Ok...there seems to be Physics Gurus here - Faster than light = time travel question

Factual Questions
21

Strictly speaking, you’re correct. That’s the sort of mathematical detail which physicists often sloppily gloss over. That said, one can construct number systems in which there’s a “number” called infinity, and where anything divided by zero equals infinity, and such number systems are occasionally useful.

Um, might I ask to what movie you refer? It’s certainly nothing I was consciously referencing…

Lumpy, basicall what you would need is for there to be some particular reference frame which is preferred by the laws of physics, in particular the laws which govern the FTL process (whatever it is). For instance, one might have a universe consisting of “normal” space and hyperspace, such that any experiment confined entirely to normal space, or one confined entirely to hyperspace, is fully consistent with relativity (no preferred frames), but that the system of normal space and hyperspace considered together would have a preferred reference frame. This is in fact the situation in many science fiction books with FTL travel, but I’ve yet to find one which explicitly puts it in those terms (probably because most SF authors aren’t as familiar with relativity as they should be).

22

That is what I meant. 5 light minutes.

Chronos…so I take it that my example is flawed - (would not work that way?)

23

Here’s a better example. Suppose a long train is fitted with bombs in the engine and caboose. These bombs are activated when a light placed 1/3 of the train’s length from the engine is observed turning on (e.g. if the train is 12 cars long–an engine, 10 freight cars, and a caboose–the light is on the 4th car).

On the train, the light goes off, and a light pulse moves toward the engine and caboose at the fixed speed c. It reaches the engine first, causing the bomb to go off before the similar bomb explodes in the caboose. The train rider will declare the engine exploded before the caboose.

But to an observer on the track, if the train is moving close to the speed of light (I think anything greater than c/3 will do the trick), the light will actually reach the caboose first, since it’s “rushing forward” to meet the emitted light while the engine is “racing away”. Again, this is because, per SR’s main postulate, the speed of light is always observed to be c in every frame of reference. The track-based observer will declare the caboose exploded before the engine.

The discrepancy in the observed order of events is chalked up to the “relativity of simultaneity”. In the grand scheme of things, it really doesn’t matter, since the results of both observations–both ends of the train exploded–are identical; there are no observable effects which lead to a conflict with reality.

However, if you allow faster-than-light travel, you could put an FTL teleporter in the engine that zipped the engineer to the caboose the moment the engine-bomb went off. Then, the engineer on the train could see the bomb in his cab exploding, zip to the back of the train faster than the light pulse rushing to the caboose, and defuse the caboose bomb before the pulse arrived. The result: Only the engine bomb went off; the caboose remained intact.

But consider this scenario from trackside. There, the caboose bomb goes off before the engine bomb, so the engineer should have been teleported to a burned-out caboose. From his/her perspective, both bombs exploded. Now we have a problem, because the train can be stopped and the two observers will disagree on whether or not the caboose exploded, a ridiculous situation.

To resolve this, we must conclude that FTL travel also moves a person backwards in time. Not from the engineer’s perspective–the steps as outlined there are at least understandable. But from the trackside perspective, what actually happened was that the engineer stepped into his FTL machine at some point in the future into the (relatively) past moment being observed: The engineer zipped spacewise to the back of the train, and timewise back to the moment before the caboose bomb would have gone off, allowing him to diffuse the bomb and keep reality sane.

If the trackside observer were looking closely enough, he may even see two engineers: One steering the train blithely unaware that the engineer will soon explode, the other in the caboose, black and shell-shocked from the hasn’t-yet-happened engine explosion, frantically pulling wires before the light pulse reaches him.

Eventually, of course, there will be only one engineer–the one in the engine will have to step into that FTL machine at some point. And at that point, the train can be stopped and both observers will agree on the results, even though they disagree on the detals of “which happened first”.

24

You’re still projecting some notion of time onto this. Just because you go out a light year doesn’t mean you’ll be there in a calendar year. A light year is the distance that light travels in a year (~5.88 trillion miles) minus 5 light minutes (55.8 million miles) is still a measure of pure distance, not time.

Wht you’re asking is this:

if I can instantly travel 5.83 trillion miles away and then instantly return to earth, can I send myself a message from the past by then travelling half that distance and then sending a message to the first destination.

The answer is obviously not, because you aren’t at the first destination any more.

25

The only way around this (for the purpose of sf stories, not as a real hypothesis) is to posit other branes where c is higher than in ours. You would never exceed c in any brane in which you traveled. This is analogous to being able to move faster than c in water, say, without violating any laws. You’d replace the limit of the speed of light in a vacuum with a limit of the speed of light in the branes through which you travel. That seems like an extension of, not a denial of, relativity.

As for the OP, I can’t figure out if the message is being sent at light speed or instantaneously. If it is being sent at light speed, he is only going to see year old messages when he travels instantaneously 1 ly away. Messages he sends back home will arrive 1 year after he returns.

26

I covered that in my previous post. Whenever you look at any combination of such branes, you’ll find that there’s a preferred reference frame, which breaks special relativity. Nor is multple branes the only way around the problem, for SF writers: There are other ways to introduce preferred frames which would work just as well, and some SF writers get around the problem by saying that yes, time travel is possible using FTL technology.

27

Hmmmm…

I’ve gone through this again and I see that it is wrong.

So…by going faster than light there is no way to go into your own past from your perspective, correct?

CJJ, that was really helpful.

28

[total aside] Man, I love this board. [/ta]

Carry on :slight_smile:

29

Sure there is. It’s just not the way you’re trying to describe (I think… What you’re saying isn’t entirely clear).

30

Do you have a relatively (heh) simple example I could use? Say to send a message to my past self using FTL so that I can pick up that hot stock? :slight_smile:

31

As for this business of “go into your own past from your perspective”, to expand on CJJ*'s train example, suppose you are the trackside viewer and you see the bomb being defused in the caboose by the engineer and a friend. At this point, you decide to FTL jump into the engine of the train for the sake of science. When you get there, you meet the engineer who has just observed the engine bomb going off, and you FTL travel with him to the caboose and defuse the bomb with him just as CJJ* described. Turns out, you in the caboose now are the very friend you observed the engineer defusing with earlier; you’ve gone into the past from your own perspective, as I would understand that phrase.

(If there’s something wrong with the above scenario, do let me know.)

32

If true, that would work, because I could where a t-shirt saying hey blinking…buy stock xyz and I would see that in my past. :slight_smile:

33

Revenge of the Nerds II. The jocks have marooned the nerds on an island, along with “Ogre”, one of the largest jocks who wasn’t jock-ish enough, or something. They find a wild-growing patch of marijuana and light up while staring at the stars. The nerds have an ongoing conversation about the nature of the universe using high-end physics and math jargon when Ogre interrupts with his “C-A-T” observation. The nerds, stoned, are impressed.

34

Before I address this, I’ve got a question. The observer is clearly equidistant from both stars. Now, where are A and B relative to the stars, and what are their velocities? I assume you have something in mind, because a traveler close to A and moving from A to B at a non-relativistic velocity will clearly see A explode first, which I’m sure is not what you mean. Someone at the midpoint, traveling from A to B, will indeed see B explode first.

35

This scenario assumes FTL travel is feasible between two different inertial frames of reference (the track and the train).

This may not be possible; the scenario above kept the engineer’s travel to a single frame of reference, and his leap into the past was observed by someone in a different frame of reference. That’s the best we can say about FTL time-travel.

In fact, suppose we analyze the reverse trip–say the conductor in the caboose decides to FTL travel to diffuse the engine when the caboose bomb explodes. On the train such a trip would always be in vain, since the caboose bomb explodes after the engine bomb. But to a trackside observer, such a trip should be feasible.

We cannot resolve this by saying the conductor goes into the past in his own frame of reference–that leads to a causal loop, and besides with respect to the train there’s no orientable difference between the engineer’s and the conductor’s trip; how does the physics change between the two?

The only way to resolve this from the trackside observer’s frame is to say the conductor’s trip causes him to jump forward in time (kind of the reverse of the engineer’s case). Thus, even though on the train he’s traveling FTL, to an observer on the track he would be taking a longer time to appear in the engine because of the jump forward, and so the observer concludes he’s not traveling FTL.

Again, this analysis–something akin to debating the color of elephant eggs–shows that FTL and time-travel under SR are really observer effects; I don’t believe they can be used to send messages to your past self, no matter how many Twilight Zone episodes you watch. :slight_smile:

36

You know, in retrospect, my example was superfluous, since Chronos’s example accomplishes the same thing. I must’ve missed it last time.

At any rate, fair enough, you need the shift in inertial frame of reference. Is that so bad, though? I mean, if you have FTL travel at all, it seems not a far leap to be able to combine it with such shifting: Start at spatial point A at velocity v relative to whatever, then FTL travel to point B, initially touching down at the same velocity v. Now, while still at point B, switch your velocity in any classical, real-world, boring manner of your choice to velocity w. This acceleration will take a little bit of time, perhaps, but it won’t be so bad. After that, FTL travel back to point A. Do it in the right way, and you’ll end up at point A at a time prior to that at which you left (like in Chronos’s example above). So it seems to me the most straightforward counterfactual account of FTL travel in a special relativistic world will have to be one which allows for “going into one’s past”, causal loops and all. (And what’s wrong with that? I kinda like causal loops…)