Exceeding the speed of light (FTL) violates causality in certain reference frames, as established by the Lorentz Transformation equations. The discussion emphasizes that if FTL were possible, it would lead to scenarios where cause and effect could be reversed, undermining the fundamental principles of Special Relativity (SR). Participants argue that while FTL may be theoretically supported by certain mathematical interpretations, such as tachyons, the preservation of causality remains a critical aspect of physical laws. The consensus is that causality is a fact, not merely a theoretical construct, and any FTL mechanism would need to align with this principle.
PREREQUISITESPhysicists, students of theoretical physics, and anyone interested in the implications of faster-than-light travel and its impact on causality and the foundations of relativity.
Typically I think people find it interesting because they usually believe strongly that causality is necessary, and therefore they take this as a demonstration that FTL is impossible. It's also a useful argument for explaining why SR's prohibition of FTL is not just a prohibition of FTL motion for particles, but a much more general prohibition of any kind of FTL transmission of cause and effect (e.g., transmission of information). This highlights the fact that relativity is fundamentally a theory of causality.ZealScience said:And why it is so significant?
bcrowell said:I think people find it interesting because they usually believe strongly that causality is necessary, and therefore they take this as a demonstration that FTL is impossible. It's also a useful argument for explaining why SR's prohibition of FTL is not just a prohibition of FTL motion for particles, but a much more general prohibition of any kind of FTL transmission of cause and effect (e.g., transmission of information). This highlights the fact that relativity is fundamentally a theory of causality.
Saw said:I am a little lost with this sort of comments you make from time to time. Let me tell you my view and you might yourself comment if you disagreed. Causality cannot be violated because it is not a theory, it is a fact. A conceptual interpretation may be subject to exceptions. But if I scratch my nose too much and due to that cause I suffer the effect that my nose aches..., that is it, no way out, no exception. As to FLT, I believe it is impossible for physical reasons. But if by chance one day a means for FLT were discovered, causality would not in the least suffer for that reason. And if some conceptual interpretation, some understanding of SR held that causality should in that case suffer, that would only mean that such interpretation is in that respect flawed, but my nose should keep aching, as judged from any reference frame...
Superstring said:therefore no signals can travel faster than light. Why?
Say, for example, that you send out a faster-than-light signal and a short time afterwards I shoot and kill you. Another person who is at a distance and moving at a velocity such that v/c > c\Delta t/ \Delta x receives your signal. But who sent it? From his frame, your death preceded your transmission of the signal.
Good treatment; I followed your equations but not the text discussion after. There is a similar discussion on:Superstring said:Look at the Lorentz Transformation for the time separating two events:
\Delta t'=\gamma (\Delta t-v\Delta x/c^2)
The primed frame sees the events reversed in time (i.e. \Delta t' is negative) when v\Delta x/c^2 >\Delta t.
Restated:
\Delta t'<0 when v\Delta x/c^2 >\Delta t.
Rearranging the condition gives:
\frac{v}{c} > \frac{c\Delta t}{\Delta x}
c\Delta t can be though of as the distance that light travels in the time separating the events. v is the velocity of the primed frame with respect to the unprimed frame, which must always be less than c (or you get imaginary numbers out of the LT). The left side of the above inequality must always, therefore, be less than one. The only way for the primed frame to see the events reversed is therefore when \Delta x > c \Delta t. In other words, the distance in space separating events must be large enough so that light does not have enough time to travel from the first event to the second event. It is therefore concluded that if light does not have enough time to travel from event A to event B, then event A could not have possibly caused event B, and therefore no signals can travel faster than light. Why?
Say, for example, that you send out a faster-than-light signal and a short time afterwards I shoot and kill you. Another person who is at a distance and moving at a velocity such that v/c > c\Delta t/ \Delta x receives your signal. But who sent it? From his frame, your death preceded your transmission of the signal.
Saw said:I am a little lost with this sort of comments you make from time to time. Let me tell you my view and you might yourself comment if you disagreed. Causality cannot be violated because it is not a theory, it is a fact.