The fallacy of the invisible cat

Isaac Newton

In Chapter 1 of his book Astrology, science or belief? published in 1992, Manuel Toharia writes:

However wise they can be about certain subject matters, there is always some element that contradicts the myth of the perfect genius. For example, it is well-known that Newton was an angry man, terribly unfriendly and probably a repressed homosexual. Lest there be any misunderstanding, we must add immediately that what we find wrong with this alleged homosexuality of the English genius is its repression, which certainly made him a bitter person, no doubt with a minimal dose of self-esteem.

Probably a repressed homosexual? And how can we know this, if it is true that Newton repressed it? Or did Toharia (or whoever was his original source) have inside information, or perhaps he came to this conclusion because he knows that Newton suffered at least two psychic crises in his life, and believes that their cause must have been his repressed homosexuality? Observe the use of the qualifiers certainly and no doubt. If so, his argument would be a textbook example of the fallacy of the invisible cat:

Computing the date of Easter

Raphael - Resurrection of Christ

The first Ecumenical Council was held in Nicaea, Asia Minor, in 325, convened by Emperor Constantine. Ecumenical councils could not be held before that date, for Christians were persecuted and had to meet in secret. This first Council had very important consequences: Aryanism, which denied the divinity of Christ, was condemned; the version of the creed still recited in mass today was defined; and the Council established the algorithm to calculate the date of Easter, which is still in use. This algorithm is so complicated that Donald Knuth included a program to perform it in his famous and classic computer encyclopedia, The Art of Computer Programming.

Easter was fixed on the first Sunday after the first full moon after the spring equinox, which that year fell in March 21st. To calculate the exact date one must take into account that the solar cycle (the year) contains 365.2421988 days, while the lunar cycle (the phases of the moon) lasts 29.530588 days, two numbers with many figures that do not have a simple relationship with one another, so the calculation is quite complex.

Can time travel paradoxes be avoided?

Cover of Fantastic SciFi with a
Porges story (The Shadowsmith)

In a science fiction story written in 1962 by Arthur Porges, entitled The rescuer, the inventors of a time machine discover that a man has entered the machine to travel back in time. To stop him, they destroy the machine with the man inside. When they are tried for murder and destruction of valuable property, they explain:

This man had taken with him a repeating rifle and five thousand rounds of ammunition. His intention was to arrive at Golgotha in time to rescue Jesus Christ from the Roman soldiers. In short, to prevent the crucifixion. And with a modern rifle, who can say he wouldn’t succeed? And then what?... What of the effect on the future, the entire stream of history, secular as well as religious?

The story is an excellent example of the paradox of predestination mentioned in a previous article, with several more that make us doubt the possibility of time travel. But is there no way to avoid the paradoxes? Is it possible to devise a theory that would remove them making time travel feasible, at least in principle? There have been several attempts to achieve this.

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).

Will time travel be possible?

Hibernation in 2001, a Space Odyssey

The obvious answer to this question, such as it is formulated, is yes, of course it’s possible! We all travel in time at the rate of 24 hours a day.

Naturally, this is not what comes to mind when this question is asked. What is usually meant is this: will we be able someday to make sudden jumps in time, either forward (to the future) or backward (to the past)?

There are several schemes for traveling to the future. If they aren’t possible just now, one day they could become so. For example, perhaps human beings will be frozen and remain in suspended animation, to wake up and resume their ordinary lives a hundred years later. Or they could take passage on a spacecraft, make a trip at relativistic speed, and return to their starting point a century later, whilst for the travelers the elapsed time would have been just one year. In both cases, from the point of view of the persons in question, this would have been a trip forward in time, but in reality no sudden leap would have happened, for time would have kept going on for the hibernated body, though the mind would not be aware, and also for the relativistic traveler, although in this case time would have been accelerated.

But when we speak of time travel, we do not refer to these cases, which are possible in principle. We mean disappearing from the present and appearing in the past or in the future. Will we be able to do this someday?