Is It True That Nothing is Faster Than Light?

Einstein's Theory of Relativity does not forbid the existence of faster-than-light elementary particles.

Is there anything that can travel faster than light? originally appeared on Quora, the place to gain and share knowledge, empowering people to learn from others and better understand the world. You can follow Quora on Twitter, Facebook, and Google Plus.

Special relativity tells us one thing: that there exists an invariant speed, which we call the (vacuum) speed of light, and which is the same for all observers.

This statement has the following rigid mathematical consequences:

1. It is not possible to smoothly accelerate a material object to, or beyond, the speed of light. Apart from the fact that it would require an infinite amount of energy, it is also a topological impossibility: The nature of spacetime is such that the “inside of the light cone” (slower-than-light trajectories) and the “outside of the light cone” (faster-than-light trajectories) are not interchangeable.

2. There is no observer reference frame moving at the speed of light. If such an observer existed, that would be a contradiction. An observer is always at rest relative to himself. But as per the basic postulate of the theory, his own speed, the speed of light, would be the same for all observers, including himself. So he would simultaneously see himself as being at rest and moving at the speed of light.

3. There are no faster-than-light observer reference frames, for similar reasons. What is faster-than-light for one observer is faster-than-light for all observers. So a faster-than-light observer would simultaneously see himself as being at rest and moving faster than light, which is a contradiction.

However, the theory does not forbid the existence of faster-than-light elementary particles. Such hypothetical particles even have a name: tachyons. The problem with tachyons is twofold. First, if tachyons existed, a clever arrangement of tachyon transceivers would allow causality violations — that is, sending messages to the past. Second, the existence of tachyons leads to an unstable universe, as tachyons can lose arbitrary amounts of energy by accelerating to infinite speed. By way of example, the so-called Higgs doublet field, which existed before symmetry breaking, was tachyonic in nature, and also unstable. This instability led to symmetry breaking: with respect to the resulting, new configuration of vacuum and fields, no tachyons exist anymore.

That said, even in the absence of tachyons, there are “things” that can move faster than light. Unfortunately, these things carry neither energy nor momentum, nor any information. As a trivial example, a thought experiment: imagine a very powerful laser pointer that you aim at the Moon. Suppose it is powerful enough so that you can see its light, and its beam is tight enough so that you see a well-defined red spot on the Moon’s surface. Now start wiggling that laser pointer back and forth several hundred times a second. A few seconds later, the red dot will also appear to start moving back and forth… and when you measure it, it will be moving faster than light across the lunar surface. Unfortunately, no resident of the Moon would have the ability to alter the red dot in any way, to use it to send a message to another lunar resident at a speed faster than light.

This question originally appeared on Quora. More questions on Quora:

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