The Paradoxes That Threaten To Tear Modern Cosmology Apart

Some simple observations about the universe seem to contradict basic physics. Solving these paradoxes could change the way we think about the cosmos

Revolutions in science often come from the study of seemingly unresolvable paradoxes. An intense focus on these paradoxes, and their eventual resolution, is a process that has leads to many important breakthroughs.

So an interesting exercise is to list the paradoxes associated with current ideas in science. It’s just possible that these paradoxes will lead to the next generation of ideas about the universe.

Today, Yurij Baryshev at St Petersburg State University in Russia does just this with modern cosmology. The result is a list of paradoxes associated with well-established ideas and observations about the structure and origin of the universe.

Perhaps the most dramatic, and potentially most important, of these paradoxes comes from the idea that the universe is expanding, one of the great successes of modern cosmology. It is based on a number of different observations.

The first is that other galaxies are all moving away from us. The evidence for this is that light from these galaxies is red-shifted. And the greater the distance, the bigger this red-shift.

Astrophysicists interpret this as evidence that more distant galaxies are travelling away from us more quickly. Indeed, the most recent evidence is that the expansion is accelerating.

What’s curious about this expansion is that space, and the vacuum associated with it, must somehow be created in this process. And yet how this can occur is not at all clear. “The creation of space is a new cosmological phenomenon, which has not been tested yet in physical laboratory,” says Baryshev.

What’s more, there is an energy associated with any given volume of the universe. If that volume increases, the inescapable conclusion is that this energy must increase as well. And yet physicists generally think that energy creation is forbidden.

Baryshev quotes the British cosmologist, Ted Harrison, on this topic: “The conclusion, whether we like it or not, is obvious: energy in the universe is not conserved,” says Harrison.

This is a problem that cosmologists are well aware of. And yet ask them about it and they shuffle their feet and stare at the ground. Clearly, any theorist who can solve this paradox will have a bright future in cosmology.

The nature of the energy associated with the vacuum is another puzzle. This is variously called the zero point energy or the energy of the Planck vacuum and quantum physicists have spent some time attempting to calculate it.

These calculations suggest that the energy density of the vacuum is huge, of the order of 10^94 g/cm^3. This energy, being equivalent to mass, ought to have a gravitational effect on the universe.

Cosmologists have looked for this gravitational effect and calculated its value from their observations (they call it the cosmological constant). These calculations suggest that the energy density of the vacuum is about 10^-29 g/cm3.

Those numbers are difficult to reconcile. Indeed, they differ by 120 orders of magnitude. How and why this discrepancy arises is not known and is the cause of much bemused embarrassment among cosmologists.

Then there is the cosmological red-shift itself, which is another mystery. Physicists often talk about the red-shift as a kind of Doppler effect, like the change in frequency of a police siren as it passes by.

The Doppler effect arises from the relative movement of different objects. But the cosmological red-shift is different because galaxies are stationary in space. Instead, it is space itself that cosmologists think is expanding.

The mathematics that describes these effects is correspondingly different as well, not least because any relative velocity must always be less than the speed of light in conventional physics. And yet the velocity of expanding space can take any value.

Interestingly, the nature of the cosmological red-shift leads to the possibility of observational tests in the next few years. One interesting idea is that the red-shifts of distant objects must increase as they get further away. For a distant quasar, this change may be as much as one centimetre per second per year, something that may be observable with the next generation of extremely large telescopes.

One final paradox is also worth mentioning. This comes from one of the fundamental assumptions behind Einstein’s theory of general relativity—that if you look at the universe on a large enough scale, it must be the same in all directions.

It seems clear that this assumption of homogeneity does not hold on the local scale. Our galaxy is part of a cluster known as the Local Group which is itself part of a bigger supercluster.

This suggests a kind of fractal structure to the universe. In other words, the universe is made up of clusters regardless of the scale at which you look at it.

The problem with this is that it contradicts one of the basic ideas of modern cosmology—the Hubble law. This is the observation that the cosmological red-shift of an object is linearly proportional to its distance from Earth.

It is so profoundly embedded in modern cosmology that most currently accepted theories of universal expansion depend on its linear nature. That’s all okay if the universe is homogeneous (and therefore linear) on the largest scales.

But the evidence is paradoxical. Astrophysicists have measured the linear nature of the Hubble law at distances of a few hundred megaparsecs. And yet the clusters visible on those scales indicate the universe is not homogeneous on the scales.

And so the argument that the Hubble law’s linearity is a result of the homogeneity of the universe (or vice versa) does not stand up to scrutiny. Once again this is an embarrassing failure for modern cosmology.

It is sometimes tempting to think that astrophysicists have cosmology more or less sewn up, that the Big Bang model, and all that it implies, accounts for everything we see in the cosmos.

Not even close. Cosmologists may have successfully papered over the cracks in their theories in a way that keeps scientists happy for the time being. This sense of success is surely an illusion.

And that is how it should be. If scientists really think they are coming close to a final and complete description of reality, then a simple list of paradoxes can do a remarkable job of putting feet firmly back on the ground.

Sure. The Special Theory of Relativity has basically two postulates: 1) Absolute Uniform motion cannot be detected. 2) The speed of light is the same for all observers in uniform reference frames.

The first postulate, that the physics of two observers moving at constant velocity relative to each other has to be the same, was already present in the Ancient Law [Newtonian Physics.]

The second postulate is the one that causes what appear to be bizarre consequences, and is "the new stuff." But you must be extremely careful about it, because it is a rigorously precise statement. It doesn't say that objects cannot move with apparent or mathematically implied velocities greater than c [the speed of light in vacuum.] But it does -- as you have correctly surmised -- have that consequence for most situations.

When can it fail? It fails in cases where the motion is not uniform. For example: inside the Schwarzschild radius of a black hole. Spacetime is curved in there, and essentially everything falling into the singularity is freefalling faster than c. Those conditions are, of course, governed by General Relativity, not Special Relativity.

Now everyone wants to look at General Relativity in terms of geometry. That is the lure of its mathematical and conceptual power. But it is also true that the best way to look at Special Relativity is also essentially geometrically.

The real deal on the Special Theory of Relativity is that time and space are not independent of each other. Our universe [where it is "flat", which is where Special Relativity Holds] is not a four dimensional hypercube at all. It is a limited four dimensional surface embedded inside that hypercube, and the limitation is that events that occur on our limited surface which can communicate with each other are required to obey an equation which says [if the event started at time t, then] c²t²≥x²+y²+z².

[Aside: This is how I get myself into heated arguments with FReepres from time to time who say "someday we are going to break the light barrier." No. We are not. The "light barrier" isn't like the sound barrier. The sound barrier is an arbitrary speed that sound travels in a particular medium. The "light barrier" isn't like that. In order to break it, you would need to actually break the physical geometry of our whole universe. The USS Enterprise's "Warp Drive" doesn't warp the starship. It warps everything. Not. Bloody. Likely.]

OK, now, here are two new assumptions, which are foundational aspects of modern cosmology. They appear to be true everywhere we look and are supported by a lot of experimental evidence. They are the following: 1) The universe, except for random clumpiness [which is interesting for other reasons, but really isn't as important as the guy writing this article thinks it is] is the same in pretty much all directions and 2) It appears to be expanding away in all directions.

If you put those two things together [isotropy of spacetime, and uniform expansion] there is an inescapable conclusion: the further away something is, the faster it will appear to be moving away from you. Steven Weinberg has a very good explanation of this in his book, The First Three Minutes. The best way to understand it is: if you look down the road and the guy in front of you seems to be pulling away from you 5 miles per hour faster than you're driving, and he looks down the road and sees the guy ahead of him pulling away -- also at five miles an hour faster than he's driving -- you cannot really come to any logical conclusion other than that the guy two cars ahead of you is pulling away at TEN miles an hour faster than you're driving. Conclusion: if all points in the universe equally distant are expanding away from each other at uniform speed, and space is the same in all directions, the further away two objects are, the faster they appear to be moving apart.

You can also do this experiment with a balloon covered with dots, which is a nice two-dimensional conceptional model of three dimensional space. [Yes, the balloon is three dimensional, but the increasing radius in that model as the balloon expands is actually t: time.] The expansion of the balloon as you blow it up at a constant rate will have this feature: all equally spaced dots will separate at the same rate, and dots spaced further will be moving faster away from each other than dots close together.

OK... now ... what is the surface of our balloon doing? Objects are not moving away from each other at uniform speeds. The further objects are, the faster they're accelerating away. Therefore ... Special Relativity does notapply! Not uniform motion. Eventually, objects will be so far away that their red-shift will be infinite. The light from them will never reach us, and, they will be receding away from us faster than the speed of light.

Effectively, they are beyond our event horizon. Nothing they do in their own part of the universe can ever reach us, or ever affect us. It's as if they're beyond the event horizon of a Black Hole.

Couple things to note: The objects themselves are not "moving that fast." Within their own little neighborhoods of a couple hundred thousand light years, they think spacetime is still flat and the Special Theory works in empty space very far from strong gravity. But as you look further and further out, it becomes clear that the expansion of space gives rise to nonuniform reference relativity if two objects are widely separated. Second: why doesn't the clumpiness really matter? It doesn't matter because we expect it on the basis of Quantum Mechanics, which we haven't yet talked about. There were random fluctuations in space at just after the instant of creation. Those fluctuations were incredibly small -- smaller even than the size of an atomic nucleus. But multiply those fluctuations of energy [which eventually became mass, then stars, and galaxies] by how fast the universe was moving and how long it's been moving, and next thing you know, you see a background of stars at large distances that doesn't appear to be uniform. And it isn't. But that doesn't really change the uniformity and isotropy of spacetime a whole lot. And it doesn't change the Hubble Law.

That's what's going on here, and what this author doesn't understand.

[Aside: There is actually a decent explanation of what happens in the other direction, as you look backward in time to the Big Bang, and what happens to past events here:http://roger.blogs.exetel.com.au/index.php?/archives/186-My-Future-Light-Cone.html If you've followed what I've said here, you should have no trouble with it. ]

Sorry for an overlong explanation. Sometimes I miss teaching physics...

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