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, ~is., 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.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. They wrote: Bohmian mechanics provides a straightforward physical explanation. First, close slit 1 and open slit 2.
The particle goes through slit 2.
It arrives at x on the plate with probability |ψ2(x)|2,
where ψ2 is the wave function which passed through slit 2.
Second, close slit 2 and open slit 1.
The particle goes through slit 1.
It arrives at x on the plate with probability |ψ1(x)|2,
where ψ1 is the wave function which passed through slit 1.
Third, open both slits.
The particle goes through slit 1 or slit 2.
It arrives at x with probability |ψ1(x)+ψ2(x)|2.
Now observe that in general,
|ψ1(x)+ψ2(x)|2 = |ψ1(x)+ψ2(x)|2= |ψ1(x)|2+|ψ2(x)|2 + 2ℜψ∗1(x) ψ2(x).
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 determines the probabilities of finding particles, as Einstein first proposed..
We consider a molecule of total spin zero consisting of two atoms, each of spin one-half. The wave function of the system is thereforeEinstein may have pressed Bohm to develop hidden variables as the source of nonlocal behavior. Einstein had heartily approved of Bohm’s textbook 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.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." Bohm's pilot-wave goes through both slits in the two-slit experiment, whereas the particle goes through only one, thus explaining what Richard Feynman called the "only mystery" in quantum mechanics.
The Measurement ProcessDavid Bohm 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 1950 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