An Odyssey in Space and Time

Hyatt Carter

In 1911, the French physicist Paul Langevin proposed the following thought experiment:

Imagine two people: a chronologer, or timekeeper on earth, and a space traveler who departs from earth on a space craft that zips away at just under the speed of light. The space craft travels for one year and then reverses direction and makes the one-year return journey to earth. At the end of this space odyssey, will the time, as experienced by the traveler and the chronologer, be the same? Far from it, says Langevin. Whereas the traveler in the space craft will have lived for only two years, two centuries will have elapsed on earth and the chronologer would be long dead. This follows from Einstein’s theory of relativity and the dilatation of time that occurs at velocities approaching the speed of light: 186,000 miles per second.

Another Frenchman, the philosopher Henri Bergson, contested this interpretation. A key idea in the theory of relativity is that there is no privileged frame of reference. Therefore, as the wily Bergson points out, it is as true to say that the earth is traveling away from the space craft as to say that the space craft is traveling away from the earth.

This allows the reverse interpretation: whereas the chronologer will have lived for only two years, two centuries will have elapsed on the space craft and the traveler would be long dead.

Which Frenchman got it right? Or . . . are they both wrong? Or both right? Or each partly wrong and partly right?

**The Perspective of Velocity**

According to the special theory of relativity, if there are two systems, **S** and **S'**, with **S'** in motion relative to **S**, then an observer in **S** will notice a dilation, a slowing down, of time in **S'**. As the velocity of **S'** approaches the speed of light, the dilation of time becomes increasingly dramatic.

The dilation of time is given by the following equation^{1}:

t' = t / √ [1−(v^{2}/c^{2})]

where **t'** is the time of system **S'** moving at the velocity **v** with respect to system **S** at the time **t**.

But, in the special theory, as Bergson correctly notes, there are no privileged frames of reference. This means that, while someone in **S** will observe a slowing down of time in **S'**, someone in **S'** will do just the same and observe a slowing down of time in **S**. There is a perfect reciprocity of appearances between the two systems.

Is this dilation of time real or apparent, a feature of reality itself or only an appearance?

It was first thought, by Lorentz and Fitzgerald, that the dilation of time was a true aspect of physical reality, and, furthermore, that this was the cause of the apparent constancy of the speed of light. But, as the special theory showed, it turned out to be exactly the other way around—it was the constancy of the speed of light that caused the apparent dilation of time.

Bergson invites us to consider an analogy, drawn, as it were, from the disciple of art:

Suppose that I am painting a picture, a landscape, wherein there are two human figures, John and James. John stands close to me, say, at arm’s length, but James, standing far off in the distance,^{2} is over two hundred yards away. I will paint John life size but, to give a sense of perspective, James will be painted much smaller.

If another painter is standing close to James, with John in the distance, his approach, and the proportions of the two human figures, will be just the opposite.

In both cases, the principle involved is the **perspective of distance**. Using this as an analogy, the dilation of time in the thought experiment can be understood as a result of perspective, but in this case, the **perspective of velocity**.

While Bergson’s insight about the reciprocity of appearances between two systems in the **special** theory is right on the mark, insight gives way to oversight and he misses the mark—this time completely—with his apparent assumption that the same reciprocity holds true in Einstein’s **general** theory.

The general theory covers the domain of gravitation and, since acceleration is equivalent to gravitation in its effects, the question is whether acceleration plays a part in the little space odyssey under discussion.

There is a massive acceleration when, at the end of the one-year journey out, the space craft slows down, stops, reverses direction, and accelerates—from zero velocity to just under the speed of light—and heads back to earth. And, with gravitation in play, the dilation of time is no longer mere **appearance**, a distortion due to the perspective of velocity, as it was in the special theory—under the influence of gravitation, it is now a **reality**. The passage of time itself is modified. The passage of time itself is modified in one system but not in the other—there is no reciprocity, no symmetry.

**The Relation of Contemporaneity**

But what does it mean to say that time is modified? Is there, then, no universal time?

What at first may seem a paradox is that two systems, although they have different times, are contemporary with each other. How can this be? Indeed, to take the space odyssey as an example, how can two years be contemporary with two centuries?

In classical physics, according to Newton’s understanding, time always flows at an even rate. To quote Sir Isaac:

“Absolute true and mathematical time, of itself and by its own nature, flows uniformly, without regard to anything external.”

But, in the understanding of the new physics, there is variety in temporal flow.

A look at how we consciously, and unconsciously, experience time can provide a helpful analogy. Imagine, if you will, the following scenario: Three men are in a room. One has recently taken amphetamine and the “speed” is beginning to kick in. The second is awake and enjoying normal metabolism. Number three nods in his chair, falls asleep, and REMs show the onset of a dream. A minute or so later, the dreamer awakes.

In a dream that lasts only a minute, the dreamer may experience an adventure that lasts for a considerably longer period of time. Someone on speed can zip through minutes in what seem seconds. And yet the time of falling asleep, and the time of awakening, for the dreamer, and the speedster, will coincide with the public time of the normal person. They share the **relation of contemporaneity**. In this case, the temporal span of the dream, one minute, was experienced by the three persons in three different rhythms. So, too, in the space odyssey—the traveler and the chronologer will experience, contemporaneously, the moment of departure and the moment of return.

What differs, in both cases, are the differing **rhythms** of time.

By way of sharper contrast, in our conscious life we humans seem to enjoy about 10-12 experiences per second, while electromagnetic entities have vibratory signatures of many trillion times per second. For them a minute must seem like a millennium. Atoms have a slower frequency, and so on up the scale.

Time is **becoming**, or what Whitehead called “the creative advance of nature,”^{3} and the matrix of creative advance is within the momentary pulsations, the moment-to-moment quantum becomings, of all the true individuals in nature—subatomic particles, atoms, molecules, living cells, animals, humans. The various individuals thus show great variety in their rhythmic adventures.

Quoting Paul Weiss:

“We must acknowledge that time is universal to account for the temporal co-presence of diverse beings and for the fact that the entities of a co-present world move into the future together, despite the diversity of their rates of change.”

To further clarify the relation of contemporaneity, let us turn once more to the space odyssey.

The two intervals of discordant time, that of the traveler and that of the chronologer, are relativistic aspects of one universal passage of nature. The duration, or temporal span, between departure and return, is not affected by relative motion or acceleration. What is affected is not time itself, but the units that measure time.

The traveler and chronologer were together at the moment of departure and they will be reunited at the moment of return.

In the universal passage of nature, a duration AB between two events, A and B, is not affected by the seeming paradoxes of relativity; but two systems coextensive with AB can experience different temporal intervals because of the relativistic variability of the units that measure time, and so it follows that, in spite of the different temporal intervals, the two systems will be contemporaneous one with the other, and also with AB.

Or, as Milic Capek puts it, the “topological **relation of contemporaneity** is thus the very essence of relativistic time-space. In this sense, relativistic time, though metrically not uniform, still remains topologically **one**. The relation of ‘being contemporary’ replaces the traditional relation of spatial simultaneous juxtaposition and thus becomes a clue to the new meaning of time and space in their synthesis into the unity of relativistic time-space.”

**Notes**

1. Notice that as the velocity, **v**, approaches **c**, the speed of light, the fraction v^{2}/c^{2} comes ever closer to 1 (one), thus making the expression under the square root sign (1 − v^{2}/c^{2}) approach 0 (zero). And, the smaller it gets, the greater the dilation of time.

Since only electromagnetic entities can enjoy the thrill of cruising along at the speed of light, **v** can never equal **c**, and so this equation cannot yield 0 (zero), which would imply a complete suspension of time—nor can it yield a negative value, which would imply a reversal of time. Time’s arrow flies ineluctably into the future with, to mix metaphors, no boomerangs into the past.

2. After the revolution in physics, in the early decades of the twentieth century, the concept of distance was no longer a matter of mere spatial relations. Space was reconceptualized as space-time or, to even better reflect the new emphasis, time-space. As Whitehead said, “spatial relations must now stretch across time.”

To say that the sun is 93 million miles from Earth tells only half the story; the whole story must state that the sun is eight light-minutes from Earth.

The inadequacy of the old concept became even more obvious with more distant objects, such as the Andromeda nebula, which is one million light-years away. A present moment on Earth, a **here-now**, does not correlate with a there-now in the Andromeda nebula, but with a **there-then**—a there-then one million years ago.

No one has the slightest clue as to what’s going on there now. For all we know, it might have disappeared in a supernova long ago. If it were to disappear today, it would be our ancestors one million years hence who would first learn about it. Provided, of course, that **humans** are still around.

3. The Buddhists say that time is “dependent origination,” or **pratitya samutpada**.

Coda

One final observation:

Capek insists throughout his 414-page book that although we may consciously acquiesce to the radical revelations of the new physics, on an unconscious level the old ideas of classical physics continue to exert influence, and we are still haunted not only by the ghost of Newton, but also Euclid and, going even further back, Democritus and Zeno.

If this be the case, the question then becomes, what can we do about this?

Following a suggestion by Gaston Bachelard, Capek proposes that a person might take up a “psychoanalysis of knowledge” to rid himself of these ghostly and antiquated notions.

Or, it could be called Hauntology: the study of those ghostly elements in our Newtonian unconscious that haunt our minds and imaginations and cause us to persist in mental and semantic inertia. When the wheels of thought run in deep ruts, it’s hard to get them going in new directions.

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Note: In this essay, I follow the analysis of Milic Capek as he presents it in his book: **The Philosophical Impact of Contemporary Physics**.

HyC