Schrödinger's Cat

1. The collapse approach

The collapse approach to quantum mechanics states that the measurement of a quantum system invokes a 'collapse' of the quantum wave function, from a superpositional state into a state that can be described classically, in accordance with the Born rule[1].

It suggests that instantaneous action at a distance should simply be accepted in quantum mechanics, as it was with English natural philosopher Isaac Newton's theory of gravitation[2].

1.1 Problems with the collapse approach

There are a number of other problems with the collapse approach:

  • Firstly, it does not adequately define what constitutes a measurement, and so it does not adequately define when the collapse of the wave function occurs.

  • Secondly, there are no collapse dynamics within quantum theory itself, and so they need to be added by hand.

  • Thirdly, the collapse approach cannot explain how the quantum world can make contact with the classical world at all, since both systems obey different physical laws.

The third problem is known as the measurement problem[3], and it is analogous to the problem of causal interaction faced by French natural philosopher Rene Descartes in 1641[4].

2. The 'Schrödinger's cat' thought experiment

These problems were highlighted in a thought experiment devised by Austrian physicist Erwin Schrödinger in 1935[5]. This was written as a response to the EPR paper, which also criticised the collapse approach[6].

Schrödinger considered an experiment where a cat is placed in a closed box with a radioactive atom. The atom has a chance of decaying - the probability determined by the Born rule - and if it does, it will trigger a device that will kill the cat.

Illustration of the ‘Schrodinger’s cat’ thought experiment, showing both possible outcomes.
Illustration of the ‘Schrodinger’s cat’ thought experiment, with a dead and live cat inside of an impossible cube, first designed by M.C. Escher.

Illustrations of Schrödinger’s cat paradox. Image credit: Dhatfield/CC-SA & Jie Qi/CC-A.

The collapse approach suggests that quantum states do not collapse until they are measured, and so suggests that the cat is entangled with the radioactive atom in a superpositional state, where it is both dead and alive at the same time. The cat remains in this state until the experimenter opens the box, thereby measuring the system.

The cat itself cannot count as a measuring device according to the collapse approach; otherwise it would collapse the state as soon as it became aware of what was happening.

Schrödinger claimed that this shows the collapse approach cannot adequately describe what happens when macroscopic objects become entangled, and German-Swiss-American physicist Albert Einstein agreed.

In a letter to Schrödinger written in 1950, Einstein stated:

"You are the only contemporary physicist, besides [German physicist Max von] Laue, who sees that one cannot get around the assumption of reality – if only one is honest. Most of them simply do not see what sort of risky game they are playing with reality – reality as something independent of what is experimentally established. They somehow believe that the quantum theory provides a description of reality, and even a complete description; this interpretation is, however, refuted most elegantly by your system of radioactive atom + Geiger counter + amplifier + charge of gun powder + cat in a box, in which the [wave]-function of the system contains the cat both alive and blown to bits…it seems certain to me that the fundamentally statistical character of the theory is simply a consequence of the incompleteness of the description"[7].

2.1 The 'Wigner's friend' thought experiment

In 1961, Hungarian-American physicist Eugene Wigner popularised the idea that the collapse occurs when a measurement registers in the mind of a conscious observer. To illustrate this, he extended Schrödinger's thought experiment to include another human observer: Wigner's friend[8a].

If Wigner's friend conducts Schrödinger's experiment while Wigner waits outside the laboratory, then the state collapses earlier from the perspective of Wigner's friend than for Wigner, who can consider his friend to be in a superpositional state until he interacts with them.

Wigner did not accept this, and argued that a self-aware consciousness is what causes the collapse. Wigner stated:

"[I]t is the entering of an impression into our consciousness which alters the wave function because it modifies our appraisal of the probabilities for different impressions which we expect to receive in the future. It is at this point that the consciousness enters the theory unavoidably and unalterably. If one speaks in terms of the wave function, its changes are coupled with the entering of impressions into our consciousness"[8b].

The idea that consciousness causes the collapse was considered a possibility because the mind exhibits properties that cannot currently be explained using classical physical laws, such as subjectivity, and Wigner suggested that scientists search for unusual effects of consciousness acting on matter.

Despite Wigner's suggestion that something must occur at the level of consciousness, there are no collapse dynamics inherent to quantum mechanics, and nothing within it suggests that consciousness is special in any way.

In 1985, Italian physicists Giancarlo Ghirardi, Alberto Rimini, and Tullio Weber suggested that collapses can occur spontaneously[9][10], and in 1994, British physicist Roger Penrose suggested that the force of gravity could cause the collapse[11].

Quantum effects are now being demonstrated in larger and larger objects. In 2009, physicist Michal Karski and colleagues exhibited quantum effects in a single atom of caesium, allowing "the observation of the quantum-to-classical transition"[12], and two groups of American physicists headed by John Jost and Keith Schwab have shown quantum effects in simple harmonic oscillators[13a].

Jost stated that:

"Such experiments may lead to the generation of entangled states of larger-scale mechanical oscillators...Mechanical oscillators pervade nature; examples include the vibrations of violin strings, the oscillations of quartz crystals used in clocks"[13b].

Schwab suggested that:

It'd be weird to think of ordinary matter behaving in a quantum way, but there's no reason it shouldn't...If single particles are quantum mechanical, then collections of particles should also be quantum mechanical. And if that's not the case-if the quantum mechanical behavior breaks down-that means there's some kind of new physics going on that we don't understand"[14].

3. Decoherence theory

While the measurement problem remains unresolved for the collapse approach, decoherence theory can explain why macroscopic objects appear to exhibit classical behaviour[15]. Decoherence theory was first suggested by German physicist Heinz-Dieter Zeh, in 1970[16], and was extended by American physicist Wojciech Zurek, in 1981[17].

When describing the quantum state of a large number of objects, a mathematical device known as a density matrix is used to determine every possibility, some of these possibilities will include the results we expect but some will include the superposition of macroscopic objects.

Zeh and Zurek showed that we never observe these possibilities because they decay exponentially. This means that they are not observable long enough for us to notice them. 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.

This process is said to be irreversible because it would be impossible for an observer to reconstruct the superpositional state after it has decayed.

Interference effects decay when quantum states become entangled with a large number of objects. Objects on Earth will become entangled with the atmosphere, for example, and so Schrödinger's cat would die within 10-27 seconds of the atom decaying whether it is observed or not.

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 cannot solve the measurement problem for the collapse approach because it does not provide any collapse dynamics, or explain how quantum and classical objects could be composed of two distinct substances.

The measurement problem may be solved by applying decoherence theory to the Bohm approach, because here there is no collapse of the wave function. The Bohm approach faces other problems, however, as it still must explain why we only observe one of any number of possible results.

The Bohm approach attempts to solve this problem with hidden variables that suppress other possible brain states, yet, like collapse dynamics, these variables are not found within quantum theory itself and must be added by hand[18].

Both Zeh and Zurek suggested that the measurement problem can be solved by applying decoherence to the Everett, or many worlds, approach[19][20].

4. References

  1. Ghirardi, G. C., 'Collapse Theories', Stanford Encyclopedia of Philosophy, last accessed 15-02-16.

  2. Berkovitz, J., 'Action at a Distance in Quantum Mechanics', Stanford Encyclopedia of Philosophy, last accessed 15-02-16.

  3. Myrvold, W., 'Philosophical Issues in Quantum Theory', Stanford Encyclopedia of Philosophy, last accessed 15-02-16.

  4. Descartes, R., Cottingham, J. (trans), Bennett, J. (trans), 2006 (1641), 'Meditations on First Philosophy', Cambridge University Press.

  5. Schrödinger, E., 1935, 'Die gegenwärtige Situation in der Quantenmechanik' ('The present situation in quantum mechanics'), Naturwissenschaften, 23, pp.823-828.

  6. Einstein, A., Podolsky, B. and Rosen, N., 1935, 'Can quantum-mechanical description of physical reality be considered complete?', Physical review, 47, pp.777-780.

  7. Einstein, A., 2011 (1950), 'Letter to Schrödinger, 22 December 1950' in 'Letters on Wave Mechanics: Correspondence with H. A. Lorentz, Max Planck, and Erwin Schrödinger', Open Road Media.

  8. (a, b) Wigner, E. P., 1995 (1961), 'Remarks on the mind-body question' in 'Philosophical Reflections and Syntheses', Springer Berlin Heidelberg.

  9. Ghirardi, G. C., Rimini, A. and Weber, T., 1985, 'A model for a unified quantum description of macroscopic and microscopic systems' in 'Quantum Probability and Applications II', Springer Berlin Heidelberg.

  10. Ghirardi, G. C., Rimini, A. and Weber, T., 1986, 'Unified dynamics for microscopic and macroscopic systems', Physical Review D, 34, pp.470-491.

  11. Penrose, R., 1999 (1989), 'The Emperor's New Mind', Oxford University Press.

  12. Karski, M., et al, 2009, 'Quantum walk in position space with single optically trapped atoms', Science, 325, pp.174-177.

  13. (a, b) Jost, J. D., et al, 2009, 'Entangled mechanical oscillators', Nature, 459, pp.683-685.

  14. Svitil, K., 'Mechanics: Nano Meets Quantum', Caltech, last accessed 15-02-16.

  15. Bacciagaluppi, G., 'The Role of Decoherence in Quantum Mechanics', Stanford Encyclopedia of Philosophy, last accessed 15-02-16.

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

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

  18. Goldstein, S., 'Bohmian Mechanics', Stanford Encyclopedia of Philosophy, last accessed 15-02-16.

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

  20. 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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