Chapter 25
The many-universes interpretation of quantum theory and its
implications
It is true that only a minority of physicists are dissatisfied
with the usual interpretation (by Niels Bohr of Copenhagen) of
the quantum theory of measurement, but at least it can be said
that members of this minority have made various proposals aimed
at overcoming our mental distaste for a completely random universe
that is comprehensible only through statistical laws.
Let us consider a stream of electrons being diffracted by a pair
of slits. The familiar wave diffraction pattern will appear on
a fluorescent screen. If one of the slits were blocked up, there
would be no interference between the two waves, and only a single
smudge would appear on the screen. If instead the other slit were
blocked up, again only one smudge would appear. But if both slits
were opened again, a complete set of fringes would build up as
more and more electrons reached the screen.
What about the first electron to pass through the pair of slits?
To which fringe does it contribute? Can quantum theory tell us
where it will go? At present it cannot, and most physicists would
give the opinion that we can never know the answer. The point
of arrival of the first electron is random and that of the second
electron is still random, and so on. But as an increasing number
pass through, the fringe pattern gradually appears. This experiment
could in principle be carried out very slowly, maybe one electron
per year; the same principle would apply, each electron path being
unpredictable. In this extreme example, quantum theory does not
seem to be very powerful. The system also seems to have non-locality
in time. But for predicting the most probable results of a large
number of electrons, quantum theory is extremely powerful; it
has developed to the extent when it can be included as part of
engineering. With the aid of solutions of the Schrodinger wave
equation, the probabilities of events happening can be calculated
with precision. These are expressed as the square of 'probability
amplitudes', which are represented by means of the bra-ket notation:
<electron arrives at y |electron leaves x>
or <y|x>. Within the limits of uncertainty determined by
the Heisenberg Principle, and within the limits imposed by sheer
mathematical difficulty, the most probable behaviour of a system
can be calculated. One can extend the calculation to that of the
probability amplitude of the electron leaving x for y. and leaving
y for x (two slits one after the other); this would be represented
as the product <x|y> <y|x>.
Now consider again the question of which of two interference slits
a single electron passes through. Since the electron has the properties
of a particle, the question is not meaningless; but quantum theory
gives no answer, unless there is some method of detecting the
passage of the electron. For example, a photon might be arranged
to pass behind one of the slits; when it is scattered by the passing
electron, detection of the electron is possible. But this introduces
an observer or apparatus into the system, and the
probability |A> of the apparatus being in a certain state A
must be taken into account, as well as the probability |s>
of the system being in a state s. The combined probability is
|s,A>= |s>|A>
The observer is an integral part of the description of the event,
and without the observer there can be no description and no complete
understanding of reality.
A similar difficulty about unpredictability is encountered in
the phenomenon of radioactive decay. Most people will be familiar
with the behaviour of a 'radioactive source', which is a sample
consisting of a species of radioactive atom. When these atoms
decay, each one emits (often by a tunneling process) a highly
penetrating particle, which is a form of nuclear radiation. These
particles can be detected by a suitable type of detector such
as the Geiger counter used in the Uri Geller experiment of chapter
15. The average time taken for a radioactive atom to decay can
be measured if sufficient atoms are available. But the exact moment
of decay of an individual atom can in no way be predicted by quantum
theory. The moments at which the Geiger counter clicks are random
within the bounds set by a probability distribution. The quantum
mechanical description of the system is a linear combination of
the wave functions not only of the undecayed atom but also of
the decayed atom. The wave function is the mathematical expression
of the form of the wave for the system, and it must satisfy the
wave equation. Schrodinger went further than demanding this inclusion
of both wave functions; he insisted that the consequential wave
functions must also be included.
He illustrated this requirement with a dramatic example of a cat
enclosed in a chamber with a sealed flask of cyanide poison, which
can be broken by a hammer which is released by a relay activated
only by the radiation pulses from a radioactive source. This source
is very weak, so that there is a chance that there will be a pulse
within the natural lifetime of the cat, and a chance that there
will be none. Since the cat is provided with adequate food, drink
and air, the question of whether the cat will live out its natural
life or be prematurely poisoned by cyanide vapour cannot be answered
with any certainty; only the probability could be calculated.
Schrodinger insisted that a complete description of the system
must include both the wave function of the living cat and that
of the dead cat.
Since no physical condition exists to determine causally the state
of a particular system at the moment of measurement, it follows
that until a measurement is carried out, a system is properly
described by what is known as a state vector, which is the linear
combination of all possible states of the system. Only after a
measurement is performed can we affirm with confidence that the
system, let us say an atom, is in a certain state. Before the
measurement, the atom is collectively in all the states.
The problem of the quantum theory of measurement was formulated
mathematically by von Neumann(75) and the short account given
by de Witt(76) will be repeated here. The world is considered
to be composed of two dynamical variables, a system s and
an apparatus A. A combined state vector is expanded in
terms of an orthonormal set of basis vectors:
|s,A>= |s>|A>
where s is an eigenvalue of some system observable and
A is an eigenvalue of some apparatus observable. The state
of the world at an initial moment is represented by:
|psi0>= |psi>|phi>,
which is a combined state vector with |psi> referring to the
system and |phi> to the apparatus. The learning of the apparatus
about the system requires a coupling between the two; the result
of this is described by a unitary operator U:
|psi>= U|phi0>
U acts as follows:
U|s,A>= |s,A +gs>= |s>|A +gs>
where g is an adjustable coupling constant, which is said
to result in an observation, the information from which is stored
in the apparatus memory by virtue of its irreversible change from
|A> to |A + gs>. Using the orthonormality
and assumed completeness of the basis vectors, the initial state
vector is found to become:
|psi1>= sum over s Cs|s>|phi[s]>
where
Cs=<s|psi>
|phi[s] >=integral |A +gs>phi(A)dA
phi(A) = <A|phi>
This final state vector is a linear superposition of vectors |s>phi[s]>,
each of which represents a possible value assumed by the system
observable, the value which has been observed by the apparatus.
The observation is capable of distinguishing adjacent values of
s (spaced by delta s) provided that A <<
g delta s where delta A is the variance in A about
its mean value relative to the distribution function |phi(A)|^2.
Under these conditions,
<phi[s] | phi[s']> = delta function of s,s'
where delta function is the Dirac delta function. The wave function
of the apparatus is initially single, but splits into a great
number of mutually orthogonal packets, one for each value of s
(i.e. s, s', s" etc.).
The apparatus cannot decide which is the correct value of the
system observable, and would have to be supplemented by a second
apparatus to observe the first one; but the second one also cannot
decide, and so must be supplemented by a third; and so on. This
'catastrophe of infinite regression' requires resolution by a
fresh approach, otherwise the whole quantum theory of measurement
remains inadequate. One cannot make predictions about the whole
universe, because the universe must contain all the observers.
This infinite regression has an affinity with Russell's paradox
and with Godel's theorem in mathematics.
To recapitulate; in the absence of any observation, matter is
in continual fluctuation. When an observation is made, a single
value of the energy is observed, and the physical observables
instantaneously take on certain single values. Until the observation
is made, at a time which is determined by a mental decision of
the observer, no certainty about the physical reality is possible.
To a second observer this system of 'wave function and first observer'
appears to be in continual fluctuation, even when the first observer
makes his observation. The second observer believes that the first
observer is in continual fluctuation, and is split into many copies
of himself, even though he is making an observation. But he must
again become singular when the second observer performs.
The conventional escape from infinite regression is that proposed
by the Copenhagen school,(77) which states that as soon as the
state vector attains the form of the equation above it collapses
into a single wave packet, so that the vector | psi> is reduced
to an element |s >|phi[s]> of the superposition.
We cannot predict which element will be formed, but there is a
probability distribution of possible outcomes. This assumption
is not a corollary of the Schrodinger equation, and it leaves
the world in an essentially unpredictable state.
A different proposal was made by David Bohm(78) with his introduction
into quantum theory of 'hidden variables', which determine the
indeterminable quantities but at the same time conform to the
probability distribution. For many years the search for these
hidden variables has continued, but up to the present none has
been found. We are now coming increasingly to believe that the
mind is the only remaining undiscovered hidden variable.
A proposal was in fact made by the theoretical physicist, Eugene
Wigner,(79) that the infinite regression could be arrested by
the intervention of mind. This was almost the first appearance
of mind in modern physics; it was accompanied by a mathematical
description of the conversion from a pure to a mixed state arising
from possible nonlinear departures from the Schrodinger equation
when consciousness intervenes. Wigner also proposed that an experimental
search be made for unusual effects of consciousness acting on
matter. It is my own conviction that the clue to paranormal phenomena
lies embedded in quantum theory.
An important formulation was made nearly twenty years ago by Everett,
Wheeler and Graham.(80) They attempted to deny the collapse of
the state vector, and take the full mathematical formalism of
quantum mechanics as it was originally presented. The world could
be represented by a vector in Hilbert space, a set of dynamical
equations for a set of operators that act on the Hilbert space,
and a set of commutation relations for the operators; always provided
that it were possible to decompose the world into systems and
apparatus. Hilbert space is the complex analogue of Euclidean
space, namely a space in which a system of orthogonal straight
line coordinates is possible. Complex vectors epsilon(i) satisfying
orthogonality relations (epsilon(i), epsilon(k)) = delta
function of i,k are employed
Every vector psi is a linear function of the unit vectors:
psi=sum over k of psi k * epsilon (k)
and
psi k = (psi, epsilon(k))
This proposal forces us to believe in the reality of all the simultaneous
universes represented in the superposition described by the above
equations. These universes cannot communicate physically with
each other, because the vectors are mutually orthogonal. In three-dimensional
space it would be possible to have only three mutually orthogonal
sets of vectors, but in a many-dimensional Hilbert space many
such vectors could simultaneously exist, so that there is here
the basis for simultaneously existing universes which cannot communicate
physically with each other. Simultaneous universes have always
been a subject which has fired the highest flights of human imagination.
One has only to think of Milton, Dante, or in recent times of
Jean Cocteau's Orphée.
It is not the existence of many simultaneous universes that is
the most difficult concept to believe, but the continual splitting
of one universe into an infinite (or very large) number each time
an observed quantum transition occurs. We can hardly conceive
of how many simultaneous universes there must be if this can
really happen. For this reason Schrodinger refused to accept the
consequences of the fully formal quantum mechanics.
I will repeat the proposal in the words of de Witt:(81)
The universe is constantly splitting into a stupendous number
of branches, all resulting from the measurement-like interactions
between its myriads of components. Moreover, every quantum transition
taking place on every star, in every galaxy, in every remote corner
of the universe is splitting our local world on earth into myriads
of copies of itself.
What is really uncomfortable about this formulation is the invasion
of our privacy. We do not like the idea of countless (>l0^100)
doppelgangers of ourselves, increasing in number all the time,
even if they can never communicate physically. Perhaps they could
communicate telepathically. But at least a proof can be given,
in quantum mechanical terms, of the fact that we cannot feel the
splits in physical terms.
Some comfort can be taken from the experience of physics, that
it is only in microscopic, atomic, terms that quantum theory gives
different results from classical mechanics. In the limit of large
numbers of energy quanta within one system - that is in the limit
of large quantum numbers there is correspondence between quantum
and classical mechanics. In classical, macroscopic, surroundings
the universes all look the same, and this is surely less uncomfortable.
Nevertheless there are quantum-determined events, such as the
mysterious death of Schrodinger's cat in the chamber, which differ
from one universe to another.
If macroscopic objects were able to make quantum transitions,
then the situation would be very much more precarious. There is
a whole field of physics in which macroscopic quantum effects
occur - namely the physics of very low temperatures, close to
absolute zero, where superfluids and superconductors exhibit their
extraordinary properties. Theorists who have worked in that field,
such as Frohlich,(82) are alive to the possibility that quantum
theory may apply macroscopically even at room temperature. If
we can describe a macroscopic object by a single mathematical
expression, a wave function, when its temperature is close to
absolute zero, then for very short periods of time macroscopic
wave functions might have significance at higher temperatures,
where the movements of the atoms obscure the regularity of the
system.
David Bohm and his colleagues(83) have proposed that there is
a characteristic time t ~= h/kT for which a macroscopic
wave function has reality. Here h is the Planck constant,
k the Boltzmann constant, and T the temperature.
This time will be appreciable at very low temperatures, but very
short, 2 * l0^-13 sec, at room temperature. Only certain types
of atomic and nuclear transition can take place in such a short
time, but the remote possibility of macroscopic quantum phenomena
in solids at room temperature remains. Normally within a solid
object the locaised wave functions may not be considered as assembling
coherently into a single macroscopic wave function; but local
coherence domains might develop, the boundaries changing with
time and with the characteristic time t determining the rate of
the process. This concept has as yet no experimental basis in
solid state physics, but it opens up many possibilities. What
is proposed is a continual fission-fusion process; the fission
of macroscopic wave functions into microscopic ones, and their
subsequent fusion into other macroscopic ones. But it is not clear
that the temperature T is the thermodynamic temperature.
What has prompted such interest in macroscopic wave functions
has been the realization by many physicists of the non-locality
of quantum theory, of both photons and particles possessing rest-mass.
The Einstein-Rosen-Podolsky paradox is at last coming to receive
the attention due to it. The situation envisaged, and now confirmed
experimentally, is that in the dissociation of a two-particle
system into single particles, with the latter travelling in space,
the relative polarizations of the particles become determined
and related only at the instant of measurement at two remote locations.
This instant can be made sufficiently short for no communication
between the two particles by (virtual) photons to be possible;
therefore the quantum description of the situation is non-local
over the space of the experiment.
The extreme position which it would be possible to adopt is that
of considering the whole universe to be described by one single
wave function; there would be myriads of stationary states, and
until an observation was made, the universe could be written as
a linear combination of all of them. This is equivalent to the
statement that the universe contains only a single electron, and
it provides some justification for the experimentally observed
constancy of electronic charge and rest-mass.
In Copenhagen quantum theory, using the wave equation, we can
predict the passage of a system of unique energy Eo into a mixture
of states, each with its own unique energy Eabc, but each
possessing a certain calculable probability of being the state
to which the first state has been changed; at any instant the
energy is equal to Eo = a*Eb + b*Eb + . . . But at the instant
of observation a discontinuous change occurs in the system by
which it collapses from a mixture of states into one state only.
But in the many-universe formulation, the wave function does not
collapse at the moment of an atomic transition; rather, it splits
into an infinite number of wave functions, each in its own set
of Hilbert space co-ordinates, and each differing from the others
in its energy, Ea, Eb, etc. The observer, in his particular
universe, is capable of measuring this energy, but another observer,
in a different but physically incommunicable universe, would measure
a different energy. Since it is purely a matter of chance which
universe the observer is in, the particular result he obtains
appears to him random. But if he repeats a similar observation
a sufficient number of times, then his result is predictable by
the wave-equation (from which the forementioned a, b, c, etc.
are derived), because all sets of co-ordinates are equally probable.
The collapse of the state vector is avoided by postulating that
within a single universe only the initial and final states are
real, the mixture having no reality unless an infinity of universes
is taken into account.
The proposal inherent in the many-universe theory, that each atomic
transition in our own insignificant bodies causes the remotest
galaxies to split into an infinite number, has resulted in the
theory having only a very limited acceptance among physicists.
Perhaps it would be more satisfactory if bounds were placed upon
the local universes. But such bounds would introduce physical
effects akin to surface phenomena, and normal effects of this
type are as yet unknown to physics. The original Everett-Wheeler-Graham
theory assumed that there was one observer in one universe, the
same universe which contains the observed phenomenon.
But if we were to allow ourselves the luxury of a dualistic system,
with non-material, or at least trans-spatial minds, then there
would be powerful possibilities for the interpretation of physical
psychic phenomena.
For example, we might speculate that the unconscious mind possesses
the facility of receiving 'trans-spatial' information from the
corresponding minds in other 'universes'. Since, because of the
orthogonality, physical signals cannot pass from one universe
to another, we would be forced to assume that the unconscious
mind has trans-spatial properties and is able to communicate with
physical reality in other universes only through other unconscious
minds.
On the parallel universe model, millions of copies of each individual
have parallel existences, but are entirely isolated physically
from each other by the orthogonality, which prevents the passage
of physical signals between universes. Let us propose that each
one of these individuals possesses his own mind, and that communication
between these corresponding minds is sometimes possible. No individual
knows of the existence of his many alter egos. But if he
were able to adopt the mind of one of these alter egos, he
would then take the other universe to be his reality, without
knowing that any change had occurred. Moreover, at the moment
he successfully does this, one might suppose that his neighbours'
minds (the observers' minds) could also come to be dominated by
those of their own alter egos, so that they would also
take the other universe to be their reality. All observers could
now notice whatever physical differences there might be between
the two universes. The differences could be that psychic phenomena,
metal-bending, psychokinesis or teleportations have taken place.
This principle could be extended in complication in two ways.
First, there is no reason to limit the number of universes to
two only, one before the mental change and one after. The only
situation in which we know the universe to be singular (locally)
is at the moment at which datum of an atomic physics experiment
is recorded. This is a comparatively rare moment, so why should
we not propose that we all pass through life in a continual state
of subtending many universes at the same moment of time? Since
these universes are in nearly all respects identical, we have
hitherto imagined them to be a single universe. Sometimes a unique
universe forces us to notice it, and it is then that we say that
an atomic physical phenomenon has occurred.
Second, it might be that some of the universes are partially incomplete
in the sense that the mind only knows of their existence locally.
the mind might actually impose spatial boundaries on some or all
of its local universes. These boundaries could be the 'surfaces
of action' at which we have observed metal-bending action to take
place. Outside the boundaries, that universe would not exist.
If the boundary were made to move through space by the action
of the psychic's unconscious mind, with which the observers' minds
concur, then one universe will actually grow, contract or change
shape; and the surface effects continually resulting from such
changes would make up the metal-bending structural and quasi-force
action. The change of shape is not noticed in other ways, because
so many universes are superposed that no mind regards any one
of them as incomplete. If the observers' minds do not concur,
then no physical changes can be measured, and the event is hallucinatory.
The fusion and fission of wave functions(83) into macroscopic
size would also be necessary to this interpretation of physical
psychic phenomena.
I include these speculations in order to show the extent to which
it would be necessary to go in order to explain physical psychic
phenomena with the aid of quantum physics.(84) I have in fact
carried the speculations a good deal further, but I will not indulge
myself at this stage, other than in a summary:
1 Teleportations could be interpreted using the hyperdimensional
character of the many-universes model. It may be that such hyperdimensionality
is strongly indicated by the discovery in the 1960s of the non-conservation
of parity.
2 Metal-bending and structural change could be interpreted in
terms of the reorganization forces which must occur in the creation
or annihilation of atoms at the inter-universe boundaries or 'surfaces
of action'. The configurations of these surfaces would have to
be very complicated, showing turbulence perhaps down to atomic
dimensions.
3 Quasi-forces would have to be interpreted in terms of a rapid
series of local transformations into universes, each one with
its own individual momentum, each slightly greater than the last.
The rate of change of momentum would then have the appearance
of a force acting on the transformed object.
4 For psychic acoustic phenomena,(85) psychometry, optical and
electromagnetic phenomena and even the insensitivity of the human
body to great heat, similar interpretations could be considered.
But if we allow ourselves the luxury of such speculations, then
we must be prepared to accept the nightmare universes that could
have evolved in continually increasing numbers since the 'big
bang'. Precisely how many degrees of orthogonality different from
our own these would have to be is difficult even to conjecture.
Since most people (including, probably, the proponents of the
original many-universe quantum theory) would stop short of this,
they find themselves drawn inevitably to the denial that physical
psychic phenomena exist at all. That is why the spearhead of research
must be not in theoretical formulations but in physical observations.
My purpose in including this chapter has been to show just how
difficult it is for a physicist to incorporate physical psychic
phenomena within existing physical theory. Once the difficulties
are faced, however, a wide variety of alternative hypotheses about
the nature of what we have called 'primary events' can readily
be envisaged.
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