When the cosmic microwave background predicted by George Gamow was discovered in 1965, the steady-state theory was doomed, although Gold continued to pursue it for a few decades.

Many of Gold's other ideas were fruitful, however, including the idea that pulsars are rotating neutron stars, that the human ear has an active audio processing system, and that magnetic fields are important in solar flares and in the earth's "magnetosphere" (a term coined by Gold).

But one of his most important suggestions is of great importance to information philosophy, namely, that the expansion of the universe provides an "arrow of time" more basic than the one implied by the second law of thermodynamics and the resulting increase in entropy.

The ultimate heat sink is always the night sky and the cosmic microwave background

The thermodynamic approach would be to explain that free energy was required for the interference, and that free energy can only be generated from the heat sources in the world by means of heat engines working between a source and a sink. There may be a variety of sources, but the sink is always eventually the depth of space, although there may be a number of intermediate cold bodies.

It is this facility of the universe to soak up any amount of radiation that makes it different from any closed box, and it is just this that enables it to define the arrow of time in any system that is in contact with this sink. But why is it that the universe is a nonreflecting sink for radiation?...

The large scale motion of the universe thus appears to be responsible for time's arrow. A picture of the world lines of galaxies would clearly reveal the sense of time, namely, the sense in which the world lines are diverging. As we go to a smaller scale, this type of divergence is, for most purposes, quite negligible, and it is thus clearly not the local effects of the universal expansion law that make themselves felt. But it is the electromagnetic radiation that brings the effects of expansion down to a small scale. Radiation in the world is almost everywhere almost all the time violently expanding. This expansion of the radiation is, however, only made possible by the expansion of the material between which the radiation makes its way, that is, the expansion of the universe.

Gold proposed his idea in an article called "The Arrow of Time" that was presented at the 1958 Solvay conference on Physics, "The Structure and Evolution of the Universe," in Brussels. This has come to be known as the "cosmological arrow of time," in contrast to the "thermodynamic arrow" proposed by Arthur Stanley Eddington in 1927, and implicit in the work of Ludwig Boltzmann.

In 1963, Gold, and his lifelong colleague Hermann Bondi, organized an experts meeting at Cornell University on "The Nature of Time." The attendees included Richard Feynman, David Layzer, Roger Penrose, and John Wheeler, among others.

At first one might think that there is no real problem there. Why should not the time coordinate be equipped, as it were, with an arrow at each point which singles out for any process the positive time direction? Why should the world not be quite unsymmetrical with respect to past and future?

We have no doubt that the world is, in fact, unsymmetrical in this way. But it is a remarkable fact that the laws of physics, one by one as they have been discovered, have been found to be quite symmetrical with respect to the sense of time. Newton's laws of gravitation and dynamics single out no sense of the time coordinate. If somebody recorded the motion of the planets and reversed the record of the time coordinate, this would leave it an example of a dynamical system that is as much in accord with Newton's laws as the actual. The change from Newton's laws to Einstein's did not affect this symmetry.

The laws of electrodynamics, the Maxwell—Lorentz theory, similarly are quite symmetrical, and so are those of quantum theory. Could we argue that all this is accidental and that we will discover some other physical law which clearly specifies the sense of time and which is responsible for giving us our ideas on the subject? This, I think, is not a plausible explanation, since systems we understand in detail seem to show time's arrow. But yet there must be some influence that serves to determine the arrow of time.

Usually at this point in the argument statistical or thermodynamical ideas are presented and the case is made out that it is through the investigation of these fields that the elusive arrow is found. "The entropy of any isolated system will always increase and never decrease"; so, it is said, you must merely look at a system at two instants of time and determine at which the entropy is greater. That will then be the later instant.

As there is no doubt about the correctness of this, the argument is usually not pursued any further. We and everything around us are simply taken to be aware of the arrow of time by the operation of the statistical processes which, after all, we understand very clearly. Why should there be anything else to think about?

One has to pursue this reasoning a little further, though. Why does the arrow of time appear when we are dealing with the statistical superposition of effects, each of which is determined by laws which have no arrow? Surely the fact that we had to deal with the problem in statistical terms rather than compute in detail the behavior of all the constituent parts of our system, constituted merely a lack of precision; surely it is not by rejecting information about our system that we can make it reveal to us the sense of time which it would otherwise not show. So let us see whether we can find the arrow without the statistics.

To see whether the system that we examine does or does not reveal the arrow of time, let us suppose that we are given a number of snapshots of it only, and we are asked whether we can be sure to sort them into the correct temporal sequence. We are told that the system was interfered with before the first and after the last of the snapshots, but was left quite undisturbed in the intervening period. Now if, for example, the system were a box full of gas and we found on our snapshots that one contained all the gas in one half of the box, another one showed 70% in that half of the box and 30% in the other half, and a third showed just 50% in each half of the box, then we should surely order the snapshots in that way. We would say that somehow the gas must have been put into that half of the box where it was found, and the first snapshot must have been taken very shortly, after it was put there, because we know that when left to itself it will quickly expand through the rest of the box and fill it uniformly. Whatever the way the box is interfered with after the last snapshot was taken does not enter into our considerations; but the interference the system received before the first is of importance in deciding the arrow of time. Of course, this argument is not absolutely certain; we might have ordered the snapshots the wrong way round, for the gas might have been uniformly distributed in the box to start with, but all the motions of its molecules might have been so contrived that by the operation of the ordinary laws that apply to the collision of molecules they will all have migrated at one time into half the box. But this, we think, is highly improbable. We can thus take on a bet and offer very high odds that we will be able to order the snapshots in the right sequence, but we cannot actually prove it. If we did a similar experiment with fewer particles, the same would apply, but we could offer only lower odds. Essentially, looking at a system of many particles is not very different from having many systems of a few particles on the same snapshots. There we would order the snapshots according to the appearance of one of the systems on the successive pictures, and we would then decide that our probability of being right increased when we saw each one of the other systems agreed with the sequence we had decided on. The certainty about the sense of the arrow of time then arises just from having many checks, and for this reason complicated systems reveal the effect most clearly; but this does not explain why each of our simple systems displayed an arrow at all.

The interference from outside clearly had something to do with it. If we take any system and isolate it from external influence completely and for a very long time and then take a series of snapshots, there will no longer be any way of deciding on the sequence from a subsequent examination of the pictures. We might still be able to recognize clearly the operation of fundamental physical laws in the changes that had taken place from one snapshot to the next. If all the snapshots were taken in sufficiently rapid sequence, we might be able to arrange them in order l to n, but we would not know whether it was l or n that was taken first. The physical laws that determine the motions that we can see all being time-symmetrical, there might be plenty of clues to demonstrate the laws and to find the neighbors in the sequence to any picture, but no clue at all about the arrow of time.

When the system was not isolated, there was, as usual, no doubt about the sense of tune. After it became isolated, the arrow of time evidently persisted for a while, not definable with certainty, but only with a probability that decreased from a high value initially to zero. The time scale of this decrease of probability depended upon the details of the system.

It is this rule that isolated systems initially, after their isolations, retain and then gradually lose the arrow of time that makes its appearance in the statistical and thermodynamical definitions. "Entropy of an isolated system always increases", is a way of saying that after the system was isolated, it still showed changes from which the sense of time could be deduced. In some systems the effect is best described in thermodynamic terms, and entropy is then the relevant quantity. But in other systems other statistical descriptions may be more convenient. It is inconsequential from this point of view whether the system is deterministic or not; that case can be argued equally well with a number of billiard balls assumed to behave accurately according to Newton's laws of motion, as with a system of photons and atoms in a box where we do not know of any way of specifying the laws of motion except through probabilities.

Some simple mechanical systems seem to give a more clear-cut answer than others, but on closer examination are really not different in principle.

So we can be confident that the same rule applies to all systems: interference from without enables them to show time's arrow, and that apply, and all those are then strictly time-symmetrical. On whatever scale we choose our system, we have to go to a larger scale to understand how it contrived to know the arrow of time.

Up to what scale, can we pursue this argument? On which scale do we find a law whose operation in fact serves to determine time's arrow for all the smaller scales? Let us take, for example, a star, and suppose we could put it inside an insulating box. It would still be true, then, that when the star has been in the box for long enough (which in this case will perhaps be rather long), time's arrow will have vanished. There is no reason to expect anything to be different in principle from the laboratory scale. But now if we were to open for a moment a small window in our box, then what would happen? Time's arrow would again be defined inside the box for some time, until the statistical equilibrium had been reestablished. But what had happened when we opened the hole? Some radiation had, no doubt, escaped from the box and the amount of radiation that found its way into the box from the outside was incomparably smaller. Some influence from outside had got in — though the only physical effect was that photons from inside got out.

The escape of radiation away from the system is, in fact, characteristic of the type of "influence" which is exerted from outside. Any outside influence to a system that gives it time's arrow can be traced to be associated with that process.

It is this facility of the universe to soak up any amount of radiation that makes it different from any closed box, and it is just this that enables it to define the arrow of time in any system that is in contact with this sink. But why is it that the universe is a nonreflecting sink for radiation? Different explanations are offered for this in the various cosmological theories and in some schemes, indeed, this would only be a temporary property. In the steady state universe it is entirely attributed to the state of expansion. The red shift operates to diminish the contribution to the radiation field of distant matter; even though the density does not diminish at great distances, the sky is dark because in most directions the material on a line of sight is receding very fast, and its radiation, therefore, shifted very far to the red.

The large scale motion of the universe thus appears to be responsible for time's arrow. A picture of the world lines of galaxies would clearly reveal the sense of time, namely, the sense in which the world lines are diverging. As we go to a smaller scale, this type of divergence is, for most purposes, quite negligible, and it is thus clearly not the local effects of the universal expansion law that make themselves felt. But it is the electromagnetic radiation that brings the effects of expansion down to a small scale. Radiation in the world is almost everywhere almost all the time violently expanding. This expansion of the radiation is, however, only made possible by the expansion of the material between which the radiation makes its way, that is, the expansion of the universe.

If we examine the pattern of world lines of systems that are open to the universe there will be much branching apart and much less convergence when looked at in the sense in which we think of time. As an example, the average hydrogen atom in the universe will suffer a conversion to helium in a time of the order of 10¹¹ years at the present rate. This corresponds to an emission into the universe of some 10⁶ photons in the visible spectrum. This photon expansion going on around most material is the most striking type of asymmetry, and it appears to give rise to all other time asymmetries that are in evidence.

The motion of the universe is thus most intimately connected with all processes down to the smallest scale. A more profound understanding of physics than we now have might, in fact, allow one to deduce the expansion of the universe from an observation of the small scale effects only.

We see the universe expanding and not contracting. Does this mean that of the two possible senses of motion, nature chose one? Surely not. This would be the case if the laws of physics were not time-symmetrical: then an expanding universe would be a system that is distinguishable from a contracting one. The laws could describe two types, and ours would be one of them. In such a case the laws of physics would be capable of defining more schemes of the world than we have to look at. The laws would be too wide to fit the case, and we would suppose this due to some misunderstanding we have made. But just this is avoided by the time-symmetry of the laws. In a universe where no arrow of time exists except that defined by the motion, there is only a single possibility. We would need an independent clock to say whether the universe is expanding or contracting, and we have none. All the clocks we do have are themselves run by the motion.

It follows that if all the laws of physics are time-symmetrical, they would not be able to describe a contracting universe. If, naively, we think that, after all, we might have seen blue shifts in the spectra of distant galaxies instead of the red shifts, we must be making an error in pursuing the detailed consequences of the motions of the galaxies. If, in calculating radiation effects, we took the particular solution (of the intrinsically time-symmetrical electrodynamic theory) given by the retarded potentials, then of course there would appear the second possibility. But that is rather like supposing that an independent clock exists and that the laws are not time-symmetrical. Wheeler and Feynman [2], and Hogarth [3] have considered the question of a time-symmetrical electromagnetic theory and the way in which the choice of retarded potentials appears appropriate depending upon the cosmological boundary conditions.

There is nothing new in the idea that the physical laws are more symmetrical than the universe to which they apply. For example, the principle of Galilean relativity states that the physical laws are the same in all inertial systems. But, on the other hand, one particular such frame can be singled out through the observation of the universe, namely, that particular frame where the observer would see the expansion of the universe occur symmetrically around him. A cosmological observation, therefore, specifies one out of an infinite set of frames that would all be equivalent from all other points of view. With the arrow of time, it is not really dissimilar. A cosmological observation, such as, for example, opening a window in a box and letting some radiation escape, is the means of distinguishing between the two otherwise quite equivalent senses of time.

At this point one should think, perhaps, why it is that we are subjectively so sure that time "really goes" in one sense and not the other. With symmetrical physical laws we can, after all, construct the present equally well from a sufficient knowledge of the future as from such a knowledge of the past. Why, then, do we give the past a status quite different from that given to the future? We do not generally think of predicting the past, of constructing it from the present and the knowledge of the physical laws, yet that is what we do with respect to the future. We think of some evidence about the past as entirely definite, and we think it a rule that the future can not be known with certainty. Why is this so in a system operating with time-symmetrical laws? Why do we believe in the cause and effect relationship between events when, after all, there is no strictly logical way with time-symmetrical laws of specifying which is the cause and which the effect? Today's position and momenta of the planets are the cause of their position and momenta tomorrow. But this could equally well be stated the other way around - that tomorrow's configuration causes today's. In more complicated systems, as we have seen, there is a general overwhelming tendency for branching of world lines in the forward direction of time. If a lot of information is lacking for precise prediction, as for example all the photons out in space that have escaped, then the configuration of the system at one instant will serve to define much better its configuration in the sense in which its world lines are generally converging than in the sense in which they are generally diverging. The past will be better known than the future. It is difficult to reconcile oneself to this explanation that the asymmetry between past and future which seems so profound to us should be no more than an asymmetry connected with the probability of "predicting" correctly into the two senses of time. The qualitative difference arises from a statistical quantitative one. But, of course, one must appreciate that we are systems of a high order of complexity, and that the statistics are concerned, therefore, with a very large number of possible states. In such systems there may be, in effect, complete certainty attached to the consequences of the laws of chance. And these consequences appear, then, as the laws of physics.

The symmetry of the laws with regard to the time axis is then just what was required to prevent them from being too wide, from being able to describe more than just our universe. What is the situation with respect to other symmetries of physical laws?

Symmetry with respect to the sign of the electric charge and with respect to mirror reflection was thought until recently to be separately obeyed by all the laws of physics. Now the discovery of the non-conservation of parity in weak interactions implies that the laws are not invariant to a mirror reflection alone. A certain "handedness" is shown to be resident in elementary particles. Since a right-handed screw becomes a left-handed screw when viewed in the mirror, such a particle will be transformed into something different by reflection. But this does not force us to believe that nature is not mirror-symmetrical, for there may be complete symmetry between matter and anti-matter. For every right-handed particle of matter there may be a left-handed one of antimatter having all the same properties, but possessing the opposite sign of electric charge or magnetic dipole moment. The symmetry may be complete, but only for the combined operation of mirror reflection and a change in the sign of the charge. I suppose that most physicists now would regard this as the most likely situation. If symmetry is preserved only with respect to the combined operation, then this could really be understood best if charge had a geometrical representation, possessing a "handedness".

Should we now think that the universe is in actual construction, symmetrical between matter and anti-matter? Or have we here another case of a symmetry in the laws not represented by symmetry of construction?

It is, of course, possible that amongst the various galaxies there are as many made of matter as of anti-matter. Not enough meeting ground exists between them for the annihilation process to be plainly demonstrable. From observation we can not yet tell. If, in fact, all galaxies were constructed from one type of matter only and anti-matter appeared everywhere, as it does here, only as a rare freak, would this, then, imply that the laws of physics are too wide? One might think that, after all, if our type of matter is the right-handed sort, the same laws of physics would have allowed the construction of a universe entirely similar to ours except made of matter of the left-handed type. Two universes would be specified by the laws and only one of them arbitrarily selected as ours.

But, do these laws really specify two different universes? The difference between a right-handed system and a left-handed system can be defined only when they can be compared. There is no absolute definition of either. If two systems cannot be compared, either directly or via some intermediary systems, then there is no way of defining whether they are of the same or the opposite handedness. But this is just the situation with respect to the two universes that would seem to be defined. If they are different universes, they cannot be brought together to be compared, and unless they can be so compared, there is no sense to be attached to the statement that they are of different handedness. The two universes, if they cannot be compared, are thus identical. We have then, again, the situation that a precise symmetry in the physical laws, namely that between matter and antimatter, is just what is required to assure that only one type of universe is specified. If any law of physics had not been accurately time-symmetrical, then an expanding and a contracting universe would be different possibilities.

If the symmetry between matter and anti-matter were not complete, then two different universes, one composed of matter and one composed of anti-matter, would be possibilities. These symmetries are, then, in each case, just what is required to allow the laws Of physics to describe as the only possibility the type of universe we have.

REFERENCES

[1] A. Grünbaum, Das Zeitproblem, Archiv für Philosophie 7, 165 (1957).
[2] J. A. Wheeler and R. P. Feynman, Rev. Mod. Phys. 21, 425 (1949).
[3] J. Hogarth, Advanced and Retarded Potentials in an Expanding Universe (unpublished thesis).