Understanding Violation of Causality: Explained by Reference Frames

[David Laz]

I was having an argument with some of my friends last night and I needed to explain why faster than light travel or infomation traveling faster than c violates causality. Unfortunately I studied this a long time ago and don't quite remember. Could anyone give me a brief explanation why? I remember a demonstration involving reference frames but I can't for the life of me put it together now.

Thanks in advance.

 

[selfAdjoint]

David, perhaps you mean how it violates causality rather than why? The how is that if you can go faster than light, SOME inertial observers will see you moving back in time; putting your own movements together with reports from those observers you can send messages or travel into your own past. This can all be diagrammed on a space-time plot.

 

[pervect]

You might try reading through

http://sheol.org/throopw/tachyon-pistols.html

Note that there can be more to this issue. There are some rather far-out schemes (like wormholes) that might theoeretically allow FTL travel without violating causality (i.e. no closed time-like curves) that are also completely compatible with relativity.

The wormhole scheme requires a "censorship" principle which destroys wormholes that become time-machines in order to maintain causality. This is not quite as far out as it seems (though it's still pretty far out), because quantum vacuum fluctuations would tend to become infinite in a wormhole at the instant it becomes a time machine. This would tend to destroy the wormhole.

There are other "preferred frame" schemes that are incompatible with relativity that would allow FTL travel without violating causality. If you can go any distance in a short amount of time in "some preferred frame", you can jump out a far distance, then jump back, but you'll never get back to before you started. However, this requires some particular "preferred frame", something that would violate relativity.

 

[selfAdjoint]

You might try reading through

http://sheol.org/throopw/tachyon-pistols.html

Note that there can be more to this issue. There are some rather far-out schemes (like wormholes) that might theoeretically allow FTL travel without violating causality (i.e. no closed time-like curves) that are also completely compatible with relativity.

The wormhole scheme requires a "censorship" principle which destroys wormholes that become time-machines in order to maintain causality. This is not quite as far out as it seems (though it's still pretty far out), because quantum vacuum fluctuations would tend to become infinite in a wormhole at the instant it becomes a time machine. This would tend to destroy the wormhole.

The censorship principle would have to be pretty strong/weird, because it isn't sufficient to censor each wormhole separately. Assume relativity is valid and you can build a wormhole that permits instant communication with your pal, who is 1.1 light years away and moving away from you at 87% of c. You use it to send him the S&P index charts for the preceding year. He likewise can use another wormhole to send that info back to you instantly. But his "instant" is canted at 30 degrees to yours in spacetime and goes a year into your past. This only one of a potential infinity of schemes involving any number of third parties; how would a censorship principle prevent them from working?

There are other "preferred frame" schemes that are incompatible with relativity that would allow FTL travel without violating causality. If you can go any distance in a short amount of time in "some preferred frame", you can jump out a far distance, then jump back, but you'll never get back to before you started. However, this requires some particular "preferred frame", something that would violate relativity.

Of course if you break the rules of relativity ("preferred frame") you don't have to obey the constraints of relativity.

 

[pervect]

The censorship principle would have to be pretty strong/weird, because it isn't sufficient to censor each wormhole separately.

Yep.

A serious reference on the issue is (which I've only read popularized summaries of) is:

Matt Visser. From Wormholes to Time Machines: Remarks on Hawking's Chronology Protection Conjecture. Physical Review D v47, n2, p554. 15-Jan-1993.

I don't think it addresses the network issue, specifically.

The basic idea is that "quantum vacuum fluctuations" build up along any closed time-like curve (CTC). This much is more or less expected.

The big issue - will these fluctuations be powerful enough to destroy any wormhole? Including any theoretically possible wormhole? Doing the analysis at all requires a lot of guessing, because we don't have a theory of quantum gravity.

Having networks of wormohles makes the problem even more difficult to analyze. I think there may be papers on the issue, even so. I've got a hazy recollection reading that the networks could be more robust than single wormholes, but I'm not sure where I read that.

It's almost enough to make one think that restricting space-time to a trivial topology might not be such a bad idea (there are some approaches that would do this automatically). Then we wouldn't have to worry about wormholes :-).

Anyway, all of this stuff is rather far out, in that I don't see experimental tests coming in any of our lifetimes. This includes testing the issue of whether or not space-time topology is trivial or not (at least by design, we can always hope we stumble across something). Though come to think of it, I think people are trying to address the global topology question by studying the CMB anisotropies, I'm just not sure if I believe this can really be convincing.

 

[David Laz]

Thanks for the responses. :)