Category Archives: Astronomy

Why NASA needs ARMs

In 2013, a small 70-meter asteroid exploded over the town of Chelyabinsk and injured 3000 people from flying glass. Had this asteroid exploded a few hours earlier over New York City, the flying glass hazard would have been lethal for thousands of people, sending thousands more into the emergency rooms of hospitals for critical-care treatment. Of all the practical benefits of space exploration, it is hard to argue that asteroid investigations are not a high priority above dreams of colonization of the moon and Mars.

So why is it that the only NASA mission to actually try a simple method to adjust the orbit of an asteroid cannot seem to garner much support?

There has been much debate over the next step in human exploration: whether to go back to the moon or take the harder path to Mars. The later goal has been much favored, and for the last decade or so, NASA has developed a step-by-step Journey to Mars approach for doing this, beginning with the development of the SLS launch vehicle, and the testing out of many necessary systems, technologies and strategies to support astronauts making this trip, both quickly and safely. Along with numerous Mars mapping and rover missions now in progress or soon to be launched, there are also technology development missions to test out such things as solar-electric ‘ion’ propulsion systems.

One of these test-bed missions with significant scientific returns is the Asteroid Redirect Mission to be launched in ca 2021 for a cost of about $1.4 billion. NASA’s first-ever robotic mission will visit a large near-Earth asteroid, collect a multi-ton boulder from its surface, and use it in an enhanced gravity tractor asteroid deflection demonstration. The spacecraft will then redirect the multi-ton boulder into a stable orbit around the moon, where astronauts will explore it and return with samples in the mid-2020s.

But all is not well for ARM.

ARM was proposed in 2010 during the Obama Administration as an alternative to the canceled Constellation Program proposed by the Bush Administration, so with the new GOP-dominated administration set on dismantling all of the Obama Administrations’ legacy work, there is much incentive to eliminate it for political reasons alone.

Reps. Lamar Smith (R-Texas), chairman of the HCSST, and Brian Babin (R-Texas), chairman of the HSST space subcommittee reportedly feel that the incoming Trump administration should be “unencumbered” by decisions made by the current one — like what they want to do with the ACA . They claim to have access to “honest assessments” of ARM’s value rather than “farcical studies scoped to produce a predetermined outcome.” The House’s version of the 2017 FY appropriations bill includes wording that would force NASA to fully defund the ARM program. Furthermore, Smith and Babin wrote, “the next Administration may find merit in some, if not all, of the components of ARM, and continue the program; however, that decision should be made after a full and fair review based on the merits of the program and in the context of a larger exploration and science strategy.” Similar arguments will no doubt be used to cancel climate change research, which has also been deemed politically biased and unscientific by the current, incoming administration.

But ARM is no ordinary ‘exploration and science’ space mission, even absent its unique ability to test the first high-power ion engines for interplanetary travel, and retrieve a large, pristine multi-ton asteroid sample. All other NASA missions have certainly demonstrated their substantial scientific returns, and this is often the key justification that allows them to proceed. Mission technology also affords unique tech spinoff opportunities in the commercial sector that makes the US aerospace industrial base very happy to participate. But these returns all seem rather abstract, and for the person-on-the-street rather hard to appreciate.

For decades, astronomers have been discovering and tracking 100s of thousands of asteroids. We live in an interplanetary shooting gallery, where some 15,000 Near Earth Objects have already been discovered, and 30 new ones added every week. NEOs, by the way, are asteroids that come within 30 million miles of Earth’s orbit. These asteroids measure 1 kilometer or more, and statistically over 90% of this population has now been identified. But only 27% of those 140 meters or larger have been discovered. Once their orbits are determined, we can make predictions about which ones will pose an danger to Earth.

Currently there are 1,752 potentially hazardous asteroids  that come within 5 million miles of Earth (20 times Earth-moon distance). There are none predicted to impact Earth in the next 100 years. But new ones are found every week, and between now and February 2017, one object called 2016YJ about 30 meters across will pass within 1.2 lunar distances of Earth. The list of closest approaches in 2016 is quite exciting to look through The object 2016 QA2 discovered in 2016 in the nick of time, was about 70 meters across and came within 53,000 miles of Earth. Upon impact, it would have been an event similar to Chelyabinsk. Even larger, and far more troubling very close encounters have been predicted for the 325-meter asteroid Apophis in 2029, and the 1-kilometer asteroid 2001WN5 in 2028 and well within the man-made satellite cloud that surrounds Earth.

The first successful forecast of an impact event was made on 6 October 2008 when the asteroid 2008 TC3 was discovered. It was calculated that it would hit the Earth only 21 hours later. Luckily it had a diameter of only three meters and did not cause any damage. Since then, some stony remnants of the asteroid have been found. But this object could just as easily have been a 100-meter object exploding over New York City or London, with devastating consequences.

So in terms of planetary defense, asteroids are a dramatically important hazard we need to study. For some asteroids, we may have as little as a year to decide what to do. Although many mitigation strategies have been proposed, none have actually been tested! We need to test as many different orbit-changing strategies as we can before the asteroid with Earth’s name written on it is discovered.

Honestly, what more practical benefit can there be for a NASA mission than to materially protect Earth and our safety?

Check back here on Thursday, January 5 for the next installment!

To Pluto in 30 days!

OK…While everyone else is worrying how to get to Mars, let’s take a really big step and figure out how to get to Pluto….in a month!

The biggest challenge for humans is surviving the long-term rigours of space hazards, but all that is nearly eliminated if we keep our travel times down to a few weeks.

Historically, NASA spacecraft such as the Pioneer, Voyager and New Horizons missions have taken many years to get as far away from Earth as Pluto. The New Horizons mission was the fastest and most direct of these. Its Atlas V launch vehicle gave it an initial speed of 58,000 km/hr. With a brief gravity assist by Jupiter, its speed was boosted to 72,000 km/hour, and the 1000-pound spacecraft made it to Pluto in 9.5 years. We will have to do a LOT better than that if we want to get there in 1 month!

The arithmetic of the journey is quite simple: Good old speed = distance / time. But if we gain a huge speed to make the trip, we have to lose this speed to arrive at Pluto and enter orbit. The best strategy is to accelerate for the first half, then turn the spacecraft around and decelerate for the second half of the trip. The closest distance of Pluto to Earth is about 4.2 billion kilometers (2.7 billion miles). That means that for 15 days and 2.1 billion kilometers, you are traveling at an average speed of 5.8 million kilometers per hour!

Astronomers like to use kilometers/second as a speed unit, so this becomes about 1,600 km/sec. By comparison, the New Horizons speed was 20 km/sec. Other fast things in our solar system include the orbit speed of Mercury around the sun (57 km/s), the average solar wind speed (400 km/s) and a solar coronal mass ejection event (3,000 km/s).

If our spacecraft was generating a constant thrust by running its engines all the time, it would be creating a uniform acceleration from minute to minute. We can calculate how much this is using the simple formula distance = ½ acceleration x Time-squared. With distance as 2.1 billion km and time as 15 days we get 0.00062 km/sec/sec or 0.62 meters/sec/sec. Earth’s gravity is 9.8 meters/sec/sec so we will be feeling an ‘artificial gravity’ of about 0.06 Gs….hardly enough to feel, so you will still be essentially weightless the whole journey!

If the rocket is squirting fuel (reaction mass) out its engines to produce the thrust, we can estimate that this speed has to be about 1,600 km/sec. Rocket engines are compared in terms of their Specific Impulse (SI), which is the exhaust speed divided by the acceleration of gravity on Earth’s surface, so if the exhaust speed is 1,600 km/sec, then the SI = 160,000 seconds. For chemical rockets like the Saturn V, SI=250 seconds!

What technology do we need to get to these speeds and specific impulses?

The most promising technology we have today is the ion rocket engine, which has SIs in the range of 2,000 to 30,000 seconds .The largest ion engine designs include the VASIMR engine; a proposed 200 megawatt, nuclear-electric ion engine design that could conceivably get us to Mars in 39 days. Ion engines are limited by the electrical power used to accelerate the ions (currently in the kilowatt-range but gigawatts are possible if you use nuclear power plants), and the mass of the ions themselves (currently xenon atoms).

Other designs propose riding the solar wind using solar sails, however although this works on the outward-bound leg of the trip, it is very difficult to return to the inner solar system! The familiar technique of ‘tacking into the wind’ will not work because for sailboats it relies on movement through manipulating pressure changes behind the sail, while solar wind pressure changes are nearly zero. Laser propulsion systems have also been considered, but the power requirements often compete with the total electrical power generated by a large faction of the world for payloads with appreciable mass.

So, some version of ion propulsion with gigawatt power plants (fission or fusion) may do the trick. Because the SIs are so very large, the amount of fuel will be a small fraction of the payload mass, and these ships may look very much like those fantastic ships we often see in science fiction after-all!

Oh…by the way, the same technology that would get you to Pluto in 30 days would get you to Mars in 9 days and the Moon in 5 minutes.

Now, wouldn’t THAT be cool?

If you want to see some more ideas about interplanetary travel, have a look at my book ‘Interplanetary Travel:An astronomer’s guide’ available at

Check back here on Monday, January 2 for the next installment!

Selling Ice to Eskimos

Looking beyond our first journeys to Mars in the 2030s, and perhaps setting up outposts there in the 2040s, a frequently-mentioned plan for commercialization of space often brings up the prospects of interplanetary mining. A bit of careful thought can define the prospects and successes for such a venture if we are willing to confront them honestly.

The biggest challenge is that the inner solar system out to the asteroid belt is vastly different than the outer solar system from Jupiter to the distant Kuiper Belt. It is as though they occupy two completely separate universes, and for all intents and purposes, they do!

The inner solar system is all about rocky materials, either on accessible planetary surfaces and their moons, or in the form of asteroids like this photo of asteroid Vesta. We have studied a representative sample of them and they are rich in metals, silicates and carbon-water compounds. Lots of fantastic raw materials here for creating habitats, building high-tech industries, and synthesizing food.

Humans tend to ‘follow the water’ and we know that the polar regions of Mercury and the Moon have water-ice locked away in permanently shadowed craters under the regolith. Mars is filthy rich with water-ice, which forms the permanent core of its polar caps, and probably exists below the surface in the ancient ocean basins of the Northern Hemisphere. Many asteroids in the outer belt are also rich in water, as are the occasional cometary bodies that pass through our neighborhood dozens of times a year.

The inner solar system is also compressed in space. Typical closest distances between its four planets can be about 30 million miles, so the technological requirements for interplanetary travel are not so bad. Over the decades, we have launched about 50 spacecraft to inner solar system destinations for a modest sum of money and rocketry skill.

The outer solar system is quite another matter.

Just to get there we have to travel over 500 million miles to reach Jupiter…ten times the distance to Mars when closest to Earth. The distances between destinations in the outer solar system are close to one billion miles! We have sent ten spacecraft to study these destinations. You cannot land on any of the planets there, only their moons. Even so, many of these moons (e.g those near Jupiter) are inaccessible to humans due the intense radiation belts of their planets.

The most difficult truth to deal with in the outer solar system is the quality of the resources we will find there. It is quite clear from astronomical studies and spacecraft visits that the easiest accessible resources are various forms of water and methane ice. What little rocky material there is, is typically buried under hundreds of kilometers of ice, like Saturn’s moon Enceladus shown here, or at the cores of the massive planets. The concept of mining in the outer solar system is one of recovering ice, which has limited utility for fabricating habitats or being used as fuel and reaction mass.

The lack of commercializable resources in the outer solar system is the biggest impediment to developing future ‘colonization’ plans for creating permanent, self-sustaining outposts there. This is dramatically different than what we encounter in the inner solar system where minable resources are plentiful, and water is far less costly to access than in the outer solar system.

Astronomically speaking, we will have much to occupy ourselves in developing the inner solar system for human access and commercialization, but there is a big caveat. Mined resources cannot be brought back to Earth no matter how desirable the gold, platinum and diamonds might be that are uncovered. The overhead costs to mine and ship these desirable resources is so high that they will never be able to compete with similar resources mined on Earth. Like they say about Las Vegas, ‘what is mined in space, stays in space’. Whatever resources we mine will be utilized to serve the needs of habitats on Mars and elsewhere, where the mining costs are just part of the high-cost bill for having humans in space in the first place.

The good news, however, is that the outer solar system will be the playground for scientific research, and who knows, perhaps even tourism. The same commercial pressures that will drive rocket system technology to get us to Mars in 150 days, will force these trips to take months, then weeks, then days. Once we can get to Mars in a week or less, we can get to Pluto in a handful of months, not the current ten-year journeys. Like so many other historical situations, scientific research and tourism became viable goals for travel as partners to the political or commercial competition to get to India in the 1500s, the Moon in the 1960s…or Mars in the 2000s.

In the grand scheme of things, we have all the time in the world to make this happen!

For more about this, have a look at my book ‘Interplanetary Travel:An Astronomer’s Guide’, for details about resources, rocket technology, and how to keep humans alive, based upon the best current ideas in astronomy, engineering, psychology and space medicine. Available at

Check back here on Friday, December 30 for the next installment!

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 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!

The Universe and Etc!

Hi there!

It’s exciting to start a fresh new blog project. It’s kind of like your first day in class with a new pencil and a binder with blank sheets of paper. Even as late as graduate school at Harvard I always found that first day of class exciting and filled with such promise.

You have probably GOOGLEd me by now and discovered I am a professional astronomer and educator. No I am obviously not one of those famous ones you may know by name. There are thousands of astronomers and physicists in this country, many of them far more famous than I am, but chances are you have never actually met one. Even fewer people have astronomers as members of their families!


So here I am, one of those back-roads professional astronomers who has also spent a lifetime studying space and delving deeply into the nuances of the physical world. If you decide to make it a habit of reading my blogs, you may be pleasantly surprised how a slightly different perspective might help you see the world around you a bit more clearly. I hope you will at least appreciate the connections that I see, and why they have been such a source of joy and wonderment to me all my life. As they say, it is not the destination that matters but the journey!

I have always been interested in science: the exploration of the physical world. My mother used to tell me that when she would take me out into the fragrant spruce forests surrounding my hometown Karlskoga in Sweden, she would always have to empty out the rocks in my stroller that I collected along the way. This evolved into a progression of interests leading to a passion for astronomy by 5th Grade.

But as I was exploring the hard facts and theories of astronomy and physics, it was hard for me to give up my interests in ESP and UFOs. For you see, well into middle school I used to plot the positions of UFO sightings on a map of the USA on my bedroom wall, and marvel at the descriptions of the many sightings reported in newspapers and magazines. By high school,  I was reading Carl Sagan’s ‘Intelligent Life in the Universe’, but I was also reading von Daniken’s  ‘Chariots of the Gods’ and Frank Edwards ‘Stranger than Science’. As a Junior in college, I had my own experience of sighting a UFO in the twilight sky.    I also developed an interest in ESP because my Swedish mother beguiled me with many family stories of spirit sightings and telepathic incidents during my early childhood. In high school, my friends and I conducted séances…which [fortunately?] failed, and I had my own experiences with family ghosts and inexplicable events.

Then something peculiar happened around age 23 when I was beginning my Senior Year at UC Berkeley working on my degree in astronomy.  By then, these interests in ESP and UFOs had subsided and simply vanished from the palette of issues I wanted to keep up with.  What had happened?

As I became more steeped in science, its history, its many spectacular successes, and endless rounds of homework to learn  physics from the inside out, I spent less and less time with ideas that entertained, but had far less substance and productivity to them. At some point, the hard data and objective mathematical rigor of science became a far more compelling story than the endless presentations of subjective evidence from ESP and UFO enthusiasts. It seemed to me  that there was not one shred of hard evidence about ESP and UFOs that could not be dismissed as wishful thinking, unsubstantiated anecdotes, statistical variation, or out-right fakery.


In science, advances are made when data is obtained under controlled, repeatable conditions by parties whose only goal is to collectively create an accurate model of how the world works. I decided in college that this was drastically different from ‘ghost chasers’ and UFO hoaxers, who often flooded these subjects for fame and personal gain. But there was one subject area that I immediately gravitated to, that replaced all of these entertaining ideas: Brain research.

I am going to try to explain advances in our understanding of both the physical world and our mental world in a series of blogs that my non-scientist mother would have enjoyed reading. If you want more extensive details, you are free to GOOGLE the words and topics and look to other professionals for explanations who are also popularizers. I will recommend their insights and explanations as my blogs develop.

So where do we start?

Well, for my next few blogs, let’s begin with the brain and how we perceive and make sense of the world around us. That, after all, seems to be the biggest ingredient in creating a rational picture of the world around us.

It is also the biggest impediment!

Return here on November 21 for my next blog in this series!