B Infinite amount of matter in the universe?

[lifeonmercury]

If the universe is indeed flat and the cosmological principle holds true, does this mean that there is an infinite amount of space in the universe as well as an infinite amount of matter?

 

[mfb]

Yes.

Edit: Merged another thread into this one.

 

[Demystifier]

Yes it does.

 

[lifeonmercury]

It appears that most scientists subscribe to the flat universe theory and believe in the cosmological principle. This means that our most up-to-date scientific findings suggest that it is more likely than not that space and matter just keep going on and on forever in all directions. That is quite a difficult one to comprehend.

 

[mfb]

There is no "flat universe theory". Our cosmological models allow a curvature, but measurements so far have been in agreement with a flat universe, with increasing precision over time. It does not have to be exactly flat, but at least very close to it. Experimentally that difference doesn't matter, so you can often just assume that the universe is flat. It does not mean that it has to be exactly flat.

and believe in the cosmological principle.

It is expected, based on existing measurements.

 

[Demystifier]

It is expected, based on existing measurements.

And a lot of extrapolation. In Ancient times, by similar reasoning people might think that the Earth is flat and infinite.

 

[lifeonmercury]

Are there any scientific models that predict a finite, bounded universe (such as one with a center and edges/borders)? I recall reading about a theory claiming that the universe is a sphere surrounded by a black hole state at the edges.

 

[phinds]

Are there any scientific models that predict a finite, bounded universe (such as one with a center and edges/borders)?

no

I recall reading about a theory claiming that the universe is a sphere surrounded by a black hole state at the edges.

this is nonsense

 

[Bandersnatch]

And a lot of extrapolation. In Ancient times, by similar reasoning people might think that the Earth is flat and infinite.

No - in this analogy, application of 'cosmological principle' to the surface of the Earth would prompt the ancient people to conclude that the Earth does not have an edge, and instead that the surface is a continuous plane. Either infinite or curved.
Providing they applied the same measurement analysis we do now, they could also measure the curvature to within some error margin.

The main difference between us and the analogy, though, is in the fact that the ancients could expand the base of their measurements to cover the whole surface. We, on the other hand, are restricted in how big a space can we use as a base for our measurements, since in our universe there exists an event horizon (mere <50% farther than the farthest objects we see now). Which is to say, while given enough effort the ancients could verify whether the application of the principle to Earth was valid globally, we won't be able to do the same with respect to the universe. Our choice to apply the principle to areas outside our potentially observable universe will be always based on mere parsimony, i.e. aesthetics.

Are there any scientific models that predict a finite, bounded universe (such as one with a center and edges/borders)? I recall reading about a theory claiming that the universe is a sphere surrounded by a black hole state at the edges.

This might help:
http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/universe.html
It ties a bit to the argument about applicability of the cosmological principle mentioned above.

 

[Chronos]

The ancients had good reason to believe Earth was of finite size. The moon was one obvious clue and lunar eclipses sealed the deal by around 500 BC. The shadow of the Earth on the moon was clearly curved suggesting it too is spherical. Eratosthenes is credited with deducing a fairly precise figure for Earth's circumference [40,000 Km] around 240 BC. Modern man has also arrived at a fairly precise figure for the size of the observable universe. There are some obvious practical difficulties in measuring the size of the unobservable universe. We have already tried the ancient approach by measuring the curvature of space. All we have managed to figure out is it must be really big - which, of course, assumes the classical rules of geometry apply to the whole of the universe. For a more comprehensive discussion on ancient measurements of the size of earth, see http://www.metrum.org/measures/measurements.htm

 

[stoomart]

Infinite matter makes as much sense as a singularity of infinite energy. I understand this is what the math predicts, but it is non-sensical to me; LQC seems to offer a reasonable explanation for the source and destination of matter/energy.

 

[phinds]

Infinite matter makes as much sense as a singularity of infinite energy.

Then you must of necessity believe that the universe cannot be infinite. You MIGHT be right but you can't prove it so that's just a personal opinion, not science.

EDIT: I assume you know by now that when it comes to cosmology (the very large) and Quantum Mechanics (the very small) human "intuition", "common sense", and so forth are less than worthless, they can actually get in the way of your understanding of reality.

 

[stoomart]

Then you must of necessity believe that the universe cannot be infinite. You MIGHT be right but you can't prove it so that's just a personal opinion, not science.

Agreed, the same is true for both sides of the argument. I think threads discussing infinite time/space/energy are too philosophical in general. It's one thing to say "this is what the math predicts", and another to say "this is what must be": my understanding is the latter is a scarce luxury.
I approach all topics from the perspective that common sense is attainable, even in the absence of observable evidence. In this case, scientific observation predicts the universe had a beginning and common sense tells me it's finite.

 

[Chronos]

We are unavoidably prisoners of human intuition. It is the bedrock of all intellectual pursuits. Intuition certainly leads us down dead end roads, where the error of our ways are exposed by paradoxes and infinities, but, that is the price that of admission to the frontiers of knowledge. That same intuition, however, warns us of the peril of forcing nature to comply with our personal preferences. Only by confronting these issues is progress achieved. The answers are not necessarily 'pretty', 'natural' or reflect any deeper, hidden order that satisfies any such expectations. As Freud might say, sometimes a cigar is just a cigar. You need not comprehend the nature of things to acknowledge their reality.

 

[phinds]

... scientific observation predicts the universe had a beginning ...

I'm not aware of any such. Citations? Our currently accepted model of the universe, the Big Bang Theory, is agnostic on the subject of a creation event.

 

[stoomart]

I'm not aware of any such. Citations? Our currently accepted model of the universe, the Big Bang Theory, is agnostic on the subject of a creation event.

I'm not talking about a creation event, I'm referring to the big bang.

 

[Chalnoth]

If the universe is indeed flat and the cosmological principle holds true, does this mean that there is an infinite amount of space in the universe as well as an infinite amount of matter?

Sort of, but only if it is exactly flat and the cosmological principle is exactly true.

The former we cannot ever be sure of, because our measurement accuracy will always have some non-zero error.
The latter we definitely know is false locally, but works pretty well for large scales within the observable universe. The cosmological principle may break down on scales much larger than our cosmological horizon, but we have no way to know at present.

Basically, as others have stated, this means that the precise answer to your question is yes. The problem is that this requires making two unfounded assumptions that we have no reason to believe are true, so this is a trivial statement: yes, if you assume the universe is infinite, then it's infinite. It's true but content-free.

 

[nikkkom]

I'm not talking about a creation event, I'm referring to the big bang.

Big Bang theory does not say that Universe definitely had a beginning. It merely says that there was a much denser, and much faster expanding state in the past. It is generally understood that before that, "something else" was happening. This "something else" can possibly extend infinitely far into the past. One class of such theories are eternal inflation theories.

 

[phinds]

I'm not talking about a creation event, I'm referring to the big bang.

Which is exactly what I am talking about. See, the clue was when I said "Our currently accepted model of the universe, the Big Bang Theory"

 

[stoomart]

Big Bang theory does not say that Universe definitely had a beginning. It merely says that there was a much denser, and much faster expanding state in the past. It is generally understood that before that, "something else" was happening. This "something else" can possibly extend infinitely far into the past. One class of such theories are eternal inflation theories.

Thanks nikkkom, this is similar to the idea I subscribe to: something along the lines of sequential universes or a multiverse, just not an infinite universe.

 

[stoomart]

Which is exactly what I am talking about. See, the clue was when I said "Our currently accepted model of the universe, the Big Bang Theory"

Ok sorry, I think the problem is my definition of the universe as the current instance of sequential universes, or a closed system connected to a multiverse.

 

[phinds]

Ok sorry, I think the problem is my definition of the universe as the current instance of sequential universes, or a closed system connected to a multiverse.

And that may well in fact be the case BUT ... it is not currently accepted theory (the Big Bang Theory is) and so is not what physicists normally mean by "the universe".

 

[stoomart]

And that may well in fact be the case BUT ... it is not currently accepted theory (the Big Bang Theory is) and so is not what physicists normally mean by "the universe".

Is there an FAQ or an accepted source that explains the why physicists accept the universe to be infinite?

 

[mfb]

why physicists accept the universe to be infinite?

That is not what happens. Physicists accept the possibility that the universe could be infinite. We simply do not know today.

An infinite universe is the easiest model that is not in disagreement with observations, but it is not the only one.

 

[phinds]

Is there an FAQ or an accepted source that explains the why physicists accept the universe to be infinite?

As mfb has already pointed out, physicists do NOT accept that as fact. The Big Bang Theory does not posit an infinite universe.

 

[stoomart]

That is not what happens. Physicists accept the possibility that the universe could be infinite. We simply do not know today.

An infinite universe is the easiest model that is not in disagreement with observations, but it is not the only one.

Fair enough, thanks guys.

 

[lifeonmercury]

Is there any consensus about whether it will ever be possible to determine with certainty if the universe is in fact infinite?

 

[phinds]

Is there any consensus about whether it will ever be possible to determine with certainty if the universe is in fact infinite?

The consensus, I believe, is that since we cannot see, and will never be able to see, outside of the Observable universe, we can never know for sure that the universe is infinite. We may be able to say, based on solid evidence, that is almost certainly has to be infinite but we will never know for sure.

 

[nikkkom]

Thanks nikkkom, this is similar to the idea I subscribe to: something along the lines of sequential universes or a multiverse, just not an infinite universe.

What's the problem with infinite Universe? Do you also have difficulty with infinite real line? Infinite number of natural numbers?

 

[lifeonmercury]

OK, so the idea is that we could never develop good enough technology to see past the cosmic horizon. However, if the universe is actually finite and wrapped around the 4th dimension, would there be some way of proving that (given that we haven't been able to thus far and it may be more difficult to do so in the future due to the continued expansion of space)?

 

[phinds]

OK, so the idea is that we could never develop good enough technology to see past the cosmic horizon. However, if the universe is actually finite and wrapped around the 4th dimension, would there be some way of proving that (given that we haven't been able to thus far and it may be more difficult to do so in the future due to the continued expansion of space)?

There is absolutely zero evidence of such a thing.

 

[ChrisisC]

Yes.

Edit: Merged another thread into this one.

But if there is a infinite amount of matter, wouldn't that require new energy to be constantly made forever, violating the law of energy conservation?

 

[phinds]

But if there is a infinite amount of matter, wouldn't that require new energy to be constantly made forever, violating the law of energy conservation?

(1) How do you figure that? I don't get that conclusion at all
(2) Irrespective of whether or not the universe is infinite, "dark energy" is being created constantly
(3) The law of conservation of energy does not apply on cosmological scales.

 

[mfb]

OK, so the idea is that we could never develop good enough technology to see past the cosmic horizon. However, if the universe is actually finite and wrapped around the 4th dimension, would there be some way of proving that (given that we haven't been able to thus far and it may be more difficult to do so in the future due to the continued expansion of space)?

Yes, and in fact scientists have looked for evidence of that (repeating structures in the cosmic microwave background). No indication of that has been found.

But if there is a infinite amount of matter, wouldn't that require new energy to be constantly made forever, violating the law of energy conservation?

No. There is no need to "make new energy" (this is identical for a finite and an infinite universe), and global conservation of energy does not hold in general relativity anyway.

 

[ChrisisC]

(1) How do you figure that? I don't get that conclusion at all
(2) Irrespective of whether or not the universe is infinite, "dark energy" is being created constantly
(3) The law of conservation of energy does not apply on cosmological scales.

If the law of energy conservation does not apply on a cosmological scale... where does the new energy come from?

 

[lifeonmercury]

Yes, and in fact scientists have looked for evidence of that (repeating structures in the cosmic microwave background). No indication of that has been found.

Not sure if I follow. If scientistics look toward
the cosmic horizon in one direction and detect radiation or star constellations that they also detect in the opposite direction, this would be evidence of a finite universe wrapped around a fourth dimension?

 

[mfb]

If the law of energy conservation does not apply on a cosmological scale... where does the new energy come from?

What new energy?
You cannot define "the total energy in the universe now" in a meaningful way, because you cannot even define a global "now" in a meaningful way. In GR there is no reason to expect that energy is conserved globally, energy does not have to "come from something" - that is the point of non-conservation. If energy would have to come from something, it would be conserved.

Not sure if I follow. If scientistics look toward
the cosmic horizon in one direction and detect radiation or star constellations that they also detect in the opposite direction, this would be evidence of a finite universe wrapped around a fourth dimension?

Forget the "fourth dimension", that concept doesn't work. It would be evidence that the universe is finite, yes, and that you get back to the starting point if you fly in one direction long enough.

 

[PeterDonis]

the law of energy conservation does not apply on a cosmological scale

It's more than that. In GR, the only law of energy conservation is local--it's that the covariant divergence of the stress-energy tensor is zero. Physically that means that stress-energy can't be created or destroyed in any infinitesimal volume of spacetime. Stress-energy includes other things besides energy, or more precisely energy density--it includes momentum flux, pressure, and shear stresses. For a simple discussion it's OK to think of it as "energy", but it's important to understand that it's a density--a local thing--not a "total energy". There is no invariant way to "add up" local contributions of stress-energy at different points to get a "total energy"--not just on cosmological scales, but strictly speaking, on any scale where spacetime curvature is large enough to be significant.

 

[stoomart]

What's the problem with infinite Universe? Do you also have difficulty with infinite real line? Infinite number of natural numbers?

Writing ∞ is one thing, actually constructing an infinite number of natural numbers or an infinite real line is non-sense.

EDIT: I should point out that philosophically I believe the quantum scale is infinitely small and the cosmological scale is infinitely great, but this is a science forum.

 

[Chronos]

Philosophy is irrelevant. Only observational evidence has any scientific validity. Apparently, that approach is a challenge, given the lack of credible citations supporting your conclusions.

 

[andrew s 1905]

What's the problem with infinite Universe? Do you also have difficulty with infinite real line? Infinite number of natural numbers?

It seems to me physicists are comfortable with some infinities but not others. Some, as in QED, are happily renormalised away while others infinities, such as the density as a singularity at the center of a black hole is approached, are seen as a sign that GR breaks down.

Regards Andrew

 

[stoomart]

Philosophy is irrelevant. Only observational evidence has any scientific validity. Apparently, that approach is a challenge, given the lack of credible citations supporting your conclusions.

My philosophy is not dependent on observational evidence, but is supported by it.

 

[phinds]

My philosophy is not dependent on observational evidence, but is supported by it.

You need to be careful about making such a claim on a science forum. If I understood your post correctly, your philosophy says that, to quote you directly, "the quantum scale is infinitely small and the cosmological scale is infinitely great". I challenge you to offer any evidence that these statements are true. Not LIKELY, but true. Science is a lot like horseshoes in some ways. "Likely" counts as zero if you are looking for "empirically verifiable with no exceptions" which is the standard for "true" in science, to the extent that anything is ever "true" in science.

 

[stoomart]

In post #13 I said these kinds of threads are too philosophical, and I'm surprised it has been allowed to continue this long. I recognize that I appear to be talking from both sides of my mouth when you look at posts #20 and #39, so let me explain why this is a fair conclusion.

My brain is simply a tool that is used by my mind (concerned with physical existence) and my soul (concerned with philosophy); most people supress one or the other to varying degrees, but I find life is more interesting and fulfilling when you give them equal freedom, because our brains are built to process both. This allows me to accept naturalism/creationism and a finite/infinite universe without conflict.

 

[PeterDonis]

It seems to me physicists are comfortable with some infinities but not others. Some, as in QED, are happily renormalised away while others infinities, such as the density as a singularity at the center of a black hole is approached, are seen as a sign that GR breaks down.

The difference in these two cases is that, in QED, the "infinities" that are "fixed" by renormalization are artifacts of a particular theoretical framework (perturbation theory), so renormalization is just a way of fixing the theoretical framework so that useful predictions can be extracted from it. The infinite terms that get renormalized away have no direct physical interpretation; and in fact, in non-perturbative models they don't appear at all. There is no need to believe that QED is telling us that there are any actual infinities in nature in this case.

The singularity at $r = 0$ in a black hole, OTOH, involves spacetime curvature invariants increasing without bound. Spacetime curvature invariants have a direct physical interpretation; there is no way to "renormalize them away" by changing your theoretical framework. So spacetime curvature invariants increasing without bound means GR is telling us that there are actual infinities in nature. Which means that, if you don't believe there can be any actual infinities in nature, you have to believe that GR breaks down deep enough inside a black hole.

 

[PeterDonis]

I'm surprised it has been allowed to continue this long.

There are genuine issues of physics being discussed in this thread (the post I just responded to raises one). But you are correct that philosophy is out of bounds.

My brain is simply a tool that is used by my mind (concerned with physical existence) and my soul (concerned with philosophy)

The latter part is out of bounds. Such beliefs can't be usefully discussed here because there is no way to test them against evidence. That doesn't mean you can't hold them; it just means they can't be usefully discussed in this forum. Please bear that in mind for future posts.

 

[Chris Miller]

Infinity, to me, isn't a number or an amount, but an algorithm (or function) that can always generate new set members. So the term "infinite mass" is kind of an oxymoron... unless the universe is an algorithm, I guess.

 

[PeterDonis]

Infinity, to me, isn't a number or an amount, but an algorithm (or function) that can always generate new set members.

This is not the standard definition. The proper way to interpret the statement "the universe contains infinite mass" using the standard definition of "infinite" is "given any real number, the amount of mass in the universe is larger than that number".

the term "infinite mass" is kind of an oxymoron

No, it isn't; it has a perfectly well-defined meaning, which I just gave above. The statement might not be true, but if it turns out not to be true it won't be because it's an oxymoron.

You can't change physics by picking new definitions of words.

 

[Ernest S Walton]

If personal opinions are to be kept out of this forum, then the opinion that physics and philosophy are incompatible should also be disallowed because that is all it is, an opinion. The idea that Plato, Kant, Descartes and other geniuses would have no place on this forum is mind-numbingly primitive.

 

[phinds]

If personal opinions are to be kept out of this forum, then the opinion that physics and philosophy are incompatible should also be disallowed because that is all it is, an opinion. The idea that Plato, Kant, Descartes and other geniuses would have no place on this forum is mind-numbingly primitive.

Why? This is not a forum about philosophy or art or music or any number of fields in which there are geniuses who have no relevance to hard science and so are not part of this forum.