Is the universe infinite?


by QuantumJG
Tags: infinite, universe
phinds
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Feb29-12, 06:25 PM
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Quote Quote by jay.yoon314 View Post
If there is indeed no such thing, at what scale does the law of conservation of mass-energy break down? It breaks down neither at the atomic nor at the level of the galaxy. If it breaks down at the level of the observable universe as a whole, shouldn't this breakdown be observed at the level of the galaxy (or galaxy clusters?)?

A conservation law that is so general cannot go from being obeyed in all instances at all scales that are smaller than some arbitrary scale, but then transition abruptly into there being existing "no such thing" as you said. In any case, the burden of proof is on your part. We both agree that there is a possibility that the universe's properties at the cosmological scale are different, even in extremely surprising ways, from the universe at smaller scales. But this doesn't eliminate the fact that such differences need to be quantified, or precisely stated. How is saying that there is no such thing as a conservation of energy on cosmological scales any different, in its radicalism, than me saying that there is a finite amount of mass-energy? At least, in my view, the law of conservation of mass-energy is obeyed, which is not at all a triviality.
Unfortunately I'm not knowledgeable enought to explain it adequately, but it has been discussed numerous times here on the forum and I assure you it is true, however non-intuitive it is. I too found it quite disagreeable when I first heard it. I suggest a forum search if you want a decent explanation.
salvestrom
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Feb29-12, 07:17 PM
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Quote Quote by phinds View Post
Unfortunately I'm not knowledgeable enought to explain it adequately, but it has been discussed numerous times here on the forum and I assure you it is true, however non-intuitive it is. I too found it quite disagreeable when I first heard it. I suggest a forum search if you want a decent explanation.
spacetime has non-zero vacuum energy. infinite spacetime automatically leads to infinite energy. it should also be kept in mind that current theory says all the mass/energy in the observable universe that isn't dark energy was created out of the vacuum energy during reheat. so again, infinite spacetime would lead to reheat that occured everywhere (in all areas of space at least equal in size to the observable universe) creating infinite mass/energy.
Drakkith
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Feb29-12, 07:54 PM
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Quote Quote by jay.yoon314 View Post
If there is indeed no such thing, at what scale does the law of conservation of mass-energy break down? It breaks down neither at the atomic nor at the level of the galaxy. If it breaks down at the level of the observable universe as a whole, shouldn't this breakdown be observed at the level of the galaxy (or galaxy clusters?)?
I could be wrong on this, but I'll go out on a limb and try to explain part of what I think is the reason for this.

Think about the expansion of space and the resulting redshift of light. If all galaxies outside our cluster are receding from us, and those galaxies in their cluster see all other galaxies receding from them as well, that means that we are losing energy. Normally redshift from a moving object is countered by the fact that the light emitted in the opposite direction is blueshifted the same amount. The galaxies at redshift z=2 or whatever are moving away from us but they are not moving towards anything else, meaning there is no blueshift, only redshift. So, since expansion doesn't happen on the galaxy cluster scale, the conservation of energy still applies. It is only above this scale that it breaks down. However this could simply be a lack of understanding about dark energy, expansion, or any number of things.

Now, think about the following. You look at a proton travelling at 10% c. How much energy does it have? Well obviously it would have a certain energy we can find by doing the math with the right equations. But wait...that energy is only for one particular frame of reference. If you were moving at 5% c in the same direction then the proton would NOT have the same energy as it did in the stationary frame. So how much energy does it "really" have? I don't think that's answerable. (This may not be relevant to conservation of energy, but I wanted to point out that some types of energy are relative)

Also, as has been explained to me, energy is ill defined in General Relativity, so it's hard to say whether it's conserved or not. I had a link to a page that explained some of it, but I don't know where it is at the moment. Even the page itself states something along the lines of "Is energy in GR conserved? Well, that depends on what you mean by energy...and what you mean by conserved...", so I really don't know for sure.

If I've made a mistake somewhere someone let me knwo.
Chalnoth
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Feb29-12, 08:53 PM
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Quote Quote by jay.yoon314 View Post
If there is indeed no such thing, at what scale does the law of conservation of mass-energy break down?
It breaks down the moment that the expansion of the universe becomes a non-negligible component to the behavior of the system. For smaller systems, you can define energy in such a way that it is conserved.

Quote Quote by jay.yoon314 View Post
In any case, the burden of proof is on your part. We both agree that there is a possibility that the universe's properties at the cosmological scale are different, even in extremely surprising ways, from the universe at smaller scales.
What you don't seem to be getting is that this fact is derived directly from physics we observe here in our own solar system. First of all, energy conservation is now understood to not be a fundamental fact of nature, but instead a consequence of a particular sort of symmetry. In fact, all conservation laws are now understood to be consequences of symmetry.

Conservation of momentum is honored whenever you have a system that is unchanged when you move the system from place to place.

Conservation of angular momentum is honored whenever you have a system that is unchanged when you rotate it through some angle.

Conservation of energy is honored whenever you have a system that is unchanged when you move the system forward or backward in time.

This fact comes directly from Noether's theorem. And the actual statement is a bit more subtle (in reality, some things can change). If you imagine our own solar system, for example, it is a periodic system: if you wait some amount of time, the planets will all be back in their previous positions. So energy is a conserved quantity for planetary motion. You can build similar arguments for most anything we do here on Earth.

In fact, for most of our laws of physics, those laws remain unchanged at all times. The specific system may change, but the laws do not. This means that energy has to be conserved for Newtonian gravity, electricity and magnetism, and quantum mechanics. However, General Relativity throws a wrench into this whole system, because there is no absolute time coordinate any longer. Time itself becomes a parameter in the theory, and this symmetry is lost. No longer can you change time without changing the laws of motion in General Relativity, and so you can't define a conserved energy.

However, General Relativity doesn't get rid of conservation of energy entirely. Instead of conserving energy, it conserves the stress-energy tensor. This tensor has ten independent components, including energy density, pressure, momentum density, and twisting forces. Conservation of the stress-energy tensor will sometimes force energy to change because the other components of the tensor change. So GR doesn't say, "anything at all can happen," but rather that we now have a new conservation law which is more correct: conservation of stress-energy. And conservation of stress-energy doesn't allow energy to be conserved in all cases.

Finally, I'd just point out that the conservation of mass is trivially disproven by the fact that we can create higher-mass particles in particle accelerators, and do so very often.
Drakkith
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Feb29-12, 09:37 PM
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Thanks Chalnoth! That's the first explanation of conservation of energy in GR that I've actually understood and learned something from.
bill alsept
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Mar14-12, 12:52 AM
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Quote Quote by jobigoud View Post
It would seem that you guys do not use the accepted definition for the word "universe".
Universe: The totality of everything that exists.

It cannot be in something, or located. It is everything.


Compared to solar systems, galaxies, clusters and super clusters we can call everything else the universe only because we are inside of it. But that doesn't mean there are not many other universes just like it all lined up forever. I believe they use to call the Milky Way the universe.
phinds
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Mar14-12, 01:51 AM
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Quote Quote by bill alsept View Post
Compared to solar systems, galaxies, clusters and super clusters we can call everything else the universe only because we are inside of it. But that doesn't mean there are not many other universes just like it all lined up forever. I believe they use to call the Milky Way the universe.
Yes, and they used to call the earth flat. What's your point? Previous ignorance should require current ignorance?

You don't get to decide what you want the definition to be even though you seem to think you can.
bill alsept
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Mar14-12, 02:21 AM
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Quote Quote by phinds View Post
Yes, and they used to call the earth flat. What's your point? Previous ignorance should require current ignorance?

You don't get to decide what you want the definition to be even though you seem to think you can.
WOW, nice input


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