Can Exceeding the Speed of Light Really Mean Time Travel?

[Sean Pan]

Your opinion on"exceeding the speed of light means the ability to return to the past"

I personally think this assertion is absurd, so I'm wondering why so many people(including physicists) think this is true.

 

[GeorgeDishman]

I personally think this assertion is absurd, so I'm wondering why so many people(including physicists) think this is true.

The equivalence of the two unavoidably comes out of the geometry of relativity.

Many people, including many physicists, think that returning to the past (or "violating causality") is absurd, hence they treat "exceeding the speed of light" through space as equally absurd.

 

[Sean Pan]

The equivalence of the two unavoidably comes out of the geometry of relativity.

Many people, including many physicists, think that returning to the past (or "violating causality") is absurd, hence they treat "exceeding the speed of light" through space as equally absurd.

Could you please explain why this comes out of the geometry of relativity. I think exceding the speed of light can only "observe" events happened in the past as can be easily found by drawing a space-time diagram, but it seemed that they still can't return to the past.

 

[harrylin]

I personally think this assertion is absurd, so I'm wondering why so many people(including physicists) think this is true.

Put like that it indeed doesn't make much sense. What no doubt is meant, is that it is inconsistent with relativity theory, as it causes a paradox: According to SR, as determined with certain reference systems that are moving relative to you, that same object will travel to the past. Of course, according to SR that cannot happen because nothing can travel faster than light.

 

[Sean Pan]

Put like that it indeed doesn't make much sense. What no doubt is meant, is that it is inconsistent with relativity theory, as it causes a paradox: According to SR, as determined with certain reference systems that are moving relative to you, that same object will travel to its past. Of course, according to SR that cannot happen because nothing can travel faster than light.

Can you show me how can an observer travel to its past when its speed is over the speed of light? As mathematics fails here ,I prefer using space-time diagram to discribe this kind of situation. In this way, in a certain reference system the world line of the object moving with its speed over c is just a space-like curve which still cannot reach the region represent the events of the past .

 

[Fredrik]

If a particle goes from Earth to the moon faster than light in one inertial coordinate system, then there's another inertial coordinate system in which the event where the particle is on the moon has a smaller time coordinate than the event where the particle is on Earth. So if we use this coordinate system to describe the events, we would have to say that the particle went from the moon to Earth, not the other way round. If we also insist on thinking of the event where the particle is on Earth as the cause of the event where the particle is on the moon, then it makes sense to say that the particle went back in time.

Of course, this is only a difference between how the same sequence of events is described in terms of two different coordinate systems. So it's not really time travel. However, if you have two devices that can send particles faster than light, it seems that you can use them to "really" send messages back in time. (See the argument in this post). Since this leads to nonsense results, the most natural conclusion is that there are no particles that move faster than light.

There are a few other possibilities, for example: 1. The time it takes to emit and/or detect an FTL particle grows at least linearly with the distance it travels. (This would prevent the recipient of the first message to send a reply that reaches the sender of the original message before he sent it). 2. The equations of motion of the matter in the universe doesn't have any solutions that describe someone who both chooses to carry out an experiment like the one I described in the post I linked to, and succeeds. (Yes, this one is even weirder than the first one).

 

[harrylin]

Can you show me how can an observer travel to its past when its speed is over the speed of light?

I hoped to have clarified that the argument is the other way round: nobody can travel over the speed of light, for it implies that he would travel to the past according to measurements with certain other inertial reference systems. (note: "its" was a bit too strong and I modified that now; and for a clear understanding it's good to avoid the word "observer").

As mathematics fails here ,I prefer using space-time diagram to discribe this kind of situation. In this way, in a certain reference system the world line of the object moving with its speed over c is just a space-like curve which still cannot reach the region represent the events of the past .

Sorry, I don't have drawing tools ready now. Why would you say that mathematics fails here? It's very simple algebra.

Also, as Fredrik pointed out, it inverses the course of events as interpreted in different systems- and that messes up such things as cause and effect. For example, consider a traveler who does that: I think that if one then interprets it as travel the other way round in a certain reference system, the traveler would magically have appeared at an earlier time and disappeared at a later time. But obviously no one would interpret such observations as either time travel or disappearances, it would simply disprove relativity.

 

[Demystifier]

I personally think this assertion is absurd, so I'm wondering why so many people(including physicists) think this is true.

I agree that it is absurd. Exceeding the speed of light is not more paradoxical than watching the movie backwards. Even if you can watch the world/movie in that way, you don't really travel to the past.

 

[GeorgeDishman]

Could you please explain why this comes out of the geometry of relativity. I think exceding the speed of light can only "observe" events happened in the past as can be easily found by drawing a space-time diagram, but it seemed that they still can't return to the past.

We can always only observe within our past light cones so just as you can't hear a bullet traveling faster than sound until it has passed you, you can't see a tachyon gun being fired until after you have been hit.

Attached are three spacetime diagrams. Worldline A-B is Albert and C-D is Cindy. Albert is evil so at event 'E' he shoots Cindy with a tachyon gun, the particles travel at 10c. Cindy is grazed on the forearm at event 'F'.

The second diagram shows those events from Cindy's frame, note that Albert's shot seems to travel backwards in time from her perspective. She picks up her tachyon gun at event 'G' and shoots back. The particles again travel at 10c hitting Albert at event 'H'. Cindy is the better shot and Albert drops dead, just before picking up his gun and firing at Cindy. His posthumous view of the whole exchange is shown in the third diagram.

The moral is don't play with tachyon guns or you might find you've been a zombie!

p.s. The applet I used for the sketches is here:
http://www.reagenix.com/personal/sci/space_time/test.html

p.p.s. To reach your own past, launch your spaceship from a tachyon cannon, the flightpath is A-E-F-G-H on the same diagrams.

 

[Naty1]

http://en.wikipedia.org/wiki/Time_travel

 

[Drakkith]

Hrmmm. I don't understand what the graphs represent very well. What are they called and where can I find out more on them?

Do they represent the sequence of events as perceived by each person? IE does graph number 2 represent the frame of Cindy and show what she sees, which is of course limited by light speed?
Is this paradoxical effect simply because the graph is set to have c as the limit?

 

[pervect]

I personally think this assertion is absurd, so I'm wondering why so many people(including physicists) think this is true.

Probably you are imagining some sort of preferred-frame theory, either by accident or design, while they are assuming that relativity is valid and specifically that the Lorentz transform applies.

The "tachyon pistol" duel is an example of some of the problems you get if you assume that things can go faster than light and that the Lorentz transform is correct.

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


The initial problem statement didn't specifically say that relativity was to be applied, so it's mildly ambiguous. However, if you post to a relativity forum it's a reasonable "implied" assumption.

Some people claim that there is a way to make tachyons (FTL waves) compatible with relativity. This seems to involve waves that can't be localized well enough in time to determine exactly when they were emitted. So the tachyon pistol example illustrates the problems classically, a full quantum treatment MIGHT give you a few more minor loopholes.

 

[GeorgeDishman]

Hrmmm. I don't understand what the graphs represent very well. What are they called and where can I find out more on them?

If you mean the ones in my post, they are just standard spacetime diagrams. The applet linked in the post let's you draw worldlines and events then the slider at the top controls the velocity of the observing frame. The java implements the Lorentz Transforms. I just used it to draw a simple demonstration of the equivalence of FTL and a time-like loop, the text explains what is shown. Basically it is just the grandfather paradox with a different storyline. The OP in message #5 said "I prefer using space-time diagram to discribe this kind of situation." so that's what I did.

 

[Drakkith]

If you mean the ones in my post, they are just standard spacetime diagrams. The applet linked in the post let's you draw worldlines and events then the slider at the top controls the velocity of the observing frame. The java implements the Lorentz Transforms. I just used it to draw a simple demonstration of the equivalence of FTL and a time-like loop, the text explains what is shown. Basically it is just the grandfather paradox with a different storyline. The OP in message #5 said "I prefer using space-time diagram to discribe this kind of situation." so that's what I did.

So if the Lorentz transformations used 10c as the speed limit instead of c, there would be no problem correct?

 

[Sean Pan]

Thanks for all of you above. When treating FTL particles, does Lorentz Boost still make sense? Anyone have studied that?

 

[GeorgeDishman]

So if the Lorentz transformations used 10c as the speed limit instead of c, there would be no problem correct?

If you move the slider on the applet to the right, vertical lines rotate clockwise while horizontal lines rotate anticlockwise. They coincide at 45 degrees. The letter 'c' is used to represent that angle which also acts as a speed limit. If you want to represent the angle by 10c then light would move at a speed of 10c and "FTL" would mean traveling faster than 10c, the physics would not be affected. The letter is only a symbol.

 

[GeorgeDishman]

Thanks for all of you above. When treating FTL particles, does Lorentz Boost still make sense? Anyone have studied that?

The transforms are purely geometric, they make as much sense as saying that a picture will rotate if you rotate the paper on which it is drawn even if you exceed 45 degrees. That is why physicists consider that exceeding the speed of light is problematic and that the consequences appear "absurd".

Have we adequately clarified the connection between the two in your original question?

 

[yuiop]

Hrmmm. I don't understand what the graphs represent very well. What are they called and where can I find out more on them?

Do they represent the sequence of events as perceived by each person? IE does graph number 2 represent the frame of Cindy and show what she sees, which is of course limited by light speed?
Is this paradoxical effect simply because the graph is set to have c as the limit?

They are called "spacetime diagrams" and yes, basically graph 2 is how things look in Cindy's rest frame. The diagrams conventionally have space (distance) along the horizontal axis and time along the vertical axis. Try out the applet posted by George http://www.reagenix.com/personal/sci/space_time/test.html. If you draw a line at 45 degrees to the vertical representing the null worldline of a photon and move the slider you will notice that the line remains at 45 degrees for all observers demonstrating the constancy of the speed of light for all observers.

Also note that in graph 2 produced by George, it can be interpreted that Cindy fired two tachyon shots at evil Alex and Alex looks like the innocent victim of an unprovoked (double) attack by Cindy. Once we accept that FTL interactions, then notions of what was the cause and what was the effect no longer make any sense. Cindy's claim that she was acting in self defence and that Alex fired the first shot, looks pretty week because Alex was dead before he made the alleged initial attack. The prosecution claim that Cindy fired the first shot instantly killing poor Alex and then fired another shot into his dead body for good measure. We also have the problem of defining histories in a universe that allows FTL interactions. For example, was Alex alive or dead between events E and H?

.. When treating FTL particles, does Lorentz Boost still make sense? Anyone have studied that?

If we take a series of events along an FTL worldine and then carry out a Lorentz boost, then the transformation makes perfect sense if we only consider the events as a series of independent (non causally linked) spacelike events. If we claim that the events are the worldline of a particle then nothing makes sense as explained elsewhere in the current thread.

 

[Drakkith]

So the graph uses a lorentz transformation correct? The tachyons appear to travel back in time because the lorentz transformation is set up as c as the speed limit? IE if 10c was the speed limit then the tachyons would not travel back in time? I'm just asking about the math aspect, not the real physical aspect.

 

[yuiop]

So the graph uses a lorentz transformation correct? The tachyons appear to travel back in time because the lorentz transformation is set up as c as the speed limit? IE if 10c was the speed limit then the tachyons would not travel back in time? I'm just asking about the math aspect, not the real physical aspect.

I think that is correct. If c is the speed limit and the speed of light was c/10 (in a given reference frame because the speed of light would no longer be invariant) then particles traveling at greater than the speed of light, but less than the maximum speed c, would not go back in time. Tachyons are generally described as particles that exceed the speed of light, but that is only accurate if we assume that the speed of light is exactly the maximum speed c (and that photons have no residual rest mass that is currently unmeasurable). If we define tachyons as particles that exceed the maximum possible speed limit c (the invariant speed), then all tachyons will appear to go backwards in time in certain reference frames.

 

[Drakkith]

Got it.

 

[GeorgeDishman]

The prosecution claim that Cindy fired the first shot instantly killing poor Alex and then fired another shot into his dead body for good measure.

Looking at events E and F, although F seems to happen "first", it is the burn on Cindy's arm produced by the firing of the gun at E by the remains of Alex, so the effect precedes the cause.

Of course that's the point, the gun was fired by the corpse unless we insist that the timelike loop must be self-consistent.

 

[GeorgeDishman]

So the graph uses a lorentz transformation correct?

Correct, the transforms are built into the applet to calculate the coordinates of the lines and events as you move the slider.

The tachyons appear to travel back in time because the lorentz transformation is set up as c as the speed limit? IE if 10c was the speed limit then the tachyons would not travel back in time? I'm just asking about the math aspect, not the real physical aspect.

The transforms are actually set up on the screen with c=1, if you draw a line and then move the slider, it limits at one horizontal unit per vertical unit. The word "tachyon" means going faster than that limiting value, there aren't two different quantities being represented either in the applet or the math or the real world physics.

 

[Drakkith]

The transforms are actually set up on the screen with c=1, if you draw a line and then move the slider, it limits at one horizontal unit per vertical unit. The word "tachyon" means going faster than that limiting value, there aren't two different quantities being represented either in the applet or the math or the real world physics.

Ok, so if the lorentz transformation is correct and the limiting speed is c, then any hypothetical tachyon would go back in time in certain frames? Thus there cannot be faster than light travel?

 

[Fredrik]

Thanks for all of you above. When treating FTL particles, does Lorentz Boost still make sense? Anyone have studied that?

Yes, they do, but keep in mind that every Lorentz transformation is associated with a velocity of magnitude less than c. So there are no Lorentz transformations that boost to a frame in which a FTL particle is at rest.

There are some really counterintuitive things about FTL particles. In particular, if I measure a particle going to the right at 10c, then someone going to the right at 0.5c will measure the particle going faster than 10c, not slower.

Ok, so if the lorentz transformation is correct and the limiting speed is c, then any hypothetical tachyon would go back in time in certain frames?

Yes.

Thus there cannot be faster than light travel?

No. It's not obvious that this implies that tachyons don't exist. You need a more sophisticated argument that involves two tachyon transmitters (like the one I linked to in post #6), and even then the conclusion is just that either FTL particles don't exist, or they have some really counterintuitive properties. (Much more counterintuitive than the weird thing I mentioned in this post).

 

[Austin0]

There are some really counterintuitive things about FTL particles. In particular, if I measure a particle going to the right at 10c, then someone going to the right at 0.5c will measure the particle going faster than 10c, not slower.

Hi Fredrik
Teleportation came up in another similar thread.
Instantaneous translation between points. Absolute simultaneity of events at separate locations.

Assuming teleportation to a distant location in the same frame; How do you calculate the proper time at the point of arrival?? Given t=0 at point of departure.

BTW Congrats.

 

[yuiop]

Looking at events E and F, although F seems to happen "first", it is the burn on Cindy's arm produced by the firing of the gun at E by the remains of Alex, so the effect precedes the cause.

Of course that's the point, the gun was fired by the corpse unless we insist that the timelike loop must be self-consistent.

Well it is not clear that Cindy's arm would be burnt as we go forward in time again, because Alex, perhaps along with his tachyon gun, has been destroyed so he is not in a position to do anything. In this case it looks like "evil" Alex is killed in a single unprovoked attack by "nice" Cindy.

As mentioned in #18, the first time around the loop, Alex is alive between events E and H and the second time around he is dead between those same two events. This requirement for different histories probably requires the concept of parallel universes to make sense. Can we say FTL interaction not only implies traveling backward in time, but also implies parallel universes?

 

[yuiop]

An energy paradox involving time travel.

Let us say we have one very large uncharged lead battery and a small solar panel to charge the battery. We follow these steps:

1)We connect the solar panel to the uncharged battery.
2)We put a note on the uncharged battery saying "When this battery is charged please send it back to time 1"
3)Our future self obliges and sends the charged battery back in time.

The first time a battery is sent back fully charged, we still have the initial uncharged battery. the second time a charged battery is sent back, we have the initial uncharged battery and two fully charged batteries. Repeat as often as required. We could in principle end up with more batteries than there is lead on the Earth to make them with and with a greater energy store than the total energy impinging on the Earth from the Sun between times 1 and 3.

 

[Sean Pan]

Have we adequately clarified the connection between the two in your original question?

Thanks a lot and I have a clearer understand of this problem now. I actually knew that if there were FTL particles, causality would be violated. My opinion is that FTL observers can never actually traveling backwards. And thanks for all above that I now understand what other physicsts mean when they are saying 'returing to the past', it's just an illusion caused by the limited speed of information-carrier. But still, to an FTL particle, γ is no longer real, so I think lorentz boost can't be applied directly here. For example, how can time dilation effect being discussed here?

 

[GeorgeDishman]

Ok, so if the lorentz transformation is correct and the limiting speed is c, then any hypothetical tachyon would go back in time in certain frames? Thus there cannot be faster than light travel?

Exactly, FTL and time travel in this sense are synonymous. Whether that makes them impossible or not is another question.