# Speed of light Described by relativistic mechanics

1. Oct 21, 2010

### bhsmith

I have been doing research lately. And I wanted to know if anyone could tell me what exactly in relativistic mechanics makes us not able to achieve the speed of light?

2. Oct 21, 2010

### bcrowell

Staff Emeritus
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.

3. Oct 21, 2010

### Passionflower

I am interested, could you tell us which program this is and where it is done?