Determinism and the speed of light
How do we know that no signal can travel faster than the speed of light? There cannot be a direct evidence of this fact. The indisputable fact is that the speed of light is the same in all reference frames.
In my knowledge, augmented with the browsing capability of my students, the only answer lies in the following deduction:
(1) The speed of light being the same in all reference frames and the principle of relativity lead, as well known, to the Lorentz transformation.
(2) Armed with the Lorentz transformation, one can rather easily show that a signal propagating faster than light could allow me to send a message to myself from the future to the past. Einstein himself was well aware of this (I don’t know if he was even the first to notice it).
Now, why is it a problem, that I can send a message to myself from the future to the past? Normally, the answer lists all kind of crazy things I could do, like winning all my bets and analog stuff. For me, the most dramatic consequence is all that I, and many others, can no longer do. First of all, when I receive a message at time t0 sent at time t1, I know that for sure I’ll have to send the message at time t1: it’s unavoidable. Moreover, all the events happened between t0 and t1 that the message informs me about have also become unavoidable. For instance, the message may inform me that a friend who is walking alongside me at t0 will be killed by a car, and even if this is going to happen one hour later, all I can do is to inform him that his life is about to end. Isn’t this absurd enough?
Well, I definitely find it is… but not necessarily someone who believes in full determinism! For such a person, all the information about what is going to happen in the future is already fully contained in the universe now, and always has been. There is nothing wrong in the physical universe that some existing piece of information gets stored in the neurons that call themselves “I” before the corresponding fact can be observed by all the brains: after all, that is what happens when we predict something with the laws of physics (say, the passing of an asteroid close to the earth).
The deduction made above is absolutely conclusive only if one believes in the possibility of creation of information that was previously not available. It is not such an outlandish belief: people believing in human free will have uphold it for centuries, and within physics, quite a few interpretations of quantum physics also uphold it. But it is funny to find it appearing in a topic usually supposed to derive from special relativity alone.
Two disclaimers. First, I am NOT claiming that I believe something can go faster than light — indeed, since I believe in free will, I do find the deduction above perfectly convincing. Second, I am also aware that, if anything would go faster than light, it should be massless: for massive objects, the Lorentz transformation predicts infinite inertia at a speed approaching that of light, independently of any argument about signaling to the past.
P.S. Within a few hours from the first post, I noticed another important assumption in the deduction above: the assumption that any physical phenomenon can be harnessed to send a signal — even more specifically, that it can be harnessed to implement the protocol that allows sending messages to the past (which implies sending the superluminal signal to an observer in relative motion and having it reflected back to myself).