The Preferred Basis Problem

1. The Preferred Basis

The Everett, or many worlds approach to quantum mechanics[1] solves the measurement problem by stating that macroscopic objects also obey the laws of quantum mechanics, but it then faces a similar problem known as the preferred basis problem.

The preferred basis problem asks why the universe is split into the 'separate worlds' we experience if it is really part of a multiverse described by Austrian physicist Erwin Schrödinger's wave equation.

American physicist Henry Stapp described how:

"if the universe has been evolving since the big bang in accordance with the Schrödinger equation [without a preferred basis], then it must by now be an amorphous structure in which every device is a smeared-out cloud of a continuum of different possibilities. Indeed, the planet earth would not have a well defined location, nor would the rivers and oceans, nor the cities built on their banks"[2].

Schrödinger first considered this problem when he discussed the realist implications of his theory in 1952. He stated that:

"nearly every result [a quantum theorist] pronounces is about the probability of this or that...happening - with usually a great many alternatives. The idea that they be not alternatives but all really happen simultaneously seems lunatic to [them], just impossible. [They think] that if the laws of nature took this form for, let me say, a quarter of an hour, we should find our surroundings rapidly turning into a quagmire, or sort of a featureless jelly or plasma, all contours becoming blurred, we ourselves probably becoming jelly fish"[3a].

Schrödinger thought that this idea must be flawed and stated that:

"the compulsion to replace the simultaneous happenings, as indicated directly by the theory, by alternatives [is] a strange decision"[3b].

2. Decoherence theory

The Everett approach was not able account for the preferred basis problem until the theory of decoherence was developed by German physicist Heinz-Dieter Zeh in 1970[4]. This theory was extended by American physicist Wojciech Zurek in 1981[5].

The superpositional effects of microscopic objects are suppressed when these objects become entangled with something that does not appear to be in a superpositional state, like a measuring device.

Decoherence theory shows that this mechanism is also responsible for the suppression of superpositional effects in macroscopic objects. This occurs when quantum states become entangled with a large number of objects. Objects on Earth will become entangled with the atmosphere, for example.

It takes about 10-27 seconds (a billionth, of a billionth, of a billionth of a second) for the interference effects of macroscopic objects to become unobservable. In contrast to this, it takes about a year for the interference effects of isolated microscopic objects to disappear, and this is why it is much easier to observe them.

Decoherence does not solve the measurement problem when combined with the collapse approach to quantum mechanics because it does not provide any collapse dynamics, or explain how quantum and classical objects could be two distinct substances. It does solve the problem for the Bohm approach to quantum mechanics, as it does not explain why all but one world is suppressed.

Zeh and Zurek both argue, however, that the preferred basis problem, and hence the measurement problem, can be resolved when the theory of decoherence is combined with the Everett approach[6][7].

Decoherence shows that a natural basis will form, which prevents us from experiencing branches that involve indeterminate macroscopic objects. Mathematically, these branches are said to decay exponentially, but they do not disappear completely and so decoherence can only give us an approximate appearance of definiteness.

The approximate nature of decoherence may not matter because our minds have evolved to only comprehend definite objects, or because decoherence is precise enough to explain our observations when combined with a functional approach to the mind.

3. References

  1. Everett, H., III, 1957, ''Relative State' Formulation of Quantum Mechanics', Reviews of Modern Physics, 29, pp.454.

  2. Stapp, H. P., 2002, 'The basis problem in many-worlds theories', Canadian Journal of Physics, 80, pp.1043-1052.

  3. (a, b) Schrodinger, E. and Bitbol, M. (ed), 1995 (1952), 'July Colloquium, 1952' in 'The interpretation of quantum mechanics: Dublin seminars (1949-1955) and other unpublished essays', Ox Bow Press.

  4. Zeh, H. D., 1970, 'On the interpretation of measurement in quantum theory', Foundations of Physics, 1, pp.69-76.

  5. Zurek, W. H., 1981, 'Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse?', Physical Review D, 24, pp.1516.

  6. Zeh, H. D., 2000, 'The Problem of Conscious Observation in Quantum Mechanical Description', Foundation of Physics Letters, 13, pp.221-233.

  7. Zurek, W. H., 1998, 'Decoherence, Einselection, and the Existential Interpretation (The Rough Guide)', Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1, pp.1793-1822.

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