During the 1970's, he published several articles on thermodynamics, cosmology, and the origin of irreversibility, including

"The Crisis about the Origin of Irreversibility and Time Anisotropy," Science, 7 April 1972, Volume 176, Number 4030

"Cosmological origin of irreversibility, time, and time anisotropies. I," Foundations of Physics 6.4 (1976): 407-426.

"The new astrophysical school of thermodynamics." Space Science Reviews, 22.2 (1978): 119-151.

In 1981 Gal-Or published a book, Cosmology, Physics, and Philosophy, a wide-ranging course curriculum that covered topics from classical and quantum physics of small systems out to questions of cosmology, then back to Earth again for philosophical questions.

Gal-Or was especially interested in "arrows of time," what Arthur Stanley Eddington had first called Time's Arrow, which Eddington attributed to the increase in entropy over time demanded by the second law of thermodynamics.

In his 1981 book Gal-Or said that irreversibility can not be deduced from quantum mechanics, that "quantum-mechanical tactics...fall into the trap of assuming that which they set out to prove. One cannot get uncertainty for certainty, nor indeterminism from determinism." (Our explanation of the origin of irreversibility in fact starts with Einstein's 1916 discovery of indeterminism when light quanta interact with the discrete quantum energy levels of atoms.)

Gal-Or wrote...

Over the last decades there have been remarkable developments in thermodynamics and quantum mechanics. Yet many of the basic problems have remained largely unsolved. In the spectrum of opinions expressed by authors who have attempted to solve these problems, one can roughly distinguish three main schools of thought:

1) Traditional axiomatic thermodynamics with some refined modifications, which however, cannot explain the origin of irreversibility and time asymmetries.

2) The statistical school, which generates “man-made irreversibility’’ or “manmade statistical evolution” by imposing asymmetric conditions on symmetric equations (or concepts) in order to describe the observed behavior of (relatively small) local systems (see below).

3) The new gravitational school, which deduces the origin of evolution, irreversibility and electromagnetic and thermodynamic time asymmetries from gravitation and the large-scale (nonequilibrium) dynamics of gravitationally-induced processes. The latter, in turm, are intimately related to the non-static properties of the (time-symmetrical) field equations of the gravitational field. This school includes some new modifications to the physics of time and is part and parcel of gravitism (Introduction).

Because the basic ideas of the first school are by far better covered in the textbooks, and because of the limited length of these lectures, the latter are concerned mainly with the last two schools of thought. We therefore turn now to examine the problems associated with the second school and, in particular, with false ideas that are traditionally associated with the concepts of “statistical evolution’’, “statistical asymmetry’’, etc.

My object in this connection would be to show that, to obtain a consistent mathematical formulation of entropy growth, irreversibility, evolution, and asymmetry in probabilistic theories, one needs ‘to break ’ the symmetric properties of the statistical-probabilistic equations. So far physicists have done this by means of (a priori) imposing on these equations an (often hidden postulate of) asymmetry (which, in itself, is equivalent to the very results that the mathematical analysis is aimed “to prove”). In other words, the (asymmetric) “results” (of classical and quantum-statistical physics) are not really results for they are deliberately enforced on, not deduced from the (symmetric) formalism (§V. 5).

Such quantum-mechanical tactics are, as I shall explain, unacceptable. Moreover, they lead to a highly misleading philosophy of science, which, in turn, has generated a ludicrously jncongruous mode of thinking in education and in general philosophy (see below). Their advocates all fall into the trap of assuming that which they set out to prove. One cannot get uncertainty for certainty, nor indeterminism from determinism (see below).* These conclusions lead to somewhat surprising results, which, in turn, are related to the very core of our physical theories and to the role of time, causality, and determinism in philosophy.

My viewpoint, as expressed in these lectures, stems from my long-time search for an explanation of time asymmetries, evolution, irreversibility and thermodynamics within the various frameworks of quantum mechanics; a search which has systematically disclosed that quantum mechanics is not a universal theory, but rather should be viewed as a practical “tool" in characterizing phenomena on a limited physical scale—a “tool” that must be incorporated into a more universal framework.

In spite of their importance in physics and philosophy alike, the fundamental problems of quantum mechanics have rarely, if ever, been evaluated from the combined points of view of the theories of time asymmetries, thermodynamics, evolution, structure, relativity, cosmology and philosophy. The present study is designed to fill this gap.

Contrary to this viewpoint, most physicists (and non-physicists) possess today an unshakable belief in the ability of quantum mechanics to explain and deduce the origin of thermodynamics, evolution, structure, and time asymmetries from its formalism. This belief stems, perhaps, from the fact that most scientists are today so thoroughly conditioned to the artificial imposition of the quantum-statistical postulates, that they hardly pause to consider their divertive consequences. With the present aversion to physico-philosophical inquiry in physics, an attempt to displace the resulting semi-sacrosanct myth calls for more than a proof of the fallacy involved: for more than the authority of Einstein; perhaps eVen for more than the full impact of a body of new empirical data in a wide spectrum of interconnected fields of study; it calls for an entirely new approach to the methodology of academe (Volume II).

Cosmology, Physics, and Philosophy, Springer-Verlag, 1981, pp.281-282

Cosmology, Information, and the Second Law

Another approach to cosmology, information, and the second law of thermodynamics has been described by Layzer(19). He discusses two paradoxical aspects with interesting implications. Assuming that the initial state of the universe was very simple (and hence required a very small quantity of information for its specification) and noting that the present state of the universe is exceedingly complex (hence requires a large quantity of information for its specification), he points out the contraction with the second law of thermodynamics, which requires, among other things, that the information contained in a macroscopic description of an isolated physical system never increase.

Relatedly, Layzer discusses the evolution in time of a universe whose mean spatial curvature is positive. Here the assumption that the initial state is one of thermodynamic equilibrium at zero temperature makes sense only if the universe returns to this state at the end of each cycle of expansion and contraction. But the identity of the initial and final states seems to contradict the fact that in the course of the expansion an irreversible generation of entropy (loss of information) must occur.

According to Layzer(19), information can always flow from the macroscopic to the microscopic degrees of freedom. Broadly speaking, this necessary condition for the law of increasing entropy to be valid is that the entropy associated with the microscopic degrees of freedom of a system should initially have its maximal possible value (that is, initial microscopic information should be absent). This is considered as an objective property of the universe. Thus, the arrow of time is transferred from the universe as a whole to the astronomical systems that separate out in the course of the expansion. Every newly formed system, no matter how complex its structure may be, is devoid of microscopic information. The justification for applying the second law of thermodynamics to the universe as a whole, according to Layzer, is the additivity of entropy (that is, if the law applies locally, it must also apply globally). The question is, then, whether entropy remains an additive quantity over large volumes of space. Up to a point, the amount of information required to describe the content of a given volume of space undoubtedly increases in direct proportion to the volume. In principle, however, the content of a volume whose dimensions greatly exceed the scale of local irregularities is largely predictable. Thus, the accuracy of predictions generally increases with volume. Since only a finite quantity of information is required to specify the entire universe, the entropy per unit volume approaches zero as the volume increases indefinitely. Consequently, the very concept of additive entropy fails. As to the origin of the electromagnetic arrow, Layzer(19) believes,contrary to Narlikar(20), that it is determined by the thermodynamic arrow of time.

"The Crisis about the Origin of Irreversibility and Time Anisotropy," Science, 7 April 1972, Volume 176, Number 4030, p.15