Much recent speculation about time in physics centres on the paradoxes
of Einstein's theories of relativity. Yet many of the interesting philosophical
issues about physical time are inherent in the whole notion of objective
time and are, I think, better discussed outside the context of relativity.
At least that's what I intend to do in the first half of this paper. I
will look first at the problems that arise from the process of objectively
measuring time, which some think amounts to treating time as space. This
leads some to think of the universe as a four-dimensional, static structure
in which two features that seem to be essential to time appear to get lost:
the flow of time, or the process of change, of becoming; and the unidirectional
nature of time in that it only goes towards the future. Then I will talk
about Newton's concept of absolute time as God's sensorium in preparation
for Einstein's attack on it in the name of humanized relativity. I will
finish by examining some of the implications of Einstein's theories for
our concepts of simultaneity, the speed of the flow of time, and the separation
of space from time.
I. THE QUANTIFICATION AND SPATIALIZATION OF PRE-SCIENTIFIC TIME
Time as we experience it has two outstanding features: it is unidirectional, and it is non-homogeneous. By unidirectional I mean that we move always from the past towards the future, that we can never return to the same moment twice, that is, the past is gone and the future still expected. Time does not look the same in both directions. By non-homogeneous, I refer to the different qualities that different times have for us; the slowness of boring lectures; the sense of suspension of time under the influence of some drugs; the rapidity with which time vanishes when with someone you love.
To compare two periods of time so qualitatively different we must pick out or abstract some common dimension, such as speed or the length of an interval. It is difficult, if not impossible to compare the length of two intervals of time even within my own experience. It is even harder to speak of equal intervals of time in the experience of two different people. Only by appealing to some external standard does the project make any sense. Presumably natural features, such as the night-day cycle, or the movements of the heavens, were the first intersubjective measures of time. They establish a common time which is objective and available to all. (Poincare says that to deal with objective time is to put ourselves in the place of God. p. 322.) Such measures were used in early astronomy, navigation, the schedule of monasteries and so on. They were supplemented by various kinds of clocks, especially after the 11th century.
Measuring sets up a mapping relationship between the quality of the phenomenon being measured and the range of rational numbers. The measures used for time pick out from the richness of our experience of time, a single feature or "dimension" to quantify. Descartes definition is clear: "All that I understand by dimension is the mode and aspect according to which something is considered to be measurable." (Rules #14: P.359) Descartes invented the notion of "Cartesian coordinates," that is, the idea of laying any rational measure along a spatial measure so as to produce a graph. By setting up spatial measures at right angles to each other, he was able to graph more than one "dimension" on the same graph. In principle, any quantified dimension can be graphed in this way. This does not imply that the original phenomenon being graphed is spatial; being graphable is simply a side-effect of quantification. For example, "Musical tones may be ordered by volume and pitch" (H. Reichenbach, The Philosophy of Space and Time, p. 111) and so they can be laid out in a two-dimensional graph form without implying that either volume or pitch are spatial, nor that notes are in some manner spatially two-dimensional.
Nevertheless, the quantification of time led inevitably to people imagining
it spatially, which leads us into paradoxes. Gassendi, for example, like
Heraclitus before him, speaks of "flowing" by analogy with a river. The
analogy raises an immediate problem, for flow presupposes speed of flow.
We can say, for instance, that the water in the river flows at a speed
of two kilometres per hour with respect to the bank as our standard of
rest, but what speed can we assign to the "flow" of time, and with respect
to what? What sense does it make to say that time flows at the rate of
1 minutes every 60 seconds? The river could have been flowing at four kph;
could time have been flowing at 2 minutes every 60 seconds? The difficulty
seems to stem not just from the river analogy, but from the spatialization
of time as such. Yet once we quantify time, the spatial analogy seems hard
II. THE FOUR-DIMENSIONAL "STATIC" UNIVERSE
We can represent any quantity graphically as a length or distance from some original point. Thus (10) may be used to represent the number of students in this class, but so may a vertical bar 10 cm high. Sometimes we need to know two dimensions of something, such as the number of students at MUN in a certain year (15000, 1990). Alternatively, we could place a dot on a graph with population and year axes. Again, (48, 53, 160000) might represent the latitude, longitude and population of St. John's, which we might draw as a vertical line upwards from the position of St. John's on a two dimensional map. The five dimensions (65, 170, 10, 48, 1941) might represent the weight, height, number of fingers, age and date of birth of someone. It is hard to imagine how we could graph this since our imagination won't take us past three graphic dimensions, although something might be done with colours.
In physics, it is useful to record four coordinates for any object,
three spatial ones and a temporal one. Thus
(48, 53, 0, 1990) might represent me in St. John's at sea-level in 1990. Physics, whether Newtonian or Einsteinian, represents any event as such a four-dimensional set of quantities. The notion of a four-dimensional universe should in principle boggle the imagination no more (nor less) than does the five-dimensional example above; we are dealing simply with a convenient mathematical model or mode of representation. The long history of our spatialization of time, however, has led many to try to "imagine" the four dimensions as if they were four spatial dimensions and the attempt to mentally contemplate the universe as four-dimensional in that sense has tied many a mind in a mystical knot. Meditation on the five-dimensional example above may act as an antidote.
In particular, many have speculated about a four-dimensional "static" universe. Edington, for example, says "events do not happen; they are just there and we come across them." (Capek, p.355.) Spatial dimensions are already laid out for us and we can imagine someone travelling along one of these dimensions. In so far as we think of time as one more spatialized dimension, we can imagine a person "travelling" along the time line (at 60 seconds per minute?) and arriving at a future that is already laid out in advance. According to this conception, "the future is already there," we have just to reach it! (Frank, Capek p. 387.)
Many have claimed that this is nonsense. It makes no more sense than thinking of time as a river that travels along (in time?). From the viewpoint of a pure physicist (God?) sitting around outside the universe looking in, (53, 48, 0, 1995) is already as much a point on the graph as (53, 48, 0, 1990). There can be no movement whatsoever. It is true that the being (me) that is around in 1995 is different than the one in 1990 in a number of ways. It has less hair, for example. More significantly, it's brain cells now have more memories than the me in 1990. As a result, the me in 1995 can remember the me in 1990 and so thinks of the 1990 me as "in the past," as "already having been lived," while the me in 1990 has no such memory of the me in 1995. Hence the biological illusion (subjective time) that I have lived the past and am about to face the future. From the "realistic" viewpoint of the physicist, of course, such change, such temporal living is pure maya, ultimate illusion. From the standpoint of thought, of science, of truth, time is not change or movement, it is just a quantity laid out spatially on an unimaginable graph of the cosmos.
Against such mystics, Reichenbach claims that the quantification of time and its representation as a "dimension" is no more a spatialization of time than is the dimensional representation of musical pitch or volume.
III. THE DIRECTION OF TIME
Easily said! Yet one change in conception is hard to avoid. Time as we experience it is unidirectional. As soon as we quantify time, however, we have the problem that any mathematical quantity can in principle either increase or decrease. That is, mathematical dimensions are "isotropic" by which I mean they are the same in both directions. Quantitative dimensions, especially when graphed, are governed by what Russell called the "axiom of free mobility:" we can in principle move either way along them. (Meyerson, in Capek p. 356.) Mathematized time, therefore, automatically abstracts from one of the most essential features of time; it fails to capture the unidirectional nature of experienced time. In so far as we conceive or imagine time as a spatial dimension, we can dream about the possibility of moving along the time axis either way. Many science fiction stories about time travel rely on our ability to treat the time dimension as if it were a spatial one.
Does this mean that from the viewpoint of physics time is actually blind to direction and it is only our accumulation of memories (as explained above) that produces the subjective illusion of unidirectionality? If the planets moved backwards they would obey the same laws. If the impact of two billiard balls is replayed in reverse no laws of mechanics are violated. Meyerson, however, argues that these are exceptions and that nature is not generally reversible.
The trouble is that in all the equations of mechanics the variable +t
can be replaced by -t and all the laws of mechanics remain valid and unchanged.
We must look outside classical mechanics to thermodynamics for a possible
solution: the law of entropy offers the possibility of finding a direction
to physical time. The law of entropy says, basically, that as time goes
on, disorder increases, a point already hinted at in the quotation from
Meyerson above. Some philosophers, such as Gruenbaum, have used this law
to claim that time, even in physics, is not isotropic, but has an intrinsic
directionality to it. Presumably it is the effects of the law of entropy
on our brain processes that produces the subjective impression of time
flowing in one direction only.
IV. ABSOLUTE NEWTONIAN TIME
For Newton, time is a pure, a one dimensional quantity to be measured by clocks and other physical systems. Such measures, however, always fall short of the ideal, for any human measuring system is to some extent irregular. He therefore distinguishes between time in itself, and time as it is measured by us.
At this stage there are three concepts of time to juggle: subjective, non-homogeneous time; relative (physical) time that human physicists measure by natural mechanisms; and absolute (physical) time, measurable only by God.
The ironies of calling on a timeless, spaceless God to overcome the
irregularities of natural mechanisms and human subjects should not be missed.
This is solution is perhaps analogous to calling in a deaf person to judge
on the merits of a piece of music, on the grounds that they will not be
distracted by the sounds. In any case, by the 20th century the appeal to
God as the final standard of measurement in physics fell out of fashion
and scientists came to rely on purely human colleagues and instruments.
V. RELATIVISTIC EINSTEINIAN TIME
It was Einstein who excluded God from the Cosmic Association of Physicists
and permitted membership only to humans. The distinction between absolute
and relative time then becomes impossible, since all time becomes a quantity
measured by a human observer. In reality, then, all time measurements are
relative to actual observers located at particular points in space and
time, having their own clocks and moving at specific velocities and accelerations.
This, more or less, is the Theory of Relativity. I will deal first with
the problem of simultaneity from this perspective, and then show the implications
of this discussion on the speed of time and then for Einstein's notion
of the union of space-time.
If time is a quantity, then it must be measurable. To measure an interval of time is to compare it with some other, standard interval (e.g., five seconds on a calibrated stopwatch). By compare, I mean ensure that both start at the same time and then observe whether they stop at the same time. So the nature of time as measurable is based on the notion of "at the same time" or "simultaneity."
As long as we only have one observer, that is, as long as the intervals to be compared are in the same place, it is easy for the unitary consciousness of the observer to judge the events as simultaneous. But what does it mean to say that two spatially separated events occur "at the same instant?" If there were a God whose substance spread over the universe so that she were present in all places, then simultaneity would be absolute for it would refer to the two events being present together in the unity of the one, non-dispersed, (divine) consciousness. As finite human beings we might be able to simulate this effect if two observers in different places had a system of communication which was instantaneous. Then, as soon as an event was observed by observer A, he could send a message at infinite speed to observer B who, observing another event in her vicinity at the same moment as receiving the message, could declare the two events to be "simultaneous.
Einstein however hypothesized that there is no communication system with infinite speed; the best we can do is rely on light, or other electro-magnetic radiation, whose fastest speed, in a vacuum, is around 300,000 Km per second. Accordingly observers A and B have to make allowance for the time lag in messages they send each other, and this is no easy task! Let's try an example.
Imagine I set out in a space craft to visit my friend on Mars and that, as I leave home, I send a radio message to her home to tell her I'm coming. Unfortunately, at "exactly the same moment," she decides to come and visit me, and sends me a message to my home as she leaves. The messages take, say, 15 minutes to arrive (alas, too late!). For practical purposes (that is, for us non-divine beings) the two spacecraft departures are "simultaneous" if neither of us get the other's message before we leave. However, there is a little leeway here. Even if I had left 14 minutes later, neither of us would still have got the message in time, that is, the departures would still be "simultaneous." The zone of "practical simultaneity" is around 15 minutes.
More technically, what we are defining is a zone of causal exclusion. Since no causal process can travel faster than light, the zone of simultaneity is the time span within which nothing at point A can be either the cause or the effect of an event at point B. (Cf. Poincare, in Capek, p. 323, and Robb, in Capek. pp. 369-386.)
There is no use saying that within that 15 minute window one moment is "really" simultaneous with my departure, but that we just cannot as human beings in practice determine which it is. That would be to say that there is a God's-eye view, which is exactly what Einstein is denying. From a human, relativistic point of view, the idea of an absolute simultaneity makes no sense; we must choose some instant within the zone at a distance place and define it to be simultaneous with the present instant here. As Robb puts it, "There is no identity of instants at different places at all. ... The present instant, properly speaking, does not extend beyond here." (Robb in Capek p. 380.) It follows that, as Reichenbach puts it, "The time-order of events separated by distance is arbitrary, within certain limits." (H. Reichenbach, From Copernicus to Einstein, p. 107.)
How can we resolve this arbitrariness and pick one instant within the zone as "simultaneous?" Well, imagine a UFO from a friendly neighbourhood galaxy, flying rapidly (very rapidly) over the solar system in the Earth-Mars direction. It will pick up the message I sent from Earth but somewhat later (say five minutes later) than I might expect, since my message will have had to chase it to catch up with it. On the other hand, the UFO will bump head-on into my friend's message from Mars and receive it earlier (five minutes) than expected. The UFO captain will therefore declare that my friend left Mars ten minutes after I left Earth. Of course, another UFO speeding in the opposite, Mars-Earth, direction would say that the event of my departure occurred ten minutes after my friend's. That is, we can arbitrarily resolve the indefiniteness of the simultaneity by accepting to define simultaneity relative to one or other of these observers.
And there is no use saying that we can rely on the "absolute" judgment of an observer who is "stopped" somewhere between Earth and Mars: that would be again to appeal to a God. The solar system, and our galaxy, are themselves moving relative to other galaxies. The notion of being "stopped" cannot be defined. Like simultaneity, all velocity, being based on the measurement of time, is relative in a Godless cosmos.
Hence the definition of which instants are simultaneous is relative to the velocity of the observer. The ramifications of this are far-reaching. It means that an event which occurs before another event for one observer may occur after it for another; The time-order of events is, within limits, not absolute, but dependent on the velocity of the observer. The arbitrariness of simultaneity means that the measure of any distant interval of time is arbitrary, since the two end-points are indefinite. Intervals of time, however, are part of the definition of velocity, and velocity in turn is part of the definition of energy. Ultimately even mass, since its inertia is related to energy, must be seen as arbitrary, within limits.
The limits, of course, depend on the speed of light. If light travelled
slower, the limits would be wider; if light travelled faster, the limits
would be narrower. Indeed, in the extreme case if light were to travel
at infinite speed the arbitrariness would be reduced to zero and we would
revert to Newton's absolute, God-based time. Since light travels at so
high a velocity, for most the distances on Earth, and at everyday velocities,
these limits are very narrow so the world appears to us as it did to Newton
(and to God). Relativistic phenomena only become apparent at higher speeds
and over longer distances.
B. THE SPEED OF TIME
I want to look at the implications of one relativistic ramification. If the length of time intervals depends on the velocity of the observer, then a period of, say, one hour as I observe it on my own watch may be measured as two hours by someone travelling very fast away from me, and as only a half hour to some approaching me. In other words, the "flow of time" may be faster or slower depending on who is observing it. We might expect that if two observers A and B are receding from each other and A observed B's clock to be running slow, that B would therefore think that A's clock was going fast. Surprisingly, this is not the case; each will each observe the other's clock to be going too slow. If the velocity of recession were increased to close to the speed of light, both would see time in the other's neighbourhood coming almost to a halt. (Remember my own observation of myself has no particular, Divine privilege; I too am speeding along at some velocity.)
This leads us to what has been called the "twins paradox." (H. Reichenbach, From Copernicus to Einstein, p. 69. See also Capek, pp. 433-455.) At the age of 25 one of the twins leaves Earth in a fast (very fast!) spacecraft and when her sister is 75 she returns to Earth, but the traveller is now only 50 years old! The notion that twins might have different ages is very counter-intuitive, but does bring out the point that relativistic effects are not just tricks of our mode of representation, but real physical phenomena. While we haven't actually done this with twins, we have experimentally achieved the same effect by comparing two identical atomic clocks, one on the Earth and one in a fast moving orbit around the Earth; they do indeed age at different rates.
I should add that in the later General Theory of Relativity, which I
have not discussed, Einstein also proves that time "slows down" in the
presence of large gravitational masses, or under conditions of high acceleration.
(These two conditions are identical under General Relativity.) Just as
space gets warped by gravitation, so does time.
C. THE UNION OF SPACE-TIME
One final point. Though I haven't discussed it, the measurement of space is subject to the same relativity as the measurement of time, and for the same reasons. The length of a body as measured by a moving observer will be shorter than if it is measured by an observer at rest relative to the body being measured. What is constant for all observers is the space-time distance between two events, that is, the length of the line joining the two event-points in a four-dimensional graph (technically, the square root of x2 + y2 + z2 + t2 ). Observers at different velocities will attribute different components of this "distance" to the space coordinates and to the time coordinates. Somewhat loosely we can say taht what is measured as a space distance to one observer will be measured as a time difference to another. In the case I mentioned above when, at almost the speed of light, when time slows almost to s stop, the length of the observed spacecraft will reduce almost to zero. As Einstein puts it: