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Metric
05-22-2006, 01:02 AM
In cosmology, there is a well-known problem known as the "cosmological constant problem" -- it's been touched on a few times here, but basically the problem is that apparently no theory is any good at predicting the observed energy density of the vacuum, from quantum field theory zero point energy, to spontaneous symmetry breaking, up to superstring theory -- it's all horribly wrong, by something like 100 orders of magnitude (ten years ago the superstring theorists would have said "we're pretty sure it's zero, but if it isn't zero it would have to be negative" -- turns out that it's measured to be non-zero and positive).

Another, lesser-known problem (not quite as severe or embarassing, but still oddly compelling) is called the "cosmological coincidence problem." When the universe was young, up until very recently, gravity on the largest scale was dominated by the energy density of matter. But as the universe expands, because galaxies are moving apart, the energy density of matter in the universe becomes less and less, while the energy density of the vacuum remains constant. So in the future, the energy density of the vacuum will dominate gravity on the largest scale.

The interesting thing, though, is that this transiton from "matter dominated universe" to "vacuum dominated universe" happens rather abruptly. See the following figure:

http://nedwww.ipac.caltech.edu/level5/Carroll2/Figures/fig11.jpeg

Here, the vertical axis represents the percent of energy in the universe due to the vacuum. The horizontal axis is the "cosmological scale factor" which you can think of simply as "time." As you can see, in the past the vacuum was totally inconsequential, but in the future, it will be everything. By now you must have noticed, however, that "now" seems to occupy a strangely special point on the graph -- the point at which the two contributions to the vacuum energy are roughly equal.

For another point of view, look at its derivative:

http://nedwww.ipac.caltech.edu/level5/March01/Carroll/Figures/figure1.jpg

As I have heard one professor remark, the transition happens exactly on September 24th, at 3:19 pm, eastern standard time -- which, lo and behold as I look at my watch, happens to be RIGHT NOW!

Now, this seems to violate the Copernican principle, which asserts that we occupy no "special" place in the universe. Yet -- there sits the data. Obviously, if you're inclined to believe that "there are no coincidences," you're very apt to think that this is a serious problem. If you don't mind occupying a special place in the universe -- well, maybe you don't think it's such a big problem.

This is one of those facts that could be pointing to some fundamental new kind of understanding -- or maybe not. Unlike the cosmological constant problem, it is irritatingly vague. If it really is "just a coincidence," then we're probably doomed to be asking the same question forever without a satisfying answer.

(Sean Carroll has a great article on this stuff here: http://nedwww.ipac.caltech.edu/level5/March01/Carroll/frames.html )

lucktard
05-22-2006, 01:20 AM
That's very weird and very cool. Thanks for posting.

I'm enjoying these physics lessons. Keep 'em coming!

Lestat
05-22-2006, 02:14 AM
I wish I understood more of what you're referring to. I'm very interested in all this.

But hasn't gravity ALWAYS been a problem? Admittedly, we don't understand it yet. So any such problem coincidental or otherwise that concerns gravity, shouldn't be taken too seriously, should it?

Metric
05-23-2006, 05:46 PM
[ QUOTE ]
But hasn't gravity ALWAYS been a problem? Admittedly, we don't understand it yet. So any such problem coincidental or otherwise that concerns gravity, shouldn't be taken too seriously, should it?

[/ QUOTE ]
There are two sides to gravity. On the one hand, some of the best agreement between theory and experiment in all of science comes from GR -- predicting energy loss due to gravitational radiation of orbiting pulsars, and so forth... On the other hand, unlike the other forces in nature, GR forces upon us a new language for doing physics (general covariance), and it's not clear how to combine other general principles (like quantum theory and statistical mechanics) with this new way of thinking. So in the weak-field regime, we have fantastic agreement with experiment -- but in sufficiently high energy/strong field regimes, it is likely that we don't even know how to make unique predictions, quite aside from knowing how to test them.

AvivaSimplex
05-25-2006, 10:59 AM
[ QUOTE ]
As I have heard one professor remark, the transition happens exactly on September 24th, at 3:19 pm, eastern standard time -- which, lo and behold as I look at my watch, happens to be RIGHT NOW!

Now, this seems to violate the Copernican principle, which asserts that we occupy no "special" place in the universe. Yet -- there sits the data. Obviously, if you're inclined to believe that "there are no coincidences," you're very apt to think that this is a serious problem. If you don't mind occupying a special place in the universe -- well, maybe you don't think it's such a big problem.

[/ QUOTE ]

Let me point out first that the graph you posted is deceiving. The x-axis is the relative distance between galaxies, on a logorhythmic scale. So at the far left of the scale is the big bang, when all matter was within a single point. Depending on how you interpret the line, the shift from energy to vacuum dominance began 1-2 billion years ago. You certainly can't pinpoint it to yesterday, and it's certainly not specific to us.

This is one issue that can resolved in a pretty satisfactory way by appeal to the anthropic principle. In the evolution of the universe, some time must elapse in order for there to be planets suitable for life. That amount of time is approximately (give or take 4-5 billion years) the same as the time it takes for the universe to switch between energy- and vacuum dominance.

Metric
05-26-2006, 08:27 AM
[ QUOTE ]
Let me point out first that the graph you posted is deceiving. The x-axis is the relative distance between galaxies, on a logorhythmic scale. So at the far left of the scale is the big bang, when all matter was within a single point. Depending on how you interpret the line, the shift from energy to vacuum dominance began 1-2 billion years ago. You certainly can't pinpoint it to yesterday, and it's certainly not specific to us.

[/ QUOTE ]
There are multiple lines on that graph, corresponding to the Planck scale, the electro-weak symmetry breaking scale, etc. all of which indicate a kind of fundamental change in the nature of the universe, and all of which are seperated by many orders of magnitude in the expansion parameter. A logarithmic plot is certainly better than a linear plot, which would scrunch every line but "now" to the far left, and hide the fact that the universe existed in many distinctly different states, on many different timescales.

[ QUOTE ]
This is one issue that can resolved in a pretty satisfactory way by appeal to the anthropic principle. In the evolution of the universe, some time must elapse in order for there to be planets suitable for life. That amount of time is approximately (give or take 4-5 billion years) the same as the time it takes for the universe to switch between energy- and vacuum dominance.

[/ QUOTE ]
That is more of a statement of the coincidence than a statement of a resolution. Why should the timescale for planets to form, life to emerge etc. (which is presumably set by a combination of gravitational, electromagnetic, and nuclear coupling constants) be at all similar -- in fact on exactly the same order of magnitude -- as the timescale for vacuum to dominate (which is presumably set by the value of the cosmological constant and the mass density of the universe)? It would be roughly like expecting life to emerge precisely during the process of electro-weak symmetry breaking -- a very specific point in time, when all epochs of the universe are considered together.