Exploring Space, Time and Energy: A Look at the Universe

[jostpuur]

Couldn't it be, that universe merely had greater energy density in the past, and that the energy density is decreasing now? Is there some reasons to assume, that the universe itself was smaller in the past, as the big bang theory says?

Is there also some reason to assume, that the spatial space is compact topologically, like $S^3$. Couldn't it be $\mathbb{R}^3$ (as it is at least is locally)?

 

[marcus]

Is there also some reason to assume, that the spatial space is compact topologically, like $S^3$. Couldn't it be $\mathbb{R}^3$ (as it is at least is locally)?

YES! it could indeed be $\mathbb{R}^3$
We don't know. My guess is that if you could get a working cosmologist to render an opinion, he would likely say he favors the non-compact $\mathbb{R}^3$ picture.

Majority hunches can change though. So I wouldn't bet on $\mathbb{R}^3$ just because a present it may have majority support.

I think we should at least TALK some about the compact alternative, part of the reason being that people tend to THINK of the big bang as occurring when the universe was very small. If you start with a finite (compact) universe and expand, it will always remain finite.

A cosmologist who pictures the universe as spatially infinite $\mathbb{R}^3$ will, to be consistent, also have a mental picture of the big bang occurring over a broad front----infinite extent. This is hard for many non-specialists to imagine----plus the media have made an indelible impression of the bang occurring at a "point" or "golf-ball" or something.
It's been drummed in.

Since there is SOME recent evidence that it MIGHT be compact, I favor thinking about that possibility, and the simplest picture by far is $\mathbb{S}^3$ . But certainly you should keep $\mathbb{R}^3$ in mind as well!

Is there some reasons to assume, that the universe itself was smaller in the past, as the big bang theory says?

YES! there are very good reasons! There is no other way to fit the observed data and the way gravity behaves. By far the best theory of gravity is General Relativity. It has past repeated tests that wiped out the competition and has been confirmed to amazing accuracty. It may in future be REFINED but the basic features will surely carry over.

One of these is that you should expect distances to expand (or in certain other cases, contract). If distances aren't nailed down with a steel bar, or a crustal plate of rock, or a stable orbit system-----some resistant physical locking mechanism---then they just change. that is what Einstein told us in 1915 and it is part of the reason his theory of gravity works so well.

So part of the reason is that we have a great theory of gravity that WORKS and which teaches us to expect a universe that is expanding (unless it is contracting)

AND THE OTHER PART of the reason is THIS IS WHAT WE ACTUALLY SEE. There is a huge amount of astronomical data, including a rich variety of different kinds collected about different objects, seen in different wavelengths, using different models, with different instruments and it all fits together. There is no way that I can conceive explaining all that with a model in which distances don't increase.

Some decades ago there used to be academic debates about this. I think it was around 50 years ago and more. But the non-expansion people must have given up or died off. The controversy was hot at one time but it's no longer interesting.

So the answer to your question is a resounding YES There are indeed excellent reasons.
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jostpuur in post 4 reminded me that I forgot to include the case where the universe is spatially infinite. in that case it has no well-defined size and one cannot say that it was smaller and is now bigger---because it has no size.
however it can still have expansion going on, two points that were some substantial distance apart when the CMB photons were born are probably 1000 times farther apart today. Even in the spatial infinite case people still talk about space expanding.

jostpuur mentioned the matter density as a handle on this. the matter density in our universe is now some (1000)³ times less than when the CMB photons were emitted. So density gives a good handle on it no matter whether space is finite or infinite.

 

[Seele]

With the recognition that were are indeed witnessing a red-shift pattern of the galaxies, that certainly indicates that they are moving away from us at an ever-growing pace, thus if you rewind time, 4 billion years ago the galaxies would be significantly closer to one another. Therefore if you desire to go back 13.7 billion years, all matter would be indeterminably close together. Though this does not necessarily condone that the big bang did indeed occur, it just simply leads intuition to that conclusion. There is a definite worthy opponent to the big bang theory, and this new theory is explained extensively in the book "Endless Universe", written by Paul J. Steinhardt and Neil Turok.

 

[jostpuur]

The first part of the marcus's response was pretty much what I wanted to hear

The second part though seemed to be result of some kind of misunderstanding. I understand that distances of different objects must have been smaller in the past, but was wondering is it necessary for the universe itself have been smaller. Universe could have been denser, but still as infinite as it is now (if it is)?

Is it clear that the density of stuff in the universe approaches infinity when we go back in time and approach some instant (big bang)? Is there evidence that contradicts an idea, that time extends into negative infinity, and matter density just keeps increasing for example exponentially there?

 

[marcus]

The first part of the marcus's response was pretty much what I wanted to hear

Splendid! that is good to know.

Is it clear that the density of stuff in the universe approaches infinity when we go back in time and approach some instant (big bang)?

I think it is pretty clear that the density gets very large as you go back in time. How large depends on the model. Some folks at Penn State who have been running computer models of the universe have found that the maximum density consistently turns out to be about 80 percent of Planck density.
At that point gravity becomes a repulsive rather than attractive force, and the universe undergoes a bounce (in their model).

that is looking back in time, so it may be confusing to say it that way.
what I mean is, they start the model running in a collapse mode and the universe density increases to about 80 percent of Planck density and then it bounces and the collapse turns around and becomes an expansion that looks like our big bang-----what follows basically matches what we see has happened.

So far the evidence for a bounce is suggestive, but not CONCLUSIVE. The new models that replace the bang singularity with a bounce (at very high density) need to be thoroughly tested.

If you are curious what Planck density is, Wikipedia should have something on it, or a general article about Planck units. roughly speaking if I remember right it is around 10⁹⁰ times the density of water, somewhat more than that, but not as much as 10¹⁰⁰ times water.

If you want a link to some of the papers written about the bounce, and the computer simulation work, let me know.

In all these models that have a bounce, it happens at the usual time of some 13.7 billion years ago. Basically the only real difference is that you don't get a singularity and there is less need for inflation----or whatever inflation you need comes about more naturally without so much in the way of extra assumptions. Otherwise it is pretty much the same old bigbang story.

 

[rcgldr]

How do "bounce theory" and "entropy theory" coexist? If the universe is infinitely old, why hasn't it settled into a stablized state due to entropy?

Then there's my issue with the concept of here and now with the infinite. Since we exist here and now, then no matter how far back of forward in time or distance you go, it's a finite distance from the "here and now". If time and/or space is infinite, then how can a "here and now" exist?

For example, if a line is infinitely long, then how can a finite segment of this line exist? Where would it's "position" be on a line that infinitely long? As the length of a line approaches infinity, the odds of a random spot on such a line existing within a finite segment of the line go to zero. On the other hand, as mentioned, if there is a "here" or "origin" on this line, then no matter how far something travels along the line, it will always be a finite distance from the origin. I'm not sure if there's a generic term for this concept.

I guess this is similar to the concept of "finite but unbounded".

 

[marcus]

How do "bounce theory" and "entropy theory" coexist? If the universe is infinitely old, why hasn't it settled into a stablized state due to entropy?

I don't think there is any "bounce theory" as such. Some theories predict bounce as one of their features. there are several theories of gravity that are candidates to replace General Relativity---they all need to be thoroughly tested against observations

The proposed improvements of Gen Rel that I know best are quantum theories of gravity (QG)

one of these is LQG (actually a cluster of related theories) and after it had been around for some 15 years and studied by various people it was discovered (in 2001) that it predicted a bounce at our bigbang

That's different from having bounce put in at the start---and it doesn't predict that our universe follows a CYCLIC pattern

there are limits to how far you can push the model and how much detail you can get out of it----all it says is that our universe had a bounce 13.7 billion years ago at the moment where Gen Rel breaks down and gives meaningless results (infinite curvature, infinite density etc.)

Any model has a limited range of applicability. LQG-cosmology, called LQC, may or may not be right (still must be tested) and if it is right, even then it does not tell you the whole history of the universe---it just describes dynamics around our bigbang event and agrees approximately with classical GR about most of what came after. It also applies to black holes, inflation, and tentatively to dark energy---so it does address a few puzzles that classical is not very clear about. But it does not tell the whole history and it is not a 'bounce theory' precisely----the bounce was not put in as an assumption, it was something discovered later that the theory predicts.

Your question is how to square this kind of theory---which predicts a bounce---with the Second Law of thermodynamics.

As I understand it, the way to reconcile these two is to note that the Second Law (with overwhelming probability, entropy is not observed to decrease) requires an OBSERVER who provides an idea of what microstates are indistinguishable and belong to the same macrostate. The observer provides a MAP of phase space depending on what he can measure and what is significant for him (pressure temperature etc.)

the point about the bounce is that observers before and after have different maps of phase space, leading to different numbers for entropy. So NOBODY SEES ENTROPY DECREASE. The Before observer sees entropy increase as his universe collapses in chaos. The After observer looks back in time and sees a highly uniform state with very low entropy----a highly NON-equilibrium state of the gravitational field---because there hasn't been time for much clumping to happen. After bounce the field is almost perfectly even, with only small fluctuations that serve as seeds for future clumping clustering coagulation etc.

The Second Law is satisfied. It works fine for either observer. You just have to be consistent about which observer you mean.

Then there's my issue with the concept of here and now with the infinite. Since we exist here and now, then no matter how far back of forward in time or distance you go, it's a finite distance from the "here and now". If time and/or space is infinite, then how can a "here and now" exist?

For example, if a line is infinitely long, then how can a finite segment of this line exist? Where would it's "position" be on a line that infinitely long? As the length of a line approaches infinity, the odds of a random spot on such a line existing within a finite segment of the line go to zero. On the other hand, as mentioned, if there is a "here" or "origin" on this line, then no matter how far something travels along the line, it will always be a finite distance from the origin. I'm not sure if there's a generic term for this concept.

In Newton's cosmology time was infinite, I believe. I think it is normal for time-axis to be infinite in both directions with no fixed reference point.

I have no trouble imagining a bug crawling along an infinite line. You seem to be saying it is impossible for the bug to be there, crawling along the line, because it wouldn't have any POSITION. More precisely it would not have any position you could express as a number of centimeters measured from some distinguished fixed point serving as reference.

In math this kind of thing is studied in several different contexts---for example Lie groups acting on homogeneous spaces. A homog. space is where there is no fixed reference point---but you can still define a group action.
the group action might be TRANSLATION. Anyway from a logical/mathematical viewpoint it is perfectly OK for the time axis to have no fixed reference point.

We can still have our instantaneous subjective reference point, the present moment. And the bug can still crawl along the line

I guess this is similar to the concept of "finite but unbounded".

You ask nice questions. I'm not sure i see a connection but maybe I do. An example of a "finite but boundaryless" space would be a RING.
there is no surrounding space, only the ring
a one-dimensional being lives there
the ring has no "north pole" or any other distinguished point
the one-dimensional being has no official "position" relative to any fixed point of reference

but he can still measure the size of his space by making a mark somewhere and then making a full circuit----timing or measuring somehow as he goes.

But we were talking about TIME. i don't know any scientific reason to suppose that time is like a ring or that it is finite. I don't know any reason to imagine that it is not infinite in both directions.

It might be finite, of course, but I don't know of any evidence to that effect.