A double-cone-shaped universe?

[Chalnoth]

http://en.wikipedia.org/wiki/Boltzmann_brain
Boltzmann proposed that we and our observed low-entropy world are a random fluctuation in a higher-entropy universe

So, "we are random fluctuation in a higher-entropy universe"
--> there are only Boltzmann brains
--> This is a bad universe as no real observers exist
--> entropy MUST be low at BB.

No. This does not follow.

The argument is as such:
1. Our universe had very low entropy at its start.
2. We assume that our universe was born out of a thermal fluctuation out of equilibrium.
3. However, small thermal fluctuations are vastly more common than large ones.
4. Therefore observers born out of small fluctuations vastly outnumber those who are born out of large fluctuations. The smallest possible fluctuation is a brain born out of this thermal bath, complete with memories and false observations of a false universe. These "Boltzmann Brains" would vastly outnumber real observers if point (2) is true.
5. Therefore our universe was not born out of a thermal bath in this sense.

Any theory, for it to say anything at all about the beginnings of our universe, must overcome this, and predict more real observers than Boltzmann Brains. Simply positing a low-entropy beginning doesn't work, as it isn't explaining anything. You have to posit why the entropy was low in the first place.

 

[Chalnoth]

Chalnoth, tell me please, do you believe that universe is spatially open, or that it is closed. Are you proponent of infinite or finite universe?

None of the above.

The observational evidence, so far, has yet to detect a definitive deviation from flatness. So at the very least it is very flat. This doesn't actually say anything about whether the universe is finite or infinite, because the curvature that we measure within our observable region may well be different outside it. So even if we had a definitive non-zero measurement of the spatial curvature within our volume, we still couldn't say whether or not our universe was finite or infinite (unless, of course, we were able to detect observational evidence of our universe wrapping back on itself, which also hasn't been detected).

Now, I personally think that the most likely answer is that as far as spatial extent is concerned, the region that was born out of our big bang event is probably quite finite. But I tend to suspect that the number of such events is actually infinite, such that the universe as a whole is very much infinite.

 

[Dmitry67]

No. This does not follow.

The argument is as such:
1. Our universe had very low entropy at its start.
2. We assume that our universe was born out of a thermal fluctuation out of equilibrium.
3. However, small thermal fluctuations are vastly more common than large ones.
4. Therefore observers born out of small fluctuations vastly outnumber those who are born out of large fluctuations. The smallest possible fluctuation is a brain born out of this thermal bath, complete with memories and false observations of a false universe. These "Boltzmann Brains" would vastly outnumber real observers if point (2) is true.
5. Therefore our universe was not born out of a thermal bath in this sense.

Any theory, for it to say anything at all about the beginnings of our universe, must overcome this, and predict more real observers than Boltzmann Brains. Simply positing a low-entropy beginning doesn't work, as it isn't explaining anything. You have to posit why the entropy was low in the first place.

What a nonsense!
1 and 2 are inconsistent! So the rest makes no sense at all.
And also our Universe was not 'born of equlibruim of something' - unless you are going 'Beyond the Standard model' into the superstrings, the Bulk which produces the universes etc. But it is an offtopic. We can just compare 2 scenarios: BB with high entropy and BB with low entropy.

At first, should we follow the commonly accepted description of Boltzmann brains (from Wiki) or not? Answer first.

 

[Chalnoth]

What a nonsense!
1 and 2 are inconsistent! So the rest makes no sense at all.

They're only inconsistent due to the Boltzmann Brain argument in the first place. That's what this argument shows.

At first, should we follow the commonly accepted description of Boltzmann brains (from Wiki) or not? Answer first.

Yes.

 

[Dmitry67]

ok, let's begin from the very beginning

"We assume that our universe was born out of a thermal fluctuation out of equilibrium"

We can not assume that. When something is "born" then there is BEFORE the birth and AFTER the birth, and a state of that something BEFORE the birth. So this statement is equivalent to the famous "What happened before the Big Bang?" or "What caused the Big Bang?"

Do you agree?

 

[Chalnoth]

ok, let's begin from the very beginning

"We assume that our universe was born out of a thermal fluctuation out of equilibrium"

We can not assume that. When something is "born" then there is BEFORE the birth and AFTER the birth, and a state of that something BEFORE the birth. So this statement is equivalent to the famous "What happened before the Big Bang?" or "What caused the Big Bang?"

Do you agree?

Let me put it this way. If you want to talk about a universe being born at random, no matter whether it was "from nothing" or from a pre-existing thermal bath, the analysis is the same. It just doesn't matter.

 

[Dmitry67]

I deny that we can use the word 'Born'

The word 'Born' uses the time.
The word 'From' assumed some time dimension and transition from something into something. I also deny that.
As a special case, the universe we discuss exists from -inf to +inf, so it was never 'born from something', including 'from nothing'. It simply existed. Like pi or sin(x)
The word 'random' and theory of probability requires multiple trials. Not applicable in this case.

So in you statement "universe being born at random, no matter whether it was "from nothing" or from a pre-existing thermal bath, the analysis is the same" there are more words I don't agree with then I agree. So it is difficult point to start.

You are trying to apply simple common sense reasoning/things to the Universe and Big Bang. We can't do it. Listen, Loop Gravity Guys even deny the 2nd law of thermodynamics, claiming that the entropy had been mysteriously 'reset to 0' at the Big Bounce. If we take another school, spuperstrings, then at BB there were more spatial directions and who-hows-how-many-of-these-dimensions-behaved as time! If we are talking about the BULK then we don't know the number of time dimensions too: it could be 0,1,2 or all.

And you are talking about the "thermal bath" before the big bang! We even don't know if there was time!

 

[gruff]

I think Dmitry67 is more convincing so far. Chalnoth, doesn't the Bolzman argument presume a classical background time and so your framing of it slips in the need for causation arbitrarily. Isn't this begging the question?

 

[Chalnoth]

I think Dmitry67 is more convincing so far. Chalnoth, doesn't the Bolzman argument presume a classical background time and so your framing of it slips in the need for causation arbitrarily. Isn't this begging the question?

Well, no. All that the Boltzmann argument presumes is that the laws of physics (including gravity) are unitary. This is a statement that even though the current, very large universe appears very very different from the minuscule inflating patch it came from, the two are, in a sense, just two different configurations of the same physical system.

And if they are just two different configurations of the same system, then the 'initial' configuration during inflation was an exceedingly special configuration indeed: there are vastly, vastly more ways for a universe to look like the universe we see around us than there are for it to look like a small inflating patch. So that if our universe is to be uncaused, then it is more likely to appear in its present state than it is to appear as a small inflating patch.

This is somewhat counterintuitive, just because it doesn't seem reasonable that our universe could possible "just appear" in its present state, complete with the photons on the way from distant stars and all. But if we are to believe unitarity, then it seems that it is necessarily the case that it is even more weird for a universe to "just appear" as a small, inflating region.

 

[Chalnoth]

You are trying to apply simple common sense reasoning/things to the Universe and Big Bang. We can't do it. Listen, Loop Gravity Guys even deny the 2nd law of thermodynamics, claiming that the entropy had been mysteriously 'reset to 0' at the Big Bounce. If we take another school, spuperstrings, then at BB there were more spatial directions and who-hows-how-many-of-these-dimensions-behaved as time! If we are talking about the BULK then we don't know the number of time dimensions too: it could be 0,1,2 or all.

It seems to me that you are trying to wiggle out of the argument by making special allowances that are pretty darned unlikely, such as the idea that the "big bang" event that we see in the past of our region of space-time was the only one.

And you are talking about the "thermal bath" before the big bang! We even don't know if there was time!

Actually, there isn't time in a thermal bath at equilibrium. At least, there is no arrow of time. There may or not be a dimension of time, but there is no arrow of time.

 

[Dmitry67]

All that the Boltzmann argument presumes is that the laws of physics (including gravity) are unitary. This is a statement that even though the current, very large universe appears very very different from the minuscule inflating patch it came from, the two are, in a sense, just two different configurations of the same physical system.

Yes, so it is applicable to 2 moments of time in our universe (if the number of time dimensions is still 1 and 2nd law is still valid - which is not guaranteed at plank times, but let's ignore it now)

But it can not be used to say something about the INITIAL conditions because they are INITIAL.

In some cases, the initial conditions are indistinguishable from the laws of physics: for example, check the Goedels Universe: http://en.wikipedia.org/wiki/Gödel_metric

This is a very interesting universe with the initial conditions are not defined at some moment of time of space, but globally. Goedels inverse is eternal: Closed time-like loops cross every point in spacetime.

 

[Dmitry67]

It seems to me that you are trying to wiggle out of the argument by making special allowances that are pretty darned unlikely, such as the idea that the "big bang" event that we see in the past of our region of space-time was the only one.

Well, I am ready to play on the superstring field:
* multiple bubble universes in the so-called BULK
* different collisions between multi-dimensional branes create these baby universes
* there are many 'big bangs', as you wanted
* there is 'something', which created these universes, as you wanted.

But now *YOU* must prove that 2nd law of thermodynamics is valid in the BULK.
To begin, try to find out how many dimensions BULK has and how many dimensions of them are TIME
It would be a great help to the superstring theory.

 

[gruff]

Well, no. All that the Boltzmann argument presumes is that the laws of physics (including gravity) are unitary. This is a statement that even though the current, very large universe appears very very different from the minuscule inflating patch it came from, the two are, in a sense, just two different configurations of the same physical system.

OK, I think I understand you: it presumes an exiting physical universe, the thermal bath, with no arrow of time.

 

[Dmitry67]

OK, I think I understand you: it presumes an exiting physical universe, the thermal bath, with no arrow of time.

... which is not compatible with GR.

 

[Chalnoth]

OK, I think I understand you: it presumes an exiting physical universe, the thermal bath, with no arrow of time.

Hmmm, not quite. Granted, the original argument presumed this, but it isn't necessary to do so. Notice that my last post didn't actually make any reference to a pre-existing state, as it's merely pointing out that the early universe had lower entropy than the current universe, and that essential fact absolutely requires explanation.

 

[Chalnoth]

Yes, so it is applicable to 2 moments of time in our universe (if the number of time dimensions is still 1 and 2nd law is still valid - which is not guaranteed at plank times, but let's ignore it now)

But it can not be used to say something about the INITIAL conditions because they are INITIAL.

Hmmm, no. You can't just pick out a specific time and say that this time is special, and the rules don't apply to it.

 

[gruff]

Hmmm, not quite. Granted, the original argument presumed this, but it isn't necessary to do so. Notice that my last post didn't actually make any reference to a pre-existing state, as it's merely pointing out that the early universe had lower entropy than the current universe, and that essential fact absolutely requires explanation.

But doesn't Boltzman's argument assume an existing (albeit timeless) physical universe in order to determine likelihood of fluctuations in it?

 

[Chalnoth]

But doesn't Boltzman's argument assume an existing (albeit timeless) physical universe in order to determine likelihood of fluctuations in it?

Well, yes, but it only requires that all possible microstate configurations are equally likely for the argument to hold. This statement holds trivially in the case of a thermal fluctuation from equilibrium, but that isn't necessarily the only way.

So another way to state the argument is that there must be some sort of physical law that makes it so that it is more likely for microstates that make for inflating regions to appear than for microstates that make for universes like those we observe appear, despite the vastly larger number of microstates that can replicate a universe like the one we observe. And preferably the physical process that causes this wouldn't be ad-hoc, and would be testable by other means.