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It’s confusing how a universe can have finite mass but infinite size. Could the universe be like a tesselation, where you always end up where you started? Not like a closed universe, but where space is just copied over and over?
It doesn't. The total mass of the universe isn't a well-defined quantity.It’s confusing how a universe can have finite mass
I don't think your first sentence is worded very well. If it's reworded as follows, it becomes (possibly) accurate:It’s confusing how a universe can have finite mass but infinite size. Could the universe be like a tesselation, where you always end up where you started? Not like a closed universe, but where space is just copied over and over?
I don't know if I buy the logic that spatial infinity implies temporal infinity. But it is definitely the case that models which are spatially-infinite are difficult to make sense of (not due to the objections in the original post, but just because it's difficult to come up with a physical process that would generate such a universe).The problem with spatial infinity is it implies temporal infinity and consensus among cosmologist is the universe is of finite age, This concession puts a strain on the concept of spatially infinite or that it eventually repeats ad nauseum over sufficiently vast distances. This leads to curious scenarios like the pac-man universe which is finite, but, unbounded [spacetime boundaries present special problems that have no easy cosmological, or philosophical, solutions]. Since the risk of being proven wrong is low, most cosmologists are content with the easy way out offered by spatial nfinity, and reply 'What can of worms?', when pressed on the issue.
I have also wondered if Cosmologists consider the possibility that the Universe is circular? (like the surface of a balloon), so that we can perhaps see the milky way one or even more times, as its light travels the universe one or multiple times. I remember playing a game called asteroids like that :)
I wouldn't go that far. Two things muck this up:(whereas they can tell us that the universe is not spatially a 3-sphere, since that requires spatial curvature)
Two things muck this up
The mathematical models used are intrinsically tied into the physical theories used. You can't separate the two.Is it possible that the mathematics currently used to speculate about the universe isn't up to the task? For example, pretend there's a civilization whose mathematical systems are all based on counting. They've developed extremely sophisticated ways to count, to describe things using counting, even to talk about counting. Sure they have some anomalies, infinities, etc. that they just shrug off, but all in all they've been able to develop sophisticated means of description. But for whatever reason they never discovered geometry. So their descriptions of the universe would be necessarily limited, though they wouldn't know it. How do we know that our cosmologists aren't in the same boat? All these anomalies and infinities and breakdowns are just because they're using the wrong type of math.
Can you explain this part a little bit more. Couldn't the same be said in the context of my example of the counting based physics? Doesn't the math preceed the physical theory?The mathematical models used are intrinsically tied into the physical theories used. You can't separate the two.
I think the point being made is that Newtonian physics isn't usually described in terms of geometry, but it can be - Cartan did it. Likewise, it would not surprise me if it's possible to develop GR without using geometry, so it's not at all clear that your hypothetical system would be different from GR. In fact, if it made the same predictions then it would not be distinct. If it made different predictions then it would be a different physical theory, one that may or may not be better than GR.Can you explain this part a little bit more. Couldn't the same be said in the context of my example of the counting based physics? Doesn't the math preceed the physical theory?
The reference to geometry was unimportant, it was just part of the analogy. Pretend I used the word "phlemomotry". I guess in terms of the second part of your response, my question is, does the math determine the predictions? Point being, if the math predicts something weird like infinities, or some of the aspects of the big bang theory (the "right way to think about it" as described in the Sci Am article), maybe it's not that the universe has those odd properties, but that the math used to get to the predictions is the wrong type of math. (I know this is straying into philosophy of physics. Pardon my wandering.) To put it extremely crudely, if all you have is a hammer (current math) then everything looks like a nail.I think the point being made is that Newtonian physics isn't usually described in terms of geometry, but it can be - Cartan did it. Likewise, it would not surprise me if it's possible to develop GR without using geometry, so it's not at all clear that your hypothetical system would be different from GR. In fact, if it made the same predictions then it would not be distinct. If it made different predictions then it would be a different physical theory, one that may or may not be better than GR.
Ah ok that makes a lot of sense. I was not aware that cosmologists think the singularities probably don't exist in reality. I thought that was the forgone conclusion which then to us laymen indicated just how strange the universe is. (I guess you can't make big budget sci fi thrillers on the reality of current theory. ;) ) Thanks for being patient and giving honest, not condescending replies.As @kimbyd says, we are fully aware that GR is very likely not completely accurate. The singularities it predicts almost certainly do not exist in reality. We continue to look for successor theories, which may or may not be expressed (or expressible) in terms of geometry. The only real constraint on the form of such a theory is that its predictions must match GR in cases we have tested to at least the precision of our tests.
Not necessarily. Experimental results have often provided hints as to new possible mathematical models that might be used. The mathematics involved in quantum mechanics, for example, would probably never have developed as far as it has if there was no demand for that kind of theory in physics. Physicists generally don't just pick pre-existing mathematical models off the shelf to make use of them. Some theorists explore new regimes of mathematics that hadn't yet been explored, or extend regimes that had only been examined briefly by mathematicians. Furthermore, many mathematicians have a great deal of interest in math as it is applied to physics, such that they pursue investigations with the specific purpose of understanding physics better.Can you explain this part a little bit more. Couldn't the same be said in the context of my example of the counting based physics? Doesn't the math preceed the physical theory?
Hi @kimbyd:But since the universe is infinite, there has to eventually be a copy somewhere.
The number of OUs is ℵ_{0}.
I think the relevant point is slightly weaker than the one that @Buzz Bloom is trying to make.Why?
One can nail down the initial conditions for the entire universe in terms of the initial conditions for a countable collection of observable universes. The uncountably many other observable universes will overlap with this set and will have their initial conditions determined thereby.
In quantum mechanics, any finite region has a finite number of degrees of freedom. In our case, as long as the cosmological constant is positive, the total number of configurations within a given cosmological horizon can be counted precisely based upon the entropy of the horizon. The finite number of degrees of freedom guarantees infinite repetitions if the universe is genuinely spatially-infinite (with the same cosmological constant everywhere).Hi @kimbyd:
I have found this thread quite interesting, and in particular the very clear explanations you made regarding the OP. However, the above quote does not quite make sense to me. There seems to me to be two problems with this assumption.
I assume the universe we are discussing to be the current best cosmological model for out actual universe.
(1) Each observable universe (OU) has its own history based on it's "initial conditions" at some arbitrarily chosen past time T using comoving coordinates. If we assume that there is some other very distant OU to ours which is identical to ours now, it must have been identical to ours at the earlier time T. My thought is that the influences of interactions among the various components of the two OUs dependent on QM effects, would necessarily introduce small changes between the two OUs over the time between T and now, and each small change would grow to become a significant change. Thus the two OUs would not be identical now even they were identical at time T.
(2) For the purpose of presenting this problem I ignore the QM influence in (1). I think you are confusing two different kinds of infinity: ℵ_{0} and ℵ_{1}.
The number of OUs is ℵ_{0}. The number of possible configurations of time T initial conditions is ℵ_{1}.
Therefore the likelihood that there is another OU with initial conditions identical to ours in infinitesimal. If the initial conditions are different, even when the difference is small, they will produce current configurations which will be greatly different for chaos theory reasons.
If you disagree with either the (1) or (2) conclusion, I would much appreciate your explanation.
Regard,
Buzz
Hmm, I'm having difficulty following this argument. When you say "any finite region", do you mean a finite 3D spacelike slice, or a general 4D spacetime volume?In quantum mechanics, any finite region has a finite number of degrees of freedom. In our case, as long as the cosmological constant is positive, the total number of configurations within a given cosmological horizon can be counted precisely based upon the entropy of the horizon.
In QM, the 4D space-time is degenerate, as you can time-evolve the state of the system at anyone time to obtain the state of the system at another. Thus the full configuration of the system is described by a single time-slicing (and it can be evolved forward and back to get the full 4D state).Hmm, I'm having difficulty following this argument. When you say "any finite region", do you mean a finite 3D spacelike slice, or a general 4D spacetime volume?
Yes, so,... what precisely did you mean earlier by "a given cosmological horizon"? Do you mean the horizon of our distant (but finite) past, or some other horizon at a finite spacelike distance from us?In QM, the 4D space-time is degenerate, as you can time-evolve the state of the system at anyone time to obtain the state of the system at another. Thus the full configuration of the system is described by a single time-slicing (and it can be evolved forward and back to get the full 4D state).
I believe the horizon in question is the cosmological event horizon, beyond which it is impossible for signals to reach a given observer. That's the horizon that has a temperature, as I understand it.Yes, so,... what precisely did you mean earlier by "a given cosmological horizon"? Do you mean the horizon of our distant (but finite) past, or some other horizon at a finite spacelike distance from us?
I'm familiar with horizons, their thermal radiation, entropy, etc, but I'm still having trouble meshing this with what you said. Could you elaborate in more detail, pls?
Oh, I see now -- like (for example) in de Sitter spacetime which has a Killing horizon at ##r = \sqrt{3/\Lambda}## .I believe the horizon in question is the cosmological event horizon, beyond which it is impossible for signals to reach a given observer. That's the horizon that has a temperature, as I understand it.