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The Essence of Quantum Computing

Copenhagen interpretation

 

The Copenhagen interpretation, named after the city in Denmark where Bohr lived and worked, was provided by Niels Bohr and Werner Heisenberg around 1927. It is the most cited Interpretation. It extends the probabilistic interpretation of the wave function proposed by Max Born.31 As Jammer notes:

The Copenhagen view is not a single, clear-cut, unambiguously defined set of ideas but rather a common denominator for a variety of related viewpoints.32

The interpretations’ interesting features include: the position of a particle is essentially meaningless; a measurement causes an instantaneous collapse of the wave function and the collapsed state is randomly picked to be one of the many possibilities allowed for by the system’s state vector; the fundamental objects handled by the equations of quantum mechanics are not actual particles that have an extrinsic reality but “probability waves” that merely have the capability of becoming “real” when an observer makes a measurement. Even then it does not explain entanglement; this observed “nonlocality” is a mathematical consequence of quantum theory33. In Bohr’s view,

there is no quantum world. There is only abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics [only] concerns what we can say about nature34(p153) .

This view is contrary to Einstein’s who believed that the job of physical theories is to ‘approximate as closely as possible to the truth of physical reality.35’ David Merman once dubbed the Copenhagen interpretation as the ‘shut up and calculate’ interpretation.36

Everett’s many world interpretation

Hugh Everett III, in his 1956 doctoral dissertation37 (journal version38), proposed his “relative state interpretation”, now generally known as the many world interpretation (the name was coined by Bryce DeWitt in the late 1960s). This interpretation is perhaps the most bizarre and yet perhaps the simplest because it circumvents the measurement conundrum. Everett posits that when a quantum system is faced with a choice as in a measurement, the entire Universe splits into a number of universes equal to the number of collapse-choices available. When a universe splits, observers in it also split. Thus, there will be parallel copies of observers in parallel universes, each of whom will see the specific outcome that appears in his respective split universe39. Variants of the many-world interpretation are the multiverse interpretation, the many-histories interpretation, and the many-minds interpretation.

Physicists, including Bohr, at the time ridiculed Everett’s interpretation (he got his PhD alright and the work was published). It was said that “Bohr gave him the brush-off when Everett visited him in Copenhagen.40” He was so discouraged by the ridicule that he left physics, became a defense analyst, then a private contractor to the U.S. defense industry which made him a multimillionaire41. “Everett advised high-level officials in the Eisenhower and Kennedy administrations on the best methods for selecting hydrogen bomb targets and structuring the nuclear triad of bombers, submarines and missiles for optimal punch in a nuclear strike.”42 Everett is also renowned for his generalized Lagrange multiplier method. After Everett’s death, his interpretation has gained widespread respect of physicists, especially of David Deutsch who believes:

The quantum theory of parallel universes is not the problem, it is the solution. It is not some troublesome, optional interpretation emerging from arcane theoretical considerations. It is the explanation, the only one that is tenable, of a remarkable and counter-intuitive reality.44

Bohm’s interpretation

 

In Bohm’s interpretation45, which appeared in 1952 predating Everett’s, the whole universe is entangled, and one cannot isolate one part of the universe from the other. In Bohm’s view, the interaction between entangled particles is not mediated by any conventional field known to physics (such as the electromagnetic field), but by an all-pervasive field that is instantaneous. He showed that the non-local interactions can be described in terms of a very special anti-relativistic quantum information field (pilot-wave) that does not diminish with distance and that binds the whole universe together. This field is not physically measurable but manifests itself in terms of non-local correlations. The idea is not only interesting but entirely derivable from the Schrödinger equation. Consequently, in Bohm’s interpretation, e.g., the electron is a particle with well-defined position and momentum at any instant. However, the path an electron follows is guided by the interaction of its own pilot wave with the pilot waves of other entities in the universe. A major supporter of Bohm’s interpretation was John Bell.


[31] Born (1926a); Born (1926b).
[32] Jammer (1974), p. 87. Quotation as reproduced in Al-Kahlili (2003), p. 134.
[33] Seife (2005)
[34] Al-Kahlili (2003).
[35] Al-Kahlili (2003), p. 153.
[36] Mermin (2004
[37] Everett (1957a).
[38] Everett (1957b).
[39] Byrne (2007).
[40] Al-Kahlili (2003).
[41]Al-Kahlili (2003).
[42] Byrne (2007).
[43] Everett (1963).
[44] Deutsch (1997), p. 51.
[45] Bohm & Hiley (1993), Chapter 3. The original paper is: Bohm (1952).

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