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This post is the second in a series of posts that met (decreasingly) with some contention from the physics community, do to my status as a pure mathematician at the very beginning of trying to discuss applications of my field of study (hyperbolic $3$-manifolds), about which I was pretty ignorant. The previous one was: Can we see enough of the universe to have a valid opinion on whether it's expanding? and the following two are Regarding the universe, doesn't "almost flat" mean "not flat?" and What are the applications of hyperbolic $3$-manifold theory to cosmology? I hope that others can appreciate my choice to evoke a potentially annoying conversation as opposed to remaining ignorant. Please be patient with me and if I say something stupid, let me know and tell me why.

When say "the universe," there is a built in problem of definition since if we really knew what it was we would be done. We often get around this by saying "the observable universe," which loosely means the portion of space which is close enough to us to be "theoretically" measurable. In fact, the very definition of observable universe includes the assumption that it is expanding because, according to the theory, that expansion is the very thing which limits the theoretical measurability.

The naive idea of the Big Bang is that, since things are drifting away from each other, we can trace back their trajectory to a single more dense object, from which they must have exploded. Given that we are only able to measure up to a certain sphere around ourselves, isn't it a bit presumptuous to say that this characterizes the entire creation of the universe? (After all we, as humans, have a long history of overestimating the scope of our observations.)

Let's grant that the observable universe 4 was the result of such an explosion (maybe we should call it "a" Big Bang). My specific question is, what evidence do we have that objects in the universe at large, beyond the observable portion, also originated from this same bang? For instance, what properties of matter can we study locally that would imply this globally, in the mathematical sense? [As I pointed out in my other post (linked at top) a homogenous dynamical system can very well have multiple repelling and attracting points and we could just be near a big repelling point.] Lastly, if we do not have reason to extrapolate such a thing, should we not caution the general community about confusing "The Universe" with the part we're studying, in this manner?

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    $\begingroup$ Obligatory reading re "single dense object": Did the Big Bang happen at a point? $\endgroup$
    – ACuriousMind ♦
    Dec 5, 2016 at 1:30
  • $\begingroup$ @ACuriousMind Okay I've looked at the post you linked. I don't think it addresses my question. The concept of a space with no center or boundary are elementary topologically speaking. My question is how we rule out that the expansion we observe could be a local phenomenon. How do we know it's not just our neck of the universe that exploded out of the explosion we are studying? How did we reach such a global solution from such local measurements? $\endgroup$
    – j0equ1nn
    Dec 5, 2016 at 3:05
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    $\begingroup$ Most of cosmology rests on the assumption that the universe is homogeneous and isotropic on large scales (and that is true for the part of the universe we can observe). It sounds as if both of your questions are essentially saying. "What if the universe isn't homogeneous and isotropic outside of what we observe?", and the "answer" to that is simply that that may well be, but we have no reason to believe so. There can't be any evidence for that about the universe beyond the observable portion because then it would be observable since there's evidence about its features! $\endgroup$
    – ACuriousMind ♦
    Dec 5, 2016 at 3:21
  • $\begingroup$ I guess I should learn what physicists mean by these terms and how it relates to their use in math. There certainly do exist dynamical systems having both expanding and contracting regions, easily found in nature (e.g. the ocean), hence not contradictory to the laws of the universe. I am not convinced that we have ruled out something of this nature on a larger scale. $\endgroup$
    – j0equ1nn
    Dec 5, 2016 at 3:26
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    $\begingroup$ I think they do explain what you're lacking, but it seems you are just too adamant about your own position to appreciate the answers there. I also disagree with your assessment of the answers there, it is not assume P, then Q therefore P but We find Q, which is likely explained by P $\endgroup$
    – Kyle Kanos
    Dec 5, 2016 at 13:57

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I can only definitively answer your last question.

Lastly, if we do not have reason to extrapolate such a thing, should we not caution the general community about confusing "The Universe" with the part we're studying, in this manner?

We do! That caveat is found in lots of answers on this site. Among non physicists, there is in my experience a huge amount of interest in fundamental questions regarding the universe (it's the basic human need to know, which strangly enough generally fades away when math is introduced :) The link you were referred to above must be amongst the most common referrals for certain classes of questions, such as "what is the universe expanding into?".

This really the only general community we can reach, apart from the rare mathematician who wanders in...

My specific question is, what evidence do we have that objects in the universe at large, beyond the observable portion, also originated from this same bang? For instance, what properties of matter can we study locally that would imply this globally, in the mathematical sense?

How can we answer this question, except on the balance of probabilities? One possible way of checking that the hidden part is much the same as the observable part is to check for gravitational anomalies. Is one part of the observable region being affected by an inhomogeneous distribution of whatever "things" are in the hidden part, and to my extremely limited knowledge, we have not detected anything in that regard.

There is an endless of possibilities of what is beyond the observable part, and it is useless to even raise one them as an example, as they are all unprovable.

Because I don't consider this as an answer, I feel it is accepable to put the question back on you. Why should there be a difference in any way between the observable and the hidden part, when we do have evidence of an initial start, we do have a good idea as to why we have this division between observable and hidden, even if we have no idea as to it's actual mechanism? Yes, I appreciate that this only applies to the observable part, but that just highlights the difficulty or impossibility of giving an answer.

Finally, I should say, as it's obvious anyway, that this simplistic, naive reply to your question is given by someone who has very limited cosmological knowledge, but I would be surprised, and also delighted, if any other answer, however sophisticated and detailed, will significantly alter anything I have written here.

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    $\begingroup$ I really appreciate this answer in light of the fact that my questions might be annoying to many physicists. I think part of my problem is that I need to understand better the difference between actual cosmology and how it's presented in popular science. People seem to think that physicists think they have a good guess about how The Universe began. Maybe it's the oversimplification that is at issue truly. But... it's not hard to find words like "proves" and "implies" on, say Wikipedia, that gives you heartburn if you're a mathematician. And I feel like extra care is in order on this topic. $\endgroup$
    – j0equ1nn
    Dec 5, 2016 at 2:54
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    $\begingroup$ Right on. It's interesting to bring up Cantor and Godel though because where that stuff ended up is with us having to accept incompleteness (Cohen). With this we learn that you can't necessarily prove something by disproving (what we think is) its opposite. I feel like that messes up a lot of experimental science ... maybe not in most areas but, well we're talking about "the universe!" I can live with representation groups not being on TV. But maybe TV-watchers could swallow a little more of "that question is too big and we don't know, but what we do know is..." $\endgroup$
    – j0equ1nn
    Dec 5, 2016 at 3:20
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    $\begingroup$ As for the universe, it is not the likelihood that the rest we can't see is the same as what we observe, it is that so much of what we observe is the same (homogeneous and isotropic, seems to follow the same laws we see here going away tens of billions of light years and going back almost 13.7 billion years. We see light emitted 380,000 years after The BIG BANG, and it reinforces what we see otherwise, with the same symmetries and just enough perturbations to cause the galaxies we observe. We predict some crazy non Euclidian space, and 100 years later observe its undulations. Next comment pls $\endgroup$
    – Bob Bee
    Dec 5, 2016 at 7:26
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    $\begingroup$ It is not physicists arrogantly saying they know something, to within certain limits and with plenty caveats, it is a mathematician arrogantly saying that because he knows about cases where there are attractors and repulsors (or whatever) that he can therefore argue that what we do know means nothing. We do know that from all our observations the universe is likely flat or slightly open (with some uncertainty, I think about 1 or 2 percent), and we have not observed attractors or big bangs or whatever elsewhere. And we keep looking. Not annoying, uneducated. $\endgroup$
    – Bob Bee
    Dec 5, 2016 at 7:33
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    $\begingroup$ @BobBee Where you lose me is where you say "We do know that from all our observations the universe is likely flat" etc. If we're assuming the universe is infinite, then what you're saying is that we have measurable confidence about something based on having sampled 0% of it. 13.7 light years out of infinity is still 0. We have not observed any other big bangs, but this one accounts for phenomenon up to our limits of observation, right? I also think the response would be more professional without the insults. I came here admitting ignorance of the topic and respectfully asking to be educated. $\endgroup$
    – j0equ1nn
    Dec 5, 2016 at 20:53

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