How did Einstein come to the conclusion

[imsmooth]

How did Einstein come to the conclusion that nothing can go faster than the speed of light?

Did he base it on the failure of the Michelson-Morley Experiment to determine a difference in the speed of light based on the measurement?

 

[Al68]

How did Einstein come to the conclusion that nothing can go faster than the speed of light?

Did he base it on the failure of the Michelson-Morley Experiment to determine a difference in the speed of light based on the measurement?

Partially, yes. He combined two postulates, one (supported by M-M) that the speed of light is a constant in any inertial reference frame, the other that the laws of physics are the same in every inertial reference frame. He went on to derive the special theory of relativity to reconcile those two (seemingly contradictory) postulates.

And when you do the subsequent math for two sequential events, for example a signal sent and received, you find that if the signal traveled faster than light, there would be inertial reference frames in which the signal was received before it was sent, violating accepted laws of causality.

In addition, it was also found that an object's resistance to acceleration increases with its velocity, reaching infinity at the speed of light, making it impossible to accelerate any object with mass to the speed of light.

Finally, the above is a completely inadequate explanation, a complete one would require a good understanding of Newtonian laws of motion, frames of reference, and why it is so bizarre that light travels at the same constant speed relative to every observer regardless of their own velocity.

 

[ghwellsjr]

He combined two postulates, one (supported by M-M) that the speed of light is a constant in any inertial reference frame, the other that the laws of physics are the same in every inertial reference frame. He went on to derive the special theory of relativity to reconcile those two (seemingly contradictory) postulates.

This is a very commonly believed but totally wrong understanding of Einstein's postulate concerning the speed of light. You should study his 1905 paper. You will see that he accepted the experimental evidence from the MMX that the measured round-trip speed of light is a universal constant. He postulated that the unmeasureable one-way (both halves of the round-trip) speed of light is a constant. This is an arbitrary definition that has nothing to do with MMX or any other experiment that has ever been done or ever could be done. It forms the basis of synchronizing clocks in any inertial frame of reference. It was this definition of the one-way speed of light that was seemingly contradictory to the other postulate, because the round-trip speed of light is not contradictory to the other postulate. Do you understand why?

 

[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.