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Is there more to quantum
theory than quantum mechanics? The former is
the departure from the continuity scheme of
Newtonian mechanics to one in which certain physical
quantities only take certain restricted discrete
values; the latter is the mathematical theory used
to predict values of measurable quantities.
From one
perspective, it can be seen that quantum physics has
a third part. The first being the theory of discrete
physical quantities, the second, the mathematics in
the form of the wave function and the probabilities
that pertain to the result of measurements and the
third is the set of symmetries which attach to the
processes which can be expressed as:
Representation —> Transformation —> Invariance These elements are uncontroversial
in so far as they do not stand in the way of the
acceptance of the various interpretations of quantum
theory. They are consistent with the Copenhagen
interpretation, the many worlds interpretation, the
transactional interpretation, Bohm's pilot wave theory
etc.
By contrast, the mysteries or weirdness which derive from quantum discreteness are controversial. They include the quantum jump, wave particle duality and the measurement problem; to name just three. These are so difficult to deal with, or accommodate in the theory, that they have generally been side-stepped. The problem, for instance, of quantum tunnelling has to be set aside even though as a physical fact it is a necessary part of nuclear theory. History is consistent with the idea that the question of how physical theory can successfully move beyond the standard model cannot be answered without first disentangling the physical meaning of the quantum mysteries and then incorporating them in a new foundation for the way ahead. The last hundred years of struggling to understand the atomic nucleus in a framework of continuous motion of quantum objects in curved space has failed. The continuity model is bankrupt. The Born interpretation It was Max Born, in 1926, who linked the quantum wave function with empirical meaning. He discovered that squaring the modulus of the wave function gives the density of the probability of an occurrence, such as observing an electron. A diffracted electron can be found in any space for which the wavefunction is not zero. If the meaning of the wavefunction is confined to what the square of the modulus refers to then what is happening between the diffraction and the ensuing detection of the electron—the intervening period—is irrelevant. This is crucially important to any realistic theory of the microscopic realm. What then of the intervening
period? Born's discovery is consistent with either the
electron being somewhere, everywhere or nowhere in the
intervening period. Perhaps even more possibilities
can be imagined! What is important is to discover the
importance or even the relevance of the difference
between the three possibilities. What we do know is
that the question has no relevance for the probability
of the electron being somewhere, when it is observed.
This is why what is going on in the intervening period
can form the basis for any number of different quantum
interpretations, provided the wavefunction and its
importance are never lost sight of. That way, every
interpretation has the same mathematical outcome—they
are all equally successful, at least they are
frequently claimed to be so.
The issue of the intervening period
becomes somewhat more complicated when it is realized
that the wavefunction is relevant to an abstract
configuration space, not physical three dimensional
space or four dimensional spacetime. This leaves open
the possibility that what is going on in configuration
space and in physical space are different, because
during the intervening period their mutual relevance
is undetermined. What is happening in configuration
space is mathematical and not physical. It is this
question of relevance which is the foundation of the
perceived incompleteness which plagues quantum
mechanics.
A minimalist interpretation
A consequence of the apparent
equivalence of the different interpretations of
quantum mechanics is that experimental differentiation
between them is not just round the corner. Thus, we
have no reason to expect that one or more
interpretations will fail some experimental test of
their correctness. Despite this, all may not be lost
in the quest for the interpretation that matches the
real world—if, indeed, one of them does. It is
generally the case that in addition to predicting the
outcome of experimental results, theories
provide explanations of formerly unexplained
phenomena, whether or not they are dependent upon
mathematical quantification or description.
Explanations derivative of a theory may embrace
phenomena, formerly considered unrelated, in a manner
which unifies them under a single principle.
In the latter half of the twentieth
century, unification of the four forces of Nature
under a single principle was a centrally important
question. As things stand at the beginning of the
twenty-first century, quantum mechanics and special
relativity are less than seamlessly unified. And
quantum field theory (QFT) is plagued with
renormalisation problems whose underlying causes have
a distinctly unnatural flavour about them. Thus, one
of the interpretations may pull ahead of the field in
the race to explain the QFT provides the framework for several theories of microscopic objects in modern physics. It is the project to combine special relativity and quantum mechanics so as to make the latter comply with the rules of the former. The result is relativistic quantum theory but it is not fully satisfactory and many would claim it remains incomplete. Any project to extend quantum mechanics must take account of the views of Bohr and Heisenberg on what quantum mechanics actually means, not just what it predicts about microscopic phenomena. This is especially important if the extension entails a reliance upon more than the mathematical formalism. And such an extra formalistic reliance underlies QFT. A simply appeal against the non reality of quantum mechanics accompanied by an insertion of classicality to correct the deficiency runs the risk of fatally damaging the whole project. When the foundations of QFT are
examined in the light of Bohr's complementarity
interpretation, the logic of one manoeuvre stands out
as a source of unease. The manoeuvre is the insistence
that evolving quantum systems have properties in
opposition to Bohr's claim that unmeasured systems
lack properties. From the point of view of the theory
of the inheritance of order, QFT extends Bohr's
concept of the unobserved system beyond the scope of
its natural limit. QFT adopts the contrary postulate:
"The property of a quantum system in the position
representation is the wavefunction and not a specific
location as in the classical case." The quantum state is a description
containing definite values of a set of physical
properties. QFT assumes that the description is
applicable to the system. Such an assumption is
unwarranted. The extrapolation of the description from
the quantum state to the quantum system is not a
simple matter. And how it differs from the relations
between the set of odds for the different horses in
the next race and the winner is also unclear.
That is not the present analysis, according to which, if it is not at a particular or definite position the electron might as well be at no position and we have no reason to go beyond that conclusion. We need to set aside all reliance upon classicality, which is sometimes called common sense. Being at no particular or definite position does not warrant any conclusion as to where the system is; or whether it is anywhere! The minimalist analysis adopted here agrees that the electron is at no definite or particular position and draws no conclusions beyond that fact. Of course, this runs counter to commonsense--but then common-sense is what tells us the earth is flat! The analysis of the logic underlying
the electron being smeared out among all the
positions, at which there is some probability of its
being found, depends upon two implied propositions:
One is that the world contains the electron and the
other is that the world includes all the positions at
which it might be found in the future. However, if we
adopt the mode of coupling space and time in the
formation of spacetime which does not reduce the time
axis to a space-like axis, and separate the concept of
action from its representation, then we can question
the idea that future spacetime loci are present before
they occur! Put simply, if space and time are merely
relations among objects and if the object has not yet
arrived then perhaps neither has the space and time
which relate it to other objects. If the world is
discrete instead of continuous, then perhaps it only The evolution of the quantum system
is inscrutable—it is private because it has no
extrinsic or classical aspect. And theory says nothing
about what is going on in the quantum domain. It only
predicts what happens when quantum objects interact
with the classical domain—when what happens is always
classical. The simplest position to take is that
nothing classical is going on in the quantum
domain—nothing that can be counted, measured or
observed.
For the abstracts of the three papers and links to the full text, as pdf files, click here.
In brief, when space and time are understood as
geometric relations for the individual electron, the
behaviour of the electron is both quantum mechanical
and gravitational. Gravity curves the space-time
trajectory of the electron, rather than a space-time
that is independent of the objects that it relates.
The pre-print abstract
is here.
For the full text, as a pdf file,
click here Notes: |

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© Peter Fimmel 2002-2009 Last page update 02/06/09 |