TIME TRAVEL: FICTION OR REALITY? (I)

In these two articles, we will attempt to answer in detail the now-famous question: Do the laws of physics allow time travel? We will also address the question of whether such travel is actually possible. The answer to the first question will greatly delight science fiction fans, although the answer to the second will not be as positive. Interest in this topic will also

It is theoretical: it tells us a lot about the Universe we inhabit, a world full of fascinating phenomena.

Why superluminal travel would allow time travel

The first thing we'll explain is why a theoretical particle traveling faster than light (such as the hypothetical tachyons) could, in principle, travel into the past in a given reference frame. Let's consider the space-time graph of a light ray emitted from a reference frame at rest at time t=0 and s=0:

In the graph we have that t=v/x, for v=c we consider a straight line of unitary slope, for this reason the light is always represented as a straight line with 45º inclination. The x axis represents the instant t=0 and the lines parallel to the x axis the instants t=1, t=2, etc.

In this graph, light always travels along straight lines with a 45º inclination. Any trajectory with an angle less than 45º will be a "usual" trajectory, that is, subluminal, while a trajectory greater than this angle will correspond to a superluminal trajectory. The x-axis represents space and all points in spacetime at the instant t=0 , the y-axis represents time and therefore represents the passage of time at the point s=0 . According to special relativity, when two reference systems move relative to each other, relativistic transformations occur (time dilation and space compression). Let us consider a reference system t' that moves at a certain speed v with respect to at, an object in this reference system will travel a greater distance s in the same time t, this is represented as follows:

The object in the reference system t' travels more space in time T, therefore the axis is represented forming an angle with respect to at such that for the same time T the vector t' is greater than the vector t

We calculate the x' axis by bisecting the line c, which represents a ray of light:

The greater the relative velocity v, the more the axes close around the 45º angle. Let's focus our attention on the x' axis: this indicates all the points in spacetime at the instant t'=0. The first line parallel to x' indicates all the points at the instant t'=1, the second at the instant t'=2 and so on, that is, the lines parallel to x' indicate the "slices" of space at a given instant in the reference frame t´-x´. Due to relativistic time dilation (represented by the inclined axes) for an observer at t, time at t' flows more slowly, this means that events located along the lines t' will happen at the same time in the reference frame t'-x' but will occur at different times in the reference frame t:

Next, we'll consider the following situation: a space station located on Alpha Centauri communicating with Earth. We'll analyze this situation in three different cases:

Station at rest - light communication

In this representation, photon 1 must meet two conditions: it must be emitted into the future in the Earth's reference system, that is, above the x-axis and move at an angle of 45° corresponding to a light trajectory. Photon 1 is received at the station at time t'=0, which corresponds to time t=1 on Earth. Photon 2 is sent back to Earth at that instant, fulfilling the same conditions as photon 1, and is received by Earth-based astronomers at time t=2.

Station with relativistic speed v-light communication

In this case, the axes of the space station's reference frame are rotated due to their relativistic motion relative to the Earth at rest. Photon 1 emitted from the Earth's reference frame meets the same conditions as in the previous case; however, due to time dilation, seen from Earth (considered at rest), time at the time station flows more slowly. Therefore, the instant t'=0 at which the station receives photon 1 corresponds to a shorter time t=0 measured from Earth (the instant t=0 in the drawing is shorter than in the previous case without time dilation). Photon 2 must meet the same requirements described and be emitted above the x' axis and at an angle of 45º.

The key point is the following: whenever the relative velocity between the Earth and the space station is less than or equal to ac the angle Ø will be positive and the x' axis marking the instant t'=0 will intersect the t axis at positive values . As we will see in the next section, this is the explanation of why for sublight velocities there are no problems of causality.

Station with relativistic velocity v-superluminal communication

This is when we come face to face with a truly strange phenomenon. If we allow velocities greater than c we can send tachyon 1 below the maximum allowed angle of 45º so that the station will receive it at time t'=0. The relativistic reference frame t'-x' is now below the 45º angle of the light cone . When receiving tachyon 1 the station emits tachyon 2 towards Earth; this tachyon must be emitted towards the future of the t'-x' reference frame (above the x' axis) and at an angle smaller than 45º (superluminal velocity). When tracing the trajectory of tachyon 2 we find something incredible: tachyon 2' cuts the t axis at negative values! This means that seen from the Earth's reference frame , tachyon 2 arrives before tachyon 1 is sent!

In fact, this strange phenomenon could be easily glimpsed just by looking at the position of the x' axis in the figure. This axis marks the instant t=0 in the reference system of the space station, and this instant coincides with a terrestrial time prior to the sending of tachyon 1! This implies the possibility of sending information to the past of the terrestrial reference system!

Sources: Lectures on Faster-than-Light Travel and Time Travel