# Speed of light - causality - etc

1. Dec 21, 2012

### DwithQs

I've seen other posts about this, but would appreciate an explanation if anyone knows.

I've read that travelling faster than the speed of light could affect causality. Example: item I travelling in a tube could be seen arriving at end B before it ever left end A.

A=======I=B

Is this an actual affect on causality or just the light reaching the observer? I am trying to compare it with speed of sound. Travelling faster than the speed of sound may affect when an observer hears something, but not actually when the sound is made.

2. Dec 21, 2012

### jbriggs444

It is one of the axioms underlying the theory of Special Relativity that the laws physics are the same no matter what inertial frame of reference you use to describe them.

So if the laws of physics allow you to send an object faster than light from the point of view of one reference frame, all you have to do is speed up your sending apparatus and you can send an object faster than the speed of light from the point of view of any other reference frame.

It is a simple consequence of Special Relativity (more specifically a property of the Lorentz transform) that an object that is moving faster than the speed of light in one frame of reference is moving backward in time as viewed from another.

Put this together just right...

Start from your choice of frame of reference. Say one in which the Earth is more or less at rest. Put a message in a cannister and launch it faster-than-light. But launch it from an apparatus that is moving fast enough that the resulting motion is backwards in time from the point of view of the Earth frame. At the far end, arrange for a receiver to catch this message, put it in another canister and launch it back. Again, launch it from an apparatus that is moving fast enough that the resulting motion is also backwards in time from the point of view of the Earth frame. Back on Earth, receive the canister, unwrap the message and read it -- before you wrote it.

That's not just a matter of light reaching the observer. That's actionable information. Fodder for all sorts of causality paradoxes if you can A) build such an apparatus, B) send information using it and C) act on it arbitrarily.

This sort of thing is sometimes referred to as a "closed timelike loop".

Last edited: Dec 21, 2012
3. Dec 22, 2012

### Greg-ulate

Its an actual affect on causality, even after the travel time of the light reaching the observer is corrected for. Its different from the way sound works because the speed of sound is not the absolute speed limit of space. What you are asking about is called Relative Simultaneity of Events. It is pretty hard to understand, visual aids help.

Energy warps space. Kinetic energy warps space in the direction of motion by compressing it in that direction. If you travel towards a distant object at relativistic speed, the amount of space between you and that object appears smaller to you, it takes less time for light to travel from that object to you, so it seems like you just jumped into that object's past (compared to a prior measurement made a rest with respect to the object) since the light (and any other form of information) you are receiving from that object is essentially the same, and you calculate that it took a shorter time to travel to you from that object through the compressed space.

Moving towards (or away from) a pair of distant objects where one is farther from you than the other compresses the distance between the two objects from your point of view. It takes less time (in your reference frame) for light to move from one to the other the faster you move toward them. If an event at the more distant object causes and event at the closer object then the causal event must precede the caused event in all inertial frames of reference. But as you travel towards them they seem to happen closer together in time, this is ok since you still see the information traveling from one to the other at less than or equal to the speed of light, its just that the space is getting smaller and smaller. However, if you are going at the speed of light exactly, the space between them becomes infinitely small, and the events happen simultaneously in your reference frame. If you were able to go even faster than that, the events would swap causal relationships, you would see time run backwards, distances would be negative... all sorts of bad things would happen. You would collapse into a black hole, I don't recommend it.

This is called relative simultaneity because events that are simultaneous in the rest reference frame are not simultaneous to an observer moving with respect to that reference frame. Simultaneous distant events are by definition not causal and can be seen to occur in different order depending on which one is farther away from you.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook