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Hugh Everett III
Hugh Everett III was one of John Wheeler's most famous graduate students. Others included Richard Feynman. Wheeler supervised more Ph.D. theses than any other Princeton physics professor.
Everett took mathematical physics classes with Eugene Wigner, who argued that human consciousness (and perhaps some form of cosmic consciousness) was essential to the collapse of the wave function. Everett was the inventor of the "universal wave function" and the "relative state" formulation of quantum mechanics, later known as the "manyworlds interpretation." The first draft of Everett's thesis was called "Wave Mechanics Without Probability." Like Albert Einstein and Erwin Schrödinger, Everett was appalled at the idea of indeterministic events. For him, it was much more logical that the world was entirely deterministic. Everett began his thesis by describing John von Neumann's "two processes." Process 1 is the sudden collapse of the wave function from a superposition of quantum states into a single state, with the probability of collapsing into a given state proportional to the overlap of the wave function of the current state with those of the superposition states. (See von Neumann Process 1.) Process 2 is the unitary time evolution of the wave function deterministically generated by the Schrödinger wave equation. (See von Neumann Process 2.) Everett then presents the internal contradictions of observerdependent collapses of wave functions with examples of "Wigner's Friend," an observer who observes another observer. For whom does the wave function collapse? Everett considers several alternative explanations for Wigner's paradox, the fourth of which is the standard statistical interpretation of quantum mechanics, which was criticized by Einstein as not being a complete description.
Alternative 4: To abandon the position that the state function is a complete description of a system. The state function is to be regarded not as a description of a single system, but of an ensemble of systems, so that the probabilistic assertions arise naturally from the incompleteness of the description.In order to be "complete, Everett thought that "hidden variables" would be necessary. Everett's "theory of the universal wave function" is the last alternative:
Alternative 5: To assume the universal validity of the quantum description, by the complete abandonment of Process 1. The general validity of pure wave mechanics, without any statistical assertions, is assumed for all physical systems, including observers and measuring apparata. Observation processes are to be described completely by the state function of the composite system which includes the observer and his objectsystem, and which at all times obeys the wave equation (Process 2).He says this alternative has many advantages. It has logical simplicity and it is complete in the sense that it is applicable to the entire universe. All processes are considered equally (there are no "measurement processes" which play any preferred role), and the principle of psychophysical parallelism is fully maintained. Since the universal validity of the state function description is asserted, one can regard the state functions themselves as the fundamental entities, and one can even consider the state function of the whole universe. In this sense this theory can be called the theory of the "universal wave function, " since all of physics is presumed to follow from this function.
Information and Entropy
In a lengthy chapter, Everett develops the concept of information  despite the fact that his deterministic view of physics allows no possibilities. For Claude Shannon, the developer of the theory of communication of information, there can be no information transmitted without possibilities. Everett correctly observes that in classical mechanics information is a conserved property, a constant of the motion. No new information can be created in the universe. As a second illustrative example we consider briefly the classical mechanics of a group of particles. The system at any instant is represented by a point...in the phase space of all position and momentum coordinates. The natural motion of the system then carries each point into another, defining a continuous transformation of the phase space into itself. According to Liouville's theorem the measure of a set of points of the phase space is invariant under this transformation. This invariance of measure implies that if we begin with a probability distribution over the phase space, rather than a single point, the total information,... which is the information of the joint distribution for all positions and momenta, remains constant in time. Everett correctly notes that if total information is constant, the total entropy is also constant. if one were to define the total entropy to be the negative of the total information, one could replace the usual second law of thermodynamics by a law of conservation of total entropy, where the increase in the standard (marginal) entropy is exactly compensated by a (negative) correlation entropy. The usual second law then results simply from our renunciation of all correlation knowledge (stosszahlansatz), and not from any intrinsic behavior of classical systems. The situation for classical mechanics is thus in sharp contrast to that of stochastic processes, which are intrinsically irreversible.
The Appearance of Irreversibility in a Measurement
There is another way of looking at this apparent irreversibility within our theory which recognizes only Process 2. When an observer performs an observation the result is a superposition, each element of which describes an observer who has perceived a particular value. From this time forward there is no interaction between the separate elements of the superposition (which describe the observer as having perceived different results), since each element separately continues to obey the wave equation. Each observer described by a particular element of the superposition behaves in the future completely independently of any events in the remaining elements, and he can no longer obtain any information whatsoever concerning these other elements (they are completely unobservable to him).
In the final chapter of his thesis, Everett gives five possible "interpretations, the "popular", the "Copenhagen", the "hidden variables", the "stochastic process", and the "wave" interpretations. a. The "popular" interpretation. This is the scheme alluded to in the introduction, where ψ is regarded as objectively characterizing the single system, obeying a deterministic wave equation when the system is isolated but changing probabilistically and discontinuously under observation.
b. The Copenhagen interpretation. This is the interpretation developed by Bohr. The ψ function is not regarded as an objective description of a physical system (i.e., it is in no sense a conceptual model), but is regarded as merely a mathematical artifice which enables one to make statistical predictions, albeit the best predictions which it is possible to make. This interpretation in fact denies the very possibility of a single conceptual model applicable to the quantum realm, and asserts that the totality of phenomena can only be understood by the use of different, mutually exclusive (i.e., "complementary") models in different situations. All statements about microscopic phenomena are regarded as meaningless unless accompanied by a complete description (classical) of an experimental arrangement.
c. The "hidden variables" interpretation. This is the position (Alternative 4 of the Introduction) that ψ is not a complete description of a single system. It is assumed that the correct complete description, which would involve further (hidden) parameters, would lead to a deterministic theory, from which the probabilistic aspects arise as a result of our ignorance of these extra parameters in the same manner as in classical statistical mechanics.Everett says that here the ψfunction is regarded as a description of an ensemble of systems rather than a single system. Proponents of this interpretation include Einstein and Bohm.
The stochastic process interpretation. This is the point of view which holds that the fundamental processes of nature are stochastic (i.e., probabilistic) processes. According to this picture physical systems are supposed to exist at all times in definite states, but the states are continually undergoing probabilistic changes. The discontinuous probabilistic "quantumjumps" are not associated with acts of observation, but are fundamental to the systems themselves. This is close to our information interpretation of quantum mechanics, which claims that collapses of the wave function result from interactions between quantum systems, independent of any observers or measurement processes.
The wave interpretation. This is the position proposed in the present thesis, in which the wave function itself is held to be the fundamental entity, obeying at all times a deterministic wave equation.Everett says that this is his thesis, that it follows most closely the view held by Erwin Schrödinger, who denied the existence of "quantum jumps" and collapses of the wave function. See Schrödinger's Are There Quantum Jumps?, Part I and Part II (and, years after Everett, John Bell (1987) and H. Dieter Zeh (1993) who wrote articles with similar titles). Everett proposed that the complicated problem of "conscious observers" can be greatly simplified by noting that the most important element in an observation is the recorded information about the measurement outcome in the memory of the observer. He proposed that human observers could be replaced by automatic measurement equipment that would achieve the same result. A measurement would occur when information is recorded by the measuring instrument. It will suffice for our purposes to consider the observers to possess memories (i.e., parts of a relatively permanent nature whose states are in correspondence with past experience of the observers). In order to make deductions about the past experience of an observer it is sufficient to deduce the present contents of the memory as it appears within the mathematical model. Everett's model of machine memory completely solves the problem of "Wigner's Friend." As in the information interpretation of quantum mechanics, it is the recording of information in a "measurement" that makes a subsequent "observation" by a human observer possible.
Summary of Everett's Ideas
References
The ManyWorlds Interpretation of Quantum Mechanics (PDF)
"Relative State" Formulation of Quantum Mechanics, Hugh Everett,III, Reviews of Modern Physics, Vol.29, No.3, 454462, July, 1957
Assessment of Everett's "Relative State" Formulation of Quantum Mechanics, John A. Wheeler, Reviews of Modern Physics, Vol.29, No.3, 463465, July, 1957 Quantum Mechanics and Reality, Bryce DeWitt, Physics Today, vol.23, no.9, pp.3035, September, 1970 Many Worlds or Many Words?, Max Tegmark, September 15, 1997, arXiv.org The Many Worlds of Hugh Everett III, Peter Byrne, Oxford University Press, 2010 For Teachers
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