What are the best lines of reasoning for why nothing can travel faster than c

[itsthemac]

The argument I've heard following from Special Relativity is as follows:

Assume a causal influence can travel faster than c in a given reference frame, and assume it starts at Event A and is the cause of Event B a short time later (Events A and B are also at different points in space). This implies that you could always choose a different reference frame in which Event B happens before Event A. So in theory, you could witness Event B happening (knowing that it could only be caused by A), and then stop Event A from ever occurring to be able to cause B in the first place, creating a paradox.

Is this the best argument for why nothing can go faster than c? Are they others that I'm not aware of? Is there a mathematical proof that shows unequivocally that it could never happen? This one paradox argument doesn't feel good enough to to me be able to claim that we know for sure that nothing could ever even hypothetically go faster than c, but maybe that's just me and I need to just accept it.

Basically what I'm asking is, what are the arguments that YOU all use to reassure YOURselves that nothing can truly ever travel faster than the speed of light? What was the big one that gave you that ah-ha moment?

 

[dacruick]

haha I guess there are a few things for me.

But any relativistic equation contains mathematical proof that something traveling at v > c, is undefined.

I like the relativistic mass. As something approaches the speed of light, its mass approaches infinity, which means that it takes an infinite amount of energy to bring a mass to the speed of light.

 

[itsthemac]

haha I guess there are a few things for me.

But any relativistic equation contains mathematical proof that something traveling at v > c, is undefined.

I like the relativistic mass. As something approaches the speed of light, its mass approaches infinity, which means that it takes an infinite amount of energy to bring a mass to the speed of light.

Woops, can't believe I forgot about that. Probably more popular than the one I mentioned.

 

[ghwellsjr]

If you understand what light is and how it interacts with matter, then you can see why nothing can ever go faster than light. Light is a changing electric field, propagating at c, caused by moving charged particles, mainly electrons but also protons. And the electric field is what causes charged particles to move which is how we impart motion to massive bodies. So you can see that if the mechanism for imparting motion between objects is itself limited to c, there is no way for one object to get another one to go faster than c.

I realize this is an over-simplification but it is how I answer your question.

 

[Buckleymanor]

Light don't have mass and it won't travel faster than c so how can you expect an object with mass to go faster

 

[bcrowell]

FAQ: Why can't anything go faster than the speed of light?

In flat spacetime, velocities greater than c lead to violations of causality: observer 1 says that event A caused event B, but observer 2, in a different state of motion, says that B caused A. Since violation of causality can produce paradoxes, we suspect that cause and effect can't be propagated at velocities greater than c in flat spacetime. Special relativity is one of the most precisely and extensively verified theories in physics, and in particular no violation of this speed limit for cause and effect has ever been detected -- not by radiation, material particles, or any other method of transmitting information, such as quantum entanglement. Particle accelerators routinely accelerate protons to energies of 1 TeV, where their velocity is 0.9999996c, and the results are exactly as predicted by general relativity: as the velocity approaches c, a given force produces less and less acceleration, so that the protons never exceed c.

The corresponding speed limit in curved spacetime is far from being established. The argument from causality is not watertight. General relativity has spacetimes, such as the Godel solution, that are valid solutions of the field equations, and that violate causality. Hawking's chronology protection conjecture says that this kind of causality violation can't arise from realistic conditions in our universe -- but that's all it is, a conjecture. Nobody has proved it. In fact, there is a major current research program that consists of nothing more than trying to *define* rigorously what the chronology protection conjecture means.

There are certain things we *can* say about faster-than-light (FTL) motion, based on the fundamental structure of general relativity. It would definitely be equivalent to time travel, so any science fiction that has routine FTL without routine time travel is just plain wrong. It would probably require the existence of exotic matter, which probably doesn't exist. If it were possible to produce FTL artificially, it would certainly require the manipulation of godlike amounts of matter and energy -- so great that it is unlikely that beings able to carry it out would have anything like ordinary human concerns.

There are many ways that velocities greater than c can appear in relativity without violating any of the above considerations. For example, one can point a laser at the moon and sweep it across, so that the spot moves at a speed greater than c, but that doesn't mean that cause and effect are being propagated at greater than c. Other examples of this kind include a pair of cosmic-sized scissors cutting through a gigantic piece of paper at greater than c; phase velocities greater than c; and distant, observable galaxies receding from us at greater than c, which can be interpreted as an effect in which space itself is expanding in the space in between.

 

[grav-universe]

I would say that the main reason is time dilation. Imagine we remain inertial but a ship accelerates from our frame that is constantly firing a rocket thruster in order to accelerate to ever greater speeds. As it approaches the speed of light, we observe the thruster firing at a lesser and lesser pace. If it could reach the speed of light, we would no longer observe it firing at all since from our perspective, time has stopped aboard the ship, so it would then just continue to travel inertially at c, never gaining any greater speed. In reality it would get closer and closer to the speed of light but never quite reach it.

 

[Joseph14]

There are certain things we *can* say about faster-than-light (FTL) motion, based on the fundamental structure of general relativity. It would definitely be equivalent to time travel, so any science fiction that has routine FTL without routine time travel is just plain wrong. .

Why would FTL be equivalent to time travel??

 

[bcrowell]

Why would FTL be equivalent to time travel??

If yo had FTL, you could get from event A to event B, where A and B are separated from one another by a spacelike interval. Then in a Lorentz-boosted frame, you would be arriving at B before you left from A.

 

[DrGreg]

Why would FTL be equivalent to time travel??

Tachyonic antitelephone

 

[Joseph14]

If yo had FTL, you could get from event A to event B, where A and B are separated from one another by a spacelike interval. Then in a Lorentz-boosted frame, you would be arriving at B before you left from A.

Even if it appears in a Lorentz-boosted frame that B occurs before A, that does not imply time travel has occurred. As a comparison if you were in battle and someone tried sniping you (and luckily misses you) you will hear the bullet hit before you here the gunshot.

 

[Phrak]

On the other hand, step on over to the quantum electrodynamics folder for a moment, and this physics will demand faster than light phase contributions to expectation values or your results will not match experimental results.

 

[ZikZak]

The causality argument doesn't mean much to me personally. I can imagine universes which violate causality but maintain a self-consistent external reality.

The relativistic mass explanation? Ew.

I think the conceptual line of thinking is very simple. No matter how fast you run to try to catch up to a light ray, it still recedes from you at c. Since you can never even make headway towards it, no external inertial observer can observe you closing distance to it, and thus no external inertial observer can observe you to travel at its speed.