What does physics tell us about time travel?

In the previous article we considered a few paradoxes that could bring us to doubt the possibility of time travel. But what does physics say about this? Is there any theory that would make time travel possible? Is it true, as some say, that Einstein’s special theory of relativity implies that it will be possible to travel in time?

First of all, we must refute a fairly widespread misconception. We often hear people saying something like this:

If it were possible to travel at speeds greater than the speed of light, we would travel backwards in time, because the passage of time would become negative.

Is this true? Consider the equation that defines the relationship between proper time and external time for a body moving with a uniform rectilinear speed, according to the special theory of relativity:

Where t is the time experienced by travelers who move at speed v; t₀ is the equivalent external time (the time experienced by an object at rest); and c is the speed of light. 

We can see that, for v < c, the term inside the square root is positive and less than 1, its root would also be less than 1, and therefore t < t₀ (the time experienced by the travelers is shortened).

Time A or Time B?

J.M.E. McTaggart, who in 1908 coined
the terms "A and B-theories of time."

Human beings seem to have an innate tendency to think that what we do not like or cannot explain does not exist. Thus in Hinduism and Buddhism, reality itself is considered an illusion (maya), something that must be discarded to achieve liberation. According to this philosophy, since it is an inseparable part of physical reality, time should also be considered as an illusion. In the Hindu Brahman and the Buddhist Nirvana, time does not exist.

In Western philosophy and science, the idea of ​​time has traditionally been quite different. Until the eighteenth century, nobody put in question the reality of reality. As an inseparable part of reality, time was absolute. In Newtonian mechanics, time plays that role. According to his theory of gravitation, the course of time is independent of the motion of the observer. Hence one can deduce the principle of relativity of classical mechanics: when several bodies are subjected to uniform rectilinear motion (at constant speed) it is impossible to distinguish which one is at rest and which is moving.

Einstein’s mistake

When Einstein formulated in 1915 his theory of general relativity, he soon applied it to the entire universe, deriving the following cosmological equation:

It is curious that this equation is identical to the equation that would result from Newton’s theory of gravitation. There is only one difference: constant k represents, in Newton’s case, the total energy of the universe; in Einstein’s case, its curvature.

Each term of this equation contains a universal constant. Besides k, G is the gravitational constant; L is called the cosmological constant, whose interpretation is not clear. Einstein initially thought he could eliminate this term by making L = 0, which simplifies the equation and makes it analytically solvable. Then he discovered that the solution, in that case, was a universe in constant expansion. Since he believed that the universe had to be stationary, he decided to assign the constant a critical value L = L_c, to make it be so.

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: