The Future of Physics?
My name is Mendel Sachs. My subject is theoretical physics. I have recently become aware of this excellent means of communicating ideas to my fellow physicists. I would like to ask your indulgence in some of my thoughts about physics today.
I have discovered during my professional career that in order to increase our comprehension of the material world, it is necessary to ask significant questions and then try to answer them, as completely and rigorously as possible –no matter how hard this may seem to be at the outset. A "significant question" to me is one whose answer could possibly increase our understanding. Of course, there is no guarantee at the outset that the question would turn out to be significant in the final analysis. On the other hand, it is often clear when a question (that a great deal of attention may be given to) is not significant! Let me start out, then, with some questions that I believe are significant, and then try to answer them, in my view.
What do we presently believe are the most fundamental assertions of the laws of nature? My answer is: The bases of the quantum theory and the theory of relativity. I am not referring here to mathematical expressions of these theories; I refer to the basic concepts that underlie these expressions. If you do not agree with this answer, or those to the questions below, please respond with your own views.
Are the quantum and relativity theories compatible with each other, in terms of their respective fundamental assertions? My answer is: No! A close examination of the irreducible premises of each of these theories reveals that they are indeed incompatible. A long treatise, or possibly a Ph.D. thesis in the Philosophy of Physics, could be written on this subject. I have discussed it in my book, Einstein Versus Bohr (Open Court Publ. Co., 1988), but there is much more to say on this subject than I have said in my book.
Briefly, examples of these incompatibilities from the point of view of logical structure are the following, for 'quantum theory' versus 'relativity theory':
- A) Principle of complementarity, implying 'pluralism', versus principle of relativity, implying 'monism'.
- B) Atomism, elementarity and seperability of particles of matter and a model in terms of an 'open system', versus the continuous field concept and a model in terms of a 'closed system' at the outset, i.e. the basic inseparability of material components from a system of matter.
- C) In our approach to what it is that we truly 'know', we have the conflict of logical positivism versus realism–the former asserting that all we can possibly know is what we can verify directly in measurements; the latter asserting that there is a real world, independent of whatever we do to find out about it, and that indeed we may learn things about the world that are not directly verifiable in measurements, though they are inferable from the logical structure of our theories, if they also predict correct empirical facts.
- D) Irreducible subjectivity in the role of measuring apparatus as a fundamental ingredient in our understanding of matter versus full objectivity, in which the 'subject' and the 'object' of an interacting system are truly interchangeable without losing the objective truth of the entire closed system.
- E) Indeterminism (all variables of matter are not 'predetermined') versus determinism (all variables of matter are predetermined).
- F) Linear mathematics versus nonlinear mathematics.
- G) A fundamental role in the laws of nature of probabilities and their calculus, versus the role of probabilities only as a tool for the observer, but playing no fundamental role in the laws of nature.
- H) Special reference frame of the measuring apparatus versus no special frame of reference for any component of a closed system, whether or not one of these components is a large macroobserver and another a small bit of micromatter.
3) Has there been any real success in unifying the quantum theory and the theory of relativity, since the discovery of quantum mechanics in the 1920s? My answer is: There has been no substantial success in this direction, essentially because of the fundamental incompatibilities, discussed above. To fully unify these two theories is like trying to forece a square peg into a round hole! In my view.
4) Is it then possible to re-express the quantum theory with the relativity requirements fully removed? My answer is: No! This is because the basic elements of the quantum theory, according to the underpinnings of the Copenhagen school, are the unbreakable triads of the measurement process: emitter-signal-absorber. The problem is the following: While the emitter and absorber components of this unbreakable triad have a nonrelativistic limit in their description , i.e. one can always find a reference frame that is at rest with respect to to them, from which we describe them mathematically, the signal component does not have such a limit. This is well known in the case of electrodynamic interaction, where the signal is a photon. But even in other types of interaction, such as the nuclear interaction, one must still be able to describe the signal (the pions, etc.) relativistically because of their fundamental high energy interaction with other matter. It then follows that the 'emitter-signal-absorber' units of measurement, according to the quantum theory itself, must necessarily be described fully in terms of the quantum theory subject to the symmetry requirements of relativity theory. When the case of special relativity is evoked (it should also be subject to the rules of general relativity, in principle) we have quantum electrodynamics, when the interaction is electromagnetic. Generally the theory is called 'Relativistic Quantum Field Theory' (RQFT) for any type of interaction.
The well known trouble with RQFT is that when its formal expression is examined for its solutions , it is found that it does not have any! This is because of infinities that are automatically generated in this formulation. After this failure of the quantum theory was discovered, renormalization computational techniques were invented that provide a recipe for subtracting away the infinities and thereby generating finite predictions–some which had amazing empirical success. But the trouble is that a) such a scheme is not demonstrably mathematically consistent (implying that, in principle, any number of predictions could come from the same physical situations, though one of them is empirically correct) and b) there still remains the problem that there are no finite solutions for the problem. Thus, if nonrelativistic quantum mechanics is supposed to to be not more than an approximation for RQFT, and if the latter does not exist as a mathematically (or logically) consistent theory, then we still do not have the right to claim the scientific truth of the bases of nonrelativistic quantum mechanics (i.e. fundamental uncertainty and probability in laws of matter, linearity, 'open system', mathematical representation with a Hilbert space, etc.). IT IS IMPORTANT TO KNOW THAT THE EMPIRICAL AGREEMENT WITH THE PREDICTIONS OF A SCIENTIFIC THEORY, WHILE BEING A NECESSARY REQUIREMENT FOR THE TRUTH OF THAT THEORY, IS NOT SUFFICIENT TO ESTABLISH ITS TRUTH. To be a scientifically true theory, its expression must also be both logically and mathematically consistent. Unforrunately, RQFT is neither.
An obvious alternative approach that might get us out of this dilemna is the following: Start at the outset with a theory that is based fully on the premises and the ensuing mathematical expression of the theory of general relativity (i.e. curved spacetime, field concept, determinism, closed system, etc. – implying a nonlocal, nonlinear field theory), yet a theory in which a part of the generally covariant formalism reduces to the formal probabilty calculus of quantum mechanics, as a linear approximation for a nonlinear, nonlocal field theory of matter. If this could be shown, rigorously, it would mean that we must abandon the assertions of the Copenhagen school approach to quantum mechanics (as well as various other offshoots, such as several of the hidden variable theories). But the linear, nonrelativistic approximation for this relativistic, nonlocal, nonlinear, deterministic (non-hidden variable) field theory of matter is precisely the formal probability calculus that is the Hilbert space expression of nonrelativistic quantum mechanics. This would be entirely analogous to what happened to Newton's theory of gravitation when it was superseded by Einstein's theory of general relativity. Newton's theory became a linear approximation for an entirely different theory of gravity; yet it remains useful in this role while its conceptual truth has to be rejected.
I have spent the past 35 years pursuing this field approach in general relativity on the way that quantum mechanics emerges as a mathematical approximation for an entirely different field theory of matter–a theory rooted in Einstein's theory of general relativity–both mathematically and conceptually. I have found, in this research program, that the generally covariant theory of matter, that quantum mechanics emerges from, as a linear approximation, is a field theory of inertia. I have found that this is an essential ingredient in any unified theory because not only does general relativity logically imply that we must unify the forces of nature, representing the actions of matter on other matter, it also implies that we must include the reaction of the latter to the former, in a truly closed system. It is an ingredient in a unified field theory that Einstein and Schrodinger did not yet consider in rigorous terms, as I did, yet an ingredient that I feel is essential to complete the theory.
I have written two monographs that summarize my research program (until 1986): General Relativity and Matter (Reidel, 1982) and Quantum Mechanics from General Relativity (Reidel, 1986). A nonmathematical discussion of the meaning of relativity theory was presented in my book, Relativity In Our Time (Taylor&Francis, 1993).
I would welcome any discussion on this subject (whether or not argumentative) in this medium of communication. I can be reached via the Contact page.
I strongly beleive that it is essential to resolve this problem of the dichotomy between the quantum and relativity theories before we can make any genuine progress in physics. I beleive that, if I haven't made any major mistakes, I have taken several positive steps toward this goal in my research program. Other approaches to resolve this problem, equally rigorous (both logically and mathematically) should also be considered seriously. But pretending that the problem does not exist does not help us to make real progress in physics!