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8.02 One familiar process which appears to be irreversible is the radiation of energy. We see examples of radiation when waves spread out from a disturbance on the surface of a pond, when sound or light are generated by a loudspeaker or a lamp, or when waves are transmitted by a radio station. In each case, if we try to imagine the process taking place in reverse, the picture is so strange that we are convinced it could not occur. In his book Time's Arrow and Archimedes' Point (OUP, p.49), the philosopher Huw Price paints an attractive picture of an otter jumping into a still Scottish loch:

... we all know what happens, at least in one respect. Circular ripples spread outwards from the otter's point of entry, across the water's surface. It turns out that this familiar and appealing image illustrates another of the puzzling ways in which nature is asymmetric in time... The asymmetry turns on the fact that the ripples always spread outwards, rather than inwards. ... It makes no difference whether the otter is entering or leaving the water, of course!

8.03 Inward moving waves, if they ever occur, are often called advanced because they seem to exist before the disturbance which is responsible for them, to distinguish them from retarded waves, the more familiar type. Several scientists and philosophers have devoted much attention to considering these advanced waves, asking whether they could ever exist, and if not, why not. If such waves were ever to be observed, there would be two different ways of describing them. We could suppose that, like retarded waves, they are nevertheless still generated by the emitter, the lamp, the loudspeaker or the otter, but that they travel backwards in time; the emitter causes the radiation, as we expect, but the radiation exists before its cause. The alternative description pictures the emitter as the destination or absorber of the radiation; here we are faced with the problem that all the radiation must have been generated at a large number of separate points, for instance all the points around the edge of the loch inhabited by our otter, and the times of generation must have been finely co-ordinated to ensure that it all arrives at the emitter at exactly the right moment. Neither of these pictures appears reasonable, and the problem is equally acute when we consider radiation of light, radio waves or sound.

8.04 Why has so much thought been dedicated to this question? After all, is not radiation just one more from the wide range of phenomena which are uni-directional because of the Second Law of Thermodynamics? Is it not merely an example of the dissipation which results from the low entropy state of the universe today? We are not perplexed to the same extent by the irreversibity of falling stones and breaking eggs; these effects are not so mysterious that we find ourselves talking about the possibility of effects existing before their causes, or going backwards through time, as we must do in discussing advanced waves. Why do we single out this particular example of the asymmetry of nature?

8.05 Perhaps the explanation lies in the work of James Clerk Maxwell, to whom we owe the electromagnetic explanation of radiation, and who is, quite rightly, still held in admiration by many of today's physicists. May we quote from Huw Price's clear description:

Maxwell's theory of electromagnetism, developed in the mid-nineteenth century, is easily seen to admit two kinds of mathematical solutions for the equations describing radiation of energy in the electromagnetic field. One sort of radiation, called the retarded solution, seems to correspond to what we actually observe in nature, which is outgoing concentric waves. The other case, the so-called advanced solution, describes the temporal inverse phenomenon -- incoming concentric waves -- which never seem to be found in nature. Thus the puzzle of temporal asymmetry here takes a particularly sharp form. Maxwell's theory clearly permits both kinds of solution, but nature appears to choose only one. (ibid.)

You drive five miles to work each morning through heavy traffic. If you could travel 10 mph faster your journey would take five minutes less. How fast do you normally travel?

[For those who want to see the mathematics:
Suppose usual speed = v mph.
So usual time = 5/v hr. = 300/v mins.
Time at faster speed = 300/(v + 10) mins.
So 300/v = 300/(v + 10) + 5
Solving (v + 30)(v - 20) = 0
So v = +20 or v = -30 ]

8.06 And yet the problem of advanced radiation has indeed attracted a great deal of attention over the years, both theoretical and experimental. The best known attempt to show theoretically why we do not witness light sources radiating into the past was devised by Richard Feynman and John Wheeler in 1941. They considered the consequences of assuming that retarded and advanced waves are indeed generated by every source of electromagnetic radiation, so that a radio station, for example, sends half its power into the future and half into the past. They came to the surprising conclusion that all the advanced waves would disappear, and we would be left with what we had always believed, that the whole power of the transmitter is directed into the future. Paul Davies describes their reasoning well:

When the retarded waves from a particular point on Earth, having spread out across the universe, encounter matter, they will be absorbed. The process of absorption involves the disturbance of electric charges by the electromagnetic waves, and as a result secondary radiation is produced by these faraway charges. The radiation too is one-half retarded and one-half advanced, in accordance with the assumption of the theory. The advanced component of this secondary radiation travels backwards in time, and some of it reaches the source on Earth. Naturally, this secondary wave is but a pale echo of the original wave, but a myriad of such pale echoes from across the universe can add up to a substantial effect. Wheeler and Feynman proved that under some circumstances the advanced secondary radiation can serve to double the strength of the retarded primary wave, bringing it up to full strength, while also canceling out the advanced wave of the original source by destructive interference. At the end of the day, when all the waves and their echoes, backward and forward in time, are totted up, the net result is to mimic pure retarded radiation. (About Time, Viking, 1995.)

8.07 In 1972 Bruce Partridge attempted to detect these advanced rays by means of an ingenious experiment. He beamed a rapid succession of radio pulses into the sky on a clear night, and during the intervals between the pulses he directed this same radio signal into a nearby absorbing screen. The Wheeler-Feynman effect demands that all the radiation emitted by a source today is absorbed somewhere, and sometime in the future, by the material of the universe. It does not matter how far into the future this occurs, for the returning advanced rays are supposed to arrive back at the point of emission at exactly the same time as the primary wave is emitted, but it is crucial that all the radiated energy is eventually absorbed. Partridge reasoned that it was unlikely this absorption would be complete, whereas he knew that all the energy fed into his local absorber was in fact absorbed. This difference would manifest itself as a difference in the power which his transmitter was drawing from the radio frequency generator, and he measured this power with great accuracy to detect any variation. Despite many careful attempts, Partridge detected no trace of the effect he was seeking. It might be, of course, that the universe of the future is a perfect absorber, and that Wheeler and Feynman were right after all, but many people would regard the experiment as confirming that advanced effects do not exist.

8.08 Most of the writers who have considered this theory have regarded it with some suspicion. Huw Price's analysis must surely be the most thorough and tightly argued treatment. He gives us twenty-nine pages of detailed and complex logical argument, and comes to the conclusion that the Wheeler-Feynman reasoning is faulty, and that assuming radiation sources to radiate equally into the past and the future does not result in the advanced waves being suppressed and the retarded waves behaving in the familiar way we experience.

8.09 We can agree with Price's conclusion, but should be surprised that so much ink and effort has been expended on the matter, by him and others. Feynman and Wheeler's premise, that a source of radiation emits retarded and advanced waves equally, is completely time-symmetric, and nowhere in their reasoning do they interpose any facts that are not symmetric. But their conclusion, that the wave travelling into the future is doubled while that going into the past is neutralised, is asymmetric. Surely there is no way by which symmetric premises can generate an asymmetric conclusion; there must be a flaw in their argument, even if it is difficult putting a finger on the precise place where it breaks down.

8.10 In Price's book, he goes on to present a slightly modified version of the Wheeler-Feynman theory. Significantly this does introduce a new element, and this is time-asymmetric. Price sums up his view as follows:

What needs to be explained is why there are large coherent sources -- processes in which huge numbers of tiny transmitters all act in unison, in effect -- and why there are not large coherent absorbers or sinks, at least in our region of the universe. Of course by now we know that the former question is the more puzzling one, for it is the abundance of large sources rather than the lack of large sinks which is statistically improbable, and associated with the fact that the universe is very far from thermodynamic equilibrium. (ibid.)

In other words, the asymmetry of the radiation process is due to the existence of objects such as the sun, or electric lamps and radio transmitting stations, which in turn display the present low entropy of the universe, or by the fact that, like everything else of interest today, it is still constrained by the big bang boundary conditions. We cannot disagree with Price's conclusion, but he could have arrived there by a shorter route.

8.11 Viewing the transmission of light from the newer quantum viewpoint, it is difficult to see what the fuss is all about. Suppose a photographic flashgun emits a short burst of light, which from one viewpoint we must regard as a large number of photons travelling outwards at the speed of light, rather than the radiation of waves. Because each photon obeys laws which are time-symmetric, we are asked why they all travel outwards after the flashbulb is activated, and why there is not another burst travelling inwards before this event, to reach the flash unit just at the moment it is fired. Suppose that, instead of a flashgun we have a bomb which explodes, scattering fragments of metal in all directions. Now (ignoring air resistance) the motion of each fragment obeys the laws of elementary physics, and its motion is reversible; viewing in reverse a motion picture of one such fragment, it would be seen to behave quite reasonably. Must we explain why the fragments all move outwards, and why there is not also an inward rush of fragments before the explosion, to assemble the bomb just prior to its subsequent dispersal? Of course not! The bomb clearly provides an example of dissipation; before the explosion it contains a high concentration of low-entropy energy, which becomes widely dispersed after the explosion, an archetypical example of an irreversible process, and the photons radiated by the flashgun illustrate the same principle. The manufacture of such a bomb, or the charging of a flashgun, is not something nature could accomplish without a highly complicated process, which according to the picture we are advocating, links it right back to the low entropy of the big bang boundary conditions. There is no essential difference between the dispersal of the bomb fragments and of the flashgun's photons.

8.12 Other types of wave motion may be explained by different arguments, but all involve a process of dissipation, and a consequent gain in entropy, which rules out the reverse process. In the case of a stone (or an otter) disturbing the surface of a pond, it is not the material of the stone which is dissipated, as was the material of the bomb, but rather its motion. Initially the energy of the moving stone arose from its unstable position on the bank, but after it tumbles into the pond the motion is gradually dispersed, firstly as water waves on the surface, and then finally as heat when the waves are damped around the shore line. It appears that the temporal asymmetry of radiation is just one example of the Second Law of Thermodynamics at work.

8.13 However, we have considered only macroscopic examples, involving large numbers of particles. At the sub-atomic level all processes (with the unimportant exception of the decay of the neutral kaon) are reversible, and yet radiation continues to play a part in their description. We have not yet explained why such radiation also is irreversible. If we consider firstly a typical experiment in which we set up some apparatus to emit large numbers of photons, it is clear that in doing so we are producing a low entropy situation, a situation very unlikely to arise by chance, and we do not expect reversibility. The photons can be considered as particles, and their dispersion is a simple thermodynamic phenomenon. We can also describe their behaviour using probability amplitudes without paradox, for probabilities (and quantum theory's complex amplitudes) behave in exactly the same way as large ensembles of particles.

8.14 The emission of a single photon, however, does present us with a problem. Considered from the particle point of view the transference of a particle from one collision to the next is a simple reversible occurrence, but the wave function which describes it appears to radiate outwards as a spherical shell, in a manner which is clearly irreversible. We have only one particle, to which we cannot apply the argument of dissipation, or appeal to the Second Law. It is here, however, that the Nodal theory comes to the rescue, and removes the paradox. That component of the wave which relates to an expanding shell of radiation, to the travelling outwards from the first node, is purely subjective. It belongs to the CWF but not the NWF. The probabilities which this conventional wave encapsulates are based on our knowledge of the starting point and our ignorance of the destination of the particle, a distinction which has no counterpart anywhere other than in our own minds. The NWF, the wave that relays information from node to node, is reversible. We will analyse the form taken by the NWF in Chapter 11.

8.15 The motivation behind the search for advanced waves, a search dedicated to explaining the irreversibility of radiation phenomena, has been misguided. There are four different models we can use in discussing the radiation of light, four different pictures we can hold in the mind.

(i) The classical picture, as advocated by Maxwell, sees the radiation as the interplay of electric and magnetic fields in the space between the source and the destination of the light rays.
(ii) In the alternative quantum view, the Schrodinger wave function takes the place of an electromagnetic disturbance, but is found to propagate in the same way. At the point of reception we convert these into probabilities, which exactly replace the Maxwell intensities.
(iii) From the Planck viewpoint we must regard light as the emission and absorption of a stream of photons, a view which is forced upon us by the particle properties revealed in some of our experiments.
(iv) The Nodal picture concentrates on the photons, but claims that these are no more real than the waves; they make themselves known only at the nodes where they "collide" with particles of matter, but the information transferred from node to node by the NWF matches exactly what we can imagine is carried by the moving photons of (iii) above.

8.16 Most of the discussion about advanced waves has been conducted in terms of the first of these representations, the Maxwellian radiation, but could equally well have embraced also the Schrodinger wave equation. In both cases, another set of solutions is obtained if we replace t by -t, giving advanced waves which seem never to be observed in practice, but we have shown above that the search for advanced waves may well have been based on an improper interpretation of these solutions. If, instead, the third picture had been adopted in the argument, the outward flow of photons from radiating bodies, it seems doubtful that advanced waves would ever have been suggested, for the situation is so like that of an exploding bomb, or the flow of water from a leaking vessel. These phenomena are readily explained by the Second Law; we do not ask why they are never observed in reverse. All the other forms of radiation, such as water ripples and sound waves, are produced by co-ordinated macroscopic events, and their directionality also is explained as thermodynamic dispersion.

8.17 The Second Law and the Nodal theory between them teach us that the search for advanced radiation has been mistaken, and absolve us from having to continue the quest.

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