All posts by StenBlog

A Life in Remission

In the midst of an active research career in astrophysics, in 2008 I was diagnosed with non-Hodgkins Lymphoma, and my world ended.

For the next eight years I learned to live with the cancer growing slowly within me like some creature out of the infamous ‘Alien’ movie series. Annual tests showed the dozens of affected lymph nodes were very slowly growing in size by the millimeter, but with luck none of them would  turn dangerous for a decade or more. But no one could predict when my cancer would ‘transform’ and become dangerously aggressive, requiring immediate chemotherapy. Actuarial forecasts said that the probability of transformation increased by 5% per year, so that after 10 years I would have a 50/50 chance of my NHL becoming aggressive, but it could happen sooner. …or much later. As a scientist, this uncertain diagnosis was devastating.

A scientist conducts research based on the a priori assumption that they will live to see the end of their work and to publish the results.  I just know you are going to say ‘Well, no one knows when they are going to die’, but among those of us who deal with cancer, these kinds of sentiments seem insensitive and a bit flippant no matter how well-intended.

How does one function when one does not know when the monster will spring out of hiding and put the kibosh on your current work? Many of my projects required several years of work, followed by months of writing-up the results and interacting with referees and journal editors to publish the results. You simply cannot muster the stamina to carry-on your research and deal with referees when you are on a short, emotional leash.

Coping with an uncertain future in research

I immediately began to wean myself away from the rigors of research and instead moved into the area of education where NASA had a huge footprint. I won two grants to develop my SpaceMath@NASA resource, which grew every year to become a significant mathematics resource for educators. I even became known in some circles as Dr. Space Math! This was an intensely therapeutic undertaking for me because could write new math problems and design new math books whenever I chose to on my timetable, and if I literally died tomorrow, I would have left behind a complete archive of fun math resources. It was an open-ended commitment that suited my new frame-of-mind, and still made me feel as though I was contributing, intellectually, to a Greater Good: The education of our children.

As the years began to add up, 5…6..7…8  I started to realize that I might be in this cancer frame-of-mind for the long haul. But by this time my hiatus from research, and my ‘advanced age’ of 64, precluded any re-entry into the level of research I had enjoyed in my earlier years. It was very sad to see this part of my career waste away, but considering I was in my peri-retirement years, perhaps as it is for so many other scientists, this transition was inevitable.

In 2016 my NHL became aggressive after eight years of near-dormancy. I was quickly rushed into a course of immunotherapy with a monthly infusion of Rituximab and Bendemustine for six months. At the end, a PET scan showed in November, 2017 that there wasn’t a sign of  the NHL anywhere, and my oncologist, Dr. Bruce Cheson at MedStar/Georgetown University Hospital in Washington DC pronounced me in remission. For the next two years, if there was no further sign of the NHL, he would consider me cured!

All of a sudden my attitude seemed to change almost literally over-night. I was anxious to start new research projects that, at least for now, could be completed in six months or less including writing up the results and submitting to the Journals. I had been out of my own research area for too long, and besides no astronomer at the age of 65 worries about new research unless they are still employed at a stable faculty or government job…which I was not. But I did have a part-time position at NASA working on citizen science activities. I was also involved in some very fun research trying to determine how well smartphones performed as scientific data-gathering sensors. That was starting to generate a pipeline of short-term projects culminating in several papers every year. But now that I was in remission, I could start to think about more complicated projects to tackle once again.

So I, basically, have come full circle in research having wandered for eight years in the dreary and uncertain desert of non-research work.

It’s good to be back!!


Quantum Gravity – Again!

In my previous blogs, I briefly described how the human brain perceives and models space (Oops one more thing), how Einstein and other physicists dismiss space as an illusion (Relativity and space ), how relativity deals with the concept of space (So what IS space?), what a theory of quantum gravity would have to look like (Quantum Gravity Oh my! ), and along the way why the idea of infinity is not physically real (Is infinity real?) and why space is not nothing (Thinking about Nothing).  I even discussed how it is important to ‘think visually’ when trying to model the universe such as the ‘strings’ and ‘loops’ used by physicists as an analog to space (Thinking Visually)

And still these blogs do not exhaust the scope of either the idea of space itself or the research in progress to get to the bottom of our experience of it.

This essay, based on a talk I gave at the Belmont Astronomical Society on October 5, 2017 will try to cover some of these other ideas and approaches that are loosely believed to be a part of a future theory of quantum gravity.

What is quantum gravity?

It is the basic idea that the two great theories of physics, Quantum Mechanics and General Relativity are incompatible with each other and do not actually deal with the same ingredients to the world: space(time) and matter. Quantum gravity is a hypothetical theory that unifies these two great ideas into a single language, revealing answers to some of the deepest questions we know how to ask about the physical world. It truly is the Holy Grail of physics.

Why do we need quantum gravity at all?

Quantum mechanics is a theory that describes matter and fields embedded in a pre-existing spacetime that has no physical effect on these fields other than to provide coordinates for describing where they are in time and space. It is said to be a background-dependent theory. General relativity is only a theory of space(time) and does not describe matter’s essence at all. It describes how matter affects the geometry of spacetime and how spacetime affects the motion of matter, but does so in purely ‘classical’ terms. Most importantly, general relativity says there is no pre-existing spacetime at all. It is called a background-independent theory. Quantum gravity is an overarching background-independent theory that accounts for the quantum nature of matter and also the quantum nature of spacetime at scales where these effects are important, called the Planck scale where the smallest unit of space is 10^-33 cm and the smallest unit of time is 10^-43 seconds.

We need quantum gravity because calculations in quantum mechanics are plagued by ‘infinities’ that come about because QM assumes space(time) is infinitely divisible into smaller units of length. When physical processes and field intensities are summed over smaller and smaller lengths to build up a prediction, the infinitesimally small units lead to infinitely large contributions which ‘blow up’ the calculations unless some mathematical method called ‘renormalization’ is used. But the gravitational field escribed by general relativity cannot be renormalized to eliminate its infinities. Only by placing a lower limit ‘cutoff’ to space(time) as quantum gravity does is this problem eliminated and all calculations become finite.

We need quantum gravity because black holes do not possess infinite entropy. The surface area of a black hole, called its event horizon, is related to its entropy, which is a measure of the amount of information that is contained inside the horizon. A single bit of information is encoded on the horizon as an area 2-Planck lengths squared. According to the holographic principle, the surface of a black hole, its 2-d surface area, encodes all the information found in the encompassed 3-d volume, so that means that the spacetime interior of a black hole has to be quantized and cannot be infinitely divisible otherwise the holographic principle would be invalid and the horizon of the black hole would have to encode an infinite amount of information and have an infinite entropy.

We also need quantum gravity because it is believed that any fundamental theory of our physical world has to be background-independent as general relativity shows that spacetime is. That means that quantum mechanics is currently an incomplete theory because it still requires the scaffolding of a pre-existing spacetime and does not ‘create’ this scaffolding from within itself the way that general relativity does.

So what is the big picture?

Historically, Newton gave us space and time as eternally absolute and fixed prerequisites to our world that were defined once and for all before we even started to describe forces and motion. The second great school of thought at that time was developed by Gottfrid Leibnitz. He said that time and space have no meaning in themselves but only as properties defined by the relationships between bodies. Einstein’s relativity and its experimental vindication has proven that Newton’s Absolute Space and Time are completely false, and replaced them by Leibnitz’s relativity principle. Einstein even said on numerous occasions that space is an imaginary construct that we take for granted in an almost mythical way. Space has no independent existence apart from its emergence out of the relationships between physical bodies. This relationship is so intimate that in general relativity, material bodies define the spacetime geometry itself as a dynamical solution to his famous relativistic equation for gravity.

How does the experience of space emerge?

In general relativity, the only thing that matters are the events along a particle’s worldline, also called its history. These events encode the relationships between bodies, and are created by the intersections of other worldlines from other particles. This network of fundamental worldlines contains all the information you need to describe the global geometry of this network of events and worldlines. It is only the geometry of these worldlines that matters to physical phenomena in the universe.

The wireframe head in this illustration is an analog to worldliness linking together to create a geometry. The black ‘void’ contains no geometric or dimensional information and any points in it do not interact with any worldline that makes up the network. That is why ‘space’ is a myth and the only thing that determine the structure of our 4-d spacetime are the worldliness.

General relativity describes how the geometry of these worldlines creates a 4-dimensional spacetime. These worldlines represent matter particles and general relativity describes how these matter particles create the curvature in the worldlines among the entire system of particles, and thereby creates space and time. The ‘empty’ mathematical points between the worldlines have no physical meaning because they are not connected to events among any of the physical worldlines, which is why Einstein said that the background space in which the worldlines seem to be embedded does not actually exist! When we look out into ‘space’ we are looking along the worldlines of light rays. We are not looking through a pre-existing space. This means we are not seeing ‘things in space’ we are seeing processes in time along a particle’s history!

There are two major quantum gravity theories being worked on today.

String theory says that particles are 1-dimensional loops of ‘something’ that are defined in a 10-dimensional spacetime of which 4 dimensions are the Big Ones we see around us. The others are compact and through their geometric symmetries define the properties of the particles themselves. It is an approach to quantum gravity that has several problems.


This figure is an imaginative rendering of a ‘string’.

First it assumes that spacetime already exists for the strings to move within. It is a background-dependent theory in the same spirit as Newton’s Absolute Space and Time. Secondly, string theory is only a theory of matter and its quantum properties at the Planck scales, but in fact the scale of a string depends on a single parameter called the string tension. If the tension is small, then these string ‘loops’ are thousands of times bigger than the Planck scale, and there is no constraint on what the actual value of the tension should be. It is an adjustable parameter.

This figure is an imaginative rendering of a ‘loop’

Loop Quantum Gravity is purely a theory of spacetime and does not treat the matter covered by quantum mechanics. It is a background-independent theory that is able to exactly calculate the answers to many problems in gravitation theory, unlike string theory which has to sneak up on the answers by summing an infinite number of alternate possibilities. LQG arrives at the answer ‘2.0’ in one step as an exact answer while for example string theory has to sum the sequence 1+1/2+1/4+1/8+1/16 +…. To get to 2.000.

LQG works with elementary spacetime ingredients called nodes and edges to create spin networks and spin foam. Like a magnetic field line that carries magnetic flux, these edges act like the field lines to space and carry quantized areas 1 Planck length squared. By summing over the number of nodes in a spin network region, each node carries a quantum unit of space volume. These nodes are related to each other in a network of intersecting lines called a spin network, which for very large networks begins to look like a snapshot of space seen at a specific instant. The change of one network into another is called a spin foam and it is the antecedent to 4-d spacetime. There is no physical meaning to the nodes and edges themselves just as there is no physical meaning to the 1-d loops than make up strings in string theory. . They are pure mathematical constructs.

So far, the best idea is that LQG forms the bedrock for string theory. String theory looks at spacetime and matter far above the Planck scale, and this is where the properties of matter particles make their appearance. LQG creates the background of spacetime that strings move through. However there is a major problem. LQG predicts that the cosmological constant must be negative and small, which is what is astronomically observed, while string theory says that the cosmological constant is large and positive. Also, although LQG can reconstruct the large 4-d spacetime that we live in, it does not seem to have have any room for the additional 6 dimensions required by string theory to create the properties of the particles we observe. One possibility is that these extra dimensions are not space-like at all but merely ‘bookkeeping’ tools that physicists have to use which will eventually be replaced in the future by a fully 4-d theory of strings.

Another approach still in its infancy is Causal Set Theory. Like LQG it is a background-independent theory of spacetime. It starts with a collection of points that are linked together by only one guiding principle, that pairs of points are ordered by cause-and-effect. This defines how these points are ordered in time, but this is the only organizing principle for points in the set. What investigators have found is that such sets create from within themselves the physical concepts of distance and time and lead to relativistic spacetimes. Causal Sets and the nodes in LQG spin networks may be related to each other.

Another exciting discovery that relates to how the elements of quantum spacetime create spacetime involves the Holographic Principle connected with quantum entanglement.

The Holographic Principle states that all the information and relationships found in a 3-d volume are ‘encoded’ on a 2-d surface screen that surrounds this volume. This means that relationships among the surface elements are reflected in the behavior of the interior physics. Recently it was discovered that if you use quantum entanglement to connect two points on the surface, the corresponding points in the interior become linked together as a physical unit. If you turn off the entanglement on the surface the interior points become unconnected and the interior space dissolves into unrelated points. The amount of entanglement can be directly related to how physically close the points are, and so this is how a unified geometry for spacetime inside the 3-d ‘bulk’ can arise from unconnected points linked together by quantum entanglement.


Additional Reading:

Exploring Quantum Space  [My book at]

Quantum Entanglement and quantum spacetime [Mark Raamsdonk]

Background-independence  [Lee Smolin]

Holographic Principle [ Jack Ng]

Causal Sets: The self-organizing universe [Scientific American]


Eclipse Postscript

In a previous blog in June , I described the August 21, 2017 eclipse and what to expect from it, along with the many resources available at the NASA website that fill-in the details of this event as we were expecting it to unfold.  This website, by the way,  went crazy for the eclipse and got over 2 billion hits from tens of millions of daily visitors. For myself, I was not prepared for the surge of emotions I would feel even after glimpsing only 15 seconds of this event between gaps in the clouds over Carbondale, Illinois. Why Carbondale? I described in a 2014 Huffington Post article how this would be the place where the eclipse lasted the longest, 2 minutes and 40 seconds, and so this is where NASA Edge decided to park us for our major public outreach activities and NASA TV interviews.

I had been interviewed by a number of TV and radio reporters as well as a memorable Facebook interview with Curiosity. My article at NASA on the airline flights that would see the eclipse got quite a bit of traction. It was fun to see my articles on smartphone eclipse photography get so much press like this one at BuzzFeed, or this one at WIRED.  I even presented my smartphone tips to 1000 students at a local high school, which was carried by the local TV station WSIL-TV. Amazingly, despite my public ‘expertise’ on the matter, I did not bother using my smartphone at all in the brief time that the eclipse showed itself!

I mentioned in an interview with Carolyn Cerda also on WSIL-TV how I had brought along my cameras and hoped to grab just one image of this event. This was after many weeks of debating with myself whether I should even bother with photography at all. I knew how easy it was to get lost among the f/stops and exposure speeds in pursuit of a trophy to commemorate this event. I certainly didn’t want to waste precious time wrestling with the very finicky smartphone telephoto lens set up. But I also wanted to spend as much time as possible letting the emotions wash over me, just as they had done for millions of other people down through the thousands of years of human history. Could I, too, experience the fear that had so commonly been the popular experience? Or would my science protect me from these irrational feelings like some coat-of-armor? I had no idea, and in many of my TV interviews I said as much.

So I compromised.

I would run my digital, Sony camcorder during totality, and on the same tripod bracket, I would set my Nikon D3000 to a fixed f/stop and exposure speed selected to highlight the dazzling bright inner corona and any prominences or blood-red chromospheric light that may be present. I would hold the shutter release down so that the camera took bursts of a dozen photos, and periodically snap photos at mid-eclipse, and on each side of the 2.5-minute window to catch Baily’s Beads and anything else going on. It sounded like a good plan, and one in which I could still spend all of my eyeball time looking at totality and not at my camera!

This turned out to be a very good choice!

The clouds did roll in and cover the entire eclipse except for the last 15 seconds of totality. I snapped a few pictures like the one above using the clouds themselves to filter the intense sunlight, revealing a diminishing crescent sun. Had my NASA activities allowed us to be located a mile east rather than by Saluki Stadium at the Southern Illinois University, Carbondale campus, I would have been treated to a full 2.5 minutes of eclipse. But 15 seconds was just enough time to send chills down my spine and have the experience of a lifetime.

My photos turned out not to be too bad. The montage below was posted on my Facebook page within an hour or so, and although a bit fuzzy for the clouds, it was clear I had seen the entire circumferential inner corona, several red spots along the solar limb as the chromosphere peaked through, and the delightful Diamond Ring of sunlight streaking through a deep lunar canyon! My camcorder also showed the emergence of the sun from totality, capturing the dense clouds and the screams from the thousands of people looking on. This also went up on my Facebook page to the delight of dozens of my friends and family!

But how did I feel?

It was frustrating to see the crescent sun dip in to the dense clouds at the start of totality, and to watch the clock tick out the next few minutes, but as we reached mid-eclipse the scenery around me turned to twilight so quickly that I actually gasped in amazement! Hopefully, and with cameras at the ready I waited and then suddenly the brightening of a small portion of the cloud heralded that the eclipsed sun was about to make its appearance. When it did, everyone shouted and I watched with amazement, not really understanding what it was I was seeing. I immediately placed my finger on the shutter button, let the camera’s machinery take a series of 100 images, and hoped for the best. Again I was not dissappointed.

A dark object appeared surrounded by an intense ring of light. I thought this was just the reflection of sunlight on the cloud, but in an instant I realized this was no sun glint for there was no brilliant solar disk to illuminate it. Instead, it was the corona itself, brighter to the naked eye than I ever could have imagined! Within a few seconds the moon began to move off the western edge of the solar disk and slowly but steadily a single bright point of light appeared and grew in brightness until I could no longer stare at it with my eye through the digital display of my camcorder.

There was so much noise and ruckus from everyone else cheering that it was hard for me to collect and reflect on my thoughts – a process that took several days and repeated sharing of my experiences with family and friends. I had only experienced the ‘tip of an iceberg’ in the emotions that had hit me, and some were no doubt muted by the confusion of what I was seeing so briefly. I could only imagine what the full two minutes would have brought to mind.

I was not prepared for the days to follow. My sense of loss was something ineffable that I could not quite shake. I drifted from day to day, occasionally gawking at the many gorgeous online photos taken by more savvy photographers and old-hands at totalities. But you have to start somewhere, and at least for the first time in my life as an astronomer I can describe to my students,not only why we have eclipses and how our ancestors regarded them, but as with the Northern Lights, I can now add my own tiny voice to describing them in purely human terms!

Thinking Visually

Look at the two images  for a few minutes and let your mind wander.

What impressions do you get from the patterns of light and dark? If I were to tell you that the one at the top is a dark nebula in the constellation Orion, and the one on the bottom is a nebula in the Pleiades star cluster, would that completely define for you what you are experiencing…or is there something more going on?

Chances are that, in the top image you are seeing what looks like the silhouette of the head and shoulders of some human-like figure being lit from behind by a light. You can’t quite put your finger on it, but the image seems vaguely mysterious and perhaps even a bit frightening the more you stare at it.

The image on the bottom evokes something completely different. Perhaps you are connecting the translucence and delicacy with some image of a shroud or silken cloak floating in a breeze. The image seems almost ghost-like in some respects…spiritual

But of course this is rather silly” you might say. “These are interstellar clouds, light-years across and all we are doing is letting our imaginations wander which is not a very scientific thing to do if you want to understand the universe.” This rational response then tempts you to reach for your mouse and click to some other page on the web.

What has happened in that split second is that a battle has been fought between one part of your brain and another. The right side of your brain enjoys looking at things and musing over the patterns that it finds there. Alas, it cannot speak because the language centers of the brain live in the left cerebral hemisphere, and it is here that rules of logic and other ‘scientific’ reasoning tools exist. The left side of your brain is vocal, and talking to you right now. It gets rather upset when it is presented with vague patterns because it can’t understand them and stamp them with a definite emotion the way the right hemisphere can. So it argues you into walking away from this challenge of understanding patterns.

If you can suspend this indignation for a moment or two, you will actually find yourself thinking about space in a way that more nearly resembles how a scientist does, though even some scientists don’t spend much time thinking about space. This indifference has begun to change during the last 20 years, and we are now in the midst of a quiet revolution.

There are three child-like qualities that make for a successful scientist:

Curiosity. This is something that many people seem to outgrow as they get older, or if they maintain it as adults, it is not at the same undiluted strength that it was when they were a child.

Imagination. This is something that also wanes with age but becomes an asset to those that can hang on to even a small vestige of it. It is what ‘Thinking out of the box’ is all about.

Novelty. As a child, everything is new. As an adult we become hopelessly jaded about irrelevant experiences like yet another sunset, yet another meteor shower, yet another eclipse. In some ways we develop an aversion for new experiences preferring the familiarity of the things we have already experienced.

If you wish to understand what space is all about, and explore the patterns hidden in the darker regions of nature, you will have to re-acquaint yourself with that child within you. You will need to pull all the stops out and allow yourself to ‘play’ with nature and the many clues that scientists have uncovered about it. You will need to do more than read books by physicists and astronomers. They speak the language of the left-brain . They can help you to see the logical development of our understanding of space and the Void, but they can not help you internalize this knowledge so that it actually means something to you. For that, you have to engage your right-brain faculties, and this requires that you see the patterns behind the words that physicists and astronomers use. To do that, you will need to think in terms of pictures and other types of images. You will need to bring something to the table to help you make sense of space in a way that you have not been able to before. You will need to expand your internal library of visual imagery to help you find analogues to what physicists and astronomers are trying to describe in words and equations. These visual analogues can be found in many common shapes and patterns, some seen under unusual and evocative circumstances. Here are some evocative images that seem to suggest how space might be put together compliments of  a diatom, the painters Miro and Mondrian, dew on a spider web, and atoms in a tungsten needle tip!

Spider web covered with dew drops

Remember, the right brain uses ALL sensory inputs to search for patterns and to understand them. It even uses imaginary information, dreams, and other free-forms to decode what it is experiencing.  

My book ‘Exploring Quantum Space’ is a guidebook that will give you some of the mental tools you will need to make sense of one of the greatest, and most subtle, discoveries in human history. Space, itself, is far from being ‘nothing’ or merely a container for matter to rattle around within. It is a landscape of hidden patterns and activity that shapes our universe and our destiny. You cannot understand it, or sense the awe and mystery of its existence, by simply reading words and following a logical exposition of ‘ifs and thens’. You also have to experience it through evocative imagery and imagination. Space is such a different medium from anything we have ever had to confront, intellectually, that we need to employ a different strategy if we wish to understand it in a personal way. Once we do this, we will be reconnected with that sense of awe we feel each time we look at the night sky.

My next blog about Nothing introduces some of the other ideas and techniques that scientists use to think about the impossible!


Thinking about Nothing

Looking back at the millennia of model building and deduction that has occurred, not a century has gone by when the prevailing opinion hasn’t been that a perfectly empty vacuum is impossible.

Aristotle’s Aether blends seamlessly into the 19th century Ether. In this century, overlapping quantum waves and virtual particles have finally taken root as the New Ether, though it is now infinitely more ephemeral than anything Aristotle or Maxwell could have imagined. We have also seen how the Atomist School of ancient Greece reached its final vindication in the hands of 19th century scientists such as Boltzman. By the 20th century, the Atomist’s paradigm has even been extended to include not just the graininess of matter, but the possible quantum graininess of the vacuum and space itself. In the virtual particles that animate matter, we finally glimpse the world which Heinrich Hertz warned us about nearly a century ago when he said that we would eventually have to reach some accommodation with “invisible confederates” existing alongside what we can see, to make our whole model of reality more logically self-consistent.

Even by the start of the 21st Century, we have reached this accommodation only by shrugging our shoulders and honestly admitting that there are things going on in the world that seem to defy human intuition. What impresses me most about the evolution of our vision of the vacuum is that the imagery we find so potent today is actually in some sense thousands of years old.

It is difficult to imagine that humans would be drawn to the same understanding of physics and astronomy that we now enjoy if our brains had been wired only slightly differently. Without sight and mobility we could not form the slightest notion of 3-D space and geometry. This is what Kant spoke about, what Henri Poincare described at great length without the benefit of 20th century neuroscience, and what Jacob Bronowski described in his book The Origins of Knowledge and Imagination with the benefit of such knowledge. But the object of science is more than just making sense of our senses. It must also guide us towards a deeper understanding of the physical world. This understanding must be self-consistent, and independent of whether we are sensorially or neurologically handicapped. Mathematics as the premier language of physical model building, seems uniquely suited to providing us with an understanding of the physical world. Mathematics lets us see the world in a way that all of the other human languages do not.

If our mathematical understanding of nature is a product of mental activity, and this activity can be physically affected by the hard-wiring of our brain, how do we arrive at a coherent model of the physical world? Can we see in this process any explanation for why certain ideas in physics appear to be so historically tenacious?

It is commonly believed that in order for mathematics and the underlying logic to exist, at the very least a conscious language must be pre-existent to support it. This is the point of view expressed by Benjamin Whorf. But the thoughtful reflections by individuals such as Einstein, Feynman and Penrose point in a very different direction. Einstein once wrote a note to Jaques Hadamard prompted by Hadamard’s investigation of creative thinking,

“…The words of language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements of thought are certain signs ( symbols ) and more or less clear images which can be voluntarily reproduced and combined…The above mentioned elements are, in my case, of visual and some muscular type…”

Roger Penrose echoes some of this same description in his book, The Emperor’s New Mind,

“…Almost all my mathematical thinking is done visually and in terms of non-verbal concepts, although the thoughts are quite often accompanied by inane and almost useless verbal commentary such as ‘that thing goes with that thing and that thing goes with that thing’..”

Freeman Dyson, one of the architects of modern QED had this to say about how Feynman did his calculations,

“…Dick was using his own private quantum mechanics that nobody else could understand. They were getting the same answers whenever they calculated the same problem…The reason Dick’s physics was so hard for ordinary people to grasp was that he did not use equations…Dick just wrote down the solutions out of his head without ever writing down the equations. He had a physical picture of the way things happen, and the pictures gave him the solutions directly with a minimum of calculation…It was no wonder that people who had spent their lives solving equations were baffled by him. Their minds were analytical; his was pictorial…”

In many instances, the conversion of abstract thinking into conventional language is seen as a laborious, almost painful process. Often words are inadequate to encompass the subtleties of the non-verbal, abstract ideas and their interrelationships. According to Penrose,

“I had noticed, on occasion, that if I have been concentrating hard for a while on mathematics and someone would engage me suddenly in conversation, then I would find myself almost unable to speak for several seconds”

In fact, abstract thinking is often argued to be a right-hemisphere function. Visual or pattern-related thinking and artistic talents are frequently coupled to this hemisphere, and since the language centers are in the left-hemisphere, with such a disconnect between language and abstract thinking, there is little wonder that theoreticians and artists find themselves tongue-tied in explaining their ideas, or are inclined to report that their work is non-verbal.

So the creation of sophisticated physical theories may involve a primarily non-verbal and visual-symbolic thinking processes, often manipulating patterns and only later, with some effort of will, translating this into spoken language or fleshing out the required mathematical details. Could this be why scientists, and artists for that matter have such difficulty in explaining what they are thinking to the rest of the population? Could this be why ancient philosophers managed to land upon archetypes for their Creation legends that seem familiar to us in the 20th century? The symbols that are used appear disembodied, and no amount of word play can capture all of the nuances and motivations that went into a particular interpretive archetypes, and make them seem compelling to the non-mathematician or non-artist. Feynman once wrote about the frustrating process of explaining to the public what goes on in nature,

“…Different people get different reputations for their skill at explaining to the layman in layman’s language these difficult and abstruse subjects. The layman then searches for book after book in the hope that he will avoid the complexities which ultimately set in, even with the best expositor of this type. He finds as he reads a generally increasing confusion, one complicated statement after another,… all apparently disconnected from one another. It becomes obscure, and he hopes that maybe in some other book there is some explanation…but I do not think it is possible, because mathematics is NOT just another language. Mathematics is a language plus reasoning…if you do not appreciate the mathematics, you cannot see, among the great variety of facts, that logic permits you to go from one to the other…”

If this is the mental frame used by some physicists to comprehend physics, it is little wonder that a great chasm exists between the lay person and the physicist in explaining what is going on. The task that even a physicist such as Freeman Dyson had in translating Feynman’s diagrammatic techniques into mathematical symbology, seems even more challenging knowing that Feynman may have had a whole other perspective on visualization via his apparent color-symbol synthesia. The equations below are the current best mathematical expression for the Standard Model in physics, which describes all known particles and fields excepting gravity.

Another feature of thinking that separates scientists and artists from everyone else seems to be the plasticity of the thinking process itself. Scientists flit from one idea to another until they arrive at a model that best explains the available data, although scientists can also get rooted to particular perspectives that are difficult to forget after decades of inculcation. The general adult population prefers a more stable collection of ideas and ‘laws’ which it can refer to over a lifetime.

Where does this all leave us?

The vacuum has been promoted to perhaps the most important clue to our own existence. The difficulty is that we lack a proper Rosetta Stone to translate the various symbolisms we use to describe it. The clues that we do have are scattered among a variety of enigmatic subjects which strain at our best intellectual resources to understand how they are linked together. Could it be that we are lacking an even more potent symbolic metaphor, and an internal non-verbal language, to give it life? Where would such a thing come from?

Spider web covered with dew drops

If we take our clue from how ideas in physics have emerged in the past, the elements of the new way of thinking may be hidden in some unexpected corner of nature. We may find an analogy or a metaphor in our mundane world which, when mixed with mathematical insight, may take us even closer to understanding gravity, spacetime and vacuum. It is no accident that string theory owes much of its success because it asks us to think about quantum fields as ordinary strings operating in an exotic mathematical setting. It is exciting to think that the essential form of the Theory of Everything could be this close to us, perhaps even lurking in a pattern we see, and overlook, in our everyday lives.

Much of this symbolic process may be performed sub-consciously, and only the form of dreams, insights or hunches seem to bring them into consciousness when the circumstances are appropriate. It is, evidently, the non-verbal and unconscious right hemisphere which experiences these ideas. Is there a limit to this process of symbolic thinking? At least a dozen times this century, physicists have had to throw up their hands over what to make of certain features of the world: the collapse of the wave function; quantum indeterminacy; particle/wave dualism; cosmogenesis. Some of these may eventually find their explanation at the next level of model building. Others such as the meaning of quantum indeterminacy and particle/wave dualism, seem to be here to stay.

In working with these contradictions, the human mind prefers the avenue of denial, you can almost hear your inner voice saying “Aw come on, quantum mechanics just can’t be that weird!” or a state of anxiety as the two hemispheres try to fabricate conflicting world models. Little wonder that we have particle/wave duality, the seeming schism between matter and energy, and a whole host of other ‘polar’ ideas in physics, as two separate minds try to resolve the universe into one model or another with the left one preferring time ordered patterns, and the right one, spatial patterns.

It is hard to believe that our brains can control what we experience of the objective world, but we need only realize that the brain actually blindsides us in a variety of subtle ways, from seeing a wider sensory world. The object of science, however, is to discern the shapes of objective laws in a way that gets to the universal elements of nature that are not coupled to a particular kind of brain circuitry. It doesn’t matter if all scientists have anasognosia and see the world differently in some consistent way, what counts is that they must still live by the laws of motion dictated by gravity and quantum mechanics.

Nils Bohr believed atoms are not real in the same sense as trees. The quantum world really does represent a different kind of reality than our apparently naive understanding of macroscopic reality implies. This being the case, we must first ask to what extent fields and the denizens of the quantum vacuum can be represented by any analogy drawn from the macroworld? We already know that the single most important distinguishing characteristic of atomic particles is their spin; far more so than mass or charge. Yet unlike mass and charge, quantum mechanical spin has ABSOLUTELY no analog in the macroscopic world. Moreover, fundamental particles cannot be thought of as tiny spheres of charged matter located at specific points in space. They have no surface, and participate in an infernal wave-like dance of probability, at least when they are not being observed. Yet despite this warning, we feel comfortable that we understand something about what reality is at this scale, in the face of these irreconcilable differences between one set of mental images and what experiments tell us over and over again. What is the true nature of the vacuum? How did the universe begin? I suspect we will not know the answer to these questions in your lifetime or mine, perhaps for the same reason that it took 3000 years for geometers to ‘discover’ non-Euclidean geometry.

At the present time we are faced with what may amount to only a single proof of the parallel-line postulate, unable to see our way through to another way of looking at the proof. There is also the very real worry that some areas of nature may require modalities of symbolic thinking beyond the archetypes that our brains are capable of providing as a consequence of their neural hard-wiring. Today, we have quantum field theory and its tantalizing paradoxes, much as the ancient geometers had their parallel-line postulate. We, like they, scratch the same figures in the sand over and over again, hoping to see the glimmerings of a new world view appearing in the shifting sands. At a precision of one part in a trillion, our quantum theories work too well, and seem to provide few clues to the new direction we must turn to see beyond them.

The primary arbiters we have at our disposal to decide between various interpretive schemes, experimental data, are not themselves in unending supply as the abrupt cancellation of the U.S. Superconducting Super Collider program in 1989 showed. It was replaced by the CERN Large Hadron Collider shown above, but even the LHC may not be large enough to access the new physics we need to explore to further our theories and understanding.

Whatever answers we need seem to be hidden, not in the low- energy world accessible to our technology, but at vastly higher energies well beyond any technology we are likely to afford in the next few centuries. It is easy to provide a jet plane with an energy of 100 billion billion billion volts — its energy of motion at a speed of a few hundred miles per hour, but it is beyond understanding how to supply a single proton or electron with the same energy. On the other hand, our internal symbolic thinking seems to lead us to similar interpretative schemes, and unconscious dualities which may only be a reflection of our own neural architecture, which we all share, and which has remained essentially unchanged for millennia. We visualize the vacuum in the same way as the Ancients did because we are still starting from the same limited collection of internal imagery. At least for some general problems, we seem to have hit a glass ceiling for which our current style of theory building seems to lead us to a bipolar and contradictory world populated by various dualities: matter/energy, space/time, wave/particle. When we finally do break through to a new kind of reality in our experiments, would we be able to recognize this event? Will our brains filter out this new world and show us only the ghostly shadows of contradictory archetypes cast upon the cave wall?

We have seen that many schemes have been offered for describing the essential difference between matter and empty space; many have failed. Theoreticians since Einstein have speculated about the geometric features of spacetime, and the structure of electrons and matter for decades. The growing opinion now seems to be that, ultimately, only the properties of space such as its geometry or dimensionality can play a fundamental role in defining what matter really is. In a word, matter may be just another form of space. If the essence of matter is to be found in the geometric properties of ’empty’ space, our current understanding of space will not be sufficient to describe all of matter’s possible aspects.

Misconceiving the Big Bang

The Big Bang was NOT a Fireworks Display!

Written by Sten Odenwald
Copyright (C) 1997. Published in the Washington Post Horizon education supplement on May 14, 1997.

The Big Bang wasn’t really big. Nor was it really a bang. In fact, the event that created the universe and everything in it was a very different kind of phenomenon than most people–or, at least, most nonphysicists–imagine.
Even the name “Big Bang” originally was a put-down cooked up by a scientist who didn’t like the concept when it was first put forth. He favored the idea that the universe had always existed in a much more dignified and fundamentally unchanging, steady state.

But the name stuck, and with it has come the completely wrong impression that the event was like an explosion and that the universe is expanding today because the objects in it are being flung apart like fragments of a detonated bomb.

Virtually every basic aspect of this intuitive image for the Big Bang (we ARE stuck with the name) is incorrect. To understand why, you need to understand Albert Einstein’s general theory of relativity. Or, at least, you need to have a sense of it. That may sound daunting, but general relativity is the most revolutionary scientific advance of the 20th century, and we all ought to acquire some feeling for it before the century ends.

After all, it’s been 82 years since Einstein put forth his theory. It’s been tested in scores of experiments and has always passed with flying colors and is now firmly established as our premier guide to understanding how gravity operates. Moreover, it is part of the foundation of Big Bang cosmology. And it is because of general relativity that we know the Big Bang was (and is, for the event is still going on) nothing like an explosion.

Albert Einstein developed general relativity in order to make his famous theory of special relativity include the effects of gravity. It is a better way than Sir Isaac Newton’s of understanding how gravity works. Like a hungry amoeba, general relativity ( or just GR for short) had absorbed both Einstein’s newly-minted special relativity and Newton’s physics, giving us the means to replicate ALL of the predictions from these two great theories, while extending them into unfamiliar realms of experience. One of these realms was the Black Hole. The other was the shape and evolution of the universe itself.

Big Bang cosmology says that the universe came into existence between 10 to 20 billion years ago, and that from a hot dense state has been expanding and cooling ever since, remains unassailable. Yet, Big Bang cosmology is vulnerable. It is based on GR being accurate over an enormous range of scales in time and space. Just how good is general relativity? So far, GR has made the following specific predictions:

1…The entire orbit of Mercury rotates because of the curved geometry of space near the sun. The amount of ‘perihelion shift’ each century was well known at the time Einstein provided a complete explanation for it in 1915.

2…Light at every frequency can be bent in exactly the same way by gravity. This was confirmed in the 1919 Solar Eclipse for optical light using stars near the Sun’s limb, and in 1969-1975 using radio emissions from star-like quasars also seen near the limb of the Sun. The deflection of the light was exactly as predicted by GR.

3…Clocks run slower in strong gravitational fields. This was confirmed by Robert Pound and George Rebka at Harvard University in 1959, and by Robert Vessot in the 1960’s and 70’s using high-precession hydrogen maser clocks flown on jet planes and on satellites.

4…Gravitational mass and inertial mass are identical. Most recently in 1971, Vladimir Braginsky at Moskow University confirmed GRs prediction of this to within 1 part in a trillion of the exact equality required by GR.

5…Black holes exist. Although these objects have been suspected to exist since they were first introduced to astronomers in the early 1970’s, it is only in 1992 that a critical acceptance threshold was crossed in the astronomical community. It was then that Hubble Space Telescope observations revealed monstrous, billion-sun black holes in the cores of nearby galaxies such as Messier 87, Messier 33 and NGC 4261.

6…Gravity has its own form of radiation which can carry energy. Russel Hulse and Joseph Taylor in 1975 discovered two pulsars orbiting each other, and through careful monitoring of their precise pulses during the next 20 years, confirmed that the system is loosing energy at a rate within 1 percent of the prediction by GR based on the emission of gravitational radiation.

7…A new force exists called ‘gravito-magnetism’. Just as electric and magnetic fields are linked together, according to GR, a spinning body produces a magnetism-like force called gravitomagnetism. GR predicts that rotating bodies not only bend space and time, but also make empty space spin. A NASA satellite called Gravity Probe B will be launched in the next few years to see whether this effect exists. This is a killer. If it is not found, GR is mortally wounded despite its long string of other successes.

8…Space can stretch during the expansion of the universe. This was confirmed by Edwin Hubble’s detection of the recession of the galaxies ca 1929. More recently in 1993, Astronomer Kenneth Kellerman confirmed that the angular sizes of distant radio sources shrink to a minimum then increase at greater distances exactly as expected for a dilating space. This is not predicted by any other cosmological model that does not also include the dilation of space as a real, physical phenomenon.

We have now boxed ourselves into a corner. If we accept the successes of GR, we are forced to see the world and the cosmos through its eyes, and its eyes alone, since it is the theory which satisfies all known tests to date.

So, how should we think about the Big Bang? Our mental ‘fireworks’ image of the Big Bang contains these basic elements: 1) A pre-existing sky or space into which the fragments from the explosion are injected; 2) A pre-existing time we can use to mark when the explosion happened; 3) Individual projectiles moving through space from a common center; 4) A definite moment when the explosion occurred; and 5) Something that started the Big Bang.

All of these elements to our visualization of the Big Bang are completely false according to GR!

Preexisting Space?

There wasn’t any!

The mathematics of GR state specifically and unambiguously that 3-dimensional space was created at the Big Bang itself, at ‘Time Zero’, along with everything else. It was a ‘singular’ event in which the separations between all particles everywhere, vanished. This is just another way of saying that our familiar 3-dimensional space vanished. Theorists studying various prototypes for the Theory of Everything have only modified this statement somewhat. During its earliest moments, the universe may have existed in a nearly incomprehensible state which may have had more than 4 dimensions, or perhaps none at all. Many of these theories of the earliest moments hypothesize a ‘mother space-time’ that begat our own universe, but you cannot at the same time place your minds eye both inside this Mother Spacetime to watch the Big Bang happen, and inside our universe to see the matter flying around. This is exactly what the fireworks display model demands that you do.

Preexisting Time?

There wasn’t any of this either!

Again, GR’s mathematics treats both space and time together as one object called ‘space-time’ which is indivisible. At Time Zero plus a moment, you had a well defined quantity called time. At Time Zero minus a moment, this same quantity changed its character in the mathematics and became ‘imaginary’. This is a mathematical warning flag that something dreadfully unexpected has happened to time as we know it. In a famous quote by Einstein, “…time and space are modes by which we think and not conditions in which we live”. Steven Hawking has looked at the mathematics of this state using the fledgling physics of Quantum Gravity Theory, and confirms that at the Big Bang, time was murdered in the most thorough way imaginable. It may have been converted into just another ‘timeless’ dimension of space…or so the mathematics seems to suggest.

Individual objects moving out from a common center?


GR says specifically that space is not a passive stage upon which matter plays out its dance, but is a member of the cast. When you treat both galaxies and space-time together, you get a very different answer for what happens than if you treat them separately, which is what we instinctively always do. Curved space distorts the paths of particles, sometimes in very dramatic ways. If you stepped into a space ship and tried to travel to the edge of the universe and look beyond, it would be impossible. Not only could you not reach a supposed “edge” of the universe no matter how long or how fast you traveled, in a closed universe, you would eventually find yourself arriving where you departed. The curvature of space would bring you right back, in something like the way the curvature of Earth would bring you home if you flew west and never changed course. In other words, the universe has no edge in space. There is nothing beyond the farthest star.

As a mental anchor, many have used the expanding balloon as an analogy to the expanding universe. As seen from any one spot on the balloon’s surface, all other spots rush away from it as the balloon is inflated. There is no one center to the expansion ON THE SURFACE of the balloon that is singled out as the center of the Big Bang. This is very different than the fireworks display which does have a dramatic, common center to the expanding cloud of cinders. The balloon analogy, however, is not perfect, because as we watch the balloon, our vantage point is still within a preexisting larger arena which GR says never existed for the real universe.

The center of the Big Bang was not a point in space, but a point in time! It is a center, not in the fabric of the balloon, but outside it along the 4th dimension…time. We cannot see this point anywhere we look inside the space of our universe out towards the distant galaxies. You can’t see time afterall! We can only see it as we look back in time at the ancient images we get from the most distant objects we can observe. We see a greatly changed, early history of the universe in these images but no unique center to them in space.

It is at this point that common sense must give up its seat on the bus, and yield to the insights provided by GR. And it is at precisely this point that so many non-physicists refuse to be so courteous. And who can blame them? But there’s more to come.

Projectiles moving through space?


GR again has something very troubling to say about this. For millions of years we have learned from experience on the savanas of the African continent and elsewhere, that we can move through space. As we drive down the highway, we have absolutely no doubts what is happening as we traverse the distance between landmarks along the roadside. This knowledge is so primal that we are incapable of mustering much doubt about it. But science is not about confirming our prejudices. It’s about revealing how things actually are.

What if I told you that you could decrease the distance from your house and the Washington Monument by ‘standing still’ and just letting space contract the distance away? GR predicts exactly this new phenomenon, and the universe seems to be the only arena we know today in which it naturally occurs. Like spots glued to the surface of the balloon at eternally fixed latitude and longitude points, the galaxies remain where they are while space dilates between them with the passage of time. There is no reason at all we should find this kind of motion intuitive.

If space is stretching like this, where do the brand new millions of cubic light years come from, from one moment to the next? The answer in GR is that they have always been there. To see how this could happen, I like to think of the shape of our universe as a “Cosmic Watermellon”. The fact that this is only the shape for a ‘closed’ finite universe is only a technicality. Finite watermellons are also cheaper to buy than infinite ones.

GR predicts the entire past, present and future of the universe all at once, and predicts its entire 4-dimensional shape. As we slice the 4-dimensional, Cosmic Watermellon at one end of the cosmic time line, we see 3-dimensional space and its contents soon after the Big Bang. At the other end of the Cosmic Watermellon in the far future, we see the collapse of space and matter just before the Big Crunch. But in between, our slices show the shape of space (closed, spherical volumes) and the locations of galaxies ( at fixed locations) as space dilates from one extreme to the other.

As a particular slice through an ordinary watermellon, we see that its meat has always been present in the complete watermellon. The meat is present as a continuous medium, and we never ask where the meat in a particular slice came from. Cosmologically, GR ask us to please think of 3-dimensional space in the same way. Space, like the meat of the watermellon, has always existed in the complete shape of the universe in 4-dimensions. But it is only in 4-dimensions that the full shape of the universe is revealed. It is a mystery why our consciousness insists on experiencing the universe one moment at a time, and that is why we end up with the paradox of where space comes from. There really is no paradox at all.

Space is not ‘nothing’ according to Einstein, it is merely another name for the gravitational field of the universe. Einstein once said, “Space-time does not claim existence on its own but only as a structural quality of the [gravitational] field”. If you could experimentally turn-off gravity with a switch, space-time would vanish. This is the ultimate demolition experiment known to physics for which an environmental impact statement would most certainly have to be filed.

The gravitational field at one instant is wedded to itself in the next instant by the incessant quantum churnings of the myriad of individual particles that like bees in a swarm, make up the gravitational field itself. In this frothing tumult, the gravitational field is knit together, quantum by quantum, from perhaps even more elemental building blocks, and it is perhaps here that we will find the ultimate origin for the expansion of the universe and the magical stretching of space. We hope the much anticipated Theory of Everything will have more to say about this, but to actually test this theory may require technologies and human resources that we can only dimly dream of.

Was there a definite moment to the Big Bang?

GR is perfectly happy to forecast that our universe emerged from an infinite density, zero-space ‘Singularity’ at Time Zero, but physicists now feel very strongly that this instant was smeared out by any number of quantum mechanical effects, so that we can never speak of a time before about 10^-43 seconds after the Big Bang. Just as Gertrude Stein once remarked about my hometown, Oakland, California that “There is no ‘There’ there”, at 10^-43 seconds, nature may tell us that before the Big Bang, “There was no ‘When’ there” either. The moment dissolves away into some weird quantum fog, and as Steven Hawking speculates, time may actually become bent into a new dimension of space and no longer even definable in this state. Ordinary GR is unable to describe this condition and only some future theory combing GR and quantum mechanics will be able to tell us more. We hope.

Something started the Big Bang!

At last we come to the most difficult issue in modern cosmology. In the fireworks display, we can trace the events leading up to the explosion all the way back to the chemists that created the gunpowder and wrapped the explosives. GR, however, can tell us nothing about the equivalent stages leading up to the Big Bang, and in fact, among its strongest statements is the one that says that time itself may not have existed. How, then, do we speak or think about a condition, or process, that started the whole shebang if we are not even allowed to frame the event as “This happened first…then this…then kerpowie!”? This remains the essential mystery of the Big Bang which seems to doggedly transcend every mathematical description we can create to describe it.

All of the logical frameworks we know about are based on chains of events or states. All of our experiences of such chains in the physical world have been ordered in time. Even when the mathematics and the theory tell us ‘What happened before the Big Bang to start it?’ is not a logical or legitimate question, we insist on viewing this as a proper question to ask of nature, and we expect a firm answer. But like so many other things we have learned this century about the physical world, our gut instincts about which questions ought to have definite answers is often flawed when we explore the extreme limits to our physical world.

I wrote this essay before seeing the new IMAX file at the Air and Space Museum ‘Cosmic Journey”, by far one of the nicest and most heroic movies of its kind I had ever seen. But of course it showed the Big Bang as a fireworks display. No matter. It doesn’t take a rocket scientist to accept the fact that the Big Bang was a spectacular moment in history. What is amazing is that the daring audacity of humans may have demystified some of it, and revealed a universe far stranger than any could have imagined.

Still, we are haunted by our hunches and intuitions gathered over millenia, and under circumstances far removed from the greater physical world we are now exploring. No wonder it all seems so alien and maddeningly complex.

Before the Big Bang

Beyond the Big Bang

Written by Sten Odenwald Copyright (C) 1987, Kalmbach Publishing. Reprinted by permission

Sometime between 15 and 20 billion years ago the universe came into existence. Since the dawn of human awareness, we have grappled with the hows and whys of this event and out of this effort have sprung many ideas. An ancient Egyptian legend describes how the universe was created by Osiris Khepera out of a dark, boundless ocean called Nu and that Osiris Khepera created himself out of this ocean by uttering his own name. Human inventiveness has not stood still in the 5000 years since these ideas were popular. The modern theory of the Big Bang states that our universe evolved from an earlier phase billions of times hotter than the core of our sun and trillions of times denser than the nucleus of an atom. To describe in detail such extreme physical conditions, we must first have a firm understanding of the nature of matter and of the fundamental forces. At the high temperatures likely to have attended the Big Bang, all familiar forms of matter were reduced to their fundamental constituents. The forces of gravity and electromagnetism together with the strong and weak nuclear forces, were the essential means through which the fundamental particles of matter interacted.
The feedback between cosmology and particle physics is nowhere more clearly seen than in the study of the early history of the universe. In October, 1985 the giant accelerator at Fermilab acheived for the first time, the collision of protons and anti-protons at energies of 1.6 trillion electron volts, about 1600 times the rest mass of the proton. This was a unique event because for one split second, on a tiny planet in an undistinguished galaxy, a small window onto the Creation Event was opened for the first time in at least 15 billion years.


The persuit by physicists of a single, all encompassing theory capable of describing the four natural forces has, as a by-product, resulted in some surprising glimpses of the Creation Event. Although such a theory remains perhaps several decades from completion, it is generally recognized that such a theory will describe physical conditions so extreme it is quite possible that we may never be able to explore them first- hand, even with the particle accelerators that are being designed today. For example, the Superconducting Supercollider to be built by the early 1990’s will cost 6 billion dollars and it will allow physicists to collide particles at energies of 40 trillion electron volts ( 40,000 GeV) matching the conditions prevailing 10 seconds after the Big Bang. The expected windfall from such an accelerator is enormous and will help to answer many nagging questions now plaguing the theoretical community, but can we afford to invest perhaps vastly larger sums of money to build machines capable of probing the quantum gravity world at 10 GeV? At these energies, the full unification of the natural forces is expected to become directly observable. How curious it is that definite answers to questions such as, ‘What was Creation like?’ and ‘Do electrons and quarks have internal structure?’ are so inextricably intertwined. Our ability to find answers to these two questions, among others, does not seem to be hampered by some metaphysical prohibition, but by the resources our civilization can afford to devote to finding the answers. Fortunatly, the situation is not quite so bleak, for you see, the ‘machine’ has already been ‘built’ and every possible experiment we can ever imagine has already been performed!


We are living inside the biggest particle accelerator ever created – the universe. Ten billion years before the sun was born, Nature’s experiment in high-energy physics was conducted and the experimental data can now be examined by studying the properties and contents of the universe itself. The collection of fundamental facts that characterize our universe is peculiar in that it derives from a variety of sources. A partial list of these ‘meta-facts’ looks like this:

1) We are here, therefore, some regions of the universe are hospitible to the creation of complex molecules and living, rational organisms.

2) Our Universe has 4 big dimensions and all are increasing in size as the universe expands in time and space.

3) There are 4 dissimilar forces acting in Nature.

4) Only matter dominates; no anti-matter galaxies exist and this matter is built out of 6 quarks and 6 types of leptons.

The task confronting the physicist and the astronomer is to create, hopefully, a single theory consistent with these metafacts that can then be used to derive the secondary characteristics of our universe such as the 2.7 K background radiation, the primordial element abundances, and galaxy formation. The interplay between the study of the macrocosm and the microcosm has now become so intense that astronomers have helped physicists set limits to the number of lepton families — No more than 4 are allowed otherwise the predicted cosmological abundance of helium would seriously disagree with what is observed. Physicists, on the other hand, use the astronomical upper limits to the current value of the cosmological constant to constrain their unification theories.

An extention to the standard Big Bang model called the Inflationary Universe (see The Decay of the False Vacuum) was created by MIT physicist Alan Guth in 1981. This theory combined Grand Unification Theory with cosmology and, if correct, allows astronomers to trace the history of the universe all the way back to 10 seconds after the Big Bang when the strong, weak and electromagnetic forces were unified into a single ‘electro-nuclear’ force. During the 4 years since the Inflationary Universe model was proposed, other theoretical developments have emerged that may help us probe events occurring at an even earlier stage, perhaps even beyond the Creation Event itself. Ten years ago, theoreticians discovered a new class of theories called Supersymmetric Grand Unified Theories ( SUSY GUTs). These theories, of which there are several competing types, have shown great promise in providing physicists with a unified framework for describing not just the electro-nuclear force but also gravity, in addition to the particles they act on (see The Planck Era: March 1984). Unfortunately, as SUSY GUTs were studied more carefully, it was soon discovered that even the most promising candidates for THE Unified Field Theory suffered from certain fundamantal deficiencies. For instance:

1) There were not enough basic fields predicted to accomodate the known particles.

2) Left and right-hand symmetry was mandated so that the weak force, which breaks this symmetry, had to be put in ‘by hand’.

3) Anomalies exist which include the violation of energy conservation and charge.

4) The Cosmological Constant is 10 times larger than present upper limits suggest.

In recent years, considerable effort has gone into extending and modifying the postulates of SUSY GUTs in order to avoid these problems. One avenue has been to question the legitimacy of a very basic premise of the field theories developed heretofore. The most active line of theoretical research in the last 25 years has involved the study of what are called ‘point symmetry groups’. For example, a hexagon rotated by 60 degrees about a point at its center is indistinguishable from one rotated by 120, 180, 240, 300 and 360 degrees. These 6 rotation operations form a mathematical group so that adding or subtracting any two operations always result in a rotation operation that is already a member of the group ( 180 = 120 + 60 etc). The Grand Unification Theories of the electro-nuclear interaction are based on point symmetry groups named SU(3), SU(2) and U(1) which represent analogous ‘rotations’ in a more complex mathematical space. In the context of ponderable matter, point symmetry groups are also the mathematical statement of what we believe to be the structure of the fundamental particles of matter, namely, that particles are point-like having no physical size at all. But what if this isn’t so? The best that experimental physics has to offer is that the electron which is one of a family of 6 known Leptons, behaves like a point particle at scales down to 10 cm, but that’s still an enormous distance compared to the gravitational Planck scale of 10 cm where complete unification with gravity is expected to occur.

By assuming that fundamental particles have internal structure, Michael Green at Queen Mary College and John Schwartz at Caltech made a remarkable series of discoveries which were anounced in the journal NATURE in April 1985. They proposed that, if a point particle were replaced by a vibrating ‘string’ moving through a 10-dimensional spacetime, many of the problems plaguing SUSY GUTs seemed to vanish miraculously. What’s more, of all the possible kinds of ‘Superstring’ theories, there were only two ( called SO(32) and E8 x E8′) that were: 1) Consistent with both the principles of relativity and quantum mechanics,2) Allowed for the asymmetry between left and right-handed processes and, 3) Were free of anomalies. Both versions were also found to have enough room in them for 496 different types of fields; enough to accomodate all of the known fundamental particles and then some! Superstring theories also have very few adjustable parameters and from them, certain quantum gravity calculations can be performed that give finite answers instead of infinite ones. In spite of their theoretical successes, Superstring theories suffer from the difficulty that the lightest Superstring particles will be completely massless while the next more massive generation will have masses of 10 GeV. It is not even clear how these supermassive string particles are related to the known particles which are virtually massless by comparison (a proton has a mass of 1 GeV!). It is also not known if the 496 different particles will cover the entire mass range between 0 and 10 GeV. It is possible that they may group themselves into two families with masses clustered around these two extreems. In the later instance, experimental physicists may literally run out of new particles to discover until accelerators powerful enough to create supermassive particles can be built.

An attractive feature of the SO(32) model, which represents particles as open-ended strings, is that gravity has to be included from the start in order to make the theory internally consistent and capable of yielding finite predictions. It is also a theory that reduces to ordinary point field theories at energies below 10 GeV. The complimentary theory, E8 x E8′, is the only other superstring theory that seems to work as well as SO(32) and treats particles as though they were closed strings without bare endpoints. This model is believed to show the greatest promise for describing real physical particles. It also includes gravity, but unlike SO(32), E8 x E8′ does seem to reduce at low energy, to the symmetry groups associated with the strong, weak and electromagnetic interactions, namely, SU(3), SU(2) and U(1).

If E8 x E8′ is destined to be the ‘ultimate, unified field theory’, there are some additional surprises in store for us. Each group, E8 and E8′, can be reduced mathematically to the products of the groups that represent the strong, weak and electromagnetic forces; SU(3) x SU(2) x U(1). If the E8 group corresponds to the known particles what does E8′ represent? In terms of its mathematical properties, symmetry considerations alone seem to require that the E8′ group should be a mirror image of E8. If E8 contains the groups SU(3), SU(2) and U(1) then E8′ contains SU(3)’, SU(2)’ and U(1)’. The primed fields in E8′ would have the same properties as those we ascribe to the strong, weak and electromagnetic forces. The E8′ particle fields may correspond to a completly different kind of matter, whose properties are as different from matter and anti-matter as ordinary matter is from anti-matter! ‘Shadow Matter’ as it has been called by Edward Kolb, David Seckel and Michael Turner at Fermilab, may actually co-exist with our own – possibly accounting for the missing mass necessary to close the universe. Shadow matter is only detectable by its gravitational influence and is totally invisible because the shadow world electromagnetic force (shadow light) does not interact with any of the particles in the normal world.


The quest for a mathematical description of the physical world uniting the apparent differences between the known particles and forces, has led physicists to the remarkable conclusion that the universe inhabits not just the 4 dimensions of space and time, but a much larger arena whose dimensionality may be enormous (see Does Space Have More Than 3 Dimensions?). Both the Superstring theories and SUSY GUTs agree that our physical world has to have more than the 4 dimensions we are accustomed to thinking about. A remarkable feature of Superstring theory is that of all the possible dimensionalities for spacetime, only in 10-dimensions ( 9 space dimensions and 1 time dimension) will the theory lead to a computationally finite and internally consistent model for the physical world that includes the weak interaction from the outset, and where all of the troublesome anomalies cancil exactly. In such a 10-dimensional world, it is envisioned that 6 dimensions are now wrapped-up or ‘compactified’ into miniscule spheres that accompany the 4 coordinates of every point in spacetime. What would a description of the early universe look like from this new viewpoint? The 6 internal dimensions are believed to have a size of order 10 cm.

As we follow the history of the universe back in time, the 3 large dimensions of space rapidly shrink until eventually they become only 10 cm in extent. This happened during the Planck Era at a time, 10 seconds after the Creation Event. The appearance of the universe under these conditions is almost unimaginable. Today as we look out at the most distant quasar, we see them at distances of billions of lightyears. During the Planck Era, the matter comprising these distant systems was only 10 cm away from the material that makes-up your own body!

What was so special about this era that only 4 of the 10 dimensions were singled-out to grow to their enormous present size?. Why not 3 ( 2 space + 1 time) or 5 ( 4 space + 1 time)? Physicists have not as yet been able to develope an explanation for this fundamental mystery of our plenum, on the other hand, it may just be that had the dimensional breakdown of spacetime been other than ‘4 + 6’, the physical laws we are the products of, would have been totally inhospitable to life as we know it.

As we relentlessly follow the history of the universe to even earlier times, the universe seems to enter a progressively more and more symmetric state. The universe at 10 seconds after the Big Bang may have been populated by supermassive particles with masses of 10^15 GeV or about 10^-13 grams each. These particles ultimatly decayed into the familiar quarks and leptons once the universe had grown colder as it expanded. In addition, there may only have been a single kind of ‘superforce’ acting on these particles; a force whose character contained all of the individual attributes we now associate with gravity, electromagnetism and the strong and weak nuclear forces. Since the particles carrying the ‘superforce’ had masses similar to those of the supermassive particles co-existing then, the distinction between the force-carriers and the particles they act on probably broke-down completely and the world became fully supersymmetric.

To go beyond the Planck Era may require a radical alteration in our conventional way of thinking about time and space. Only glimpses of the appropriate way to think about this multidimensional landscape can be found in the equations and theories of modern-day physics. Beyond the Planck Era, all 10 dimensions (and perhaps others) become co-equal at least in terms of their physical size. The supermassive Superstring particles begin to take-on more of the characteristics of fluctuations in the geometry of spacetime than as distinguishable, ingredients in the primordial, cosmological ‘soup’. There was no single, unique geometry for spacetime but, instead, an ever-changing quantum interplay between spacetimes with an unlimited range in geometry. Like sound waves that combine with one another to produce interference and reinforcement, the spacetime that emerged from the Planck Era is thought to be the result of the superposition of an infin ite number of alternate spacetime geometries which, when added together, produced the spacetime that we are now a part of.

Was there light? Since the majority of the photons were probably not created in large numbers until at least the beginning of the Inflationary Epoc, 10^-36 seconds after the Big Bang, it is not unthinkable that during its earliest moments, the universe was born out of darkness rather than in a blinding flash of light. All that existed in this darkness before the advent of light, was an empty space out of which our 10-dimensional spacetime would later emerge. Of course, under these conditions it is unclear just how we should continue to think about time itself.

In terms of the theories available today, it may well be that the particular dimension we call Time had a definite zero point so that we can not even speak logically about what happened before time existed. The concept of ‘before’ is based on the presumption of time ordering. A traveler standing on the north pole can never move to a position on the earth that is 1 mile north of north! Nevertheless, out of ingrained habit, we speak of the time before the genesis of the universe when time didn’t exist and ask, “What happened before the Big Bang?”. The list of physicists investigating this ‘state’ has grown enormously over the last 15 years. The number of physicists, worldwide, that publish research on this topic is only slightly more than 200 out of a world population of 5 billion!


In the early 1970’s Y. Zel’dovitch and A. Starobinski of the USSR along with Edward Tryon at Hunter College proposed that the universe emerged from a fluctuation in the vacuum. This vacuum fluctuation ‘ran away’ with itself, creating all the known particles out of empty space at the ‘instant’ of no-time. To understand what this means requires the application of a fundamental fact of relativistic quantum physics discovered during the latter half of the 1920’s. Vacuum fluctuations are a direct consequence of Heisenberg’s Uncertainty Principle which limits how well we can simultaneously know a particle’s momentum and location (or its total energy and lifetime). What we call empty space or the physical vacuum is a Newtonian fiction like absolute space and time. Rather than a barren stage on which matter plays-out its role, empty space is known to be filled with ‘virtual particles’ that spontaneously appear and disappear beyond the ability of any physical measurement to detect directly. From these ghost particles, a variety of very subtle phenomena can be predicted with amazing accuracy. Depending on the total rest mass energy of the virtual particles created in the vacuum fluctuation, they may live for a specific lifetime before Heisenberg’s Uncertainty Principle demands that they vanish back into the nothingness of the vacuum state. In such a quantum world, less massive virtual particles can live longer than more massive ones. Edward Tyron proposed that the universe is just a particularly long-lived vacuum fluctuation differing only in magnitude from those which occur imperceptably all around us. The reason the universe is so long lived in spite of its enormous mass is that the positive energy latent in all the matter in the universe is offset by the negative potential energy of the gravitational field of the universe. The total energy of the universe is, therefore, exactly zero and its maximum lifetime as a ‘quantum fluctuation’ could be enormous and even infinite! According to Tryon, “The Universe is simply one of those things which happens from time to time.”

This proposal by Tryon was regarded with some scepticism and even amusement by astronomers, and was not persued much further. This was a fate that had also befallen the work on 5-dimensional general relativity by Theodore Kaluza and Oskar Klein during the 1920’s which was only resurrected in the late 1970’s as a potent remedy for the ills plaguing supersymmetry theory.

In 1978, R. Brout, P. Englert, E. Gunzig and P. Spindel at the University of Brussels, proposed that the fluctuation that led to the creation of our universe started out in an empty, flat, 4-dimensional spacetime. The fluctuation in space began weakly, creating perhaps a single matter- antimatter pair of supermassive particles with masses of 10^19 GeV. The existence of this ‘first pair’ stimulated the creation from the vacuum of more particle-antiparticle pairs which stimulated the production of still others and so on. Space became highly curved and exploded, disgorging all of the superparticles which later decayed into the familiar leptons, quarks and photons.

Heinz Pagels and David Atkatz at Rockefeller University in 1981 proposed that the triggering agent behind the Creation Event was a tunneling phenomenon of the vacuum from a higher-energy state to a lower energy state. Unlike the Brout-Englert-Gunzig-Spindel model which started from a flat spacetime, Pagels and Atkatz took the complimentary approach that the original nothingness from which the universe emerged was a spatially closed, compact empty space, in other words, it had a geometry like the 2-D surface of a sphere. but the dimensionality of its surface was much higher than 2. Again this space contained no matter what-so-ever. The characteristics (as yet unknown) of the tunneling process determined, perhaps in a random way, how the dimensionality of spacetime would ‘crystallize’ into the 6+4 combination that represents the plenum of our universe.

Alex Vilenkin at Tufts University proposed in 1983 that our spacetime was created out of a ‘nothingness’ so complete that even its dimensionality was undefined. In 1984, Steven Hawkings at Cambridge and James Hartle at UCSB came to a similar conclusion through a series of quantum mechanical calculations. They described the geometric state of the universe in terms of a wavefunction which specified the probability for spacetime to have one of an infinite number of possible geometries. A major problem with the ordinary Big Bang theory was that the universe emerged from a state where space and time vanished and the density of the universe became infinite; a state called the Singularity. Hawkings and Hartle were able to show that this Big Bang singularity represented a specific kind of geometry which would become smeared-out in spacetime due to quantum indeterminacy. The universe seemed to emerge from a non-singular state of ‘nothingness’ similar to the undefined state proposed by Vilenkin. The physicist Frank Wilczyk expresses this remarkable situation the best by saying that, ” The reason that there is Something rather than Nothing is that Nothing is unstable.”


Theories like those of SUSY GUTS and Superstrings seem to suggest that just a few moments after Creation, the laws of physics and the content of the world were in a highly symmetric state; one superforce and perhaps one kind of superparticle. The only thing breaking the perfect symmetry of this era was the definite direction and character of the dimension called Time. Before Creation, the primordial symmetry may have been so perfect that, as Vilenkin proposed, the dimensionality of space was itself undefined. To describe this state is a daunting challenge in semantics and mathematics because the mathematical act of specifying its dimensionality would have implied the selection of one possibility from all others and thereby breaking the perfect symmetry of this state. There were, presumably, no particles of matter or even photons of light then, because these particles were born from the vacuum fluctuations in the fabric of spacetime that attended the creation of the universe. In such a world, nothing happens because all ‘happenings’ take place within the reference frame of time and space. The presence of a single particle in this nothingness would have instantaneously broken the perfect symmetry of this era because there would then have been a favored point in space different from all others; the point occupied by the particle. This nothingness didn’t evolve either, because evolution is a time-ordered process. The introduction of time as a favored coordinate would have broken the symmetry too. It would seem that the ‘Trans-Creation’ state is beyond conventional description because any words we may choose to describe it are inherently laced with the conceptual baggage of time and space. Heinz Pagels reflects on this ‘earliest’ stage by saying, “The nothingness ‘before’ the creation of the universe is the most complete void we can imagine. No space, time or matter existed. It is a world without place, without duration or eternity…”

A perusal of the scientific literature during the last 20 years suggests that we may be rapidly approaching a major crossroad in physics. One road seems to be leading to a single unification theory that is so unique among all others that it is the only one consistent with all the major laws we know about. It is internally consistent; satisfies the principles of relativity and quantum mechanics and requires no outside information to describe the particles and forces it contains . A prototype of this may be superstring theory with its single adjustable parameter, namely, the string tension. The other road is much more bleak. It may also turn out that we will create several theoretical systems that seem to explain everything but have within them hard to detect flaws. These flaws may stand as barracades to further logical inquiry; to be uncovered only through experiments that may be beyond our technological reach. It is possible that we are seeing the beginning of this latter process even now, with the multiplicity of theories whose significant deviations only occur at energies near 10^19 GeV.

I find it very hard to resist the analogy between our current situation and that of the Grecian geometers. For 2000 years the basic postulates of Eulidean geometry and the consequences of this logical system, remained fixed. It became a closed book with only a few people in the world struggling to find exceptions to it such as refutations of the parallel line postulate. Finally during the 19th century, non-euclidean geometry was discovered and a renaissance in geometry occurred. Are physicists on the verge of a similar great age, finding themselves hamstrung by not being able to devise new ways of thinking about old problems? Egyptian cosmology was based on motifs that the people of that age could see in the world around them; water, sky, land, biological reproduction. Today we still use motifs that we find in Nature in order to explain the origin of the universe; the geometry of space, virtual particles and vacuum fluctuations. We can probably expect that in the centuries to follow, our descendents will find still other motifs and from them, fashion cosmologies that will satisfy the demands of that future age with, possibly, much greater accuracy and efficiency than ours do today. Perhaps, too, in those future ages, scientists will marvel at the ingenuity of modern physicists and astronomers, and how in the space of only 300 years, we had managed to create our own quaint theory as the Egyptians had before us.

In the meantime, physicists and astronomers do the best they can to fashion a cosmology that will satisfy the intellectual needs of our age. Today, as we contemplate the origin of the universe we find ourselves looking out over a dark, empty void not unlike the one that our Egyptian predecessors might have imagined. This void is a state of exquisite perfection and symmetry that seems to defy description in any linguistic terms we can imagine. Through our theories we launch mathematical voyages of exploration, and watch the void as it trembles with the quantum possibilities of universes unimaginable.

Decay of the False Vacuum

The Decay of the False Vacuum

Written by Sten Odenwald. Copyright (C) 1983 Kalmbach Publishing. Reprinted by permission

In the recently developed theory by Steven Weinberg and Abdus Salam, that unifies the electromagnetic and weak forces, the vacuum is not empty. This peculiar situation comes about because of the existence of a new type of field, called the Higgs field. The Higgs field has an important physical consequence since its interaction with the W, W and Z particles (the carriers of the weak force) causes them to gain mass at energies below 100 billion electron volts (100 Gev). Above this energy they are quite massless just like the photon and it is this characteristic that makes the weak and electromagnetic forces so similar at high energy.

On a somewhat more abstract level, consider Figures 1 and 2 representing the average energy of the vacuum state. If the universe were based on the vacuum state in Figure 1, it is predicted that the symmetry between the electromagnetic and weak interactions would be quite obvious. The particles mediating the forces would all be massless and behave in the same way. The corresponding forces would be indistinguishable. This would be the situation if the universe had an average temperature of 1 trillion degrees so that the existing particles collided at energies of 100 Gev. In Figure 2, representing the vacuum state energy for collision energies below 100 Gev, the vacuum state now contains the Higgs field and the symmetry between the forces is suddenly lost or ‘broken’. Although at low energy the way in which the forces behave is asymmetric, the fundamental laws governing the electromagnetic and weak interactions remain inherently symmetric. This is a very remarkable and profound prediction since it implies that certain symmetries in Nature can be hidden from us but are there nonetheless.

During the last 10 years physicists have developed even more powerful theories that attempt to unify not only the electromagnetic and weak forces but the strong nuclear force as well. These are called the Grand Unification Theories (GUTs) and the simplist one known was developed by Howard Georgi, Helen Quinn,and Steven Weinberg and is called SU(5), (pronounced ‘ess you five’). This theory predicts that the nuclear and ‘electroweak’ forces will eventually have the same strength but only when particles collide at energies above 1 thousand trillion GeV corresponding to the unimaginable temperature of 10 thousand trillion trillion degrees! SU(5) requires exactly 24 particles to mediate forces of which the 8 massless gluons of the nuclear force, the 3 massless intermediate vector bosons of the weak force and the single massless photon of the electromagnetic force are 12. The remaining 12 represent a totally new class of particles called Leptoquark bosons that have the remarkable property that they can transform quarks into electrons. SU(5) therefore predicts the existence of a ‘hyperweak’ interaction; a new fifth force in the universe! Currently, this force is 10 thousand trillion trillion times weaker than the weak force but is nevertheless 100 million times stronger than gravity. What would this new force do? Since protons are constructed from 3 quarks and since quarks can now decay into electrons, through the Hyperweak interaction, SU(5) predicts that protons are no longer the stable particles we have always imagined them to be. Crude calculations suggest that they may have half-lives between 10^29 to 10^33 years. An immediate consequence of this is that even if the universe were destined to expand for all eternity, after ‘only’ 10^32 years or so, all of the matter present would catastrophically decay into electrons, neutrinos and photons. The Era of Matter, with its living organisms, stars and galaxies, would be swept away forever, having represented but a fleeting episode in the history of the universe. In addition to proton decay, SU(5) predicts that at the energy characteristic of the GUT transition, we will see the affects of a new family of particles called supermassive Higgs bosons whose masses are expected to be approximately 1 thousand trillion GeV! These particles interact with the 12 Leptoquarks and make them massive just as the Higgs bosons at 100 GeV made the W, W and Z particles heavy. Armed with this knowledge, let’s explore some of the remarkable cosmological consequences of these exciting theories.

The GUT Era

To see how these theories relate to the history of the universe, imagine if you can a time when the average temperature of the universe was not the frigid 3 K that it is today but an incredable 10 thousand trillion trillion degrees (10^15 GeV). The ‘Standard Model’ of the Big Bang, tells us this happened about 10^-37 seconds after Creation. The protons and neutrons that we are familiar with today hadn’t yet formed since their constituent quarks interacted much too weakly to permit them to bind together into ‘packages’ like neutrons and protons. The remaining constituents of matter, electrons, muons and tau leptons, were also massless and traveled about at essentially light-speed; They were literally a new form of radiation, much like light is today! The 12 supermassive Leptoquarks as well as the supermassivs Higgs bosons existed side-by-side with their anti-particles. Every particle-anti particle pair that was annihilated was balanced by the resurrection of a new pair somewhere else in the universe. During this period, the particles that mediated the strong, weak and electromagnetic forces were completely massless so that these forces were no longer distinguishable. An inhabitant of that age would not have had to theorize about the existence of a symmetry between the strong, weak and electromagnetic interactions, this symmetry would have been directly observable and furthermore, fewer types of particles would exist for the inhabitants to keep track of. The universe would actually have beed much simpler then!

As the universe continued to expand, the temperature continued to plummet. It has been suggested by Demetres Nanopoulis and Steven Weinberg in 1979 that one of the supermassive Higgs particles may have decayed in such a way that slightly more matter was produced than anti-matter. The remaining evenly matched pairs of particles and anti-particles then annihilated to produce the radiation that we now see as the ‘cosmic fireball’.

Exactly what happened to the universe as it underwent the transitions at 10^15 and 100 GeV when the forces of Nature suddenly became distinguishable is still under investigation, but certain tantalizing descriptions have recently been offered by various groups of theoriticians working on this problem. According to studies by Alan Guth, Steven Weinberg and Frank Wilczyk between 1979 and 1981, when the GUT transition occured, it occured in a way not unlike the formation of vapor bubbles in a pot of boiling water. In this analogy, the interior of the bubbles represent the vacuum state in the new phase, where the forces are distinguishable, embedded in the old symmetric phase where the nuclear, weak and electromagnetic forces are indistinguishable. Inside these bubbles, the vacuum energy is of the type illustrated by Figure 2 while outside it is represented by Figure 1. Since we are living within the new phase with its four distinguishable forces, this has been called the ‘true’ vacuum state. In the false vacuum state, the forces remain indistinguishable which is certainly not the situation that we find ourselves in today!

Cosmic Inflation

An exciting prediction of Guth’s model is that the universe may have gone through at least one period in its history when the expansion was far more rapid than predicted by the ‘standard’ Big Bang model. The reason for this is that the vacuum itself also contributes to the energy content of the universe just as matter and radiation do however, the contribution is in the opposite sense. Although gravity is an attractive force, the vacuum of space produces a force that is repulsive. As Figures 1 and 2 show, the minimum energy state of the false vacuum at ‘A’ before the GUT transition is at a higher energy than in the true vacuum state in ‘B’ after the transition. This energy difference is what contributes to the vacuum energy. During the GUT transition period, the positive pressure due to the vacuum energy would have been enormously greater than the restraining pressure produced by the gravitational influence of matter and radiation. The universe would have inflated at a tremendous rate, the inflation driven by the pressure of the vacuum! In this picture of the universe, Einstein’s cosmological constant takes on a whole new meaning since it now represents a definite physical concept ; It is simply a measure of the energy difference between the true and false vacuum states (‘B’ and ‘A’ in Figures 1 and 2.) at a particular time in the history of the universe. It also tells us that, just as in de Sitter’s model, a universe where the vacuum contributes in this way must expand exponentially in time and not linearly as predicted by the Big Bang model. Guth’s scenario for the expansion of the universe is generally called the ‘inflationary universe’ due to the rapidity of the expansion and represents a phase that will end only after the true vacuum has supplanted the false vacuum of the old, symmetric phase.

A major problem with Guth’s original model was that the inflationary phase would have lasted for a very long time because the false vacuum state is such a stable one. The universe becomes trapped in the cul-de-sac of the false vacuum state and the exponential expansion never ceases. This would be somewhat analogous to water refusing to freeze even though its temperature has dropped well below 0 Centigrade. Recent modifications to the original ‘inflationary universe’ model have resulted in what is now called the ‘new’ inflationary universe model. In this model, the universe does manage to escape from the false vacuum state and evolves in a short time to the familiar true vacuum state.

We don’t really know how exactly long the inflationary phase may have lasted but the time required for the universe to double its size may have been only 10^-34 seconds. Conceivably, this inflationary period could have continued for as ‘long’ as 10^-24 seconds during which time the universe would have undergone 10 billion doublings of its size! This is a number that is truely beyond comprehension. As a comparison, only 120 doublings are required to inflate a hydrogen atom to the size of the entire visible universe! According to the inflationary model, the bubbles of the true vacuum phase expanded at the speed of light. Many of these had to collide when the universe was very young in order that the visible universe appear so uniform today. A single bubble would not have grown large enough to encompass our entire visible universe at this time; A radius of some 15-20 billion light years. On the other hand, the new inflationary model states that even the bubbles expanded in size exponentially just as their separations did. The bubbles themselves grew to enormous sizes much greater than the size of our observable universe. According to Albrecht and Steinhardt of the University of Pennsylvania, each bubble may now be 10^3000 cm in size. We should not be too concerned about these bubbles expanding at many times the speed of light since their boundaries do not represent a physical entity. There are no electrons or quarks riding some expandind shock wave. Instead, it is the non-material vacuum of space that is expanding. The expansion velocity of the bubbles is not limited by any physical speed limit like the velocity of light.

GUMs in GUTs

A potential problem for cosmologies that have phase transitions during the GUT Era is that a curious zoo of objects could be spawned if frequent bubble mergers occured as required by Guth’s inflationary model. First of all, each bubble of the true vacuum phase contains its own Higgs field having a unique orientation in space. It seems likely that no two bubbles will have their Higgs fields oriented in quite the same way so that when bubbles merge, knots will form. According to Gerhard t’Hooft and Alexander Polyakov, these knots in the Higgs field are the magnetic monopoles originally proposed 40 years ago by Paul Dirac and there ought to be about as many of these as there were bubble mergers during the transition period. Upper limits to their abundance can be set by requiring that they do not contribute to ‘closing’ the universe which means that for particles of their predicted mass (about 10^16 GeV), they must be 1 trillion trillion times less abundant than the photons in the 3 K cosmic background. Calculations based on the old inflationary model suggest that the these GUMs (Grand Unification Monopoles) may easily have been as much as 100 trillion times more abundant than the upper limit! Such a universe would definitly be ‘closed’ and moreover would have run through its entire history between expansion and recollapse within a few thousand years. The new inflationary universe model solves this ‘GUM’ overproduction problem since we are living within only one of these bubbles, now almost infinitly larger than our visible universe. Since bubble collisions are no longer required to homogenize the matter and radiation in the universe, very few, if any, monopoles would exist within our visible universe.


A prolonged period of inflation would have had an important influence on the cosmic fireball radiation. One long-standing problem in modern cosmology has been that all directions in the sky have the same temperature to an astonishing 1 part in 10,000. When we consider that regions separated by only a few degrees in the sky have only recently been in communication with one another, it is hard to understand how regions farther apart than this could be so similar in temperature. The radiation from one of these regions, traveling at the velocity of light, has not yet made it across the intervening distance to the other, even though the radiation may have started on its way since the universe first came into existence. This ‘communication gap’ would prevent these regions from ironing-out their temperature differences.

With the standard, Big Bang model, as we look back to earlier epochs from the present time, the separations between particles decrease more slowly than their horizons are shrinking. Neighboring regions of space at the present time, become disconnected so temperature differences are free to develope. Eventually, as we look back to very ancient times, the horizons are so small that every particle existing then literally fills the entire volume of its own, observable universe. Imagine a universe where you occupy all of the available space! Prior to the development of the inflationary models, cosmologists were forced to imagine an incredably well-ordered initial state where each of these disconnected domains (some 10^86 in number) had nearly identical properties such as temperature. Any departure from this situation at that time would have grown to sizable temperature differences in widely separated parts of the sky at the present time. Unfortunately, some agency would have to set-up these finely-tuned initial conditions by violating causality. The contradiction is that no force may operate by transmitting its influence faster than the speed of light. In the inflationary models, this contradiction is eliminated because the separation between widely scattered points in space becomes almost infinitly small compared to the size of the horizons as we look back to the epoc of inflation. Since these points are now within each others light horizons, any temperature difference would have been eliminated immediatly since hotter regions would now be in radiative contact with colder ones. With this exponentially-growing, de Sitter phase in the universe’s early history we now have a means for resolving the horizon problem.

Instant Flat Space

Because of the exponential growth of the universe during the GUT Era, its size may well be essentially infinite for all ‘practical’ purposes . Estimates by Albrecht and Steinhardt suggest that each bubble region may have grown to a size of 10^3000 cm by the end of the inflationary period. Consequently, the new inflationary model predicts that the content of the universe must be almost exactly the ‘critical mass’ since the sizes of each of these bubble regions are almost infinite in extent. The universe is, for all conceivable observations, exactly Euclidean (infinite and flat in geometry) and destined to expand for all eternity to come. Since we have only detected at most 10 percent of the critical mass in the form of luminous matter, this suggests that 10 times as much matter exists in our universe than is currently detectable. Of course, if the universe is essentially infinite this raises the ghastly spectre of the eventual annihilation of all organic and inorganic matter some 10^32 years from now because of proton decay.

In spite of its many apparent successes, even the new inflationary universe model is not without its problems. Although it does seem to provide explainations for several cosmological enigmas, it does not provide a convincing way to create galaxies. Those fluctuations in the density of matter that do survive the inflationary period are so dense that they eventually collapse into galaxy-sized blackholes! Neither the precise way in which the transition to ordinary Hubbel expansion occurs nor the duration of the inflationary period are well determined.

If the inflationary cosmologies can be made to answer each of these issues satisfactorily we may have, as J. Richard Gott III has suggested, a most remarkable model of the universe where an almost infinite number of ‘bubble universes’ each having nearly infinite size, coexist in the same 4-dimensional spacetime; all of these bubble universes having been brought into existence at the same instant of creation. This is less troublesome than one might suspect since, if our universe is actually infinite as the available data suggests, so too was it infinite even at its moment of birth! It is even conceivable that the universe is ‘percolating’ with new bubble universes continually coming into existence. Our entire visible universe, out to the most distant quasar, would be but one infinitessimal patch within one of these bubble regions. Do these other universes have galaxies, stars, planets and living creatures statistically similar to those in our universe? We may never know. These other universes, born of the same paroxicism of Creation as our own, are forever beyond our scrutiny but obviously not our imaginations!

Beyond The Beginning…

Finally, what of the period before Grand Unification? We may surmise that at higher temperatures than the GUT Era, even the supermassive Higgs and Leptoquark bosons become massless and at long last we arrive at a time when the gravitational interaction is united with the weak, electromagnetic and strong forces. Yet, our quest for an understanding of the origins of the universe remains incomplete since gravity has yet to be brought into unity with the remaining forces on a theoretical basis. This last step promises to be not only the most difficult one to take on the long road to unification but also appears to hold the greatest promise for shedding light on some of the most profound mysteries of the physical world. Even now, a handful of theorists around the world are hard at work on a theory called Supergravity which unites the force carriers (photons, gluons, gravitons and the weak interaction bosons) with the particles that they act on (quarks, electrons etc). Supergravity theory also predicts the existence of new particles called photinos and gravitinos. There is even some speculation that the photinos may fill the entire universe and account for the unseen ‘missing’ matter that is necessary to give the universe the critical mass required to make it exactly Euclidean. The gravitinos, on the other hand, prevent calculations involving the exchange of gravitons from giving infinite answers for problems where the answers are known to be perfectly finite. Hitherto, these calculations did not include the affects of the gravitinos.

Perhaps during the next decade, more of the details of the last stage of Unification will be hammered out at which time the entire story of the birth of our universe can be told. This is, indeed, an exciting time to be living through in human history. Will future generations forever envy us our good fortune, to have witnessed in our lifetimes the unfolding of the first comprehensive theory of Existence?

What is Space? Part I

Does Space Have More Than 3 Dimensions?
Written by Sten Odenwald
Copyright (C) 1984 Kalmbach Publishing. Reprinted by permission

The intuitive notion that the universe has three dimensions seems to be an irrefutable fact. After all, we can only move up or down, left or right, in or out. But are these three dimensions all we need to describe nature? What if there aree, more dimensions ? Would they necessarily affect us? And if they didn’t, how could we possibly know about them? Some physicists and mathematicians investigating the beginning of the universe think they have some of the answers to these questions. The universe, they argue, has far more than three, four, or five dimensions. They believe it has eleven! But let’s step back a moment. How do we know that our universe consists of only three spatial dimensions? Let’s take a look at some “proofs.”

On a 2-dimensional piece of paper you can draw an infinite number of polygons.  But when you try this same trick in 3-dimensions you run up against a problem.There are five and only five regular polyhedra. A regular polyhedron is defined as a solid figure whose faces are identical polygons – triangles, squares, and pentagons – and which is constructed so that only two faces meet at each edge. If you were to move from one face to another, you would cross over only one edge. Shortcuts through the inside of the polyhedron that could get you from one face to another are forbidden. Long ago, the mathematician Leonhard Euler demonstrated an important relation between the number of faces (F), edges (E), and corners (C) for every regular polyhedron: C – E + F = 2. For example, a cube has 6 faces, 12 edges, and 8 corners while a dodecahedron has 12 faces, 30 edges, and 20 corners. Run these numbers through Euler’s equation and the resulting answer is always two, the same as with the remaining three polyhedra. Only five solids satisfy this relationship – no more, no less.

Not content to restrict themselves to only three dimensions, mathematicians have generalized Euler’s relationship to higher dimensional spaces and, as you might expect, they’ve come up with some interesting results. In a world with four spatial dimensions, for example, we can construct only six regular solids. One of them – the “hypercube” – is a solid figure in 4-D space bounded by eight cubes, just as a cube is bounded by six square faces. What happens if we add yet another dimension to space? Even the most ambitious geometer living in a 5-D world would only be able to assemble thee regular solids. This means that two of the regular solids we know of – the icosahedron and the dodecahedron – have no partners in a 5-D universe.
For those of you who successfully mastered visualizing a hypercube, try imagining what an “ultracube” looks like. It’s the five- dimensional analog of the cube, but this time it is bounded by one hypercube on each of its 10 faces! In the end, if our familiar world were not three-dimensional, geometers would not have found only five regular polyhedra after 2,500 years of searching. They would have found six (with four spatial dimension,) or perhaps only three (if we lived in a 5-D universe). Instead, we know of only five regular solids. And this suggests that we live in a universe with, at most, three spatial dimensions.

All right, let’s suppose our universe actually consists of four spatial dimensions. What happens? Since relativity tells us that we must also consider time as a dimension, we now have a space-time consisting of five dimensions. A consequence of 5-D space-time is that gravity has freedom to act in ways we may not want it to.

To the best available measurements, gravity follows an inverse square law; that is, the gravitational attraction between two objects rapidly diminishes with increasing distance. For example, if we double the distance between two objects, the force of gravity between them becomes 1/4 as strong; if we triple the distance, the force becomes 1/9 as strong, and so on. A five- dimensional theory of gravity introduces additional mathematical terms to specify how gravity behaves. These terms can have a variety of values, including zero. If they were zero, however, this would be the same as saying that gravity requires only three space dimensions and one time dimension to “give it life.” The fact that the Voyager space- craft could cross billions of miles of space over several years and arrive vithin a few seconds of their predicted times is a beautiful demonstration that we do not need extra-spatial dimensions to describe motions in the Sun’s gravitational field.

From the above geometric and physical arguments, we can conclude (not surprisingly) that space is three-dimensional – on scales ranging from that of everyday objects to at least that of the solar system. If this were not the case, then geometers would have found more than five regular polyhedra and gravity would function very differently than it does – Voyager would not have arrived on time. Okay, so we’ve determined that our physical laws require no more than the three spatial dimensions to describe how the universe works. Or do they? Is there perhaps some other arena in the physical world where multidimensional space would be an asset rather than a liability?

Since the 1920s, physicists have tried numerous approaches to unifying the principal natural interactions: gravity, electromagnetism, and the strong and weak forces in atomic nuclei. Unfortunately, physicists soon realized that general relativity in a four-dimensional space-time does not have enough mathematical “handles” on which to hang the frameworks for the other three forces. Between 1921 and 1927, Theodor Kaluza and Oskar Klein developed the first promising theory combining gravity and electromagnetism. They did this by extending general relativity to five dimensions. For most of us, general relativity is mysterious enough in ordinary four-dimensional space-time. What wonders could lie in store for us with this extended universe?

General relativity in five dimensions gave theoreticians five additional quantities to manipulate beyond the 10 needed to adequately define the gravitational field. Kaluza and Klein noticed that four of the five extra quantities could be identified with the four components needed to define the electromagnetic field. In fact, to the delight of Kaluza and Klein, these four quantities obeyed the same types of equations as those derived by Maxwell in the late 1800s for electromagnetic radiationl Although this was a promising start, the approach never really caught on and was soon buried by the onrush of theoretical work on the quantum theory of electromagnetic force. It was not until work on supergravity theory began in 1975 that Kaluza and Klein’s method drew renewed interest. Its time had finally come.

What do theoreticians hope to gain by stretching general relativity beyond the normal four dimensions of space-time? Perhaps by studying general relativity in a higher-dimensional formulation, we can explain some of the constants needed to describe the natural forces. For instance, why is the proton 1836 times more massive than the electron? Why are there only six types of quarks and leptons? Why are neutrinos massless? Maybe such a theory can give us new rules for calculating the masses of fundamental particles and the ways in which they affect one another. These higher-dimensional relativity theories may also tell us something about the numbers and properties of a mysterious new family of particles – the Higgs bosons – whose existence is predicted by various cosmic unification schemes. (See “The Decay of the False Vacuum,” ASTRONOMY, November 1983.)

These expectations are not just the pipedreams of physicists – they actually seem to develop as natural consequences of certain types of theories studied over the last few years. In 1979, John Taylor at Kings College in London found that some higher- dimensional formalisms can give predictions for the maximum mass of the Higgs bosons (around 76 times that of the proton.) As they now stand, unification theories can do no more than predict the existence of these particles – they cannot provide specific details about their physical characteristics. But theoreticians may be able to pin down some of these details by using extended theories of general relativity. Experimentally, we know of six leptons: the electron, the muon, the tauon, and their three associated neutrinos. The most remarkable prediction of these extended relativity schemes, however, holds that the number of leptons able to exist in a universe is related to the number of dimensions of space-time. In a 6-D space-time, for example, only one lepton – presumably the electron – can exist. In a 10-D space-time, four leptons can exist – still not enough to accommodate the six we observe. In a 12-D space- time, we can account for all six known leptons – but we also acquire two additional leptons that have not yet been detected. Clearly, we would gain much on a fundamental level if we could increase the number of dimensions in our theories just a little bit.

How many additional dimensions do we need to consider in order to account for the elementary particles and forces that we know of today? Apparently we require at least one additional spatial dimension for every distinct “charge” that characterizes how each force couples to matter. For the electromagnetic force, we need two electric charges: positive and negative. For the strong force that binds quarks together to form, among other things, protons and neutrons, we need three “color” charges – red, blue, and green. Finally, we need two “weak” charges to account for the weak nuclear force. if we add a spatial dimension for each of these charges, we end up with a total of seven extra dimensions. The properly extended theory of general relativity we seek is one with an 11 -dimensional space-time, at the very least. Think of it – space alone must have at least 10 dimensions to accomodate all the fields known today.

Of course, these additional dimensions don’t have to be anything like those we already know about. In the context of modern unified field theory, these extra dimensions are, in a sense, internal to the particles themselves – a “private secret,” shared only by particles and the fields that act on them! These dimensions are not physically observable in the same sense as the three spatial dimensions we experience; they’stand in relation to the normal three dimensions of space much like space stands in relation to time.

With today’s veritable renaissance in finding unity among the forces and particles that compose the cosmos, some by methods other than those we have discussed, these new approaches lead us to remarkably similar conclusions. It appears that a four-dimensional space-time is simply not complex enough for physics to operate as it does.

We know that particles called bosons mediate the natural forces. We also know that particles called fermions are affected by these forces. Members of the fermion family go by the familiar names of electron, muon, neutrino, and quark; bosons are the less well known graviton, photon, gluon, and intermediate vector bosons. Grand unification theories developed since 1975 now show these particles to be “flavors” of a more abstract family of superparticies – just as the muon is another type of electron. This is an expression of a new kind of cosmic symmetry – dubbed supersymmetry, because it is all-encompassing. Not only does it include the force-carrying bosons, but it also includes the particles on which these forces act. There also exists a corresponding force to help nature maintain supersymmetry during the various interactions. It’s called supergravity. Supersymmetry theory introduces two new types of fundamental particles – gravitinos and photinos. The gravitino has the remarkable property of mathematically moderating the strength, of various kinds of interactions involving the exchange of gravitons. The photino, cousin of the photon, may help account for the “missing mass” in the universe.

Supersymmetry theory is actually a complex of eight different theories, stacked atop one another like the rungs of a ladder. The higher the rung, the larger is its complement of allowed fermion and boson particle states. The “roomiest” theory of all seems to be SO(8), (pronounced ess-oh-eight), which can hold 99 different kinds of bosons and 64 different kinds of fermions. But SO(8) outdoes its subordinate, SO(7), by only one extra dimension and one additional particle state. Since SO(8) is identical to SO(7) in all its essential features, we’ll discuss SO(7) instead. However, we know of far more than the 162 types of particles that SO(7) can accommodate, and many of the predicted types have never been observed (like the massless gravitino). SO(7) requires seven internal dimensions in addition to the four we recognize – time and the three “every day” spatial dimensions. If SO(7) at all mirrors reality, then our universe must have at least 11 dimensions! Unfortunately, it has been demonstrated by W. Nahm at the European Center for Nuclear Research in Geneva, Switzerland that supersymmetry theories for space-times with more than 11 dimensions are theoretically impossible. SO(7) evidently has the largest number of spatial dimensions possible, but it still doesn’t have enough room to accommodate all known types of particles.

It is unclear where these various avenues of research lead. Perhaps nowhere. There is certainly ample historical precedent for ideas that were later abandoned because they turned out to be conceptual dead-ends. Yet what if they turn out to be correct at some level? Did our universe begin its life as some kind of 11-dimensional “object” which then crystallized into our four- dimensional cosmos?

Although these internal dimensions may not have much to do with the real world at the present time, this may not always have been the case. E. Cremmer and J. Scherk of I’Ecole Normale Superieure in Paris have shown that just as the universe went through phase transitions in its early history when the forces of nature became distinguishable, the universe may also have gone through a phase transition when mensionality changed. Presumably matter has something like four external dimensions (the ones we encounter every day) and something like seven internal dimensions. Fortunately for us, these seven extra dimensions don’t reach out into the larger 4-D realm where we live. If they did, a simple walk through the park might become a veritable obstacle course, littered with wormholes in space and who knows what else!

Alan Chocos and Steven Detweiler of Yale University have considered the evolution of a universe that starts out being five- dimensional. They discovered that while the universe eventually does evolve to a state where three of the four spatial dimensions expand to become our world at large, the extra fourth spatial dimension shrinks to a size of 10^-31 centimeter by the present time. The fifth dimension to the universe has all but vanished and is 20 powers of 10 – 100 billion billion times – smaller than the size of a proton. Although the universe appears four- dimensional in space-time, this perception is accidental due to our large size compared to the scale of the other dimensions. Most of us think of a dimension as extending all the way to infinity, but this isn’t the full story. For example, if our universe is really destined to re-collapse in the distant future, the three- dimensional space we know today is actually limited itself – it will eventually possess a maximum, finite size. It just so happens that the physical size of human beings forces us to view these three spatial dimensions as infinitely large.

It is not too hard to reconcile ourselves to the notion that the fifth (or sixth, or eleventh) dimension could be smaller than an atomic nucleus – indeed, we can probably be thankful that this is the case.

The Cosmological Redshift

Galaxy Redshifts Reconsidered

Written by Sten Odenwald 
Copyright (C) 1993 Sky Publishing Corporation. Reprinted by permission. See February 1993 issue

Since its discovery nearly 65 years ago, the cosmological redshift has endured as one of the most persuasive ‘proofs’ that our universe is expanding. The steps leading to its discovery are well known. Soon after Christian Doppler discovered that motion produces frequency shifts in 1842, astronomers began an aggressive spectroscopic program to measure the velocities of stars and planets using their Doppler shifts. This continued through the first few decades of the 20th century ‘culminating’ in the work by Vesto Slipher, Edwin Hubble and Milton Humason on the so-called spiral nebulae — distinctly non- stellar objects that also seemed to display star-like Doppler shifts. So long as velocities of only a few hundred kilometers per second were measured, no one questioned that the frequency shifts for the spiral nebulae indicated relative motion just as they had for stars and planets.
But, during the 1920’s and 30’s spiral nebulae with Doppler shifts of over 34,000 kilometers per second were discovered. In a letter by Hubble to the Dutch cosmologist Willem De Sitter in 1931, he stated his concerns about these velocities by saying “… we use the term ‘apparent velocities’ in order to emphasize the empirical feature of the correlation. The interpretation, we feel, should be left to you and the very few others who are competent to discuss the matter with authority.” Dispite this cautionary note, the fact of the matter was that the redshifts measured for the distant galaxies LOOKED like Doppler shifts. The terms ‘recession velocity’ and ‘expansion velocity’ were quickly brought into service by astronomers at the telescope, and by popularizers, to describe the physical basis for the redshift.

As astronomers explored the universe to greater depths, galaxies and quasars appeared to be rushing away at faster and faster speeds. It seems to be a completely natural consequence of the outrushing of matter from the big bang. Like a sparkling display of fireworks on a warm summer evening, we imagine ourselves standing on one of those galactic ‘cinders’, watching the others rush past us into the dark void of infinite space. Upon closer examination, however, this intuitively-compelling and seductive mental image is both inadequate and misleading.

The Mysteries of Relativity

Big bang cosmology is based on Einstein’s general theory of relativity. It is a theory transcending both Newton’s mechanics and Einstein’s special theory of relativity, introducing us to concepts that do not exist within the older theories. Nor are these concepts easily comprehensible by our common sense which has been honed by organic evolution to see the world only through a narrow set of glasses.

For example, special relativity is based on the difficult-to-fathom postulate that the speed of light is absolutely constant when measured in reference frames moving at a constant speed. From this emerges the concept of ‘spacetime’ which then becomes the arena for all phenomena involving time dilation, length contraction and the Twin Paradox. Beyond special relativity lies the incomparably more alien landscape of general relativity. Gravitational fields now become geometric curvatures of spacetime. This has no analog in special relativity based as it is on a perfectly flat spacetime that remains aloof from any influence on it by matter or energy.

Just as the constancy of the speed of light led to the Twin Paradox, the curvature of spacetime leads to its own menageri of peculiar phenomena. One of these involves the slowing-down of clocks in the presence of a strong gravitational field. Related to this is the “gravitational redshift” which occurs when the frequency of light sent from the surface of a body is shifted to lower frequencies during the journey to the observer. This redshift is not related to the famous Doppler shift since the observer is not in motion relative to the body emitting the light signal!

A second phenomenon predicted by general relativity that also has no analog in special relativity is the cosmological redshift. Simply stated, the cosmological redshift occurs because the curvature of spacetime was smaller in the past when the universe was younger than it is now. Light waves become stretched en route between the time they were emitted long ago, and the time they are detected by us today.

The Doppler shift and cosmology

It is tempting to refer to cosmological redshifts as Doppler shifts. This choice of interpretation has in the years since Hubble’s work led to an unfortunate misunderstanding of big bang cosmology, obscurring one of its most mysterious beauties. As noted with a hint of frustration by cosmologists such as Steven Weinberg and Jaylant Narlikar and John Wheeler, “The frequency of light is also affected by the gravitational field of the universe, and it is neither useful nor strictly correct to interpret the frequency shifts of light…in terms of the special relativistic Doppler effect.”.

By refering to cosmological redshifts as Doppler shifts, we are insisting that our Newtonian intuition about motion still applies without significant change to the cosmological arena. A result of this thinking is that quasars now being detected at redshifts of Z = 4.0 would have to be interpreted as traveling a speeds of more than V = Z x c or 4 times the speed of light. This is, of course, quite absurd, because we all know that no physical object may travel faster than the speed of light.

To avoid such apparently nonsensical speeds, many popularizers use the special relativistic Doppler formula to show that quasars are really not moving faster than light. The argument being that for large velocities, special relativity replaces Newtonian physics as the correct framework for interpreting the world. By using a special relativistic velocity addition formula the quasar we just discussed has a velocity of 92 percent the speed of light. Although we now have a feeling that Reason has returned to our description of the universe, in fact, we have only replaced one incomplete explanation for another. The calculation of the quasar’s speed now presupposes that special relativity ( a theory of flat spacetime) is applicable even at cosmological scales where general relativity predicts that spacetime curvature becomes important. This is equivalent to a surveyor making a map of the state of California, and not allowing for the curvature of the earth!

The adoption of the special relativistic Doppler formula by many educators has led to a peculiar ‘hybrid’ cosmology which attempts to describe big bang cosmology using general relativity, but which is still firmly mired in the ruberik of special relativity. For instance, under the entry ‘redshift’ in the Cambridge Encyclopedia of Astronomy it is explicitly acknowledged that the redshift is not a Doppler shift, but less than two paragraphs later, the special relativistic Doppler formula is introduced to show how quasars are moving slower than the speed of light! It is also common for popularizers of cosmology to describe how ‘space itself stretches’ yet continue to describe the expansion of the universe as motion governed by the restrictions of special relativity. What’s going on here?

General relativity to the rescue

By adopting general relativity as the proper guide, such contradictions are eliminated. General relativity leads us to several powerful conclusions about our cosmos: 1) special relativity is inapplicable for describing the larger universe; 2) the concepts of distance and motion are not absolutely defined and 3) Preexisting spacetime is undefined. Each of these conclusions are as counter-intuitive as the Twin Paradox or as the particle/wave dualism of quantum mechanics. As Nobel Physicist John Wheeler once put it “If you are not completely confused by quantum mechanics, you do not understand it” The same may be said for general relativity.

The first conclusion means that we cannot trust even the insights hard won from special relativity to accurately represent the ‘big picture’ of the universe. General relativity must replace special relativity in cosmology because it denies a special role to observers moving at constant velocity, extending special relativity into the arena of accelerated observers. It also denies a special significance to special relativity’s flat spacetime by relegating it to only a microscopic domain within a larger geometric possibility. Just as Newtonian physics gave way to special relativity for describing high speed motion, so too does special relativity give way to general relativity. This means that the special relativistic Doppler formula should not, in fact cannot, be used to quantify the velocity of distant quasars. We have no choice in this matter if we want to maintain the logical integrity of both theories.

Distance and motion

The second conclusion is particularly upsetting because if we cannot define what we mean by distance, how then can we discuss in meaningful terms the ‘motion’ of distant quasars, or a Hubble Law interpreted as a distance versus velocity relation? In a small region of spacetime, we can certainly define motion as we always have because space has a static, flat geometry. When a body moves from point x to point y in a time interval, T, we say it is moving with a speed of S = (x – y)/T. There are also specific experimental ways of measuring x, y and T to form the quotent S by using clocks and rulers. The crucil feature behind these measurements is that nothing happens to the geometry of space during the experiment to change the results of the measuring process.

In the cosmological setting which we believe is accurately described by general relativity, we have none of these luxuries! Astronomers cannot wait millions of years to measure quasar proper motions. They cannot, like Highway Patrol officers, bounce radar beams off distant galaxies to establish their relative distances or speeds. Unlike all other forms of motion that have been previously observed, cosmological ‘motion’ cannot be directly observed. It can only be INFERRED from observations of the cosmological redshift, which general relativity then TELLS US means that the universe is expanding.

In big bang cosmology, galaxies are located at fixed positions in space. They may perform small dances about these positions in accordance with special relativity and local gravitational fields, but the real ‘motion’ is in the literal expansion of space between them! This is not a form of movement that any human has ever experienced. It is, therefore, not surprising that our intuition reels at its implication and seeks other less radical interpretations for it including special relativity. But even the exotic language and conundrums of special relativity cannot help us. Instead we are forced to interrogate the mathematics of general relativity itself for whatever landmarks it can provide. In doing so, we are left, however, with a riddle as profound as that of the Twin Paradox, and equally challenging to explain.

Two galaxies permanently located at positions (x1 , y1 , z1 ) and ( x2 , y2 , z2 ) at one time find themselves one billion light years apart. Then a few billion years later while located at the same coordinates, they find themselves 3 billion light years apart. The galaxies have not ‘moved’, nevertheless, their separations have increased. In fact, when the universe was only one year old, the separations between these galaxies were increasing at 300 times the speed of light! Space can expand faster than the speed of light in general relativity because space does not represent matter or energy. The displacements that arise from its dilation produce an entirely new kind of motion for which even our special relativistically-trained intuitions remain profoundly silent. Like that gentleman from Main once said “You can’t get there [to general relativity] from here [special relativity]”. To the extent that general relativity has been tested and found correct, we have no choice but to accept its consequences at face value.

Space, time and matter

The last conclusion drawn from general relativistic cosmology is that, unlike special relativity, it is not physically meaningful to speak of spacetime existing independently of matter and energy. In big bang cosmology, both space and time came into existence along side matter and energy at ‘time zero’. If our universe contains more than a critical density of matter and energy, its spacetime is forever finite and bounded, in a shape analogous to a sphere. Beyond this boundary, space and time simply do not exist. In fact, general relativity allows the Conservation of Energy to be suspended so that matter and energy may be created quite literally from the nothingness of curved spacetime. General relativity provides a means for ‘jump-starting’ Creation!

Big bang cosmology is both a profoundly beautiful, and disturbing, model for our universe, its shape and its destiny. It contains many surprises which have yet to be completely worked-out. But one feature of the evolving universe seems absolutly clear, the big bang was not some grand fireworks display, but an event of a completely different order. It resembled more an expanding soap bubble film upon which galactic dust motes are carried along for the ride. This film represents the totality of all the space and matter in our universe, and it expands into a mysterious primordial void which is itself empty of space, dimension, time or matter.

In the future it is hoped that a death knell will finally have sounded for the last vestage of the older thinking. With the Doppler interpretation of the cosmological redshift at last reconsidered, and rejected, we will finally be able to embrace the essential beauty and mystery of cosmic expansion as it was originally envisioned by its discoverers.