Stephen Hawking and time travel

[jhe1984]

Hi,

In Hawking's A Brief History of the Universe, he describes a scenario in which it is possible to travel "back" in time. He says, if faster-than-light time travel is possible, it would then be possible to see a race in one location in space, travel to another part of space to relate the news, and arrive back all before the race actually ends (I'm possibly misrepresenting the description, but i don't think it affects question).


How can this be if a person had to exist in Point A for 1 second (assumed time it takes to observe and process event), travel at beyond-light speed to Point B, exist long enough to explain the answer (assumed explanation to conclusion time is also 1 sec) and then travel back to original point A in under 2 seconds?

I am probably misunderstanding the concept of relativity but if you wouldn't mind enlightening me, I'd be much obliged.

 

[JesseM]

It has to do with the fact that different frames define "simultaneity" differently--two events that happened "at the same time" in one frame (ie they are assigned the same time-coordinate in that coordinate system) will happen at different time-coordinates in other frames which are moving relative to the first one. If you have two events such that a signal moving at the speed of light or slower, then it works out so every reference frame will agree on which happens first and which happens second, meaning that in the absence of FTL signals, different frames don't disagree about cause and effect. But if you could have FTL signals, then different frames would disagree on the order of two events along the signal's path--if the FTL signal was emitted at one location and received at another, there would be some frames where the signal was actually received before it was sent. And one of the basic postulates of relativity is that the laws of physics should work the same in all reference frames, so according to this principle, if it is possible in some frames to send signals which move back in time, it must be possible to do this in all frames. This means that if you and I are moving apart, I could send you a signal which goes FTL in my frame and backwards in time in your frame, then you could send a reply which goes FTL in your frame but back in time in mine, and the end result would be that I would receive your reply before I sent the original signal. Thus, if FTL is possible and the postulates of relativity are correct, this implies it would be possible to send signals backwards in time.

 

[jhe1984]

Thanks for replying. I am not completely understanding what you mean when you say "frame". Let me ask you a specific question and tell me whether this is possible and, if not, why?

Is it possible for a human (who is able to travel FTL) to see an event, travel FTL to a different point in a different galaxy, slow down enough to tell them about the event, return FTL, and not miss a step? Or even, is it possible for a man to see who won a race and travel back in time to place a bet on that race? Surely that can't be.

I think I am missing something. Wouldn't he miss something seeing that it had to take him some time?

Sorry, this whole thing is a little foreign to me. Crazy...

 

[Ich]

The point is: If FTL travel is possible, and the principle of relativity still holds, all those weird things like time travel and causality violations are also possible. Because those things are widely considered as not possible (at least causality violations), FTL travel is also considered impossible.

 

[JesseM]

Thanks for replying. I am not completely understanding what you mean when you say "frame".

A frame is basically a coordinate system for assigning space and time coordinates to different events--each observer has his own rest frame, a coordinate system where he isn't moving. For example, if in my rest frame you're flying by at 0.5c to the right, then in your rest frame you'll be at rest and I'll be moving at 0.5c to the left. The physical idea behind these coordinate systems can be understood that each observer has a network of rulers and synchronized clocks which are at rest relative to himself, so if I look at a given event and see it happened at the 60-meter mark along the ruler that serves as my x-axis, and I see that at the moment the event happened the clock that was sitting at the 60-meter mark read "15 seconds", then I would assign this event coordinates x=60 meters, t=15 seconds. The tricky part is what it means to "synchronize" different clocks in my network with each other--I can't just set them to read the same time when they are next to each other and then move them apart, because when I move them apart they will experience time dilation. So instead, the standard procedure in relativity is for each observer to synchronized different clocks in his network using the assumption that light travels at the same speed in all directions in his own frame; so he can synchronize different clocks by setting off a flash at the midpoint of the line between two clocks, and then set each to read the same time at the moment the light reaches them. But if every observer synchronizes their clocks using this assumption, then each observer will see everyone else's clocks as out-of-sync. Just imagine that you're traveling in a rocket at high velocity relative to me, and you synchronize clocks at either end of your ship by setting off a flash in the middle and setting them to read the same time at the moment the light hits them. If I assume those two light beams moved at the same speed in my frame, though, then they cannot have reached the two clocks at the same time, since the clock at the front of the ship was moving away from the point where the flash was set off, while the clock at the back of the ship is moving towards it. So clocks which are synchronized in your frame will appear out-of-sync in mine, and vice versa. But it so happens that when you define different observer's coordinate systems in this way, the equations for the laws of physics will be the same when expressed in each observer's coordinate system, and it's a postulate of relativity that all laws of physics have the property of appearing the same in different coordinate systems defined this way. But again, if this postulate applies to the laws governing hypothetical FTL signals as well, then since we know that signals which move FTL in one frame move backwards in time in other frames, then it must be possible to send signals backwards in time in any frame, which means by bouncing signals between two observers, you should be able to send a message and get the reply before the time you sent it.

Is it possible for a human (who is able to travel FTL) to see an event, travel FTL to a different point in a different galaxy, slow down enough to tell them about the event, return FTL, and not miss a step?

If FTL were possible in the first place, sure.

Or even, is it possible for a man to see who won a race and travel back in time to place a bet on that race? Surely that can't be.

Again, if FTL were possible, and if it respected the postulate that the laws of physics should work the same way in every reference frame, then this would be possible as well. But since most physicists are averse to the idea of people or information going back in time, they consider this a good reason to suspect FTL will turn out not to be possible.

I think I am missing something. Wouldn't he miss something seeing that it had to take him some time?

Not if he was moving backwards in time relative to the frame where the race is taking place--in this frame he would return before he departed, just like the reply to the signal in my other example would be received before the original signal was sent.

 

[jhe1984]

For second to above statement: If there is beyond inconclusive evidence that FLT is indeed not possible, then I agree with your statement. If there aren't, then I think a case could be made that FTL ability is inconclusive.

However, how can we measure whether or not something can go beyond the speed of light using light as our measuring tool? (By light, I mean the electromagnetic spectrum)

For above statement:

Ok, here is where I am breaking down with your rocket synchronizing clocks example:

I understand that it appears to the on-the-ground observer that the distances between the flash were not equal and therefore not synchronized, but are you saying that it is not possible to adjust for the relative difference comparing distances in some way? As in, couldn't you have some sort of buzzer that zapped you at the exact moment the light went off and, if the distances were far enough, then look up and see the event taking place. Is this what you mean by faster than light travel?

If my grandmother died and was dead for several years, in which time I learned to travel faster than light, you're saying that I could go back to a frame in which see was still alive? Wouldn't that then mean that my grandmother is currently, in some frame outside of mine, at this very moment still alive in a way that I could interact with her again? This would be different from just beating a signal to a far away location and watching the past.