Neues vom Nordkap

19.08.2006 21:39

Inflation and sheep

Last week as part of the concluding conference of the NBI Summer institute there was a very nice talk by Paul Steinhardt from Princeton University on "the origin, structure and future of the universe".

According to the standard model of cosmology there was a big bang, where everything, the universe, space and time began. Shortly after our universe entered a period of inflation, where it expanded at an exponential rate. Inflation accounts for the homogeneous microwave background which we measure nowadays (COBE, WMAP) This background radiation is very uniform, it is 3 K everywhere modified by tiny quantum fluctuations as you can see from that fameous WMAP pictures. According to Steinhardt this process can be modelled by a scalar field which moves in a potential. Classically, the scalar would be developping towards the minimum of the potential where inflation eventually stops, and the universe is flat and uniform as we see it. But due to quantum fluctations there will allways be regions where inflation goes on. (The scalar field jumps "back up the potential".) Since these regions expand exponentially most of the universe in fact continues expanding. In the end we have an eternally inflating universe full with causally disconnected "bags" where expansion has stopped. This theory is called "eternal inflation". Steinhardt said that he finds this idea very disturbing because apart from explaining how the part of the universe we see, came about, it tells as that indeed most of the universe is not at all like the place we live in and there must be infinitely many other "bags" in the universe of every physically possible type. However since there is no causal connection they are out of our reach.

I like the picture. First of all I have never understood why there shouldn't be any other worlds where physics is very different? Many physicists search for a ultimate theory which explains for every constant that there is, why it has the value it has. The goal is to explain that it could not have been otherwise or at least that every other solution would be very improbable. I never really understood why there should be such a theory at all. I suspect that behind this quest there is an anthropic principle lurking: Since if there is no other possible way the universe could develop then it is necessary that mankind came into existence. Why shouldn't it be just coincidence? Due to a quantum effect at the very beginning somewhere? And suppose that quantum physics is objectively random, then we are just a coincidence. Of course in an eternally expanding universe there are so many "bags" that there will be a whole lot of them where some kind of living creatures developped. There might even be infinitely many universes which are very similar to ours, which contain men and fish and sheep.

Now the sheep: Some days ago, I claimed that there can be at most $\aleph_0$ sheep, since sheep are discrete things and I intuitively thought that a set of discrete things just cannot be uncountably large (Do you know any mathematical set, i.e. set of discrete number which is larger than $\aleph_0$ . But in view of eternal inflation I must admit that there are possibly many more sheep. Since it seems to me that there might well be uncountably many such bags in the universe which contain sheep. So even if there was only one solitary sheep in each of them, that makes them many many more in total.

Comments

This expansion happens faster than light as far as I understand it. Now, don't ask me how this is possible, but I am sure they have found a loophole there to allow this. The point is, I believe, that the uniformity of the CMB is explained by claiming that all parts of the universe which we observe were in close contact such that they reached thermodynamical equilibrium. And this is only possible if there has been expansion at a speed above c.

Well it could of course turn out that all the bags are similar or even the same at a fundamental level. Say, that at least a subset of the fundamental constants we observe, is unviversal, but then there must be a reason for it. Otherwise I don't see why all possible types shouldn't exist.
Hm yes, it is something like $\Diamond p \to p$ at the level of facts or states of the universe.

Magdalena said:
"I like the picture. First of all I have never understood why there shouldn't be any other worlds where physics is very different? Many physicists search for a ultimate theory which explains for every constant that there is, why it has the value it has. The goal is to explain that it could not have been otherwise or at least that every other solution would be very improbable. I never really understood why there should be such a theory at all."

Hi, I don't like it one bit.

There "should be such a theory" because there should be some good physical reason why the configuration of the universe follows the least action principle via whatever constraint is imposed by the *good physical reason* why no practical model of turbulence-driven structuring has ever been derived.

Figure out how the evolution of the universe still manages to follow the least action principle, in dramatic contrast to the normal expectation, and you will then know why there is only one possible configuration, (without infinite need for excuses why they can't do physics)... ;)

You will also then know the real reason for the anthropic principle, rather than some hype about an infinite potential that is neither necessary nor justified.

Magdalena said:
"The point is, I believe, that the uniformity of the CMB is explained by claiming that all parts of the universe which we observe were in close contact such that they reached thermodynamical equilibrium. And this is only possible if there has been expansion at a speed above c."

No, the issue is also more-simply resolved if the universe simply had volume when we had the big bang since there is also causal contact and asymmetry is inherent. This resolves every problem that got created by physicists that didn't pay attention when projecting backwards to the point that they had to *assume* a period of extraordinary inflation to fill in the gap that was created because they had already *assumed* an absolute cosmic singularity.

They were wrong.

island:
why should there be a reason, why the configuration of the universe follows the least action principle? It just does. It's the other way round: the least action principle is the reason why the universe is in a certain configuration. But this doesn't exclude the possibility of there being several local or degenerate minima and therefore being several distinct configuration possible, does it?

If the universe had volume at the time of the big bang, then space existed and how did it come there? Has it allways been there? I agree that all this singularity business is strange but, first of all gravitational singularities do exist, and what would be banging in that previousely empty space? Matter? But that would curve your space quite a lot.

Hi again, Magdalena, and thank you for the considered reply. I don't disagree with your first statement, but I don't think that you got the full meaning of my first point. Yes, the least action principle must be the reason why the universe is configured the way that it is, but the expansion event is constrained in a manner that restricts it to produce a LOT more structuring than any normal modeling of turbulence driven structuring derives. It's not even close, the lack of a "better" supression mechanism is the reason that the anthropic principle came to be, and the first words out of Brandon Carter's mouth in Cracow, were, "John Wheeler ask me to...".

Okay, so nobody buys Wheeler's idea, but that doesn't mean that carbon based life isn't relevant, and my own understanding is that the least action principle requires that the universe be constrained to the observed minimal entropy configuration so that work can be maximized, or energy is not going to be universally conserved. And that only applies to one kind of universe...

Barring random quantum fluctuations, the least action principle would tend to prohibit a variety of differing configurations, so I would argue that these extra entities aren't justified until you've exhausted every other possibility. That's not the kind of stability mechanism that is *normally expected*... rather, it's giving up hope of ever finding "causality-responsible" physics for one.

Won't "space" cease to exist and then be recreated if we have a big bang right now, for example? (*that's also a clue about the good physical reason for the anthropic principle btw).

Hawking might disagree with you about gravitational singularities and information loss. So would I...

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