Amount of Matter in the Universe

[loseyourname]

Is there any consensus on what the total mass of all matter in the universe is, or even whether or not there is a finite amount? I ask because the claim recently came up in discussion that recent cosmology research indicates that there is both an infinite amount of space and an infinite amount of matter in the universe. No source was cited, but the name Max Tegmark came up, associated with the claim that there is an "infinite amount of space with matter uniformly distributed throughout."

I have very little knowledge of cosmology, but this immediately sets off my BS meter. Doing a search of Tegmark on the web, I can't find anything like this (but it was only a very quick search), but I did find the rather speculative and unscientific hypothesis that every entity that exists mathematically also exists physically. Any word on this guy in general and particularly the infinite space and uniform distribution of matter thing?

 

[pervect]

In another recent thread, I've quoted some of the specific warnings in textbooks about attributing a total mass to a closed universe.

I'm not aware of any specific quotes that give the same warning for an open universe. But since theoretically, an open universe should be infinite, I would guess that the textbook authors didn't think such warnings were necessary in that case.

Next we get into the issue of "the universe" vs "the observable universe". Usually, the observable universe is taken to be some small part of a much larger total entity.

This entity is usually thought to be infinite, but since we can't actually observe it (we can only observe the observable universe) there's no sensible way to argue about whether it actually is infinite or not. All we can really say is that there doesn't seem to be any particular evidence that the part of the universe that we can see (the observable universe) has any sort of "edge" - the observable universe appears to be homogeneous and isotropic. If the universe is not closed (i.e. a compact manifold, like a sphere), the only way for it to be homogenoeous everywhere is to make it infinite. So that's the usual assumption.

Current theories tend to favor an open universe over a closed one.

I'm not particularly familiar with the particular author you quote (Max Tegmark) BTW.

 

[SpaceTiger]

Any word on this guy in general and particularly the infinite space and uniform distribution of matter thing?

Max is a respected cosmologist who spends a lot of time explaining the standard cosmological model to professionals and amateurs alike. He works a lot on the Sloan Digital Sky Survey (SDSS) and is noted for having measured the power spectrum of matter from the galaxy distribution observed by SDSS, though his work is certainly not limited to that.

I'm pretty much agnostic on the finite/infinite issue and would share your skepticism towards any claim that we had strong evidence for an infinite universe. Yes, the observable universe is consistent with an infinite and flat large-scale geometry, but I see no reason to assume that the cosmological principle (from which this conclusion would be drawn) will continue to hold on all scales, especially considering that inflation would produce local flatness independent of the large-scale geometry.

 

[pervect]

I'm pretty much agnostic on the finite/infinite issue and would share your skepticism towards any claim that we had strong evidence for an infinite universe. Yes, the observable universe is consistent with an infinite and flat large-scale geometry, but I see no reason to assume that the cosmological principle (from which this conclusion would be drawn) will continue to hold on all scales, especially considering that inflation would produce local flatness independent of the large-scale geometry.

I wouldn't want anything I've said to be interpreted that I strongly support the idea that the universe must be infinite.

However, I would definitely suggest that for accuracy and clarity that it is much, much better to talk about the density of the universe than it is to talk about the "total mass of the universe".

Aside from neatly sidestepping the whole "finite/infinite/observable" issue, talking about density instead of "total mass" get's rid of several subtle technical issues relating to how mass and energy are defined in GR and when they can be considered to be conserved.

The sci.physics.faq (previously mentioned but quoted below for definiteness)

http://www.math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

does as good a job as anything I'm aware of as to explaining the ins and outs of energy conservation in GR without getting too technical.

The differential conservation laws for energy and momentum are built into the theory from the ground up, but they do not generalize as one might expect into a globally conserved quantity, except under certain special conditions as described in the FAQ.

More specifically - total energy is not necessarily equal to density * volume.

Note as well that the FAQ is specific to GR, it won't cover "dark horse" theories like Garth's SCC.

In addition to talking about the matter density of the universe, it is occasionally necessary to talk about the radiation density (aka the pressure) as well, especially in the early history of the universe.

 

[SpaceTiger]

I wouldn't want anything I've said to be interpreted that I strongly support the idea that the universe must be infinite.

My post wasn't in response to yours, I was just giving my own perspetive on his question. I don't have any objections to what you said and agree that it's better to talk about the density than the total mass.

 

[EL]

As he says on his website,
http://space.mit.edu/home/tegmark/index.html ,
Max Tegmark's research "is focused on precision cosmology, e.g., combining theoretical work with new measurements to place sharp constraints on cosmological models and their free parameters."
Max is originally from Stockholm, Sweden, and currently works at MIT. He is probably one of the most frequently cited Swedish researcher at the moment.
Besides his scientific success, he is also a brilliant lecturer...

 

[pervect]

My post wasn't in response to yours, I was just giving my own perspetive on his question. I don't have any objections to what you said and agree that it's better to talk about the density than the total mass.

Thanks for clarifying that. Actually, my concern was not that you disagreed with me - from my recollection of your pasts posts on the topic of energy & GR I was pretty sure that that was not the case. Rather, my concern was the perception of the OP here, "loseyourname".

Basically, I realized that I'd allowed myself to be pulled off on some interesting (though rather philosphical) tangents about the finiteness or infiniteness of the universe that were only periphierally related to the original question about the mass of the universe.

 

[loseyourname]

Well, the main questions were two:

1) Is there an infinite amount of matter in the universe?
2) Did Tegmark actually make that claim?

The reason the claim didn't jive with my limited knowledge of cosmology is that it seemed there must be some limitation to how far matter could be spread out, since the big bang occurred at a point finitely, not infinitely, in the past, so where would an infinite amount of matter spread out into an infinite amount of space have come from? How could it have gotten there?

The other reason was the whole observable/unobservable thing. The original guy was obviously trying to get technical in citing current research, but what research could possibly suggest an "infinite amount of space with matter evenly distributed thoughout?" I cannot imagine a way to observe, let alone measure, the density of matter in unobservable parts of the universe that are infinitely far away. Then again, scientists have done things before that I would never have imagined were possible to do, so I didn't want to simply dismiss the claim. Ergo, I asked the experts here what they knew about this.

I get from SpaceTiger's post that the claim can only be an extrapolation based on matter distribution and spatial geometry in the portion of the universe over which we can measure these things, assuming the distribution and geometry hold "to infinity and beyond," so to speak, but there really is no good reason to conclude this any more than there is to conclude based on a survey of the land I'm on right now that the whole Earth is flat and paved over in concrete.

Don't worry about the tangents, pervect. You wouldn't believe the reason this ever came up in the first place.

 

[EL]

The reason the claim didn't jive with my limited knowledge of cosmology is that it seemed there must be some limitation to how far matter could be spread out, since the big bang occurred at a point finitely, not infinitely, in the past, so where would an infinite amount of matter spread out into an infinite amount of space have come from? How could it have gotten there?

A common misunderstanding about the Big Bang is that it happened at a single point in space. Big Bang took place at all points in space at the same time! When one speaks about the Big Bang singularity one means that the density at that moment was infinite, which need not imply a finite amount of matter.
Maybe you'll find it useful to think like this: Imagine a 2-dimensional universe living on an infinite plane, with points representing matter evenly distributed all over it . Since the plane is infinite we have an infinite amount of matter (points) in this toy-universe.
Now, by shrinking this infinite plane (i.e. going backwards in time) more and more, the points will get closer and closer, representing an increasing density. However, the plane will of course still remain infinite.
After infinitely many "shrinkings" we'll reach the Big Bang singularity (that is infinite density) without having stuffed all matter into a single point!

So in summary the infinite amount of matter need not "spread out" since it was everywhere already at the Big Bang!

Now one can always discuss wheter it's really meaningful to discuss about anything but the observable universe, which of course is finite. But I hope I could give you some kind of insight about what is probably ment by "an infinite amount of matter in the universe".

 

[pervect]

The CMB is at very nearly the same temperature viewed at any angle. This does suggest that all the parts of the universe we see are causally related.

This is actually a problem in standard GR, known as "the horizon problem", but a problem with a standard resolution. The standard resolution is inflation.

There is another issue that inflation resolves, which is the "flatness-oldness problem". Basically, the universe appears to be almost perfectly flat spatially as far as we can tell.

To use inflation to explain the flatness of the universe, though, the inflationary period must have lasted a long time - at least 100 doublings.

http://www.astro.ucla.edu/~wright/cosmo_04.htm

This solves the flatness-oldness problem as long as the exponential growth during the inflationary epoch continues for at least 100 doublings. Inflation also solves the horizon problem, because the future lightcone of an event that happens before inflation is expanded to a huge region by the growth during inflation.

Now 100 doublings is a lot. If we take the inflation explanation of the flatness-oldness problem as the proper explanation, we can see that the entire universe is at least 2^100 times bigger (that's 2^10^)^10 = 10^30 times bigger after inflation than before it.

This suggests that the entire observable universe is only a small part of the universe.

Thus the usual model is of an observable universe that's only a very small part of a much larger entity. The actual argument stops short of arguing that the obserable universe is infinitely smaller, but suggests that infinity is a perfectly fine approximation.

 

[loseyourname]

A common misunderstanding about the Big Bang is that it happened at a single point in space. Big Bang took place at all points in space at the same time! When one speaks about the Big Bang singularity one means that the density at that moment was infinite, which need not imply a finite amount of matter.
[...]
Now one can always discuss wheter it's really meaningful to discuss about anything but the observable universe, which of course is finite. But I hope I could give you some kind of insight about what is probably ment by "an infinite amount of matter in the universe".

Thanks a ton, El. My conceptual understanding was mistaken. Your post clarified what I wanted clarified.

 

[EL]

Glad to help!

 

[SpaceTiger]

A portion of this thread has been moved here:

https://www.physicsforums.com/showthread.php?t=125870"