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## Contents

## The Measurement Problem

In quantum physics the probability of an event is deduced by taking the square of the **amplitude** for an event to happen. The term "amplitude for an event" arises because of the way that the Schrodinger equation is derived using the mathematics of ordinary, classical waves where the amplitude over a small area is related to the number of photons hitting the area. In the case of light, the probability of a photon hitting that area will be related to the ratio of the number of photons hitting the area divided by the total number of photons released. The number of photons hitting an area per second is the intensity or amplitude of the light on the area, hence the probability of finding a photon is related to "amplitude".

However, the Schrodinger equation is not a classical wave equation. It does not determine events, it simply tells us the probability of an event. In fact the Schrodinger equation in itself does not tell us that an event occurs at all, it is only when a measurement is made that an event occurs. The measurement is said to cause *state vector reduction*. This role of measurement in quantum theory is known as the **measurement problem**. The measurement problem asks how a definite event can arise out of a theory that only predicts a continuous probability for events.

Two broad classes of theory have been advanced to explain the measurement problem. In the first it is proposed that observation produces a sudden change in the quantum system so that a particle becomes localised or has a definite momentum. This type of explanation is known as *collapse of the wavefunction*. In the second it is proposed that the probabilistic Schrodinger equation is always correct and that, for some reason, the observer only observes one particular outcome for an event. This type of explanation is known as the *relative state interpretation*. In the past thirty years relative state interpretations, especially Everett's relative state interpretation have become favoured amongst quantum physicists.

## The quantum probability problem

The measurement problem is particularly problematical when a single particle is considered. Quantum theory differs from classical theory because it is found that a single photon seems to be able to interfere with itself. If there are many photons then probabilities can be expressed in terms of the ratio of the number hitting a particular place to the total number released but if there is only one photon then this does not make sense. When only one photon is released from a light source quantum theory still gives us a probability for a photon to hit a particular area but what does this mean at any instant if there is indeed only one photon?

If the Everettian interpretation of quantum mechanics is invoked then it might seem that the probability of the photon hitting an area in your particular universe is related to the occurrences of the photon in all the other universes. But in the Everrettian interpretation even the improbable universes occur. This leads to a problem known as the **quantum probability problem**:

If the universe splits after a measurement, with every possible measurement outcome realised in some branch, then how can it make sense to talk about the probabilities of each outcome? Each outcome occurs.

This means that if our phenomenal consciousness is a set of events then there would be endless copies of these sets of events, almost all of which are almost entirely improbable to an observer outside the brain but all of which exist according to an Everrettian Interpretation. Which set is you? Why should 'you' conform to what happens in the environment around you?

## The preferred basis problem

It could be held that you assess probabilities in terms of the branch of the universe in which you find yourself but then why do you find yourself in a particular branch? Decoherence Theory is one approach to these questions. In decoherence theory the environment is a complex form that can only interact with particles in particular ways. As a result quantum phenomena are rapidly smoothed out in a series of micro-measurements so that the macro-scale universe appears quasi-classical. The form of the environment is known as the preferred basis for quantum decoherence. This then leads to the **preferred basis problem** in which it is asked how the environment occurs or whether the state of the environment depends on any other system.

According to most forms of decoherence theory 'you' are a part of the environment and hence determined by the preferred basis. From the viewpoint of phenomenal consciousness this does not seem unreasonable because it has always been understood that the conscious observer does not observe things as quantum superpositions. The conscious observation is a classical observation.

However, the arguments that are used to derive this idea of the classical, conscious observer contain dubious assumptions that may be hindering the progress of quantum physics. The assumption that the conscious observer is simply an information system is particularly dubious:

"Here we are using aware in a down - to - earth sense: Quite simply, observers know what they know. Their information processing machinery (that must underlie higher functions of the mind such as "consciousness") can readily consult the content of their memory. (Zurek 2003).

This assumption is the same as assuming that the conscious observer is a set of measurements rather than an observation. It makes the rest of Zurek's argument about decoherence and the observer into a tautology - given that observations are measurements then observations will be like measurements. However, conscious observation is not simply a change of state in a neuron, a "measurement", it is the entire manifold of conscious experience.

In his 2003 review of this topic Zurek makes clear an important feature of information theory when he states that:

There is no information without representation.

So the contents of conscious observation are states that correspond to states of the environment in the brain (ie: measurements). But how do these states in the brain arise? The issue that arises here is whether the representation, the contents of consciousness, is entirely due to the environment or due to some degree to the form of conscious observation. Suppose we make the reasonable assumption that conscious observation is due to some physical field in the dendrites of neurons rather than in the action potentials that transmit the state of the neurons from place to place. This field would not necessarily be constrained by decoherence; there are many possibilities for the field, for instance, it could be a radio frequency field due to impulses or an electromagnetic field (cf: Anglin & Zurek (1996)) or some quantum state of macromolecules etc.. Such a field might contain many superposed possibilities for the state of the underlying neurons and although these would not affect sensations, they could affect the firing patterns of neurons and create actions in the world that are not determined by the environmental "preferred basis".

Zeh (2000) provides a mature review of the problem of conscious observation. For example he realises that memory is not the same as consciousness:

"The genuine carriers of consciousness ... must not in general be expected to represent memory states, as there do not seem to be permanent contents of consciousness."

and notes of memory states that they must enter some other system to become part of observation:

"To most of these states, however, the true physical carrier of consciousness somewhere in the brain may still represent an external observer system, with whom they have to interact in order to be perceived. Regardless of whether the ultimate observer systems are quasi-classical or possess essential quantum aspects, consciousness can only be related to factor states (of systems assumed to be localized in the brain) that appear in branches (robust components) of the global wave function — provided the Schrodinger equation is exact. Environmental decoherence represents entanglement (but not any “distortion” — of the brain, in this case), while ensembles of wave functions, representing various potential (unpredictable) outcomes, would require a dynamical collapse (that has never been observed)."

However, Zeh (2003) points out that events may be irreversibly determined by decoherence before information from them reaches the observer. This might give rise to a multiple worlds and multiple minds mixture for the universe, the multiple minds being superposed states of the part of the world that is the mind. Such an interpretation would be consistent with the *apparently* epiphenomenal nature of mind. A mind that interacts only weakly with the consensus physical world, perhaps only approving or rejecting passing actions would be an ideal candidate for a QM multiple minds hypothesis.

## Further reading and references

- Anglin, J.R. & Zurek, J.H. (1996). Decoherence of quantum fields: decoherence and predictability. Phys.Rev. D53 (1996) 7327-7335 http://arxiv.org/PS_cache/quant-ph/pdf/9510/9510021.pdf

- Baker, D.J. (2004). Lingering Problems with Probability in Everettian Quantum Mechanics http://www.princeton.edu/~hhalvors/teaching/phi538_f2004/LingeringProbsEverett.pdf

- Lockwood, M. (1996) Many Minds Interpretations of quantum mechanics. The British Journal of the Philosophy of Science. 47: 2 (159-188). http://www.ibiblio.org/weidai/Many_Minds.pdf

- Pearl, P. (1997). True collapse and false collapse. Published in Quantum Classical Correspondence: Proceedings of the 4th Drexel Symposium on Quantum Nonintegrability, Philadelphia, PA, USA, September 8-11, 1994, pp. 51-68. Edited by Da Hsuan Feng and Bei Lok Hu. Cambridge, MA: International Press, 1997. http://arxiv.org/PS_cache/quant-ph/pdf/9805/9805049.pdf

- Squires, E.J. (1996). What are quantum theorists doing at a conference on consciousness? http://arxiv.org/PS_cache/quant-ph/pdf/9602/9602006.pdf

- Zeh, H. D. (1979). Quantum Theory and Time Assymetry. Foundations of Physics, Vol 9, pp 803-818 (1979). http://xxx.lanl.gov/PS_cache/quant-ph/pdf/0307/0307013.pdf

- Zeh, H.D. (2000) THE PROBLEM OF CONSCIOUS OBSERVATION IN QUANTUM MECHANICAL DESCRIPTION. Epistemological Letters of the Ferdinand-Gonseth Association in Biel (Switzerland) Letter No 63.0.1981, updated 2000. http://arxiv.org/PS_cache/quant-ph/pdf/9908/9908084.pdf

- Zeh, H.D. (2003). Decoherence and the Appearance of a Classical World in Quantum Theory, second edition, Authors:. E. Joos, H.D. Zeh, C. Kiefer D. Giulini, J. Kupsch, and I.-O. Stamatescu. Chapter 2: Basic Concepts and their Interpretation. http://www.rzuser.uni-heidelberg.de/~as3/index.html

- Zurek, W.H. (2003). Decoherence, einselection and the quantum origins of the classical. Rev. Mod. Phys. 75, 715 (2003) http://arxiv.org/PS_cache/quant-ph/pdf/0105/0105127.pdf

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