One commonly-known fact in physics is that you cannot move faster than the speed of light. While that's basically true, it's also an over-simplification. Under the theory of relativity, there are actually three ways that objects can move:
- At the speed of light
- Slower than the speed of light
- Faster than the speed of light
Moving at the Speed of Light
One of the key insights that Albert Einstein used to develop his theory of relativity was that light within a vacuum always moves at the same speed.
The particles of light, photons, therefore move at the speed of light. This is the only speed at which photons can move. They can't ever speed up or slow down. (Note: Photons do change speed when they pass through different materials. This is how refraction occurs. It's the photon's absolute speed in a vacuum that cannot change.)
In fact, all of the bosons move at the speed of light, so far as we can tell.
Slower Than the Speed of Light
The next major set of particles (so far as we know, all of the ones that aren't bosons) move slower than the speed of light. Relativity tells us that it is physically impossible to ever accelerate these particles fast enough to reach the speed of light.
Why is this? It actually amounts to some basic mathematical concepts.
Since these objects contain mass, relativity tells us that the equation kinetic energy of the object, based upon its velocity, is determined by the equation:
E_{k} = m_{0}(γ - 1)c^{2}
E_{k} = m_{0}c^{2} / square root of (1 - v^{2}/c^{2}) - m_{0}c^{2}
There's a lot going on in the above equation, so let's unpack those variables:
- γ is the Lorentz factor, which is a scale factor that shows up repeatedly in relativity. It indicates the change in different quantities, such as mass, length, and time, when objects are moving. Since γ = 1 / / square root of (1 - v^{2}/c^{2}), this is what causes the different look of the two equations shown.
- m_{0} is the rest mass of the object, obtained when it has a velocity of 0 in a given frame of reference.
- c is the speed of light in free space.
- v is the velocity at which the object is moving. The relativistic effects are only noticeably significant for very high values of v, which is why these effects could be ignored for long before Einstein came along.
Notice the denominator which contains the variable v (for velocity). As the velocity gets closer and closer to the speed of light (c), that v^{2}/c^{2} term will get closer and closer to 1 ... which means that the value of the denominator ("the square root of 1 - v^{2}/c^{2}") will get closer and closer to 0.
As the denominator gets smaller, the energy itself gets larger and larger, approaching infinity. Therefore, when you try to accelerate a particle nearly to the speed of light, it takes more and more energy to do it. Actually accelerating to the speed of light itself would take an infinite amount of energy, which is impossible.
By this reasoning, no particle that is moving slower than the speed of light can ever reach the speed of light (or, by extension, go faster than the speed of light).
Faster Than the Speed of Light
So what about if we did have a particle that moves faster than the speed of light.
Is that even possible?
Strictly speaking, it is possible. Such particles, called tachyons, have shown up in some theoretical models, but they almost always end up being removed because they represent a fundamental instability in the model. To date, we have no experimental evidence to indicate that tachyons do exist.
If a tachyon did exist, it would always move faster than the speed of light. Using the same reasoning as in the case of slower-than-light particles, you can prove that it would take an infinite amount of energy to slow a tachyon down to light speed.
The difference is that in this case you end up with the v-term being slightly greater than one, which means the number in the square root is a negative. This results in an imaginary number, and it's not even conceptually clear what having an imaginary energy would really mean.
(No, this is not dark energy.)
Faster Than Slow Light
As I mentioned earlier, when light goes from a vacuum into another material, it slows down. It is possible that a charged particle, such as an electron, can enter a material with sufficient force to move faster than light within that material. (The speed of light within a given material is called the phase velocity of light in that medium.) In this case, the charged particle emits a form of electromagnetic radiation that's become called Cherenkov radiation.
The Confirmed Exception
There is one way around the speed of light restriction. This restriction only applies to objects that are moving through spacetime, but it's possible for spacetime itself to expand at a rate such that objects within it are separating faster than the speed of light.
As an imperfect example, think about two rafts floating down a river at a constant speed. The river forks into two branches, with one raft floating down each of the branches. Though the rafts themselves are each always moving at the same speed, they are moving faster in relation to each other because of the relative flow of the river itself. In this example, the river itself is spacetime.
Under the current cosmological model, the distant reaches of the universe is expanding at speeds faster than the speed of light. In the early universe, our universe was expanding at this rate, as well. Still, within any specific region of spacetime, the speed limitations imposed by relativity do hold.
The Possible Exception
One final point worth mentioning is a hypothetical idea put forth called variable speed of light (VSL) cosmology, which suggests that the speed of light itself has changed over time. This is an extremely controversial theory and there's little direct experimental evidence to support it. Mostly, the theory has been put forward because it has the potential to solve certain problems in the evolution of the early universe without resorting to inflation theory.