Category Archives: Physics

Death By Vacuum

As an astrophysicist, this has GOT to be one of my favorite ‘fringe’ topics in physics. There’s a long preamble story behind it, though!

The discovery of the Higgs Boson with a mass of 126 GeV, about 130 times more massive than a proton, was an exciting event back in 2012. By that time we had a reasonably complete Standard Model of how particles and fields operated in Nature to create everything from a uranium atom and a rainbow, to lighting the interior of our sun. A key ingredient was a brand new fundamental field in nature, and its associated particle called the Higgs boson. The Standard Model says that all fundamental particles in Nature have absolutely no mass, but they all interact with the Higgs field. Depending on how strong this interaction, like swimming through a container of molasses, they gain different amounts of mass. But the existence of this Higgs field has led to some deep concerns about our world that go well beyond how this particle creates the physical property we call mass.

In a nutshell, according to the Standard Model, all particles interact with the ever-present Higgs field, which permeates all space. For example, the W-particles interact very strongly with the Higgs field and gain the most mass, while photons interact not at all, remain massless.

The Higgs particles come from the Higgs field, which as I said is present in every cubic centimeter of space in our universe. That’s why electrons in the farthest galaxy have the same mass as those here on Earth. But Higgs particles can also interact with each other. This produces a very interesting effect, like the tension in a stretched spring. A cubic centimeter of space anywhere in the universe is not at all perfectly empty, and actually has a potential energy ‘stress’ associated with it. This potential energy is  related to just how massive the Higgs boson is. You can draw a curve like the one below that shows the vacuum energy  and how it changes with the Higgs particle mass:

Now the Higgs mass actually changes as the universe expands and cools. When the universe was very hot, the curve looked like the one on the right, and the mass of the Higgs was zero at the bottom of the curve. As the universe expanded and cooled, this Higgs interaction curve turned into the one on the left, which shows that the mass of the Higgs is now X0 or 126 GeV. Note, the Higgs mass represented by the red ball used to be zero, but ‘rolled down’ into the lower-energy pit as the universe cooled.

The Higgs energy curve shows a very stable situation for ‘empty’ space at its lowest energy (green balls) because there is a big energy wall between where the field is today, and where it used to be (red ball). That means that if you pumped a bit of energy into empty space by colliding two particles there, it would not suddenly turn space into the roaring hot house of the Higgs field at the top of this curve.

We don’t actually know exactly what the Higgs curve looks like, but physicists have been able to make models of many alternative versions of the above curve to test out how stable the vacuum is. What they  found is something very interesting.

The many different kinds of Higgs vacuua can be defined  by using two masses: the Higgs mass and the mass of the top quark. Mathematically, you can then vary the values for the Higgs boson and the Top quark and see what happens to the stability of the vacuum. The results are summarized in the plot below.

The big surprise is that, from the observed mass of the Higgs boson and our top quark shown in the small box, their values are consistent with our space being inside a very narrow zone of what is called meta-stability. We do not seem to be living in a universe where we can expect space to be perfectly stable. What does THAT mean? It does sound rather ominous that empty space can be unstable!

What it means is that, at least in principle, if you collided particles with enough energy that they literally blow-torched a small region of space, this could change the Higgs mass enough that the results could be catastrophic. Even though the collision region is smaller than an atom, once created, it could expand at the speed of light like an inflating bubble. The interior would be a region of space with new physics, and new masses for all of the fundamental particles and forces. The surface of this bubble would be a maelstrom of high-energy collisions leaking out of empty space! You wouldn’t see the wall of this bubble coming. The walls can contain a huge amount of energy, so you would be incinerated as the bubble wall ploughed through you.

Of course the world is not that simple. These are all calculations based on the Standard Model, which may be incomplete. Also, we know that cosmic rays collide with Earth’s atmosphere at energies far beyond anything we will ever achieve…and we are still here.

So sit back and relax and try not to worry too much about Death By Vacuum.

Then again…

 

Return here on Wednesday, February 22 for my next blog!

The Particle Desert

For the last 100 years physicists have built exotic “atom smashers” to probe the innermost constituents of matter. Along the way they created a breathtakingly elegant mathematical theory called the Standard Model that seems to explain all of the physics we see at the atomic scale. It describes how a collection of twelve fundamental matter particles (electrons, quarks neutrinos etc) generate three fundamental forces in Nature, and how these forces are related to twelve other particles called the gauge bosons. A final 25th particle, the Higgs boson, rounds out the ensemble and embues some of the 24 particles with that mystical property we call mass.

During all this time, teams of physicists working in the “data dumps” of billion-dollar colliders have sifted through terabytes of information to refine the accuracy of the Standard Model and compare its predictions with the real world. The predictions always seemed to match reality and push the testing of the Standard Model to still higher energies. But at the Large Hadron Collider at CERN, among the trillions of interactions studied up to energies of 13,000 GeV, no new physics has been seen in the furthest decimal points of the Standard Model predictions since 2012; not so much as a hint that something else has to be added to bring it back in line with actual data. It is a theory that appears not to be broken at energies over 1000 times higher than it was designed for!

In the history of all previous colliders beginning in the 1950s, something new has always been found to move the development of physic’s explanatory capabilities forward. In the 1970s it was the discovery of quarks. In the 1980s it was the W and Z0 particles, and even recently in 2012 it was the Higgs boson. All these particles were found below an energy of 200 GeV. But now, as the LHC has spent the last year at 13,000 GeV, a desperate mood has set in. No new particles or forces have been discovered in this new energy landscape.

Nada. Nothing. Zippo.

Most of the theories that go beyond the Standard Model provide ways to unify the strong force with the electromagnetic and weak forces. At some very high energy, they say, all three forces have the same strength, unlike their present circumstance where the strong nuclear force is 100 times as strong as the electromagnetic force. The predicted energy where this unification happens is about 1000 trillion GeV — the so-called grand unification theory (GUT) energy.

According to popular supersymmetry theory calculations, there should be a large population of new particles above an energy of 1000 GeV. Each a partner to the known 25 particles, but far more massive. Some of these particles, such as the neutralino, are even candidates for dark matter! Above the masses of these new supersymmetry particles, however, there ought to be no new particles to discover from perhaps 100, 000 GeV to the GUT energy of 1000 trillion GeV. They say that without this energy desert, any particles there would cause the proton to decay much faster than current limits predict.

So although it is a frustrating prospect that no new particles may exist in this desert, this is a vital feature of our physical world that literally prevents all matter (protons) from disintegrating! But unlike the Sahara Desert, where we can at least drive through it to get to a different world beyond, there are apparently no easily reachable oases of new particles along the way to which physicists can target new generations of expensive colliders.

It remains to be seen whether the results from the Large Hadron Collider after 2016 will confirm our greatest hopes or validate our worst fears. Either way, stay tuned for some exciting news headlines!

 

Return here on Thursday, February 9 for my next blog!

 

Running on Empty

I don’t think that many people realize that right now, but a few miles north of Geneva, Switzerland and a few hundred meters below the sleepy, bucolic countryside, a leviathan machine 27 km in diameter works round-the-clock to recreate a glimpse of the Big Bang.

Called the Large Hadron Collider (LHC) it is the world’s largest particle collider created in 1998-2008 by a collaboration of over 10,000 scientists and engineers from over 100 countries. It cost $13 billion dollars, and consumes 1 billion kilowatt-hours of electricity each year; enough to run a city of 300,000 homes!


The aim of the LHC is to allow physicists to test the predictions of different theories of particle physics, including measuring the properties of the Higgs boson and searching for the large family of new particles predicted by supersymmetric theories, as well as other unsolved questions of physics.

Since it began full-power operation in 2009, it has made a series of major discoveries that have rocked the physics world. The first of these, some 50 years after its prediction, was the discovery in 2012 of the Higgs Boson; a missing particle in the Standard Model that imbues most particles with their masses. Two years later, two new heavy sub-atomic particles were discovered called the Xi-prime and the Xi-star. Each consists of a bottom-quark, a down-quark and a strange-quark. Then a four-quark particle called the Z(4430) was found in 2014, along with signs of a five-quark combination that decayed into other, more stable particles. By 2016, LHC physicists had detected the light from antimatter hydrogen atoms (an anti-proton orbited by a positron). The findings were that this light was exactly the same as from a normal-matter hydrogen atom, so you really can’t tell the difference between matter and anti-matter from the light it emits!

But there was one other search going on that hasn’t been quite as successful, and with serious consequences.
Since 1978, physicists have explored the mathematical wonders of a new symmetry in nature called supersymmetry. This one shows how the particles that carry forces in the Standard Model (photons, gluons, w-bosons) are related to the matter particles they interact with (electrons, neutrinos, quarks). This symmetry unifies all of the known particles in the Standard Model, and also predicts that all normal particles will have supersymmetry partners with far-higher masses. The electron has a partner called the slectron. The quark has a partner called the squark, and so on. The simplest change in the Standard Model that includes this new mathematical symmetry ( called the Minimal Supersymmetric Standard Model or MSSM) adds 12 new matter particles and 12 new force particles beginning at masses that are 3 times greater than the mass of the normal proton. Amazingly, one of these partners to the normal-matter neutrinos would exactly fit the bill for the dark matter that astronomers have detected across the universe! MSSM predicts the eventual unification of all three forces; electromagnetism, strong and weak. MSSM would also let us accurately predict what happened before the universe was a microsecond old after the Big Bang!

Unfortunately, the search for any signs of supersymmetry particles is not going so well after seven years of sifting through data.

In one strategy, physicists look for any signs that the predictions made by the Standard Model are not accurate as a sign of New Physics. In another strategy, physicists look for the specific signs of the decays of these new, massive particles into the familiar matter particles.

On 8 November 2012, physicists reported on an experiment seen as a “golden” test of supersymmetry by measuring the very rare decay of the Bs meson into two muons. Disconcertingly, the results matched those predicted by the Standard Model rather than the predictions of many alternate versions of the Standard Model with supersymmetry included. New data with the collider now operating at higher energies than ever before, 13 trillion electron volts; 13 TeV) show no traces of superpartners.

As of the start of 2017, it really does look as though the LHC has given us a complete and well-tested Standard Model including the Higgs Boson, but has refused to hand over any signs of new particles existing between 190 GeV and 2,500 GeV (see the predicted particle plot below). This represents a distressing, barren desert which, had it looked as supersymmetry had predicted, should have been filled with dozens of new particles never before seen.

Many physicists are adopting an attitude of “keep calm and carry on.” “I am not yet particularly worried,” says theoretical physicist Carlos Wagner of the University of Chicago. “I think it’s too early. We just started this process.” The LHC has delivered only 1 percent of the data it will collect over its lifetime. But if no firm evidence is found for supersymmetry with the LHC, that also spells the end of another marvelous, mathematical theory that proposes to also unify gravity with the Standard Model. You know this theory by its popular name String Theory.

So a lot is still to come with the LHC in the next 5 years, and in no way is the current machine ‘running on empty’! Even its failure to find new physics will be revolutionary in its own right, and force an exciting re-boot of the entire theoretical approach in physics during the 2020s and beyond.

Check back here on Thursday, January 26 for the next blog!

Cancer and Cosmology

For the treatment of my particular cancer, small B-cell follicular non-Hodgkins Lymphoma, I will soon be starting a 6-month course of infusions of Rituximab and Bendamustine. The biology of these miracle drugs seems to be very solid and logically sound. This one-two chemical punch to my lymphatic system will use targeted antibodies to bind with the CD20 receptor on the cancerous B-cells. This will set in motion several cellular mechanisms that will kill the cells. First, the antibody bound to the CD20 receptor attracts T-cells in the immune system to treat the cancerous B-cell as an invader. Thus begins my immune system’s process of killing the invader. The antibody also triggers a reaction in the cell to commit suicide called apoptosis. Even better, Rituximab does not set in motion the process to kill normal B-cells!

The promise is that my many enlarged lymph nodes chock-a-block with the cancerous B-cells will be dramatically reduced in size to near-normal levels as they are depopulated of the cancerous cells. So why do some patients not all show the same dramatic reductions? About 70% respond to this therapy to various degrees while 10% do not. Why, given the impeccable logic of the process, aren’t the response rates closer to 100%?

Meanwhile, in high-energy physics, supersymmetry is a deeply beautiful and lynch-pin mathematical principle upon which the next generations of theories about matter and gravity are based. By adding a teaspoon of it to the Standard Model, which currently accounts in great mathematical detail for all known particles and forces, supersymmetry provides an elegant way to explore an even larger universe that includes dark matter, unifying all natural forces, and explaining many of the existing mysteries not answered by the Standard Model.
Called the Minimal Supersymmetric Standard Model (MSSM), Nature consistently rewards the simplest explanations for physical phenomena, so why has there been absolutely no sign of supersymmetry at the energies predicted by MSSM, and being explored by the CERN Large Hadron Collider?

In both cases, I have a huge personal interest in these logically compelling strategies and ideas: One to literally save my life, and the other to save the intellectual integrity of the physical world I have so deeply explored as an astronomer during my entire 40 year career. In each case, the logic seems to be flawless, and it is hard to see how Nature would not avail itself of these simple and elegant solutions with high fidelity. But for some reason it chooses not to do so. Rituximab works only imperfectly, while supersymmetry seems an un-tapped logical property of the world.

So what’s going on here?

In physics, we deal with dumb matter locked into simple systems controlled by forces that can be specified with high mathematical accuracy. The fly in the ointment is that, although huge collections of matter on the astronomical scale follow one set of well-known laws first discovered by Sir Isaac Newton and others, at the atomic scale we have another set of laws that operate on individual elementary particles like electrons and photons. This is still not actually a problem, and thanks to some intense mathematical reasoning and remarkable experiments carried out between 1920 and 1980, our Standard Model is a huge success. One of the last hold-outs in this model was the discovery of the Higgs Boson in 2012, some 50 years after its existence was predicted! But as good as the Standard Model is, there seem to be many loose ends that are like red flags to the inquiring human mind.

One major loose end is that astronomers have discovered what is popularly called ‘dark matter’, and there is no known particle or force in the Standard Model to account for it. Supersymmetry answers the question, why does nature have two families of particles when one would be even simpler? Amazingly, and elegantly, supersymmetry answers this question by showing how electrons, and quarks, which are elementary matter particles, are related to photons and gluons, which are elementary force-carrying particles. But in beautifully unifying the particles and forces, it also offers up a new family of particles, the lightest of which would fit the bill as missing dark matter particles!

This is why physicists are desperately trying to verify supersymmetry, not only to simplify physics, but to explain dark matter on the cosmological scale. As an astronomer, I am rooting for supersymmetry because I do not like the idea that 80% of the gravitating stuff in the universe is not stars and dust, but inscrutable dark matter. Nature seems not to want to offer us this simple option that dark matter is produced by ‘supersymmetric neutralinos’. But apparently Nature may have another solution in mind that we have yet to stumble upon. Time will tell, but it will not be for my generation to discover.

On the cancer-side of the equation, biological systems are gears-within-gears in a plethora of processes and influences. A logically simple idea like the Rituximab treatment looks compelling if you do not look too closely at what the rest of the cancerous B-cells are doing, or how well they like being glommed onto by a monoclonal antibody like Rituximab. No two individuals apparently have the same B-cell surfaces, or the same lymphatic ecology in a nearly-infinite set of genetic permutations, so a direct chemical hit by a Rituximab antibody to one cancerous B-cell may be only a glancing blow to another. This is why I am also rooting for my upcoming Rituximab treatments to be a whopping success. Like supersymmetry, it sure would simplify my life!

The bottom line seems to be that, although our mathematical and logical ideas seem elegant, they are never complete. It is this incompleteness that defeats us, sometimes by literally killing us and sometimes by making our entire careers run through dark forests for decades before stumbling into the light.

 

Check back here on Wednesday, December 28 for the next installment!

Rainbow image credit: Daily Mail: UK
http://www.dailymail.co.uk/news/article-1354580/UK-weather-Rainbow-dominates-skyline-winter-storms.html

Oops…One more thing!

After writing thirteen essays about space, I completely forgot to wrap up the whole discussion with some thoughts about the Big Picture! If you follow the links in this essay you will come to the essay where I explained the idea in more detail!

Why did I start these essays with so much talk about brain research? Well, it is the brain, after all, that tries to create ideas about what you are seeing based on what the senses are telling it. The crazy thing is that what the brain does with sensory information is pretty bizarre when you follow the stimuli all the way to consciousness. In fact, when you look at all the synaptic connections in the brain, only a small number have anything to do with sensory inputs. It’s as though you could literally pluck the brain out of the body and it would hardly realize it needed sensory information to keep it happy. It spends most of its time ‘taking’ to itself.

The whole idea of space really seems to be a means of representing the world to the brain to help it sort out the rules it needs to survive and reproduce. The most important rule is that of cause-and-effect or ‘If A happens then B will follow’. This also forms the hardcore basis of logic and mathematical reasoning!
But scientifically, we know that space and time are not just some illusion because objectively they seem to be the very hard currency through which the universe represents sensory stimuli to us. How we place ourselves in space and time is an interesting issue in itself. We can use our logic and observations to work out the many rules that the universe runs by that involve the free parameters of time and space. But when we take a deep dive into how our brains work and interfaces with the world outside our synapses, we come across something amazing.

The brain needs to keep track of what is inside the body, called the Self, and what is outside the body. If it can’t do this infallibly, it cannot keep track of what factors are controlling its survival, and what factors are solely related to its internal world of thoughts, feelings, and imaginary scenarios. This cannot be just a feature of human brains, but has to also be something that many other creatures also have at some rudimentary level so that they too can function in the external world with its many hazards. In our case, this brain feature is present as an actual physical area in the cerebral cortex. When it is active and stimulated, we have a clear and distinct perception of our body and its relation to space. We can use this to control our muscles, orient ourselves properly in space, walk and perform many other skills that require a keen perception of this outside world. Amazingly, when you remove the activity in this area through drugs or meditation, you can no longer locate yourself in space and this leads to the feeling that your body is ‘one’ with the world, your Self has vanished, and in other cases you experience the complete dislocation of the Self from the body, which you experience as Out of Body travel.

What does this have to do with space in the real world? Well, over millions of years of evolution, we have made up many rules about space and how to operate within it, but then Einstein gave us relativity, and this showed that space and time are much more plastic than any of the rules we internalized over the millennia. But it is the rules and concepts of relativity that make up our external world, not the approximate ‘common sense’ ideas we all carry around with us. Our internal rules about space and time were never designed to give us an accurate internal portrayal of moving near the speed of light, or functioning in regions of the outside world close to large masses that distort space.

But now that we have a scientific way of coming up with even more rules about space and time, we discover that our own logical reasoning wants to paint an even larger picture of what is going on and is happy to do so without bothering too much with actual (sensory) data. We have developed for other reasons a sense of artistry, beauty and aesthetics that, when applied to mathematics and physics, has taken us into the realm of unifying our rules about the outside world so that there are fewer and fewer of them. This passion for simplification and unification has led to many discoveries about the outside world that, miraculously, can be verified to be actual objective facts of this world.

Along this road to simplifying physics, even the foundations of space and time become players in the scenery rather than aloof partners on a stage. This is what we are struggling with today in physics. If you make space and time players in the play, the stage itself vanishes and has to somehow be re-created through the actions of the actors themselves .THAT is what quantum gravity hopes to do, whether you call the mathematics Loop Quantum Gravity or String Theory. This also leads to one of the most challenging concepts in all of physics…and philosophy.

What are we to make of the ingredients that come together to create our sense of space and time in the first place? Are these ingredients, themselves, beyond space and time, just as the parts of a chain mail vest are vastly different than the vest that they create through their linkages? And what is the arena in which these parts connect together to create space and time?

These questions are the ones I have spent my entire adult life trying to comprehend and share with non-scientists, and they lead straight into the arms of the concept of emergent structures: The idea that elements of nature come together in ways that create new objects that have no resemblance to the ingredients, such as evolution emerging from chemistry, or mind emerging from elementary synaptic discharges. Apparently, time and space may emerge from ingredients still more primitive, that may have nothing to do with either time or space!

You have to admit, these ideas certainly make for interesting stories at the campfire!

Check back here on Monday, December 26 for the start of a new series of blogs on diverse topics!

Quantum Gravity…Oh my!

So here’s the big problem.

Right now, physicists have a detailed mathematical model for how the fundamental forces in nature work: electromagnetism, and the strong and weak nuclear forces. Added to this is a detailed list of the fundamental particles in nature like the electron, the quarks, photons, neutrinos and others. Called the Standard Model, it has been extensively verified and found to be an amazingly accurate way to describe nearly everything we see in the physical world. It explains why some particles have mass and others do not. It describes exactly how forces are generated by particles and transmitted across space. Experimenters at the CERN Large Hadron Collider are literally pulling out their hair to find errors or deficiencies in the Standard Model that go against the calculated predictions, but have been unable to turn up anything yet. They call this the search for New Physics.

Along side this accurate model for the physical forces and particles in our universe, we have general relativity and its description of gravitational fields and spacetime. GR provides no explanation for how this field is generated by matter and energy. It also provides no description for the quantum structure of matter and forces in the Standard Model. GR and the Standard Model speak two very different languages, and describe two very different physical arenas. For decades, physicists have tried to find a way to bring these two great theories together, and the results have been promising but untestable. This description of gravitational fields that involves the same principles as the Standard Model has come to be called Quantum Gravity.

The many ideas that have been proposed for Quantum Gravity are all deeply mathematical, and only touch upon our experimental world very lightly. You may have tried to read books on this subject written by the practitioners, but like me you will have become frustrated by the math and language this community has developed over the years to describe what they have discovered.

The problem faced by Quantum Gravity is that gravitational fields only seem to display their quantum features at the so-called Planck Scale of 10^-33 centimeters and  10^-43 seconds. I cant write this blog using scientific notation, so I am using the shorthand that 10^3 means 1000 and 10^8 means 100 million. Similarly, 10^-3 means 0.001 and so on. Anyway, the Planck scale  also corresponds to an energy of 10^19 GeV or 10 billion billion GeV, which is an energy 1000 trillion times higher than current particle accelerators can reach.

There is no known technology that can reach the scales where these effects can be measured in order to test these theories. Even the concept of measurement itself breaks down! This happens because the very particles (photons) you try to use to study physics at the Planck scale carry so much energy  they turn into quantum black holes and are unable to tell you what they saw or detected!

One approach to QG is called Loop Quantum Gravity.  Like relativity, it assumes that the gravitational field is all there is, and that space and time become grainy or ‘quantized’ near the Planck Scale. The space and time we know and can experience in-the-large is formed from individual pieces that come together in huge numbers to form the appearance of a nearly-continuous and smooth gravitational field.

The problem is that you cannot visualize what is going on at this scale because it is represented in the mathematics, not by nuggets of space and time, but by more abstract mathematical objects called loops and spin networks. The artist rendition above is just that.

So here, as for Feynman Diagrams, we have a mathematical picture that represents a process, but the picture is symbolic and not photographic. The biggest problem, however, is that although it is a quantum theory for gravity that works, Loop Quantum Gravity does not include any of the Standard Model particles. It represents a quantum theory for a gravitational field (a universe of space and time) with no matter in it!

In other words, it describes the cake but not the frosting.

The second approach is string theory. This theory assumes there is already some kind of background space and time through which another mathematical construct called a string, moves. Strings that form closed loops can vibrate, and each pattern of vibrations represents a different type of fundamental particle. To make string theory work, the strings have to exist in 10 dimensions, and most of these are wrapped up into closed balls of geometry called Calabi-Yau spaces. Each of these spaces has its own geometry within which the strings vibrate. This means there can be millions of different ‘solutions’ to the string theory equations: each a separate universe with its own specific type of Calabi-Yau subspace that leads to a specific set of fundamental particles and forces. The problem is that string theory violates general relativity by requiring a background space!

In other words, it describes the frosting but not the cake!

One solution proposed by physicist Lee Smolin is that Loop Quantum Gravity is the foundation for creating the strings in string theory. If you looked at one of these strings at high magnification, its macaroni-like surface would turn into a bunch of loops knitted together, perhaps like a Medieval chainmail suit of armor. The problem is that Loop Quantum Gravity does not require a gravitational field with more than four dimensions ( 3 of space and one of time) while strings require ten or even eleven. Something is still not right, and right now, no one really knows how to fix this. Lacking actual hard data, we don’t even know if either of these theories is closer to reality!

What this hybrid solution tries to do is find aspects of the cake that can be re-interpreted as particles in the frosting!

This work is still going on, but there are a few things that have been learned along the way about the nature of space itself. At our scale, it looks like a continuous gravitational field criss-crossed by the worldlines of atoms, stars and galaxies. This is how it looks even at the atomic scale, because now you get to add-in the worldlines of innumerable ‘virtual particles’ that make up the various forces in the Standard Model.  But as we zoom down to the Planck Scale, space and spacetime stop being smooth like a piece of paper, and start to break up into something else, which we think reveals the grainy nature of gravity as a field composed of innumerable gravitons buzzing about.

But what these fragmentary elements of space and time ‘look’ like is impossible to say. All we have are mathematical tools to describe them, and like our attempts at describing the electron, they lead to a world of pure abstraction that cannot be directly observed.

If you want to learn a bit more about the nature of space, consider reading my short booklet ‘Exploring Quantum Space‘ available at amazon.com. It describes the amazing history of our learning about space from ancient Greek ‘common sense’ ideas, to the highlights of mind-numbing modern quantum theory.

Check back here on Thursday, December 22 for the last blog in this series!

What IS space?

One thing that is true about physics is that it involves a lot of mathematics. What this means is that we often use the mathematics to help us visualize what is going on in the world. But like I said in an earlier blog, this ‘vision thing’ in math can sometimes let you mistake the model for the real thing, like the case of the electron. The same problem emerges when we try to understand an invisible  thing like space.

The greatest discovery about space  was made by Einstein just before 1915 as he was struggling to turn his special theory of relativity into something more comprehensive.

Special relativity was his theory of space and time that described how various observers would see a consistent world despite their uniform motion at high speeds. This theory alone revolutionized physics, and has been the main-stay of modern quantum mechanics, as well as the designs of powerful accelerators that successfully and accurately push particles to nearly the speed of light. The problem was that special relativity did not include a natural place for accelerated motion, especially in gravitational fields, which are of course very common in the universe.

Geometrically, special relativity only works when worldlines are perfectly straight, and  form lines within a perfectly flat, 4-dimensional spacetime (a mathematical arena where 3 dimensions of space are combined with one dimension of time). But accelerated motion causes worldlines to be curved, and you cannot magically make the curves go straight again and keep the spacetime geometrically flat just by finding another coordinate system.

Special relativity, however, promised that so long as motion is at constant speed and worldlines are straight, two different observers (coordinate systems) would agree about what they are seeing and measuring by using the mathematics of special relativity. With curved worldlines and acceleration, the equations of special relativity, called the Lorentz Transformations, would not work as they were. Einstein was, shall we say, annoyed by this because clearly there should be some mathematical process that would allow the two accelerated observers to again see ( or calculate) consistent physical phenomena.

He began his mathematical journey to fix this problem by writing his relativity equations in a way that was coordinate independent using the techniques of tensor analysis. But he soon found himself frustrated by what he needed in order to accomplish this mathematical miracle, versus his knowledge of advanced analytic geometry in four dimensions. So he went to his classmate and math wiz, Marcel Grossman, who immediately recognized that Einstein’s mathematical needs were just an awkward way of stating certain properties of non-Euclidean geometry developed by Georg Riemann and others in the mid-to-late 1800s.

This was the missing-math that Einstein needed, who being a quick learner, mastered this new language and applied it to relativity. After an intense year of study, and some trial-and-error mathematical efforts, he published his complete Theory of General Relativity in November 1915. Just like the concept of spacetime did away with space and time as independent ideas in special relativity, his new theory made an even bigger, revolutionary, discovery.

It was still a theory of the geometry of worldlines that he was proposing, but now the geometric properties of these worldlines was controlled by a specific mathematical term called the metric tensor. This mathematical object was fundamental to all geometry as Grossman had showed him, and allowed you to calculate distances between points in space. It also defined what a ‘straight line’ meant, as well as how curved the space was. Amazingly, when you translated all this geometric talk into the hard, cold reality of physics in 4-dimensions, this metric tensor turned into the gravitational field through which the worldline of a particle was defined as the straightest-possible path.

An interesting factoid, indeed, but why is it so revolutionary?

All other fields in physics (e.g like the electromagnetic field) are defined by some quantity, call it A, that is specified at each coordinate point in space and time: A(x,y,z,t). If you take-away the field, the coordinate grid remains intact. But with the gravitational field, there is no background coordinate grid to define its intensity, instead, the gravitational field provides its own coordinate grid because it is identical to the metric tensor!!

This is why Einstein and physicists say that gravity is not a force like the others we know about, but instead it is a statement about the shape of the geometry of spacetime through which particles move. (Actually, particles do not move through spacetime. Their histories from start to finish simply exist all at once like a line drawn on a piece of paper!)

So, imagine a cake with frosting on it. The frosting represents the various fields in space, and you can locate where they are and how much frosting is on the cake from place to place. But the bulk of the cake, which is supporting the frosting and telling you that ‘this is the top, center, side, etc of the cake’ is what supports the frosting. Take away the cake, and the frosting is unsupported, and can’t even be defined in the first place. Similarly, take away the gravitational field, symbolized by Einstein’s metric tensor, and spacetime actually disappears!

Amazingly, Einstein’s equations say that although matter and energy produce gravitational fields, you can have situations where there is no matter and energy and spacetime still doesn’t vanish! These vacuum solutions are real head-scratchers when physicists try to figure out how to combine quantum mechanics, our premier theory of matter, with general relativity: our premier theory of gravity and spacetime. These vacuum solutions represent gravitational fields in their purest form, and are the starting point for learning how to describe the quantum properties of gravitational fields. They are also important to the existence of gravity waves, which move from place to place as waves in the empty spacetime between the objects producing them.

But wait a minute. Einstein originally said that ‘space’ isn’t actually a real thing. Now we have general relativity, which seems to be bringing space (actually spacetime) back as something significant in its own right as an aspect of the gravitational field.

What gives?

To see how some physicists resolve these issues, we have to delve into what is called quantum gravity theory, and this finally gets us back to some of my earlier blogs about the nature of space, and why I started this blog series!

 

Check back here on Wednesday, December 21 for the last installment on this series about space!

Is Infinity Real?

In the daytime, you are surrounded by trees, buildings and the all-too-familiar accoutrements of Nature, to which by evolution we were designed to appreciate and be familiar. But at night, we see an unimaginably different view: The dark, starry night sky, with no sense of perspective or depth. It is easy to understand how The Ancients thought it a celestial ceiling with pinpoint lights arrayed in noteworthy patterns. Many millennia of campfires were spent trying to figure it out.

We are stuck in the middle ground between two vast scales that stretch before us and within us. Both, we are told, lead to the infinitely-large and the infinitely-small. But is this really true?

Astronomically, we can detect objects that emerged from the Big Bang nearly 14 billion years ago, which means their light-travel distance from us is 14 billion light years or 13,000,000,000,000,000,000,000,000,000 centimeters. This is, admittedly, a big number but it is not infinitely-large.

In the microcosm, we have probed the structure of electrons to a scale of 0.000000000000000000001 centimeters and found no signs of any smaller distance yet. So again, there is no sign that we have reached anything like an infinitely-small limit to Nature either.

When it comes right down to it, the only evidence we have for the universe being infinitely large (or other aspects of it being infinitely small) is in the mathematics and geometry we use to describe it. Given that infinity is the largest number you can count to, it is pretty obvious that even the scale of our visible universe of 13,000,000,000,000,000,000,000,000,000 centimeters falls woefully short of being even a relatively stupendous number by comparison to infinity.

Infinity is as old as the Ancient Greeks. But even Aristotle (384 – 322 BCE) would only allow the integers (1,2,3,…) to be potentially infinite, but not actually infinite, in quantity. Since then, infinity or its cousin eternity, have become a part of our literary and religious vernacular when we mention something really, really, really….. big or old! Through literary and philosophical repetition, we have become comfortable with this idea in a way that is simply not justifiable.

Mathematics can define infinity very precisely, and even the mathematician Cantor (1845 – 1918) was able to classify ‘transfinite numbers’ as being either representing countable infinities or uncountable infinities. To the extent that mathematics is also used in physics, we inherit infinity as the limit to many of our calculations and models of the physical world. But the problem is that our world is only able to offer us the concept of something being very, very, very… big, like the example of the visible universe above.

If you take a sphere a foot across and place an ant on it, it crawls around and with a bit of surveying it can tell you the shape is a sphere with a finite closed surface. But now take this sphere and blow it up so that it is 1 million miles across. The ant now looks across its surface and sees something that looks like an infinite plane. Its geometry is as flat as a sheet of paper on a table.

In astronomy we have the same problem.

We make calculations and measurements within the 28 billion light years that spans our visible universe and conclude that the geometry of the universe is flat, and so geometrically it seems infinite, but the only thing the measurements can actually verify is that the universe is very, very, very large and LOOKS like its geometry is that of an infinite, flat, 3-dimensional space. But modern Big Bang cosmology also says that what we are seeing within our visible universe is only a portion of a larger thing that emerged from the Big Bang and ‘inflated’ to enormous size in the first microseconds.  If you identify our visible universe out to 14 billion light years as the size of the period at the end of this sentence, that larger thing predicted by inflation may be millions of miles across at the same scale. This is very, very big, but again it is not infinite!

Going the other way, the current best theoretical ideas about the structure of the physical world seems to suggest that at some point near a so-called Planck scale of 0.0000000000000000000000000000000015 centimeters we literally ‘run out of space’. This mathematical conclusion seems to be the result of combining the two great pillars of all physical science, quantum mechanics and general relativity, into a single ‘unified’ theory.  The mathematics suggests that, rather than being able to probe the nature of matter and space at still-smaller scales, the entire edifice of energy, space, time and matter undergoes a dramatic and final change into something vastly different than anything we have ever experienced: elements that are beyond space and time themselves.  These ideas are captured in theories such as Loop Quantum Gravity and String Theory, but frankly we are still at a very early stage in understanding what this all means. Even more challenging is that we have no obvious way to make any measurements that would directly test whether physical reality simply comes to an end at these scales or not.

So on the cosmological scene, we can convincingly say we have no evidence that anything as large as ‘infinity’ exists because it is literally beyond our 14 billion light-year horizon of detection. The universe is simply not old enough for us to sample such an imponderably large realm. Advances in Big Bang cosmology can only propose that we live in an incomprehensively alien ‘multiverse’ or that we inhabit one miniscule dot in a vastly larger cosmos, which our equations extrapolate as infinity. Meanwhile, the world of the quantum hints that no infinitely-small structures exist in the universe, not even what we like to call space itself can be indefinitely sub-divided below the Planck scale.

In the end, it seems that infinity is a purely  mathematical ideal that can be classified by Cantor’s transfinite numbers manipulated symbolically, and thought about philosophically, but is never actually found among the objects that inhabit our physical world.

Now let’s go back to the issue of space after the relativity revolution and try to make sense of where we stand now!

Check back here on Monday, December 19 for the next installment!

Relativity and Space

Psychologists and physicists often use a similar term to describe one of the most fundamental characteristics of humans and matter: The Story. Here, for example, is the timeline story for key events in the movie The Hunger Games.

Oliver Sacks, in his book ‘The Man Who Mistook His Wife for a Hat’ describes the case of Jimmy G who was afflicted with Korsakov’s Syndrome. He could not remember events more than a few minutes in the past, and so he had to re-invent his world every few minutes to account for new events. As Sacks notes ‘If we wish to know about a man, we ask ‘what is his story – his real, inmost story? – for each of us is a biography, a story..[and a] singular narrative, which is constructed, continually, unconsciously, by, through, and in us – through our perceptions, our feelings, our thoughts, our actions..and our narratives…we must constantly recollect ourselves’.

Physicist Lee Smolin, in his book ‘Three Roads to Quantum Gravity’ , describes the essential foundation of relativity as the ‘story’ about processes and not the things-as-objects.   “A marble is not an inert thing, it is a process…There are only relatively fast processes and relatively slow processes. And whether it is a short story or a long story, the only kind of explanation of a process  that is truly adequate is a story.”

In both cases, we cannot define an object, be it a human, a table, or an electron by merely describing its properties at one instant in time. We can only define an object in terms of a process consisting of innumerable events, which create the story that defines it. This is very obvious when we are talking about humans, but it also applies to every object in the universe.

In relativity, the history or ‘story’ of a process such as a football or a galaxy, consists of a series of events that are tied together by cause-and-effect to create the process that you see at any particular moment. These events include the interactions of one process with others that cumulatively create what you see as the history of the process at a particular moment. In relativity, we call this history of a process its worldline.

This is a worldline map (Credit Aaron Koblin / BBC)of airlines traveling to and from the United States. The lines give the history of each flight on the 2-d surface of Earth. Each worldline consists of a huge number of ‘hidden’ events contributed by each passenger! By carefully studying these worldlines you could mathematically deduce that Earth is a sphere.

What Einstein said is that only worldlines matter, because that is the only thing we have access to. Even better than that, we are only able to see that part of a processes that can be communicated to us by using light, which is the fastest signal we can ever use to transfer information. When we are ‘looking’ at something, like a car or a star, what we are actually doing is looking back along its history carried to us as information traveling by photons of light.

In an earlier essay, I mentioned how we do not see objects in space, but only the end points of a light ray’s history as, for example, it leaves the surface of an object (Event 1) arrives at dust mote along the way and was re-emitted (Event 2) to arrive at our retina, and cause a rod or a cone cell to fire (Event 3). Because these events are strictly determined by cause-and-effect, and travel times are limited by the speed of light, we can organize these events in a strict history for the object we viewed (which was in fact a ‘process’ in and of itself!).

So, what does this say about space? Space  is irrelevant, because we can completely define our story only in terms of the ‘geometry’ of these history worldlines and the causal connections between events on these worldlines, without any mention of space as a ‘background’ through which things move.

This leads to another problem.

Einstein’s new relativistic theory of gravity makes use of a convenient mathematical tool called 4-dimensional spacetime. Basically we live in a world with three dimensions of space and one dimension of time, making a 4-dimensional thing called spacetime. Without knowing, you live and work in 4-dimensions because there is nothing about you that does not ‘move’ in time as well as space from second to second. All physical process take place in 4 dimensions, so all theories of physics and how things work are necessarily statements about 4-dimensional things.

It is common to refer to gravity as a curvature in the geometry of this spacetime ‘fabric’, but we can just as easily talk about the curvature of worldlines defining gravity and not even bother with the idea of spacetime at all! Remember, when you look at an object, you are ‘just’ looking back through its history revealed by the network of photons of light.

So we have used a mathematical tool, namely spacetime, to make visualizing the curvature of worldlines easier to describe, but we now make the mistake of thinking that spacetime is real because we have now used the mathematical tool to represent the object itself. This is similar to what we did with the idea of Feynman Diagrams in the previous blog! As Lee Smolin says ‘When we imagine we are seeing into an infinite three-dimensional space, we are actually falling for a fallacy in which we substitute what we actually see [a history of events] for an intellectual construct [space]. This is not only a mystical vision, it is wrong.”

But what about infinity?

In my next essay I will discuss why infinity is probably not a real concept in the physical world.

 

Check back here on Friday, December 16 for the next installment!

Physicist Lee Smolin’s book ‘The Three Roads to Quantum Gravity’ discusses many of these ideas in more detail.

Is Space Real?

I take a walk to the store and can’t help but feel I am moving through something that is more than the atmosphere that rushes by my face as I go. The air itself is contained within the boundaries of the space through which I pass. If I were an astronaut in the vacuum of outer space, I would still have the sense that my motion was through a pre-existing, empty framework of 3-dimensions. Even if I were blind and confined to a wheelchair, I could still have the impression through muscular exertion that I was moving through space to get from my kitchen to my living room ‘over there’. But what is space as a physical thing? Of all the phenomena, forces and particles we study, each is something concrete though generally invisible: a field; a wave; a particle. But space, itself, seems to be none of these. WTF!

Spider web covered with dew drops

Way back in the early 1700s, Sir Isaac Newton proposed that space was an ineffable, eternal framework through which matter passed. It had an absolute and immutable nature. Its geometry pre-existed the matter that occupied it and was not the least bit affected by matter. A clever set of experiments in the 20th century finally demonstrated rather conclusively that there is no pre-existing Newtonian space or geometry ‘beneath’ our physical world. There is no absolute framework of coordinates within which our world is embedded. What had happened was that Albert Einstein developed a new way of thinking about space that essentially denied its existence!

Albert Einstein’s relativity revolution completely overturned our technical understanding of space and showed that the entire concept of dimensional space was something of a myth. In his famous quote he stressed that We entirely shun the vague word ‘space’ of which we must honestly acknowledge we cannot form the slightest conception. In the relativistic world we live in, space has no independent existence. “…[prior-geometry] is built on the a priori, Euclidean [space], the belief in which amounts to something like a superstition“. So what could possibly be a better way of thinking about space than the enormously compelling idea that each of us carries around in our brains, that space is some kind of stage upon which we move?

To understand what Einstein was getting at, you have to completely do away with the idea that space ‘is there’ and we move upon it or through it. Instead, relativity is all about the geometry created by the histories (worldlines) of particles as they move through time. The only real ‘thing’ is the collection of events along each particle’s history. If enough particles are involved, the histories are so numerous they seem like a continuous space. But it is the properties of the events along each history that determine the over-all geometry of the whole shebang and the property we call ‘dimension’, not the other way around.

This figure is an example where the wires (analogous to worldlines) are defining the shape and contours of a dimensional shape. There is nothing about the background (black) space that determines how they bend and curve. In fact, with a bit of mathematics you could specify everything you need to know about the surface of this shape and from the mathematics tell what the shape is, and how many dimensions are required to specify it!

Princeton University physicist Robert Dicke expressed it this way, “The collision between two particles can be used as a definition of a point in [space]…If particles were present in large numbers…collisions could be so numerous as to define an almost continuous trajectory…The empty background of space, of which ones knowledge is only subjective, imposes no dynamical conditions on matter.”

What this means is that so long as a point in space is not occupied by some physical event such as the interaction point of a photon and an electron, it has no effect on a physical process ( a worldline) and is not even observable. It is a mathematical ‘ghost’ that has no effect on matter at all. The interstitial space between the events is simply not there so far as the physical world based upon worldlines is concerned. It is not detectable even by the most sophisticated technology, or any inventions to come. It does not even supply something as basic as the ‘dimension’ for the physical world!

We should also be mindful of another comment by Einstein that “…time and space are modes by which we think and not conditions in which we live“. They are free creations of the human mind, to use one of Einstein’s own expressions. By the way, the 18th century philosopher Immanuel Kant also called the idea of ‘space’ an example of a priori knowledge that we are born with to sort out the world, but it is not necessarily a real aspect of the world outside our senses.

Like a spider web, individual and numerous events along a worldline define the worldline’s shape, yet like the spider web, this web can be thought of as embedded in a larger domain of mathematically-possible events that could represent physical events…but don’t. The distinction between these two kinds of points is what Einstein’s revolutionary idea of relativity provided physicists, and is the mainstay of all successful physical theories since the 1920s. Without it, your GPS-enabled cell phones would not work!

So what are these events? Simply put, according to Physicist Lee Smolin, they are exchanges of information, which are also the interaction points between one particle’s worldline and another particle’s world line. If you think at the atomic level, each time a particle of light interacts with (collides or is emitted by) an electron it generates an event. These events are so numerous the electron’s worldline looks like a continuous line with no gaps between the events. So the shape of one worldline, what we call its history, is a product of innumerable interactions over time with the worldlines of all other objects (photons etc) to which it can be in cause-and-effect contact.

Even though this new idea of space being a myth has gained enormous validity among physicists over the last century, and I can easily speak the language of relativity to describe it, personally, my mind has a hard time really understanding it all. I also use the mathematical theory of quantum mechanics to make phenomenally accurate predictions, but no Physicist really understands why it works, or what it really means.

Next time I want to examine how the history of a particle is more important than the concept of space in Einstein’s relativity, and how this explains the seeming rigidity of the world you perceive and operate within.

Check back here on Thursday, December 15 for the next installment!