# Consciousness Studies/Measurement In Quantum Physics And The Preferred Basis Problem

## 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 Schrödinger 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 Schrödinger equation is not a classical wave equation. It
does not determine events, it simply tells us the probability of an
event. In fact the Schrödinger 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 Schrödinger 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:

`<font face="times new roman">`{=html}\"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. `</font>`{=html}(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 (i.e.: 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
some other 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:

`<font face="times new roman">`{=html}\"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.\"`</font>`{=html}

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

`<font face="times new roman">`{=html}\"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).\"`</font>`{=html}

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 Asymmetry. Foundations of
    Physics, Vol 9, pp 803--818 (1979).
-   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/abs/quant-ph/9908084>
-   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/abs/quant-ph/0105127>

