Thursday, April 30, 2015

The v>c world

Albert Einstein
In 1967, Gerald Feinberg game the name tachyon (from the Greek tacus, fast) to hypothetical particles whose possible existence had been proposed five years before by other researchers. Tachyons would have a unique property: they always move at speeds greater than the speed of light. Their mathematical behavior would not infringe the limitations of the special theory of relativity, which prohibits bodies with mass reaching the speed of light. Unfortunately this would cause other problems.
The idea of ​​the possible existence of tachyons was embraced with joy by science fiction writers, for they seemed to make interstellar travel possible in a reasonable time. For this, the following procedure would be effective:

  1. A spacecraft is built of ordinary matter.
  2. All the particles in the ship and its contents (including the crew) are replaced by tachyons. That is, the ship must be disintegrated and reintegrated into the world of tachyons. Do we know how to do this without destroying the ship and killing the crew? No, but maybe one day we’ll know.
  3. The tachyon ship is accelerated to a speed as large as we wish. This is not difficult, for in the world of tachyons you don’t have to expend energy to accelerate, quite the opposite.
  4. When the ship reaches its destination, it is disintegrated/reintegrated back into the world of ordinary matter, and presto! we are there.
Easy, right? We just need to find how to disintegrate/reintegrate matter from one world to another. But the writers of science fiction forget that things are not so simple. Tachyons can be mathematically correct, but the math is a bit exotic. Let's see how:
         The mass of the tachyons would be imaginary.
         The proper time of tachyons would be imaginary.
         The length of an object built with tachyons would be imaginary.
         The speed of a tachyon would tend to infinity when its energy tends to zero, and to the speed of light when its energy goes to infinity.
Some people say that, if we could go at a speed greater than the speed of light, we would travel back in time. That’s not true. This would happen if time became negative, but it doesn’t, it would become imaginary. The fact that both time and space become imaginary complicates things: an imaginary time behaves as a spatial dimension, an imaginary space as a time dimension. The world of tachyons would have one space dimension and three in time. How can you live with that? How can you get to the desired destination with such exotic coordinates?
Moreover, theory seems to show that, if there were tachyons, they would appear spontaneously from the vacuum and fill all available space, so they probably do not exist at all, so traveling at ultra-light speeds would be impossible.
If we can’t travel, could we at least send messages at such speeds? Einstein proved that, if it were possible, the principle of causality (causes are always prior to effects) could be violated, because the answer to a message would arrive before the message itself had been sent. Benford and colleagues showed that in this case, destructive paradoxes would occur:
Alice and Bob agree to a way to send messages at superluminal speed: Alice will send a message to Bob at time t2 if and only if she didn’t receive Bob’s message at time t1. Bob will send a message to Alice on receiving Alice’s message. If messages are sent at superluminal speed, the answer will arrive before the message was sent. Then two paradoxical situations may happen:
·         Alice doesn’t receive Bob’s answer, therefore she sends her message, but then Bob will answer and she would have received it (contradiction).
·         Alice does receive Bob’s message, therefore she does not send her own, but then Bob can’t answer (contradiction).


Manuel Alfonseca

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