# Faster than light? Faster than light! Faster than light

## Main Question or Discussion Point

I'm amazed at how often the question arises, and how many people are interested in "faster-than-light" travel. So in anticipation of the next passer-byes who may want to ask the question, here is a preemptive, answer (yeah, a jeopardy-type thread I guess), just to show how it can make perfect layman sense that it is the physical speed limit. (I don't claim it to be rigorous.)

1. Either the speed of light is finite or infinite. Experiments have shown that it is finite.

2. In vacuum, light interacts with nothing, so it cannot slow down or accelerate. It is thus a constant.

3. Since light has no mass (less than anything else observed), even common sense would suggest that anything with mass will be slower.

So in summary: Things have mass, that's why nothing travels faster than light. Unless you're writing science-fiction novels or seriously studying the field, that's all there is to it.

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bcrowell
Staff Emeritus
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2. In vacuum, light interacts with nothing, so it cannot slow down or accelerate. It is thus a constant.
Constancy of c in relativity refers to the fact that a certain velocity, c, is the same in all frames. It doesn't have anything to do with light, vacuum, or changes in speed over time. I could use your argument like this: In vacuum, a hydrogen atom interacts with nothing, so it cannot slow down or accelerate. Its velocity is thus a constant. That would be true, but it wouldn't mean that there was some special "speed of hydrogen" that had a definite numerical value and had special status in relativity.

3. Since light has no mass (less than anything else observed), even common sense would suggest that anything with mass will be slower.
No, this doesn't follow from common sense. No physicist in the world believed this before 1905, but many of them had good common sense.

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 is interpreted as an effect in which space itself is expanding in the space in between.

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 is interpreted as an effect in which space itself is expanding in the space in between.
But those are not examples of MASS moving at c.

Einstein was more intelligent then you (and me), accept it.

bcrowell
Staff Emeritus
Gold Member
bcrowell said:
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 is interpreted as an effect in which space itself is expanding in the space in between.
But those are not examples of MASS moving at c.
See the text in bold. For more about this: Davis and Lineweaver, Publications of the Astronomical Society of Australia, 21 (2004) 97, msowww.anu.edu.au/~charley/papers/DavisLineweaver04.pdf

The reason for so many people asking the same question is because there is no place to turn to for answers. Just look at some general relativity wikipedia pages and you'll see a truckload of formulas that confuse more than they explain.

On top of it all you got "bizzareness" and lack of explanation of concepts and assumptions. Two people think differently and everyone's brain is tuned the same.

Here's one for you: "I can travel faster than light. Give me a 10G massless accelerator and I'll reach Andromeda in less than 2 million years!". In fact I'll probably reach it in a year! And light takes 2.5 million years to reach it. And in fact, in a few months after that I'll be 15 billion light years away from you at the "edge of space". There's your FTL. Quite reasonable, when interpreted properly, but unrealistic.

2. In vacuum, light interacts with nothing, so it cannot slow down or accelerate. It is thus a constant.
In a Schwarzschild spacetime light actually decelerates when it falls in and accelerates when it moves out. This deceleration when falling in is even true for massive objects that have a proper velocity above some critical value.