David Bohm is perhaps best known for new experimental methods to test Einstein’s supposed suggestion of “hidden variables” that would explain the EPR paradox by providing the information needed at the distant “entangled” particle, so it can coordinate its properties perfectly with the “local” particle. Bohm wrote in 1952,But Bohm changed his mind about irreversibility when he developed his more realistic and deterministic theory. Now he became concerned with the classic "problem" of microscopic irreversibility, namely how can the increase of entropy involve macroscopic irreversibility if microscopic collisions of particles are reversible?
The usual interpretation of the quantum theory is based on an assumption having very far-reaching implications, ~i.e., that the physical state of an individual system is completely specified by a wave function that determines only the probabilities of actual results that can be obtained in a statistical ensemble of similar experiments. This assumption has been the object of severe criticisms, notably on the part of Einstein, who has always believed that, even at the quantum level, there must exist precisely definable elements or dynamical variables determining (as in classical physics) the actual behavior of each individual system, and not merely its probable behavior. Since these elements or variables are not now included in the quantum theory and have not yet been detected experimentally, Einstein has always regarded the present form of the quantum theory as incomplete, although he admits its internal consistency.Einstein may have pressed Bohm to develop hidden variables as the source of nonlocal behavior. Einstein had heartily approved of Bohm’s textbook Quantum Theory and was initially supportive of Bohm’s new mechanics. Einstein thought Bohm was young enough and smart enough to produce the mathematical arguments that the older generation of “determinist” physicists like Erwin Schrödinger, Max Planck, and others had not been able to accomplish. But when Bohm finished the work, based on Louis de Broglie’s 1923 “pilot-wave” idea (which Einstein had supported), Einstein rejected it as inconsistent with his theory of relativity. Einstein wrote to Max Born on May 15, 1952,
Have you noticed that Bohm believes (as de Broglie did, by the way, 25 years ago) that he is able to interpret the quantum theory in deterministic terms? That way seems too cheap to me. But you, of course, can judge this better than I.Five years later, Bohm and his Israeli student Yakir Aharonov reformulated the original EPR argument in terms of electron spin. They said experimental tests with continuous variables would be much more difficult than tests with discrete quantities, such as the spin of electrons or polarization of photons. Bohm and Aharonov described the preparation of two particles, such that a measurement of one at a later time determines a measurement in the same direction of the other particle at any distance away.
We consider a molecule of total spin zero consisting of two atoms, each of spin one-half. The wave function of the system is therefore
Conservation of Angular Momentum (and Spin)Bohr and Aharonov gave a rare discussion of the role of conservation of angular momentum as explaining the fact (for the total spin zero state) that spin of the particle (B) will be found opposite to that of A. They also reacted to a hypothesis by Harvard professor Wendell Furry. Six years later Eugene Wigner also cited the conservation of angular momentum as explaining perfect correlations (or anti-correlations) in Bell-Bohm experiments.
Evidently, the foregoing interpretation is not satisfactory when applied to the experiment of ERP. It is of course acceptable for particle A alone (the particle whose spin is measured directly). But it does not explain why particle B (which does not interact with A or with the measuring apparatus) realizes its potentiality for a definite spin in precisely the same direction as that of A. Moreover, it cannot explain the fluctuations of the other two components of the spin of particle B as the result of disturbances due to the measuring apparatus. One could perhaps suppose that there is some hidden interaction between B and A, or between B and the measuring apparatus, which explains the above behavior. Such an interaction would, at the very least, be outside the scope of the current quantum theory. Moreover, it would have to be instantaneous, because the orientation of the measuring apparatus could very quickly be changed, and the spin of B would have to respond immediately to the change. Such an immediate interaction between distant systems would not in general be consistent with the theory of relativity. This result constitutes the essence of the paradox of Einstein, Rosen, and Podolsky... At first sight it would seem then that there exists at present no experimental proof that the paradoxical behavior described by ERP will really occur... In fact, Einstein has (in a private communication) actually proposed such an idea; namely, that the current formulation of the many-body problem in quantum mechanics may break down when particles are far enough apart.Bohr and Aharonov also gave a powerful explanation for the The consequences of such an idea have already been discussed by Furry.4 To illustrate Furry’s conclusions in terms of our problem, we may consider the possibility that after the molecule of spin zero decomposes, the wave function for the system is eventually no longer given by Eq. (1), which implies the puzzling correlations of the spins of the two atoms. Instead, we suppose that in any individual case, the spin of each atom becomes definite in some direction, while that of the other atom is opposite. The wave function will be the product two-slit experiment. They wrote:
Bohmian mechanics provides a straightforward physical explanation. First, close slit 1 and open slit 2.The last term comes from the interference of the wave packets ψ1 and ψ2 which passed through slit 1 and slit 2. The probabilities of finding particles when both slits are open are different from the sum of slit 1 open and slit 2 open separately. The wave function ψ(x) (squared), |ψ(x)|2, determines the probability of finding a particle at x, as Einstein first suggested and Max Born later described as his "statistical interpretation" (the so-called "Born Rule"). Now Richard Feynman's path integral formulation of quantum mechanics describes supraluminal paths and even some things moving backwards in time, so we must take a careful look at Bohm's work. Bohm's search for "hidden variables" inspired John Bell to develop a theorem on "inequalities" that would need to be satisfied by hidden variables. To this date, every test of Bell's theorem has violated his inequalities and shown that the quantum theory cannot be replaced by one with "local" hidden variables. If they exist at all, "hidden variables" must also be "nonlocal."
The Measurement ProcessBohm was particularly clear on the process of measurement. He said it involves macroscopic irreversibility, which was a sign and a consequence of treating the measuring apparatus as a macroscopic system that could not itself be treated quantum mechanically. The macroscopic system could, in principle, be treated quantum mechanically, but Bohm said its many degrees of internal freedom would destroy any interference effects. This is the modern theory of quantum decoherence. Bohm's view is consistent with the information-philosophy solution to the measurement problem. A measurement has only been made when new information has come into the world and adequate entropy has been carried away to insure the stability of the new information, long enough for it to be observed by the "conscious" observer. In his 1951 textbook Quantum Theory, Bohm discusses measurement in chapter 22, section 12.
ReferencesA Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. II Discussion of Experimental Proof for the Paradox of Einstein, Rosen, and Podolsky