Albert Einstein |

In 1967,
Gerald Feinberg game the name

**(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.***tachyon*
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:

- A spacecraft is built of ordinary matter.
- 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.
- 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.
- When the ship reaches its destination, it
is disintegrated/reintegrated back into the world of ordinary matter, and
we are there.*presto!*

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 (

**) 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:***causes are always prior to effects*

*Alice and Bob agree to a way to send messages at superluminal speed: Alice will send a message to Bob at time t*_{2}if and only if she didn’t receive Bob’s message at time t_{1}. 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).***Thematic thread on Standard Cosmology: Preceding Next**

**Manuel Alfonseca**

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