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Warning: I'm trying to obfuscate much of this question, and hiding the key elements in spoiler blocks..but some spoilers will probably be inevitable.

At the ending of the book Tau Zero the ending seems odd:

the spaceship, travelling at close to the speed of light, is able to have eons pass by in instants, which allows it to travel far, far into our future. It eventually ends up circling around the eventually collapsing universe, and is able to watch as the universe is reborn in a new big bang.

Now, I'm not asking whether the big-crunch theory is out of date, whether the universe is slated to eventually collapse, or about the relative (no pun intended) likelyhood of the creation of a spaceship that can travel near the speed of light. He makes these assumptions/assertions, backs them up as he sees fit, and moves on.

But I was under the understanding that the matter that takes up space in our universe is inately connected with the space of the universe...that during a big-crunch type event, it would not just be the matter within the universe collapsing, but space itself collapsing to a singularity...which would leave the ending not making any sense. Yet, with the amount of effort he puts into explaining the effects of time dialation and the irrationality of the notion of simultaneity at near-light speeds, it seems odd that something like this would be left hanging.

Is there a solution?

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5 Answers 5

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Note that as you accelerate a spaceship towards the speed of light you will blue shift the microwave radiation and increase it's temperature. Eventually you'll roast the ship and all aboard! This is actually happening for the Earth (well, not the roasting bit) as the microwave background is slightly hotter in one direction and cooler in the opposite direction. The effect is small, but it's actually a lot larger than the variations astronomers are trying to measure, so it has to be subtracted out.

Anyhow, back to the question, and I'd like to expand a bit on DVK's answer. It's common to think of the big crunch/bang happening at a point, so you could in principle navigate the spaceship away from that point. That is entirely wrong!

Imagine drawing out a grid with spacing of 1 light year. Although obviously we can't do this, you can easily imagine putting the Earth at (0, 0), Alpha Centauri at (4.37, 0) and plotting out all the stars on this grid. The key thing is that this grid is infinite i.e. there is no point where you can't extend the grid any further.

Now wind time back to 7 billion years after the big bang, i.e. about halfway back. Our grid now has a spacing of half a light year, but it's still infinite - there is still no edge to it.

Now wind back to 0.0000000001 seconds after the big bang. There's no special significance to that number; it's just meant to be extremely small. Our grid now has a very small spacing, but it's still infinite. No matter how close we get to the big bang we still have a infinite grid filling all of space. You may have heard pop science programmes describing the big bang as "happening everywhere" and this is what they mean. The universe didn't shrink down to a point at the big bang, it's just that the spacing between any two randomly selected spacetime points shrank down to zero.

In DVKs ballon analogy, you have to imagine shrinking the ballon down to a point of zero size, but all the surface of the ballon still exists.

Incidentally, if you try to calculate the size of the universe at the big bang itself you get zero times infinity i.e. zero spacing of the grid but it's still infinitely big. That's because the above is based on General Relativity and GR cannot describe what happened at the big bang itself. You just get sums like zero times infinity that don't make physical sense.

Gosh I've rambled on a bit! Anyway after all this my point is that the big crunch is approximately a time reversed big bang, so my argument above applies. The spaceship would get shrunk down to zero size and neither it nor it's passengers could possibly survive this.

Some notes: you'll have spotted that I casually stated the universe is infinte. By this it means it has no edge. Current observations suggest the universe is flat, i.e. not like a ballon, so having no edge means it goes on forever. The universe could be curved on a scale too large for us to measure. Either way we'll never know for sure.

Secondly, as DVK noted, it's widely believed that as you approach the big bang/crunch quantum gravity of some form will take over and the grid spacing wouldn't fall to zero. Both String and Loop Quantum Cosmology predict the spacing would decrease to some minimum size then bounce and start increasing again. Both theories are still speculative, but in any case it would make little difference to the spaceship since that minimum grid spacing would be around 10e-35 meters.

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Interestingly, the blue shifted radiation is handled in the book, and is, in fact, critical to the plot, so that's not an issue in this case. It seems as though your answer and DVK's are similar in what they're describing, though he describes a finite, positively curved universe, while you're describing an infinite flat universe (which, I guess, would be nearly the same as a infinite negatively curved "saddle" type universe for these purposes.) –  Beska Feb 10 '12 at 12:24
I'll have to go back and reread the book. I remember the book described the optical effects of relativistic speeds, but I'm pretty sure it didn't include the cosmic microwave background. If it had correctly described the CMB the ship would have ended up being vaporised! –  John Rennie Feb 10 '12 at 15:47
Excellent description of the nature of cosmological expansion. (Also, I haven't heard about string theory predicting a minimum size for the universe - any chance you could point me to something to read for that? Should I ask on Physics?) –  David Z Feb 16 '12 at 3:26
There are a few of us refugees from the Physics Stack echange hereabouts :-) I don't think string cosmology is well enough developed for ideas about bounces to be more than speculative. The bounce seems more firmly established in LQG. Anyhow, see arxiv.org/abs/1108.2660 section 3.3 for some comments on the latest ideas. –  John Rennie Feb 16 '12 at 10:20
@John Rennie - This answer from the Usenet Physics FAQ on John Baez's site mentions another possible cosmological model different from the FLRW model, in which the Big Bang is actually a giant white hole spewing out matter in a larger asymptotically flat space...the Big Crunch could then be the matter collapsing back into a black hole. They say that if the size of the dust sphere were larger than the size of the observable universe, this would be observationally indistinguishable from the FLRW model. –  Hypnosifl Jan 3 at 0:07

Yes, there are solutions, but none are compatible with the current cosmological theories to the best of my knowledge.

For a really dumb analogy, imagine 1 2-D being living on a Surface of a balloon.

If the being moves really fast, they are still on the surface of a balloon.

So, if the whole balloon inflates, then deflates, then collapses... the speed of the being doesn't make ANY difference, since they are STILL situated on the balloon surface.

The only way to watch it and escape is to jump OFF the balloon surface, into an extra 3rd dimension.

As far as I know, there are no cosmological theories that posit a collapse of 3 main dimensions while leaving one of the rest non-collapsed (assuming the prevailing 11-D superstring based cosmology), so Paul's scenario doesn't make sense assuming standard physics, either with the "remain on our 3-D balloon space" case or "Jump off 3-D balloon onto another dimension".

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As a note - I'm very very far from an expert on String theory - you are better off posting on Physics.SE if you correctly word your question to be pertaining to actual physics laws as they are –  DVK Feb 10 '12 at 0:07
Yep. The balloon analogy is the one I often use when thinking about such things, which is why this struck me as such a glaring error in an otherwise well concieved book. –  Beska Feb 10 '12 at 12:16

The solution is: we don't know either way, so Anderson picked what was best for the story.

Despite the advances of modern cosmology, we still don't have a better idea of would really truly happen if the Big Crunch hypothesis were true than they did in 1970 - particularly since these days it looks like there probably isn't going to be a Crunch, so people haven't been doing as much theoretical work on it.

It may very well be the case that during a Big Crunch the metric expansion of space reverses itself and all the places in which one could exist collapse down into a teeny little point of nothing which then explodes, but on the other hand there might be some leftover space to float around in as the protagonists do; it's impossible to know without a better theory of what's actually causing space to inflate the way it is (we actually have no idea!).

Poul Anderson simply chose a formulation that allowed his protagonists to continue existing through the next Big Bounce, is all.

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As I understand, it could make sense. Going to basic distance, time and velocity formulas we find that as velocity approaches C, distance approaches 0, time approaches 0 and mass (relativistic mass) approaches infinity; in short, space and time collapse.

Take the first derivatives of d=t*v, t=d/v & v=d/t as v approaches C and it becomes clearer. Could something survive that? Anderson uses artistic license I think and supposes v never actually attains C, subjectively the universe shrinks to almost nothing, then re-expands.

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Agreed. The actual story is a nonsense. Even if you can travel at relativistic speeds approaching infinity, you're hardly going to outrun the gravity of the big crunch. –  Richard Feb 17 '14 at 23:26
He gets around this problem by the ship not being part of the big crunch...it is circling outside the universe, watching it shrink, crunch, and then re-expand (assuming I remember correctly; it's been a while now). So, not being in the universe, they're not affected by the space time relativistic problems. HOWEVER, this leaves the obvious question of "does it make any sense for them to have somehow left the universe?", which is what I was trying to get at. From what I know, it doesn't...but I thought I'd throw it out there. –  Beska Feb 18 '14 at 15:07

Its been a while since I read that book, but what I remember is that the author stated that they were able to orbit the singularity only because it wasn't total. The entire universe in the story did not crunch 100% before the next big bang.

Because they had accelerated to a significant velocity to escape its mass (possibly not really plausible), they were able to remain in the small part of the universe that didn't crunch, and ride the expanding wave of the next bang as it began to reach them.

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