TIME TRAVELING IS IMPOSSIBLE

by MILTON KALETSKY

We present herewith the most scientific, logical, and thoro treatment ever made on the much-debated question of the possibilities of time traveling. Milton Kaletsky, who takes the negative side, is a college graduate with A's in his physics and higher mathematics majors. While we personally believe Mr. Kaletsky's arguments definitely settle the question of time traveling, we will be interested in hearing from any of our readers who may have different ideas on the subject.

I

Occasionally there appears a story in which the characters travel to the past or to future times in a non-material form. In such cases, the author assumes that they can only watch events occur and that they are incapable of participating therein because of the absence of their physical selves. That this mode of time traveling is absurd should be immediately apparent: if it is admitted that the characters can not participate in whatever occurs because they are physically absent, how could they hear with immaterial ears and see with non-existent eyes, inasmuch as hearing and seeing depend on the physical presence of the respective sensory organs?

II

Probably the best method of proving the impossibility of traveling in time is by use of Logic, the science of correct thinking, the science of the rules of proper reasoning. Scientific theory comes and goes and is but theory; even scientific laws are occasionally altered. Logic however, is universal, every rational mind on earth reasoning similarly. In logic there are no theories, only facts, and this science is the closest approach to a truth of nature that exists.

The discussion of time traveling must be preceded by an exposition of the logical idea of contradictories. Contradictories are two statements such that if either is true, the other must be false; and if either is false, the other must be true.

An example of contradictories is: a) a thing exists, and b) that thing does not exist. Obviously, if it is true that if a thing exists, it must be false that it does not exist. And if it is false that a certain thing exists, it must be true that it does not exist.

What is to be remembered is that it is impossible, in the strictest sense of the word, for two contradictory statements to be true simultaneously. Thus, it is impossible for the thing in the above example to exist and not exist at the same time.

Applying this principle to the problem of time traveling, let us assume that construction of the time machine was begun on January 1, 1935, and completed on July 1, 1935. Should the time traveler return to any date in 1934, this situation is produced: a) the time machine exists in 1934, and, b) the time machine does not exist in 1934 (as construction was not begun until 1935). Such a situation is logically absurd. The time machine cannot both exist and not exist at the same time. Time travelling into the past inevitably leads to the simultaneous existence of these contradictory conditions. But the latter is an impossibility. Hence, leading as it does to logical absurdity, to an impossibility, time travelling into the past is also impossible.

As for traveling into the future, suppose the traveler to journey at some rate such as one year per hour, i.e., he travels for one hour earth-time and finds himself one year in the future. Specifically, he starts his voyage at 9:00 a.m. and at 10:00 a.m. on the clocks he has taken with him he terminates his motion thru time, finding himself then on Earth one year later. How much time has actually passed? 1 year? 1 hour?

The problem resolves itself into this: how much older the entire universe became while he was time traveling. If he traveled one year in one hour, then only one hour elapsed on earth, yet he finds himself on earth one year later. In other words, he caused every living thing on earth, the solar system, the galaxy, the entire universe, to age by one year, tho but one hour passed.

This is sheer nonsense. A year cannot elapse in one hour for the simple reason that an hour is defined as less than a year. A fraction and the whole cannot be equal; a year and an hour cannot elapse in the same interval of time because they are different intervals of time, by definition. (Had the traveling in time required no time at all, or only a minute fraction of a second, the paradoxical situation is only aggravated). Time traveling into the future would produce the simultaneous existence of contradictory conditions in this equality of time intervals defined as unequal. Hence leading as it does to logical absurdity, to an impossibility, time traveling into the future is impossible.

III

One of the cardinal principles of inductive logic, the science of original thinking, by following the rules of which most present scientific knowledge was arrived at, is that for a hypothesis or theory to be accepted, there must be positive evidence for it. The absence of evidence against a hypothesis is not sufficient to justify assumption of its validity. For example, there is no evidence against the assumption that somewhere in the universe there is a solid chunk of radium a million miles thick. Logic, however, forbids the acceptance of this hypothesis because of the lack of evidence for it.

Similarly with the hypothesis of the possibility of time traveling. We do not know what "time" is; we do not know whether that which we describe as the passage of time has any real objective existence; the idea of traveling in time was merely the invention of an author with a fine imagination; and no one has even the vaguest idea how this feat can be accomplished. Indeed there is some indication that time traveling has never been and never will be realized! For if at any time in the past a successful time machine was developed, it is reasonable to assume that sooner or later the inventor thereof or other persons would have traveled sufficiently far into what was to them the future to have arrived within recorded history. Similarly, should a time machine be built at any future time, it is equally reasonable to assume that eventually someone would return into what would be the past to him and would thus arrive within historical times. But there is no legend, no myth, no recorded event which can be safely interpreted as an account of a visit of people from either the past or the future. This is a good indication, but only an indication, that time traveling was never realized in the past and will never be realized in the future.

Summarizing, there is absolutely no evidence substantiating the hypothesis of the possibility of time traveling. Logic requires that this hypothesis be rejected at once, even without taking into account the powerful arguments against it.

IV

The belief that time traveling ought to be possible because time is a dimension is based on the fallacious notion that time is a dimension like those of three-dimensional space. This is not so. Time is not a geometrical extension, but a 4th independent variable in addition to the three independent space variables: right-left, backward-forward, up-down. Those who have studied the calculus will recall the problems in which the position of a body was expressed as a function of the time, that is, in those problems time was a variable. Yet the body was not supposed to be time-traveling nor moving along any fourth dimension. When time is spoken of as a dimension, the term is used in its sense of a measurable property. In modern mathematics, time is, as stated above, merely another independent variable.

V

If the voice of authority carries any weight, we may point out that Sir James Jeans discusses the possibility of time travel on page 109 of his "New Backgrounds of Science," concluding that this mode of travel is impossible.

VI

For those familiar with the calculus of functions, this proof that time traveling is impossible is given:

dx | dt is the rate of change of x with respect to t, where x is any quantity, and t is the time. If dx | dt=one, the change in x is one unit per unit change in t. If dx | dt=2, the change in x is two units per unit change in t. Etc. dx | dt may have any real or imaginary value, except when x happens to be time. Then dt | dt is the rate of change of t with respect to t, where again t is time. Were a time traveler to travel at some rate such as two seconds per second, or one year per hour, as in the discussion in part II, then the rate of change of t with respect to itself would be 2, in the first case, or 8766 (no. of hours in a year) in the second case. But recall that the derivative of a variable with respect to itself is one and cannot be anything other than one. Hence dt | dt can equal nothing but 1, and if dt | dt=one, the change in time is one unit per change in time, which is not time traveling but merely ordinary existence, ordinary passage of time. That is, time traveling would require the derivative, dt | dt, to have impossible values, impossible because of the inherent nature of our universe. Hence, because it would require the existence of an impossibility, time traveling is also impossible.

Q. E. D.

Author's Note: Readers will see that the foregoing arguments, based on logic and mathematics, and not on any abstractions nor on hypothetical "methods" of time traveling, cannot therefore be refuted by anything other than logic and mathematics. All arguments based on ad hoc axioms are by their very nature inadequate to refute the above discussion. Anyone familiar with logic and mathematics who wishes to continue this discussion is invited to write the author, care of FANTASY.
Data entry by Judy Bemis