Hyperluminal speed in real life

Cherenkov radiation

We know that the special theory of relativity states that the speed of a body with rest mass greater than zero must be less than the speed of light in a vacuum, i.e., about 300,000 km/second. However, sometimes examples are given that seem to indicate, at first glance, that this limit can be transgressed. Let's look at them:

1. Two elementary particles may have some of their properties, such as their spin, entangled. According to the Copenhagen interpretation of quantum mechanics, both particles have both spins (positive or negative) at the same time, until someone measures the spin of one of them. The two particles may separate and travel a very long distance away (such as one light-year). Then, we measure the spin of the particle that remained here. As soon as we measure it, it collapses. The result of the measurement may be (for instance) positive. We automatically know that the other particle entangled with it must have collapsed with a negative spin. Has there been transmission of information at hyperluminal speed (instantaneous, in this case)? Well, no, because if there were persons next to the other particle and we wanted to inform them of its spin, the information would take a year to arrive. It would be more effective if those persons did their own measurement. We know the result they’ll get, but they won’t know until they have made the measurement. So nothing moved at hyperluminal speed here.
2. With a very powerful laser, we aim at the moon from Earth and shoot a beam of light. In the area of ​​the moon where the laser light hits, we see a point of reflected light. The laser cannon is one meter long and is fixed at its lower end. Now we rotate the laser cannon around the fixed point with a speed of one meter per second. The point of light that we can see on the moon also moves. At what velocity? The triangle similarity theorem tells us: at a speed 380 million times greater than the speed with which the laser rotates, for the distance from the Earth to the moon is about 380,000 km. But that speed turns out to be equal to 380,000 km/second, and is therefore greater than the speed of light in a vacuum. Did we have here a transgression of special relativity? No, because no material point has moved with that speed. What was displaced was not an object, but a reflection. The photons we have received did not move on the surface of the moon, but from the Earth to the moon, and from the moon to the Earth.
3. The Lemaître-Hubble law tells us that the universe expands, that distant galaxies move away from us with a speed more or less proportional to their distance. It is not exactly proportional, because the Hubble constant is not constant, but varies with time. We call observable universe the set of all things that move away from us at a speed less than that of light. This means that we suspect that there are galaxies moving away from us faster than the speed of light, even though we cannot observe them. Doesn't that violate the theory of relativity? No, for those galaxies do not move away from us; rather the space between them and us is expanding.
4. Cherenkov radiation occurs spontaneously when a charged particle travels through a medium at a speed greater than the speed of light. Can a particle go faster than light? Yes! The refractive index of a substance, which is used to calculate the angle at which a light ray is refracted when passing from one transparent substance to another, can be calculated by dividing the speed of light in a vacuum by the speed of light in that substance. In water, for example, its value is about 4/3. In glass, 1.45. That means that the speed of light in water is about 225,000 km/sec, and in glass about 207,000 km/sec. Now, it is possible to launch a particle through glass or water at a speed greater than these. If the particle has charge (as an electron), Cherenkov radiation is generated. But that does not mean that special relativity has been transgressed, because the absolute speed limit of a body with mass is the speed of light in a vacuum, not the speed of light in another substance, such as water or glass.

So, despite appearances, it’s not possible to travel faster than light in a vacuum, and no example proves otherwise.

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Manuel Alfonseca