Time Travel and the Conservation of Matter Problem

[spl3001]

Imagine the following experiment:

Scientists have made a machine that can create a traversable wormhole and can also accelerate one end at near the speed of light and bring it back. A time machine. Suppose the dilation between the two ends is 10 years.

As soon as the experiment brings the traveling end back, my future self walks through. He decides to stay with me until 10 years have passed the usual way: a long ten year wait. Present self, now 10 years later, is about to walk through the worm hole to go back 10 years. I bid goodbye to future self, who remained with me this whole time (because I am such a swell future guy), and step through.

Who is waiting on the other side, 10 years in the past? Is it:

1.) Just present self when the machine was first turned on?
2.) Present self and future self #1
3.) A black hole that destroys the machine because of the possible infinite numbers of me showing up simultaneously, thus self consistency or worse, paradox.

This poses another issue: does traveling into the past create matter?

Consider the following:

I go back 100 years into the past via some fantastic means (and avoiding parallel universes for the moment). 100 years ago, the specific particles/atoms/molecules that are going to make me up maybe in the soil, part of an animal, floating in the atmosphere at that time. So, I now have two sets of me: present me as a person and what will come to be me 100 years later stuck in a tree/soil/etc. Does this form of time travel violate the conservation of matter/energy?

 

[bcrowell]

GR allows closed timelike curves. For a good popular-level discussion of this, see Gott, Time Travel in Einstein's Universe, or the final chapter of Thorne, Black Holes and Time Warps.

GR does not have global conservation laws. This is discussed in Misner, Thorne, and Wheeler, Gravitation, p. 457.

So, yes, CTCs would violate global conservation laws, but even without CTCs (which may not exist in our universe, if the chronology protection conjecture is true), you don't have global conservation laws in GR anyway.

GR *does* have local conservation laws, and those are not violated by CTCs.

 

[Andrey]

Imagine the following experiment:

Scientists have made a machine that can create a traversable wormhole and can also accelerate one end at near the speed of light and bring it back. A time machine. Suppose the dilation between the two ends is 10 years.

As soon as the experiment brings the traveling end back, my future self walks through. He decides to stay with me until 10 years have passed the usual way: a long ten year wait. Present self, now 10 years later, is about to walk through the worm hole to go back 10 years. I bid goodbye to future self, who remained with me this whole time (because I am such a swell future guy), and step through.

Who is waiting on the other side, 10 years in the past? Is it:

1.) Just present self when the machine was first turned on?
2.) Present self and future self #1
3.) A black hole that destroys the machine because of the possible infinite numbers of me showing up simultaneously, thus self consistency or worse, paradox.

This poses another issue: does traveling into the past create matter?

Consider the following:

I go back 100 years into the past via some fantastic means (and avoiding parallel universes for the moment). 100 years ago, the specific particles/atoms/molecules that are going to make me up maybe in the soil, part of an animal, floating in the atmosphere at that time. So, I now have two sets of me: present me as a person and what will come to be me 100 years later stuck in a tree/soil/etc. Does this form of time travel violate the conservation of matter/energy?

OK let’s address your first experiment. Since atoms carry information and information can multiply itself in great numbers, it is logical to assume that all three outcomes are possible. However, the reason why you as a traveller only experience one of those outcomes is determined solely by you. You decide which of the outcomes you choose to experience. This decision is based on understanding that you have of the Matrix, i.e. the fabric of space-time continuum. In other words if you know how space-time continuum works, you can choose how you wish to experience the outcomes of it.

What people fail to realize is that they and the reality they percieve is one and the same. There is no out there or in here. It's all one. Connected. The outer reality is mostly determined by our perception and perception is determined by how brain decodes light into meaningful reality. The way brain decodes light into reality is determined by mental defilements, i.e. the the concepts people have. In other words, if people believe reality to be this then that's how they'll see it. If they believe it to be that, then again, that's how they'll see it. It's all about their mental and physiological make up.

Hence all posibilities are possible when dealing with quantum field because after all it contains everything and all posible outcomes. The difference, however, which posibility will you choose to experience when steping into time machine and traveling back.

:-)

 

[spl3001]

GR allows closed timelike curves. For a good popular-level discussion of this, see Gott, Time Travel in Einstein's Universe, or the final chapter of Thorne, Black Holes and Time Warps.

GR does not have global conservation laws. This is discussed in Misner, Thorne, and Wheeler, Gravitation, p. 457.

So, yes, CTCs would violate global conservation laws, but even without CTCs (which may not exist in our universe, if the chronology protection conjecture is true), you don't have global conservation laws in GR anyway.

GR *does* have local conservation laws, and those are not violated by CTCs.

I'm not sure what the difference is between global and local conservation laws, but since CTCs don't have global conservation laws, would that allow this instantaneous build up?

And does the following re explanation make sense:

Year 2050: generate traversable wormhole. Start moving one end at close to c.
Year 2100: wormhole end returns. Aged 1 minute (lets assume we had the ability to accelerate/decelerate to the necessary velocity for this to occur).
Year 2100: Creator of wormhole (now very old) jumps through to go back to 2050.

Year 2050: out comes old creator. Meets young creator. They hang out for 50 years.
Year 2100: "Ahh, let's both jump through now that it's back!" says REALLY old creator. Both jump through.

Year 2050: Now there are three: one young, one old, and one very old. They hang out for 50 years.
Year 2100: "OK, let's all three (two guys and probably a coffin at this point) jump through!"

And so on. Could this happen? And would this loop happen instantly, all at once, at both ends? First one to have enough mass build up would collapse and produce a black hole with a mass increase in the Universe. Where is the paradox prevention here?

 

[bcrowell]

I'm not sure what the difference is between global and local conservation laws,

An example of a local conservation law is $\nabla\cdot J$ in electromagnetism, where J is the current density. This is a statement of local conservation of charge. An example of a global conservation law is that if you add up all the charge in the universe at one time, and then do that again at a later time, it's the same.

but since CTCs don't have global conservation laws, would that allow this instantaneous build up?

It's not that CTCs break global conservation laws, it's that GR in general doesn't have such conservation laws.

 

[JesseM]

GR allows closed timelike curves. For a good popular-level discussion of this, see Gott, Time Travel in Einstein's Universe, or the final chapter of Thorne, Black Holes and Time Warps.

GR does not have global conservation laws. This is discussed in Misner, Thorne, and Wheeler, Gravitation, p. 457.

So, yes, CTCs would violate global conservation laws, but even without CTCs (which may not exist in our universe, if the chronology protection conjecture is true), you don't have global conservation laws in GR anyway.

GR *does* have local conservation laws, and those are not violated by CTCs.

Although energy conservation does not generally hold globally in general relativity, this page on the subject says:

In certain special cases, energy conservation works out with fewer caveats. The two main examples are static spacetimes and asymptotically flat spacetimes.

And ideal wormhole spacetimes are asymptotically flat, so I think energy conservation actually would hold in these cases. Pervect's comments here suggest that in the case of a wormhole, whenever an object enters one mouth the mouth's own mass will increase by the same amount, and likewise whenever an object comes out of a mouth the mouth's own mass decreases by the same amount. So, this could explain why there's no violation of conservation of energy even when an object entering one mouth will exit the other in the past.

 

[Passionflower]

As soon as the experiment brings the traveling end back, my future self walks through.

Hold on, your future self? How do you imagine to get in that situation?

 

[spl3001]

Hold on, your future self? How do you imagine to get in that situation?

I think the second thought experiment expresses what I envisioned more clearly. Sorry about that.

[QUOTE}And ideal wormhole spacetimes are asymptotically flat, so I think energy conservation actually would hold in these cases. Pervect's comments here suggest that in the case of a wormhole, whenever an object enters one mouth the mouth's own mass will increase by the same amount, and likewise whenever an object comes out of a mouth the mouth's own mass decreases by the same amount. So, this could explain why there's no violation of conservation of energy even when an object entering one mouth will exit the other in the past. [/QUOTE]

So, is there a limit to how much "stuff" can travel in one direction in a wormhole? Could it reach zero mass/energy and just quietly close up once enough stuff "clogged" it up?

 

[JesseM]

So, is there a limit to how much "stuff" can travel in one direction in a wormhole? Could it reach zero mass/energy and just quietly close up once enough stuff "clogged" it up?

In pervect's post which I linked to above, he said that as more objects exited a given mouth, that mouth's mass could go lower than zero, becoming negative:

The wormhole mouth at the bottom will get "heavier" because of all the matter entering it. The worm hole mouth at the top will get lighter, eventually acquiring a negative mass!

Negative mass may sound strange, but in fact it's already known that to make a traversable wormhole, you'd need a certain amount of "exotic matter" with negative mass to hold the wormhole open. Whether or not the necessary type of "exotic matter" is actually allowed by other laws of physics besides general relativity is not known yet (the question is discussed a bit in this section of wikipedia's 'wormhole' article), it may turn out that traversable wormholes are actually impossible.