Special Relativity states that nothing that is moving initially slower than the speed of light can be accelerated to exceed it or it is impossible for some object with mass to travel at speed of light. However, it is possible that particles exist which move faster than light from the moment they are created. These particles are known as Tachyons. If such particles exist, could they be used to send signals faster than light into one’s own past?
In 1962, O. M. P. Bilaniuk, V. K. Deshpande, and E. C. G. Sudarshan first proposed the possibility of particles moving faster than light and named them “meta particle”. The term “tachyon” was coined by Gerald Feinberg in a 1967 paper titled “Possibility of Faster-Than-Light Particles”. The term comes from the Greek word “tachy ” meaning “rapid”.
Tachyons are theoretically postulated particles that always move faster than light and have ‘imaginary’ masses. One curious effect is that, unlike ordinary particles, the speed of a tachyon increases as its energy decreases. In particular, E approaches zero when v approaches infinity. This is unlike ordinary bradyonic matter (particles which travel slower than c) , E increases with increasing speed, becoming arbitrarily large as v approaches c, the speed of light. Therefore, just as bradyons are forbidden to break the light-speed barrier, so too are tachyons forbidden from slowing down to below c, because infinite energy is required to reach the barrier from either above or below.
As noted by Einstein, Tolman, and others, special relativity implies that faster-than-light particles, if they existed, could be used to communicate backwards in time. But travelling back in time comes with its own complications such as the paradox of causality. Causality is the relationship between cause and effect. Causality means that an effect cannot occur from a cause which is not in the back (past) light cone of that event. Similarly, a cause cannot have an effect outside its front (future) light cone. But faster than light events occur in space-like four-momentum meaning neither event lies in the future light cone i.e. people can disagree on the order of 2 events which can cause severe logical paradoxes and causal loops.
For example, if you sent a message back in time that caused your grandfather to be killed before your father was conceived, then you would not be around to send the message that prevented your birth so that you would be around to send the message so that you wouldn’t be around….etc. Therefore, it can be concluded that superluminal particles such as tachyons are not allowed to convey signals.
As of now Tachyons have no compelling evidence of their existence, but various theorists have suggested that the neutrino might have a tachyonic nature, while others have disputed the possibility. In recent decades, there have been various proposed ways to possibly remove such paradoxes, either by invoking the Novikov self-consistency principle(if an event exists that would cause a paradox or any “change” to the past whatsoever, then the probability of that event is zero.) or through the idea of branching timelines in the context of the many-worlds interpretation. Therefore, I think that time travel is not absolutely impossible. I will merely take a rather weak stance on the matter and simply say that based on physics as we know it today, there are some substantial difficulties that must be overcome before time travel becomes a reality.