The world of tachyons and science fiction

In previous posts in this blog I have mentioned various procedures often used by the authors of science fiction novels to make interstellar travel almost as simple and brief as today's airplane trips to different points on Earth. One of these procedures consists of disintegrating the ship and reintegrating it into the universe of tachyons: hypothetical particles, compatible with the theory of relativity, that would always travel at speeds greater than the speed of light. Thus it would be possible (in principle) to travel very fast to the point we are interested to go to, reintegrate the ship into the world of tardions (in other words, into our world), and presto! We have traveled faster than the speed of light.

In fact, the authors of these novels (of which I am one) don’t usually go into detail about what the world of tachyons would be like. We simply assume three necessary conditions for interstellar travel to be possible:

1. That the world of tachyons exists (which may very well not be true).
2. That we will know how to disintegrate and reintegrate from one world to the other as many times as we want (which is even less certain).
3. And that pilots of the interstellar ships will find their bearings in the world of tachyons and reach the point they want to go to.

In fact, point 3, which at first glance would seem the easiest to solve, turns out to be impossible. Let’s see why. But first we must point out that the world of tachyons is compatible with the special theory of relativity under quite special conditions, which make this world very strange.

We know that when a moving body travels at a relativistic speed (above 10% of the speed of light, i.e. between 30,000 and 300,000 km/second) the following phenomena take place:

• Its length, seen from outside, is shortened, because it is multiplied by the following number, which when v<c (when the speed of the moving body is less than the speed of light) is always less than 1:

• The time elapsed during the trip, measured outside the moving body, is lengthened, because it is divided by that same number.
• The mass of the moving body, seen from outside, increases, because it is divided by the same number.

When the speed of the mobile approaches the speed of light, its length, seen from outside, tends to zero; the elapsed time tends to infinity; and the mass also tends to infinity. This is the reason why we say that, for an object with non-zero rest mass, the speed of light is unattainable.

What happens in the world of tachyons? If we assume that the same relativistic laws can be applied there, as v>c in this case, we must extract the square root of a negative number, which would give an imaginary result. In other words, the length, the time and the mass of the moving body would become imaginary.

So what, we might say. We’ll travel through a world whose dimensions are imaginary. With time, we’ll learn how to do it. But things are not so simple, because we must consider the Minkowski invariant, whose value is always the same, whatever the speed at which an object moves:

x² + y² + z² – c².t²

Note that, in such an invariant, the spatial coordinates (x, y, z) appear in positive terms, while time appears in a negative term. So, if the spatial and temporal coordinates were imaginary (as they would be in the world of tachyons) the invariant, which should always keep the same value (that is why it is an invariant), would take this form:

(ix)² + (iy)² + (iz)² – c².(it)² = - x² - y² - z² + c².t²

In other words, the terms in x, y, z would have a negative sign (they would become time dimensions), while the term in t would be positive (it would be a spatial dimension). Therefore, the world of tachyons would not have one time dimension and three space dimensions (like ours), but one space dimension and three time dimensions. Is it possible to get one’s bearings in such a world?

Apparently not. In an article published in 1997, entitled On the dimensionality of spacetime, Max Tegmark, who has been mentioned here in connection with one of the multiverse theories, offers a mathematical proof that [in the world of] tachyons, with imaginary rest mass... an observer would be unable to make any predictions. In other words, they couldn’t get their bearings.

In previous posts of this blog I have mentioned my science fiction novel The History of the Earth-9 Colony, which I wrote in 2008 and deals with interstellar travel, colonization of other planets and encounters with extraterrestrial intelligences. The argument of the novel has a double meaning, easy for the reader to discover.

Fourteen years later, I have just written and published the second part of this book, because a reader of the first part asked for a sequel. As soon as I started writing, I realized that the first book really required a second part. Its title is this: The Earth-9 Colony Revisited, and it begins where the previous book ended. Once again, this book has a double meaning, which, as in the first case, is not difficult to discover.

In both novels, interstellar travel is carried out by moving to the world of tachyons, where, according to Tegmark, it would be impossible to find one's bearings. Therefore, traveling in this way wouldn’t be possible. What a pity! My novels will probably never come true. But knowing this does not rule out the fun I had while I was writing them, or the fun that my readers may have while reading them.

The same post in Spanish

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Manuel Alfonseca