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I am having trouble understanding, from a conceptual point of view, why it would be impossible to travel faster than the speed of light.

I have read one explanation given in the form of an example to explain why causality would make it impossible to travel faster than light. The example was if say for instance a bullet were to travel faster than light, then the bullet would hit the target before the trigger was pulled.

At first I thought this kind of made sense, but then the more I thought about it I do not think it does. My problem with this example is I do not see why that proves anything. In my mind it is entirely conceivable that the bullet could hit the target before the observer sees the trigger being pulled, that does not violate causality if the bullet is travelling faster than light, much the same way one sees an axe fall on a tree before the sound reaches their ears, so they see it fall before the sound is perceived. It doesn't violate causality. I guess I do not see what is different when talking about light.

What it seems like to me is that we are making the assumption that unless and until we "see" it happen, it has not yet happened. I do not understand why this is the case. Doesn't the fact that we have not "seen" the event occur yet simply mean that those photons have not yet reached our view, not that the event hasn't yet occurred, we just haven't seen it yet? Does this question make sense?

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The problem with FTL and causality has to do with two issues: 1) the relativity of simultaneity between inertial frames (not an issue in classical physics with sound waves, since in classical physics all inertial frames agree about simultaneity), which implies that a signal moving FTL but forward in time in one frame is moving backwards in time in other frames (i.e. different frames disagree on the order of the events of the signal being sent and the signal being received), and 2) the fact that any laws governing FTL signals must work the same way in all frames according to the first postulate of special relativity, so if it's possible to have an FTL signal go back in time in one frame this must be possible in all frames. Clear frame-independent causality violations crop up in situations where slower-than-light observers in different frames bounce a signal back and forth in two directions, as opposed to your example where the bullet constitutes a simple one-way signal--see my answer here for more details. As for why light is different than sound more generally, and why physicists would not make the same conclusions about sound that they make about light even if they were unaware of anything that could move faster than sound, see my answer here.

'What it seems like to me is that we are making the assumption that unless and until we "see" it happen, it has not yet happened.'

No, simultaneity in relativity is not defined by when we see an event happen, but rather based on each observer assuming that light travels at a constant speed relative to themselves. So if in my frame I see an event in 2010 that happened 10 light-years away according to a measuring-stick at rest in my frame, and in 2020 I see an event that happened 20 light-years away according to the same measuring-stick, I conclude that in my frame both events happened simultaneously in 2000 (before I actually saw either event). But if different observers all define simultaneity based on the assumption that light moves at the same speed in all directions relative to themselves, this leads to disagreements about simultaneity--see the example in this video with lightning flashes on either end of a train.

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  • $\begingroup$ I am not a physicist, but I am fascinated by it and I read about it a lot out of pure curiosity...so in my readings I have read what you just stated above and I see it is internally consistent based on certain assumptions, biggest one being that light travels at a constant speed relative to the observer. But it seems that in order to make the equations consistent, we just added plugs. What I hope to find is an explanation that intuitive makes sense without the need for equations and I have yet to find that, maybe it never will be intuitive even though true, I just have a hard time with that. $\endgroup$ – Jeremy Olson Dec 9 '14 at 20:35
  • $\begingroup$ @Jeremy Olson - Note that "light travels at a constant speed relative to the observer" is more of a recipe for constructing inertial frames (coordinate systems) for different observers, not a physical claim--it would likewise be possible to construct a set of inertial frames such that sound traveled at the same speed in every frame. The physical prediction of relativity is that once you have constructed such a set of coordinate systems, you will find that the laws of physics obey the same equations when expressed in terms of any system's position and time coordinates. $\endgroup$ – Hypnosifl Dec 9 '14 at 20:45
  • $\begingroup$ (continued) This feature of the laws of physics is known as "Lorentz-invariance", and it leads to all sorts of more specific predictions which have been verified time and again by experiment. $\endgroup$ – Hypnosifl Dec 9 '14 at 20:46
  • $\begingroup$ Wow, lots of food for thought! Thanks, I think you have pointed me in the right direction. Can you elaborate a little more on your statement, "...it would likewise be possible to construct a set of inertial frames such that sound traveled at the same speed in every frame." I think if I understand what you mean by that, i.e. how that is true and why that makes sense, I think then I would be much closer to "getting it" as it relates to light as well. $\endgroup$ – Jeremy Olson Dec 9 '14 at 20:52
  • $\begingroup$ The fact that light travels at a constant speed in all inertial coordinate systems is guaranteed by the coordinate transformation that relates the space and time coordinates of a physical event in one frame to the coordinates of the same physical event in another coordinate system. This coordinate transformation is called the Lorentz transformation. If you learn how to use it you can check that any pair of events whose spatial separation divided by the time between them is equal to c in $\endgroup$ – Hypnosifl Dec 9 '14 at 22:11
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Stated simply, causality means that all causes should precede their effects, for all observers. The timings of the causes and effects aren't the times at which a human registers them, they are the times at which they occur in an observers reference frame - i.e. the time on the observer's watch at the moment they occur.

If faster-than-light signals were possible and I sent one from $A$ to $B$, there would exist an observer (a reference frame) in which the signal arrived at $B$ before I sent it at $A$.

No such temporal paradoxes occur if you send signals faster than the speed of sound. For example, in principle, you may see a falling tree before you hear it the axe, but that doesn't indicate that there exists an observer for whom effects preceded causes.

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  • $\begingroup$ Yes, but isn't that based on the assumption that until I see it, it hasn't happened? I mean, just because you haven't yet seen the effect why does that necessarily mean the cause has not yet happened. That is what I do not understand. $\endgroup$ – Jeremy Olson Dec 9 '14 at 16:58
  • $\begingroup$ No, the timings of the causes and effects are NOT the times at which a human registers them, they are the times at which they actually occur (in an observer's reference frame). $\endgroup$ – innisfree Dec 9 '14 at 18:24
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You can of course easily define for example a computer simulated universe where light behave exactly like soundwaves (but faster), and it would have the results you suggest - it's just an annoyance that light is not instantaneous but not of any profound character.

The difference between this alternate world and our normal physics, is that in the alternate world, you could send out a beam of light and then accelerate to overtake it, see it "stand still" relative you, and then kick on the accelerator and outrun it.

This is experimentally not the case in our normal world - no matter your velocity relative to others or to the light emitter, you will measure the speed of light to be the same.

It is when you try to reconcile this experimental fact into the theory, that you end up in the causality problems, that time is variable etc. I guess it's out of scope to describe all that here, and it's described in better detail in the other answers here, I just wanted to make the point about where the suggested physics doesn't correlate with experiment.

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  • $\begingroup$ "This is experimentally not the case in our normal world" What experiments prove this is not true, I am intrigued. I like your explanation so far I think you are on the right track of explaining it in an understandable way...so now I just want to look at the experiments and then think about that for a while and digest it to see if that helps my feeble understanding. $\endgroup$ – Jeremy Olson Dec 9 '14 at 20:43

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