The universe seems to have a speed limit, a maximum speed that nothing can exceed. But why is this speed not infinite? And why is it impossible to reach it with any object that has mass?

The universe has a speed limit: the speed of light in a vacuum. This limit prevents fundamental particles from traveling faster, regardless of their energy, prevents fundamental interactions from propagating immediately (making it take us more than 8 minutes to feel the Sun’s gravity), and generally prevents any kind of information propagates above this speed. Although there are certain “things” that seem to move faster, none of them do. Neither the path of a laser on the Moon after shaking it, nor a possible spaceship that managed to use some type of warpdrive technology.

In the first case, because there is really nothing “moving”, beyond the photons that travel at the speed of light. The trail that those photons leave when we shake the laser is not a structure, nor can information be transmitted with it. In the case of warp engines, or curvature of space because, if feasible (which is questionable), they would be deforming spacetime in such a way that, rather than traveling very fast, we would be shortening the distance to our destination.

Therefore, the maximum speed that any object in the universe is capable of reaching is the speed of light, so called because light was the first phenomenon we knew of that traveled at that speed. We now know that this speed is not specific to light, but to any massless particle. In fact, this concept is closely related to the speed limit of our universe. Being massless and traveling at the speed of light seem to be the same thing. So let’s ask ourselves, what does it mean for a particle to have no mass?

To answer this we will first need to know what a particle is and what mass is. So let’s start with what a particle is. Perhaps now you have in mind a little ball of some striking color, moving through space. The concept of a particle as a very small ball is something that we have invented to make our lives (and physics) easier. To understand certain equations and many phenomena, that particle image is very useful, but the universe is not that simple and particles, at least as we imagine them, do not exist. What exist are quantum fields. Therefore, to continue talking about particles, we will content ourselves with saying that a particle is anything that can be detected with a particle detector.

That is, imagine that you have a source of photons: a star, a light bulb, or a laser. Also imagine that you have a device that every time a photon hits it emits a beep or increases a number on a counter. In some way or another you could reduce the amount of photons that reach this detector, placing filters or screens with slots and holes right in front of it, getting them to end up being detected one by one. Each of those objects that arrive at the detector one at a time is a particle.

On the other hand, the mass According to special relativity, the energy of a particle has two fundamental contributions, when it moves freely through space. One of them is the energy that the particle has due to the fact that it is moving at a certain speed, its kinetic energy. The other is its energy at rest, when it is not moving, its mass. So what does it mean for a particle to have no mass? It means that it does not have this energy contribution at rest, so all its energy is kinetic energy, energy due to motion. This will mean that a photon, since its only energy is due to movement, must necessarily move. You will not be able to rest.

But rest is relative, it depends on who measures it. If you are flying in an airplane, you are clearly not at rest, because you are moving at 1000 kilometers per hour with respect to the ground. However, for all intents and purposes, the person sitting next to you, the rest of the crew, and the fuselage of the plane are at rest with respect to you. Its velocity is zero with respect to you. They are neither moving away nor coming closer and, from your point of view, it is the ground, the clouds and the air around the plane that are moving.

Therefore, if a photon had any speed, a speed that was not the maximum allowed in the universe, in principle you could get on a spaceship, put yourself at that speed and say that the photon is at rest with respect to you. But that is impossible, because the photon has no energy at rest. So the photon has no choice but to travel at the maximum possible speed, the speed of light. Or the speed of light has no choice but to be the speed at which photons and any massless particles travel.

The speed of light is the speed at which particles whose energy is completely (100% and no less) kinetic energy move. For a particle with mass, its energy will never be completely kinetic, because no matter how colossal it is, the small contribution corresponding to the mass will always remain. And this means that having no mass and traveling at the speed of light mean the same thing.

We could only make a particle with mass reach the speed of light by giving it infinite kinetic energy. This of course is not possible. So the universe seems to have an arbitrary speed limit because we’re looking at the wrong magnitude. What is important is not really the speed of the particle, but its kinetic energy. Specifically the relationship between kinetic energy and energy at rest. If we think of it this way, the limit of the universe is at infinity (a very good place to put a limit), at an infinitely greater amount of kinetic energy than rest energy.

References:

E. F. Taylor, J. A. Wheeler, 1992, Spacetime Physics: Introduction to Special Relativity, W. H. Freeman, ISBN 978-0-7167-2327-1