Time travel and CoM

[Dooey Jo]

CoM means Conservation of Mass, obviously.

So I was thinking about the Grandfather Paradox, and ways to resolve it - alternate timelines and stuff; not important to this thread I think, but that's how I got the idea. Now, imagine a slightly different scenario from the classical one where you go back in time to kill your grandfather. This time you back in time to stop yourself from going back in time. Now, instead of killing yourself before you enter the wormhole (or whatever, let's say the time machine here is a wormhole), you destroy the wormhole. So what are we left with? That's right; there are now two of you, ignoring the paradox that it means (although the violation would occur even if you didn't stop yourself, it just makes it more obvious).

If it's not immediately obvious how that violates CoM, imagine the two of you finds another wormhole, and goes through it with the intent of stopping yourselves from entering, by destroying the wormhole; now there are (at least) four of you. Repeat ad infinitum. You wouldn't even have to destroy the wormholes, just stop the other "yous" from going through it until you can team up with them. It would be sort of like an audio feedback loop, only with people and mass instead of sound...

If you have a big wormhole, you could apply the same technique and get millions of crewed Death Stars (if you have one to start with) without having to do anything but getting it through the wormhole and go back to such a point in time so that you can send a message to the "original" Death Star not to go through the wormhole.


This is a point I've never seen raised in discussions about time travel, but since it seems so obvious I assume that there is some huge flaw in my reasoning that I just can't seem to see. Would the fact that the mass of the person follows a different time mean that it somehow still exists within the same system and so no violation of CoE has occurred (but CoM still would have to be violated because there would actually be two you and the combined mass larger than it was "before"). Or maybe enough negative energy matter would be spontaneously created to nullify the difference (maybe it would be created at the exit point of the wormhole to nullify you). And there is also the question exactly when this violation would occur; the second you enter the wormhole, or when you exit it or when?

So could someone please debunk this idea, because it seems to be way too good to actually be possible; the endless supply of materials and energy it could potentially be...

[NecronLord]

CoM is generally interpreted as Conservation of Momentum, by me at least. CoME is Conservation of Mass-Energy. Anyway...

It's impossible. That is a paradox, and you would simply fail in your endevour to destroy the wormhole.

[The Aliens]

You'd need the whole 'many worlds' thing to come into play, where conservation of mass-energy is true for the multiverse, but not necessarily one universe within it. To clarify- it doens't matter if you're missing in one universe, as long as you're present in another one, because the net result is the same- there's an average of one Dooey Jo per universe.

[Kuroneko]

Stopping yourself should be impossible--it is not a self-consistent scenario, as well as inconsistent with treating spacetime as fundamental. However, it is still classically possible to interact with yourself in other ways as long as the result is consistent. At least, there is no classical reason why this would be forbidden--how exactly time-traveling wormholes would behave under quantum effects is a rather speculative topic.

Similarly to one of Maxwell's laws of the non-divergence of the magnetic field, the general-relativistic conservation of energy[/mass]-momentum does not say that "the energy-momentum stays constant" but rather "energy-momentum is not created or destroyed anywhere in spacetime." (Except, of course, this divergence is done covariantly in the context of possibly curved spacetime, but the intuitive picture is similar.) Therefore, there is no violation, since the second "you" didn't actually get created or destroyed anywhere, instead simply travelling along a rather interesting path in spacetime. The global non-constancy of energy-momentum is actually a much more common relativistic situation that is in no way limited to such exotic scenarios involving wormholes. If a spacetime is not stationary, e.g., the spacetime of the FRW metric (the conventional big bang scenario), then it is under no obligation to conserve energy, or even having any sort of meaningful measure of global energy at all, particularly if the spacetime is also not asymptotically flat. In general, global conservation laws are associated with certain kinds of symmetries, which may or may not exist in an arbitrary situation.

[Dooey Jo]

Very interesting. So if one could create such a wormhole it indeed could be used as a sort of free-energy device. One could, for example, send some anti-matter back in time to double one's amount of anti-matter. Then one sends, not only the original anti-matter back in time, but also some of the future anti-matter, to gradually increase the total amount of anti-matter in the past. It needn't be anti-matter of course; it could be uranium, or oil or whatever. Or is that paradoxal? Perhaps because the amount of anti-matter sent back through time is different every time, but is that really a paradox?

You'd need the whole 'many worlds' thing to come into play, where conservation of mass-energy is true for the multiverse, but not necessarily one universe within it. To clarify- it doens't matter if you're missing in one universe, as long as you're present in another one, because the net result is the same- there's an average of one Dooey Jo per universe.

I see. But then wouldn't CoME be kind of irrelevant anyway, since it would not apply to any single universe, but only the largely unobservable multiverse (and of course, locally as it does normally)? In any case, it would mean that one universe actually could get an arbitrary number of copies of me.
Then I would rule that universe!

CoM is generally interpreted as Conservation of Momentum, by me at least. CoME is Conservation of Mass-Energy. Anyway...

It's impossible. That is a paradox, and you would simply fail in your endevour to destroy the wormhole.

You're probably right on the CoM vs. CoME thing, but that's why I wrote the clarification
And like I wrote, you wouldn't need to destroy the wormhole to increase the total mass. In fact, it would seem that any travel back in time would do, even if it's to a point where you don't yet exist; the matter that you will eventually be made of still does...

But if space-time actually isn't under any obligation to conserve energy-momentum, then I guess my idea was confirmed (as in that it would apply to universes where such time travel is possible) rather than debunked, correct?
So logically, the next question would be: Why isn't this way of generating energy widely used in science fiction? Wormholes and time travel certainly are (and they even get to ignore the paradoxes most of the time)...

[Wyrm]

Very interesting. So if one could create such a wormhole it indeed could be used as a sort of free-energy device. One could, for example, send some anti-matter back in time to double one's amount of anti-matter. Then one sends, not only the original anti-matter back in time, but also some of the future anti-matter, to gradually increase the total amount of anti-matter in the past. It needn't be anti-matter of course; it could be uranium, or oil or whatever. Or is that paradoxal? Perhaps because the amount of anti-matter sent back through time is different every time, but is that really a paradox?

You have a poor description of the situation. What happens for you, the sniveling little antimatter salesman, is you first recieve a really big heaping lot of antimatter from the future. Then, you go and sell it to some person looking for some black-market antimatter, and show him the antimatter as proof. Eventually, however, you must send an equal amount of antimatter back equal to the amount you received in the first place (think about it a minute to see why). Then the disgruntled customer beats the living shit out of you for swindling him.

[Kuroneko]

You have a poor description of the situation. What happens for you, the sniveling little antimatter salesman, is you first recieve a really big heaping lot of antimatter from the future. Then, you go and sell it to some person looking for some black-market antimatter, and show him the antimatter as proof. Eventually, however, you must send an equal amount of antimatter back equal to the amount you received in the first place (think about it a minute to see why). Then the disgruntled customer beats the living shit out of you for swindling him.

For the manifold realist, absolutely--one can't send anything different than what you sent "the first time." However, under a looser Novikov self-consistency criterion, it is possible to replicate the antimatter. Say, one sends an amount x, which arrives before the sending, so that one has 2x. Sending 3x/2 through the wormhole and palming the x/2 to store somewhere else, one can repeat the operation. This causal loop is self-consistent, although inconsistent with manifold realism. However, even under this scenario, it's not really a free lunch...

Very interesting. So if one could create such a wormhole it indeed could be used as a sort of free-energy device. ...

Not quite that much. There's only so much energy that can travel through a wormhole without destablizing it. It is not quite a free energy machine, although it may be a pretty good replicator.

But if space-time actually isn't under any obligation to conserve energy-momentum, then I guess my idea was confirmed (as in that it would apply to universes where such time travel is possible) rather than debunked, correct?

I definitely wouldn't say that. Rather, the relativistic conservation law holds (it is, in fact, a theorem following from the field equation) but has a different form. It would also be not quite correct to say that the quantity of energy can change globally--rather, that the concept "quantity of global energy" is not meaningfully definable for many spacetimes.

So logically, the next question would be: Why isn't this way of generating energy widely used in science fiction? Wormholes and time travel certainly are (and they even get to ignore the paradoxes most of the time)...

I have doubts that the work keeping the wormhole from collapsing, assuming one somehow does that, will be less than that stored in antimatter. Still, even it is at least "close", antimatter has more recoverable energy when paired with matter, so that one might still come out on top if the matter-antimatter reactors have more than 50% efficiency.

[The Aliens]

You'd need the whole 'many worlds' thing to come into play, where conservation of mass-energy is true for the multiverse, but not necessarily one universe within it. To clarify- it doens't matter if you're missing in one universe, as long as you're present in another one, because the net result is the same- there's an average of one Dooey Jo per universe.

I see. But then wouldn't CoME be kind of irrelevant anyway, since it would not apply to any single universe, but only the largely unobservable multiverse (and of course, locally as it does normally)? In any case, it would mean that one universe actually could get an arbitrary number of copies of me.
Then I would rule that universe!

You would need to keep transferring yourself into that universe- if there's a finite number of universes, that's no problem. As long as there's an average of one Dooey Jo per universe, CoME isn't violated. Of course, this assumes the multiple universes theory is valid.