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I apologize if this question may seem fantastical.

Since the heat death of universe is said to be inevitable, is it possible to travel back in time to a younger universe when the time comes? Is that physically possible (assuming time travel is possible)? Would that break any entropy laws as you can essentially do this indefinitely and thus extend the life of the universe in extension to yourself?

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    $\begingroup$ Hi Arnold. We have no accepted theory for what will happen in the far distant future (though there is no shortage of speculative theories). We also have no theory describing how time travel from the far distant future to a younger universe might work. So an answer to your question is going to be science fiction not physics. You might be interested to read up on conformal cyclic cosmology as this is the nearest thing to your idea that I know of. $\endgroup$ Aug 21, 2015 at 15:11
  • $\begingroup$ Time travel is science fiction, Arnold. $\endgroup$ Aug 21, 2015 at 15:40

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Imagine a 1d space and a little vector in it that can change its location but not its length. It can't continuously change in a way that turns it around. If that vector was the momentum this says in 1d you can't continuously change you direction without your momentum being zero.

A similar thing happens in relativity. A massive object has a location in 4d spacetime and it has a scalar energy and a vector of momentum and they combine together into a single 4d vector. And that vector points in the direction in spacetime the particle is going. And it has a length equal to the mass of the object.

But length is measured in a different way in spacetime, it measured in a way where everyone will agree that a massless object going at light speed has an equal amount of energy and momentum. This forces all the massive particles to have more energy than they have momentum (so the direction they are going in spacetime is less than light speed).

Because of this you don't have a 2d space of time directions and you have a vector (your energy momentum vector) with a nonzero length so you can't continuously change in a way to turn around. That is because forces act continuously and whatever you change to needs to have more energy than momentum (less than light speed) so is pointing inside this cone of vectors with more energy than momentum so you can't point in the opposite direction.

Just like the 1d example. So there is no force that can make you travel back in time.

So there are two options. Either there can be life where entropy decreases and so their subjective experience is that time flows the other way and the heat death is their past and our past is there future. But we aren't them. Or else we need spacetime itself to connect the future to the past in a way that allows us to travel from one to the other.

This is possible. For instance the set $$\{(w,W,x,y,z)\in\mathbb R^5: w^2+W^2=1\}$$ with metric $d\tau^2=dw^2+dW^2-dx^2-dy^2-dz^2$ is such a spacetime and it satisfies all classical laws of physics. Ad you can see it basically has a 2d space of time directions (the $w,W$ plane) but then only keeps 1d worth of them ($w^2+W^2=1$) and calls that the universe so time bends around like ants stuck on a cylinder they don't even notice a thing until they get back to the same place. We don't notice until we get back to the same time.

But that space requires the past and the future look the same. That isn't our universe. And any section of it where you don't go around a complete circle in $w,W$ space looks just like a section of

$$\{(t,x,y,z)\in\mathbb R^4\}$$ with metric $d\tau^2=dt^2-dx^2-dy^2-dz^2$ with your times coming from some interval. So as your time goes from 0/to $2\pi$ in this spacetime and as tour angle goes from 0 to $2\pi$ in the $w,W$ plane everything looks the same. Then all of a sudden one takes you to the past and the other doesn't.

There is no way to make the latter spacetime turn into the former one even if they looked exactly the same for every event for every interval less than $2\pi$ in length. So even when your spacetime allows you to travel in time, forcing it to do so is a different question.

And if your future isn't the same as the past how can a continuous spacetime connect them? It can't. So you could try to find a small region that is the same and maybe those can be connected. Like a wormhole that connects two times as well as to spaces. But even if a wormhole connects them it might not be traversable by things that travel less than light speed.

Imagine a bunch of people building a very long bridge all working on different section. The connected bridge is a lightyear long. Maybe they all finish connecting the parts at the same time and you can try to cross now but then the assembly crew stays right there and rests and then start disconnecting it a day later. If so, there is absolutely no person that could cross from one end of the lightyear long bridge to the other. It turns out most wormholes are like that. They could connect to regions but not in a way where something can traverse from one side to the other.

I'd you want it to be traversable then you generally need exotic matter. Exotic matter has a negative amount of energy per volume.

But again how are you going to make it connect to the place you want if the past didn't actively construct a wormhole too? And if the past didn't have you coming out of that wormhole then I'd be skeptical that you will come out intact in the past if you go in in the future. But you'd only truly be scared if in the past you saw say a giant explosion come out of the wormhole.

But you do. When you look at how quantum fields interact it looks like there might be a giant explosion as soon as a wormhole gets it ends out of sync enough to be used as a time machine and then the wormhole collapses. So it is exactly like that long bridge with say the two ends aging at different rates and when the bridge path and the path not in the bridge (im normal space) allow a time travel path when you combine together then the whole thing goes boom (the explosion of energy is a bit inconsistent with negative energy).

So if you know that wormhole had a giant explosion and was destroyed the instant it allowed time travel then you should be afraid about trying to run into the future end at the moment it is about to explode (connect to the past). So again it looks like you can traverse it (maybe) if you have exotic matter but not to go back to your own past.

And this seems to happen in general when you include quantum effects. So classical physics says maybe if you have exotic matter. But then quantum seems to say no. So it sounds like we need quantum gravity to know for sure. And we don't have a theory of quantum gravity.

Which is way I had to say maybe and looks like a few times. But now let's get to the thermodynamics, because that's what you asked about.

Look at a plant growing from a seed. It has water and sunlight and gases that get absorbed and it make complex carbohydrates. Isn't that decreasing the entropy of all the hydrogen and oxygen and carbon? Yes. But it increases he entropy of its environment more.

And here is the key. At the moment you decrease your entropy you also increase the entropy of your environment by a larger amount.

Imagine some people take a genome for a plant and use the information to then synthesis it. Then they grow it and then freeze it and put it in a time capsule and have it orbit a black hole close the the event horizon so that a century to it is a 100 trillion years to the outside (this requires fuel, a free fall orbit can't do that).

Then in 100 trillions years people find it and extract the genome. You could then pretend that they send that information back (even though they don't). But the point is that at each event entropy increased. There isn't some magic that goes in a loop around and around and needs to make new entropy each time it rewatches the movie of its life.

Because think of that first universe the one that repeated after an angle of $2\pi$ in the $w,W$ plane. From the perspective of each part of a path in that space everything looks normal. You get some light and gases and you make some sugar and entropy goes up overall but your entropy goes down. If your entropy goes up and down that's fine as long as you throw off thibgs that increase the entropy of your environment every time you decrease your entropy.

So classical physics with exotic matter might allow time travel through a wormhole and there might be a plant that sometimes increases its entropy and sometimes decreases it and when it decreases its own entropy it sends entropy in the universe.

You can break the movie of its life into short films each of which film a short time interval and a little region of space. None of which break the laws of physics. And classical Generality is literally just about making such short films and sewing them together.

Thing of it as a gold thread on a piece of cloth that has numbers stitched next to it and eveyt place where the number on the thread changes from higher to lower you see a silver thread come out of it. Then the gold thread might be a closed loop but every little piece is following the rules it is supposed to.

In classical physics the rules themselves. The laws of physics themselves are local rules. We write the rules, they are local, and they do have to get together.

Basically entropy is not a problem because there is no rule about following something around a loop multiple times. The rules say to look at little pieces and make sure each is right and that the pieces line up correctly.

Like an Escher drawing. Or one of those impossible objects. The laws of physics are written that way. If you want to forbid time travel you have to explicitly forbid it (like with caudal dynamic triangulation) or hope that it is technically impossible (e.g. no exotic matter) or hope that a nonlocal physics forbids it (like quantum mechanics).

Entropy is not the problem.

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