# I got a question.

## Main Question or Discussion Point

Let's say that somehow a car moved with speed greater than the speed of light, would that mean that time is going backwards?

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pervect
Staff Emeritus
ludi_srbin said:
Let's say that somehow a car moved with speed greater than the speed of light, would that mean that time is going backwards?
Nope. The Lorentz time dilation fatctor would become imaginary, not negative. See some of the sci.physics.faqs about tachyons, for instance. Note that tachyons are not believed to actually exist.

JesseM
pervect said:
Nope. The Lorentz time dilation fatctor would become imaginary, not negative. See some of the sci.physics.faqs about tachyons, for instance. Note that tachyons are not believed to actually exist.
In a sense his/her statement is correct though--for any signal moving faster than light, there will be some slower-than-light reference frames where it's moving backwards in time (ie the event of the signal being received is judged to happen before the event of it being sent). So, if the laws governing FTL signals were assumed to work the same way in every reference frame, then it must be true that it is possible to send a signal backwards in time in every frame, which means that if you and me are moving apart I can send you a signal which travels FTL in my frame but backwards in time in yours, and you can send me a reply which travels FTL in your frame but backwards in time in mine, and it will be possible for me to receive your reply before I sent the original signal, which is a clear causality violation in all frames.

The problem is that tachyons don't have valid rest frames of their own, so you can't apply the Lorentz transformation to see what things would look like from the tachyon's point of view or how fast a tachyonic clock would tick relative to our own--this is what you were referring to in your answer I think.

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if you moved faster than speed of light your time would not go backwards!

the speed of light C represents universal speed limit, which in your case the speed of car would be placed in there which would mean that time actually dilates by a factor of infinet.

JesseM
bayan said:
if you moved faster than speed of light your time would not go backwards!

the speed of light C represents universal speed limit, which in your case the speed of car would be placed in there which would mean that time actually dilates by a factor of infinet.
Again, relativity just doesn't give an answer to the question of how much time dilation a tachyon would experience, i.e. how fast a tachyon clock would tick compared to our own. But it does say that tachyons go back in time from the point of view of some slower-than-light reference frames, meaning that in these frames, a tachyon signal can be received before it is sent, and if the laws governing tachyons work the same way in all frames, then two people could exchange messages and the first person could receive a reply before sending the original message, gaining information about his own future.

But it does say that tachyons go back in time from the point of view of some slower-than-light reference frames
Yep, space-like trajectory.
http://www.absoluteastronomy.com/encyclopedia/s/sp/space-like.htm [Broken]
http://en.wikipedia.org/wiki/Special_relativity

Note that tachyons are not believed to actually exist.
I think that in the past so teams have been looking for them (by looking for Cherenkov radiations that should be produced), with no success...seems that nature likes causalty principle.
http://www.faqs.org/faqs/astronomy/faq/part4/section-12.html

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But how can something go faster then the speed of flight?? ( Ignoring some quantum effects) How can you apply relativity to a situation where it is not applicable? Or does relativity infact allow for things to travel faster then light?

I think that the answer is in JesseM message #5 ...
JessM said:
Again, relativity just doesn't give an answer to the question of how much time dilation a tachyon would experience, i.e. how fast a tachyon clock would tick compared to our own. But it does say that tachyons go back in time from the point of view of some slower-than-light reference frames, meaning that in these frames, a tachyon signal can be received before it is sent, and if the laws governing tachyons work the same way in all frames, then two people could exchange messages and the first person could receive a reply before sending the original message, gaining information about his own future.
How can you apply relativity to a situation where it is not applicable?
To my knowledge, the only place where you cannot apply SR is in the framework of a photon (because of the postulates of SR : http://nobelprize.org/physics/educational/relativity/postulates-1.html ). In other words you can never make v=c in SR.

Or does relativity infact allow for things to travel faster then light?
Only if the object has an imaginary mass. Moreover, an object that has an imaginary mass can only travel faster than light. To reduce their speed you have to give them more and more energy. To make them go at c you have to give them infinite amount of energy.

Benjamin

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Tzar said:
But how can something go faster then the speed of flight?? ( Ignoring some quantum effects) How can you apply relativity to a situation where it is not applicable? Or does relativity infact allow for things to travel faster then light?
Relativity doesn't prohibit objects from traveling faster than c. What it prohibits is objects accelerating from a speed less than c to a speed greater than c or vice versa. There are hypothetical particles which, if they exist, always travel faster than the speed of light. These particles are called tachyons, but there isn't any evidence of their existance and no reason to believe they should exist. However, the equations of relativity do allow for them to exist, but, as BioBen pointed out, if they do exist they must have an imaginary mass, and, as JesseM has pointed out, if they ever are found to exist, it'll through a loop-hole in our current understanding of causality.

I see. But surely if these particles are even spoken about there must be some reason for people to think they exist. Why were they brought up in the first place?

Staff Emeritus
Gold Member
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Tzar said:
I see. But surely if these particles are even spoken about there must be some reason for people to think they exist. Why were they brought up in the first place?
Precisely because they are permitted by the formalism. Physics has a history of success (not complete but suggestive) with pushing the formalism beyond where intuition leaves it; look at the quantum vacuum! Or Dirac's deduction of the positron. So people will go and see what the far-out consequences of any mathematical model are. Maybe it will produce some valid new physics, maybe not, but it's worth checking up on.

After the tachyons had been introduced as curiosities of relativity, they turned up in string theory*. There they have had a checkered history, sometimes being shunned as unphysical, smetime beeng seein as clues to real physics (vacuum decay). Or as real as string physics gets, before Juan R. jumps on me!

*The lightest vibration modes of a bosonic string have $$m^2 < 0$$. There are other places too.

Hmm

ludi_srbin said:
Let's say that somehow a car moved with speed greater than the speed of light, would that mean that time is going backwards?
Good question. But like some people already mentioned... it would become imaginary.
I wish I could move as fast as the infinite, but then I would need infinite power/force. Because if I moved in infinite speed, my mass woul also become infinite.
a=F/M

But to be more specific to your question...
t=t'/sqrt(1-v^2/c^2)
where t is the time you were looking for. And if t' was the other... relative time (if you know what I mean).
And if your car's speed was faster than the speeed of light, the calculator would show "Invalid input for function" as an answer, because you can't sqrt the negative value.

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bayan said:
if you moved faster than speed of light your time would not go backwards!
the speed of light C represents universal speed limit, which in your case the speed of car would be placed in there which would mean that time actually dilates by a factor of infinet.
is it possible AT ALL, any way taht it could ever happen, that that limit could be broken?

cd

Ich