Although David Bohm is perhaps best known for his work exploring the possibilities of "hidden variables" that would eliminate quantum indeterminacy
and restore complete determinism
to physics, he was a first-class quantum physicist who understood the quantum theory better than most working physicists who never questioned its formalism.
Bohm was pressed to develop hidden variables by his mentor Albert Einstein
, who 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 Einstein, who admired Bohm's pioneering text on quantum theory
, found that Bohm's new formulation of quantum mechanics as a deterministic
theory was "too cheap," perhaps because Bohm includes a vector potential that travels faster than light speed, apparently violating Einstein's special theory of relativity.
Now Richard Feynman
's path integral formulation describes supraluminal paths and even some 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 Process
David 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.
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.
In his 1950 textbook Quantum Theory
, Bohm discusses measurement in chapter 22, section 12.
12. Irreversibility of Process of Measurement and Its Fundamental Role in Quantum Theory.
From the previous work it follows that a measurement process is irreversible in the sense that, after it has occurred, re-establishment of definite phase relations between the eigenfunctions of the measured variable is overwhelmingly unlikely. This irreversibility greatly resembles that which appears in thermodynamic processes, where a decrease of entropy is also an overwhelmingly unlikely possibility.*
* There is, in fact, a close connection between entropy and the process of measurement. See L. Szilard, , 53, 840, 1929. The necessity for such a connection can be seen by considering a box divided by a partition into two equal parts, containing an equal number of gas molecules in each part. Suppose that in this box is placed a device that can provide a rough measurement of the position of each atom as it approaches the partition. This device is coupled automatically to a gate in the partition in such a way that the gate will be opened if a molecule approaches the gate from the right, but closed if it approaches from the left. Thus, in time, all the molecules can be made to accumulate on the left-hand side. In this way, the entropy of the gas decreases. If there were no compensating increase of entropy of the mechanism, then the second law of thermodynamics would be violated. We have seen, however, that in practice, every process which can provide a definite measurement disclosing in which side of the box the molecule actually is, must also be attended by irreversible changes in the measuring apparatus. In fact, it can be shown that these changes must be at least large enough to compensate for the decrease in entropy of the gas. Thus, the second law of thermodynamics cannot actually be violated in this way. This means, of course, that Maxwell's famous "sorting demon " cannot operate, if he is made of matter obeying all of the laws of physics. (See L. Brillouin, American Scientist, 38, 594, 1950.)
Because the irreversible behavior of the measuring apparatus is essential for the destruction of definite phase relations and because, in turn, the destruction of definite phase relation's is essential for the consistency of the quantum theory as a whole, it follows that thermodynamic irreversibility enters into the quantum theory in an integral way. This is in remarkable contrast to classical theory, where the concept of thermodynamic irreversibility plays no fundamental role in the basic sciences of mechanics and electrodynamics. Thus, whereas in classical theory fundamental variables (such as position or momentum of an elementary particle) are regarded as having definite values independently of whether the measuring apparatus is reversible or not, in quantum theory we find that such a quantity can take on a well defined value only when the system is coupled indivisibly to a classically describable system undergoing irreversible processes. The very definition of the state of any one system at the microscopic level therefore requires that matter in the large shall undergo irreversible processes. There is a strong analogy here to the behavior of biological systems, where, likewise, the very existence of the fundamental elements (for example, the cells) depends on the maintenance of irreversible processes involving the oxidation of food throughout an organism as a whole. (A stoppage of these processes would result in the dissolution of the cell.)