This article was inspired by Karl Popper's 1965 lecture Beyond the search for invariants. It complements another article by me, inspired by Thomas Kuhn's 1959 lecture The essential tension. In my previous article I argued that Kuhn's sociological analysis of the tension between `normal' and `revolutionary' science actually reflects a philosophical tension between two rival modes of analysis of physical processes. Now I see that these two rival modes have been explored extensively in Popper's lecture, where he traces them back to the beginnings of Western philosophy. Crudely speaking, Popper describes the tension between the unchanging `block universe' of Parmenides and the constantly changing universe of Heraclitus. However, Popper considers that this crude description does not do justice to the very rich Parmenidean picture. Indeed, for him, Parmenides was the first to pose, in modern terms, what we understand as the Problem of Change in physics, and he tries to relate the Parmenidean `solution' to this problem to the more recent attempts of Boltzmann, Einstein and Schrodinger. Popper's lecture raises many fascinating questions. In the area of Classical Philosophy, one may question whether the atomism of Democritus and Lucretius, and thence Boltzmann, came from Parmenides or from Heraclitus. In Philosophy of Science, one may, following Popper's own line of investigation, ask whether thermodynamic irreversibility can possibly be explained in Boltzmann's atomistic, and Parmenidean, world.
Popper states the Problem of Change as follows
All change is change of something. There must be a thing that changes; and that thing must remain, while it changes, identical with itself. But if, we must ask, it remains identical, how can it ever change?.
The question seems to reduce to absurdity the idea that any particular thing can change.
A green leaf changes when it becomes brown; but not if we replace it with a brown leaf; it is essential for change that the changing leaf remains the same during change. But it is also essential that it becomes something else: `it was green, and it becomes brown; it was moist, and it becomes dry; it was hot, and it becomes cold.'
In the universe of Parmenides there is no change. He achieves change only by making what Popper calls a Parmenidean Apology (PA), which actually destroys the whole Parmenidean programme. Just as Parmenides refuted the programme of Heraclitus, so, says Popper, some element of the Heraclitean programme must be deployed in order to repair this breakdown. The classical atomists, Democritus and Lucretius, are often classified as followers of Heraclitus, but Popper classifies the programme of their modern successor, Ludwig Boltzmann, as Parmenidean. He locates the point at which Boltzmann makes the PA, and proposes, instead of Boltzmann's inadequate solution, a different solution of his own. I shall try to show that Popper's solution is a good one, and that, sufficiently developed, it may solve the even more intractable problems associated with the physics of our century, namely those described by Popper in his book The Quantum Schism.
Boltzmann considered a mechanical system consisting of a box of volume 2V divided, for times t less than 0, into two equal volumes by a partition. In the left-hand box there are N identical atoms (I shall refer to "atoms" throughout, even though, in modern terminology, it would be more correct to say "molecules". The Greek atomists, of course, knew nothing of this distinction, and, even nowadays, it still customary to describe Boltzmann as an atomist, rather than a moleculist.) whose total energy is UL, and in the right-hand box there are N identical atoms, of the same species as in the left-hand box, whose total energy is UR which is less than UL. Now suppose that, at t=0, the partition is removed, and that, at some later time t1, it is replaced. Then thermodynamics, which Popper classifies as a non-Parmenidean discipline, says that the new value of UL, that is UL(t1), is less than UL(0), and that it is greater than [UL(0)+UR(0)]/2. Of course this also means that UR(t1) lies between UR(0) and [UL(0)+UR(0)]/2; there is a tendency towards the equipartition of energy. We may, in analogy with Popper's leaf, say that the `green' state [UL(0),UR(0)] changes into the `brown' state [UL(t1),UR(t1)].
Boltzmann tried to explain this thermodynamic process by assuming, at t=0, a certain (Maxwellian) distribution of speeds and directions among the atoms on both sides of the partition. He was then able, after making what he considered the very plausible and reasonable additional Hypothesis of Molecular Chaos (or Stosszahlansatz), to explain the above tendency to equipartition of energy.
This was a revolutionary claim by the young Boltzmann - he made it in 1871, at the age of 27. It seemed to derive, from an atomistic, therefore determinist and Parmenidean, model of the gas, an evolutionary and irreversible property which has been observed for real gases. Surely, such a mode of explanation may now be used to explain how green leaves turn brown? But his analysis was soon challenged, first by his Vienna colleague Josef Loschmidt, and later by Max Planck and Henri Poincare, all of whom were in broad agreement with Boltzmann's atomism. This crisis was, of course exploited by Boltzmann's philosophical opponents, notably Ernst Mach, and there seems little doubt that the subsequent psychological stress contributed to his tragic death in 1906.
Essentially the Loschmidt refutation of Boltzmann's argument is that we may, at the moment t=t1/2, imagine that some mischievous demon intervenes in the process and reverses the directions of motion of every one of all the 2N atoms. In that case the whole gas retraces, in reverse, between t=t1/2 and t=t1, the evolution which had occurred between t=0 and t=t1/2, thereby recovering, at t=t1, the state at t=0. On Boltzmann's definition of the entropy, we may say that it increases from t=0 to t=t1/2, in accordance with the observed thermodynamic behaviour, but decreases from t=t1/2 to t=t1. At this stage Boltzmann introduced his Stossszahlansatz, in an attempt to argue that the state produced by the demon's intervention was enormously less probable than any of the 'naturally occurring' states, but all of his efforts were unsuccessful. To make matters worse, Ernst Zermelo, with the encouragement of Max Planck, showed that, even without the intervention of a demon, a Boltzmann gas must return arbitrarily closely to its initial state within a certain (rather large) time period.
The whole programme was fully analysed, a few years after Boltzmann's death, by the Ehrenfests, who had collaborated closely with him during his latter years. As Popper puts it, Boltzmann's Stosszahlansatz is an example of a PA; it is not only incompatible with his atomistic model; it effectively destroys that model; like any other purely Parmenidean system, Boltzmann's gas cannot undergo change!
The problem about Boltzmann's gas is that it has a finite, albeit large, number of degrees of freedom - 12N for a gas of 2N molecules - and, as a related property, its total energy is constant. The atoms of a real gas lose energy whenever they collide, either with each other or with the walls of the container. Thus there is a dissipation process. This is compensated by a corresponding fluctuation, which arises because, in addition to the 12N atomic degrees of freedom, there are an infinite number of degrees of freedom, associated with the force fields involved in the collisions. It is a general Law of Nature that these two types of process are a complementary pair, and their joint effect is that, in a real gas as opposed to a Boltzmann gas, individual atoms have only a very short memory of their initial state. This means that neither the Loschmidt nor the Zermelo mechanisms apply in a real gas. The origin of the entropy increase lies in this fluctuation-dissipation mechanism, and not, as Boltzmann supposed, in any Law of Large Numbers arising from the largeness of N.
But, we may ask, what is the origin of the fluctation-dissipation mechanism? The point is that atoms are not billiard balls, but are made of positive and negative electric charges, which radiate away energy in the form of electromagnetic radiation whenever the atom undergoes a change of its overall velocity. As Popper remarks in his lecture, it is a property of radiation that it always propagates as an outgoing spherical wave, and never as an ingoing wave. This enables us to distinguish between a moving picture of a real physical phenomenon (the outward wave), and the pseudophenomenon which we see if the cinefilm is reversed. We may now distinguish, with equal confidence, between a cinefilm of 2N atoms, showing a sharing out of an initially uneven energy distribution, and the same film run backwards. For a more detailed discussion of the latter process see Refs.[9,10,11,12].
In summary we may say that the Atomists, from Democritus to Boltzmann, tried to explain Change by the movement of atoms. As Popper says, this was a noble endeavour which ultimately failed. However, this purely atomist programme may be repaired by recognizing, alongside of the finite degrees of freedom of the atoms, the infinite degrees of freedom of the force fields. This means recognizing that the motion of the atoms is inelastic. The agent of irreversible change in Nature is, just as Popper supposes, the outgoing nature of the radiation fields.
The fluctuations of the electromagnetic field, referred to in the previous section, are always present, even at the absolute zero of temperature, and must be taken into account whenever any object containing electric charges undergoes acceleration. This is something which profoundly affects the whole question of Quantum Indeterminacy, for example the Heisenberg Principle; since there are fluctuating fields, the chaotic motion of subatomic particles no longer has to be, as Niels Bohr claimed, unanalysable. In 1927, when Einstein and others made the first objections to the new quantum mechanics, the zeropoint fluctuations (ZPF) had not been discovered; they became established as a real phenomenon only in the late 1940s, with the discovery of the Lamb shift and of the Casimir effect.
What has been really difficult to understand is the unwillingness of the scientific community to take account of the ZPF, but now Popper's lecture gives us some help with this problem also. As I indicated in my earlier article, it is more of a sociological than a scientific one, but now Popper shows that it is also philosophical, and furthermore of great antiquity. Popper classifies Quantum Mechanics (QM) as Parmenidean, but in contrast to Boltzmann's atomism, which is determinist and based on a realist metaphysics, QM is indeterminist and based on an idealist metaphysics. Popper, following on his criticism of Boltzmann, classifies himself as indeterminist and realist. Indeed, to avoid any misunderstanding he said, in a lecture of 1983, that he was, in common with Boltzmann, a metaphysical realist. But QM and Boltzmann share one most important feature; they are both Parmenidean programmes, that is they are closed systems with finite degrees of freedom. When they fail to describe change, they try to escape by making a Parmenidean apology, but, says Popper, this is equivalent to conceding failure. The trouble is that, having themselves failed, they do not wish their Heraclitean rivals to succeed. Instead, like that other great failed philosopher and clever mathematician, Pythagoras, they go to great lengths to hide their failure from the "ignorant" public.
QM, as opposed to Quantum Field Theory, describes static systems; as Schrodinger remarked, nothing ever happens in QM, because, in a unitary time-evolution of the state function, the only quantities which change are the phases of the various stationary states. Thus QM exhibits its Parmenidean nature. It requires the intervention of an observer, through the mechanism known as "collapse of the state function", to produce a transition, and Popper has identified this collapse mechanism as an example of a Parmenidean apology (PA). Not surprisingly, given the long history of the PA, stretching from Parmenides to Boltzmann, a substantial group of physicists now find this description unconvincing.
The crisis of confidence in QM has deepened since the discovery by John Bell, in 1964, that the collapse mechanism requires us to believe that a measurement in one part of space can result in an instantaneous change of the system in a distant part of space. Systems in QM are said to be "entangled", a new buzzword which could have been applied to all Parmenidean systems from the very birth of western philosophy 2500 years ago! Like lemmings, intent on not merely self-destruction, but also the destruction of their own science, various Parmenidean Young Turks have been claiming, ever since 1964, to have found experimental evidence for entanglement[17,18,19,20], but every time their logic, their experimental practice, or their analysis of data has been shown to be faulty.
For a detailed indictment of this, unfortunately widespread, bad science, I refer to my Internet page. Here I want to dwell on some more positive aspects of the Bell programme, which I believe could lead to a resolution of the Quantum Schism. As I indicated above, the problem with QM lies in the M rather than the Q. Like Popper, I label myself as indeterminist, and I take the Q of QM to be shorthand for the underlying stochasticity produced by zeropoint fields. Thus it seems to me quite possible that Quantum Field Theory (QFT), which does not have the Parmenidean features of QM, will, properly developed, be found not to exhibit nonlocal entanglement.
In this area I claim that my school (which we call Stochastic Electrodynamics) has made some real scientific progress. On the one hand we have been able to establish close parallels between the formalism of Quantum Electrodynamics (a branch of QFT) and Stochastic Electrodynamics (SED). On the other hand we have been able to show that all of the Young Turks' experiments, referred to in the previous paragraph, may be explained by normal, that is local, electrodynamics once the role of the zeropoint field has been recognized. Thus, by introducing the infinite number of degrees of freedom present in the field, SED can rescue QM from its stasis, in more or less the same manner as it has already rescued the Boltzmann gas. For details I again refer to my Internet page, and to the extensive bibliography quoted there.
It is, I think, crucial to recognize the materiality or "thinginess" of the electromagnetic field. As Popper says in his lecture, Parmenides was the first to distinguish between things and processes. But, with respect to light, Popper makes a misclassification, in saying it is a process rather than a thing. Commenting on the "entanglement" experiments in 1979, Bernard d'Espagnat said
The doctrine that the world is made of objects independent of human consciousness is in contradiction with quantum mechanics, and with the results of recent experiments.
As far as QM goes, d'Espagnat was correct; in the static Parmenidean world of QM, no change occurs except through the intervention of a (human) observer. But the objects, or things, on whose capricious behaviour d'Espagnat was commenting were the mythical atoms of light which he, in common with a large uncritical community of theoretical physicists, calls photons. In the analysis of SED, photons have always been a doubtful concept, and this is a view which Willis Lamb, the discoverer of the Lamb shift and of the laser, shares. It turns out that all of the phenomena, such as the photoelectric effect and Compton scattering, which have been held up as evidence for the quantization (that is, atomization) of the light field, have a much simpler explanation once we recognize the reality of the ZPF. The electromagnetic field, including this noisy ZPF substratum, is a real physical object with an infinite number of degrees of freedom. When this field interacts with any distribution of electric charge - an electron, an atom or a nonlinear crystal, for example - waves of different frequencies are coupled together, that is scattering occurs, with the outgoing frequencies different from the ingoing.
The materiality of the electromagnetic field was already established well over 100 years ago, by scientists like Maxwell, Hertz, Heaviside and Lorentz. In the course of establishing its materiality, a distinction was made between light and heat; in particular the Wave Theory of Heat, which had a lot of support during the first half of the 19th century, was superseded by the Kinetic Theory championed by Boltzmann. This established that heat is not a thing, but rather a process among atoms, which, of course, are things. Light, by contrast, is a thing. Precisely because it is a thing, it requires no medium to facilitate its transmission; this means that light waves are fundamentally different from sound waves. Now the SED school is claiming that full recognition of light's materiality will resolve Popper's Quantum Schism, and thereby recover for science a large body of knowledge which has fallen temporarily into the hands of a magical priesthood.