NotI
2013-01-17 04:53:39 UTC
[[Mod. note -- Please limit your text to fit within 80 columns,
preferably around 70, so that readers don't have to scroll horizontally
to read each line. I have manually reformatted this article. -- jt]]
Journal Ref: EJTP 10, No. 28 (2013) 27?80
http://www.ejtp.com/articles/ejtpv10i28p27.pdf
In QED, The Strange Theory of Light and Matter, Feynman describes
the electromagnetic force as transmitted by photons, or particles
of light. The photon carries momentum from one electron to the
other, pushing them apart and explaining the Coulomb force. Many
physicists reject this conception, claiming that the photon in the
diagram is ?virtual?, a device which does not really exist. My paper
demonstrates that Feynman?s view is correct; photons transmitting
a real force can be regarded as real, but quantum fields are virtual.
The debate on the fundamental nature of light has swung to and fro
for 350 years. Corpuscular theory, influenced by Epicurean atomism,
was proposed by Pierre Gassendi and published posthumously in the
1660s, but Hook published a wave theory also in the 1660s and Huygens
described waves in his Treatise on Light (written 1678, published
1690). The development of corpuscular theory in Newton?s Opticks,
published in 1705, made particles dominant, but the argument was
thought to have been resolved in favour of waves by Young?s experiment
in 1801. In 1905 Einstein explained the photoelectric effect in
terms of quanta of light, and Dirac and Feynman clearly favoured a
particulate interpretation of quantum phenomena, but the orthodoxy
over the last 50 years has been that quantum electrodynamics is a
quantum field theory, based on quantisation of the wave function
(second quantisation).
Since the late 1940s, quantum electrodynamics has given some of the
most accurate predictions known to science, but at the same time
it has been beset with problems of the infinite, meaning that it
is mathematically incorrect, at least in some details. Some infinities
have been removed by ad hoc procedures known as renormalisation.
But renormalisation has no proper mathematical justification and
was severely criticised by two of the founders of qed. Feynman
called it a ?shell-game? (i.e. a fraud), a ?dippy process? and
?hocus-pocus?. Dirac said ?This is just not sensible mathematics.
Sensible mathematics involves neglecting a quantity when it is small
? not neglecting it just because it is infinitely great and you do
not want it!?.
Many physicists embrace renormalisation. They argue that physics
consists of nothing more than rules for calculation, and are satisfied
if the results agree with observation. They claim that the photons
appearing in Feynman diagrams are ?virtual?, and cannot be regarded
as particles with the real effect of transmitting the electromagnetic
force.
But the historical purpose of physics has been to describe the
workings of nature. This requires a single comprehensive theory
applying to all phenomena, not one theory for non-relativistic
quantum mechanics, another for relativistic quantum theory, and a
third for classical electrodynamics. The Landau pole and the Dyson
instability show that, even after renormalisation, standard qed
does not make mathematical sense. It is at best a collection of
algorithms leading to a number of correct physical predictions. It
is thought of as a ?field theory?, and is not a consistent part of
a single theory incorporating either standard quantum mechanics or
classical electromagnetism.
My paper, published in the open access, peer reviewed, Electronic
Journal of Theoretical Physics seeks to change all of this. It is
a mathematically rigorous construction of full quantum electrodynamics
from first principles in foundations of quantum mechanics, avoiding
all infinite quantities, and yielding classical electrodynamics in
the appropriate correspondence. In this form, qed is mathematically
consistent and unified with other areas of physics. It is a theory
of particles, as conceived by Dirac and Feynman, not a theory of
fields as described in most ?modern? accounts.
I make explicit Von Neumann?s interpretation of quantum mechanics,
that quantum logic is a language which tells us what can be known
about the results of measurements, by showing that the language
makes statements in the subjunctive mood. The wave function, f(x),
is identified with the statement ?if we were to do a measurement,
we would find the particle at position x?. The superposition, f(x)
+ f(y), simply means ?we would find the particle at either x or y?.
We find where photons are created or annihilated, rather than where
they are, but the principle is the same. When we will do a measurement,
the subjunctive is replaced by the future tense and a probability
can be calculated. I show that the mathematical structure of formal
sentences in the subjunctive is precisely the structure of quantum
mechanics, and that consistency with probability theory requires
that Schr?dinger?s equation is obeyed. Waves are an illusion generated
by mathematical structure. Quantum fields appear in mathematical
structure, not in underlying physics. Space appears as an emergent
property from the interactions of many particles, not as a background
into which particles can be placed.
As with Einstein?s treatment of special relativity, My treatment
of quantum theory is formulated in terms of the results of measurement.
All physical properties arise from interactions, including the
property of position. It only makes sense to describe position
relative to other objects, not with respect to a prior space or
spacetime. Quantum uncertainty arises precisely because space is
not a fundamental physical concept.
Measurement necessarily has finite range and resolution. The only
physical processes are discrete particle interactions, which are
again finite. A key mathematical step in my treatment is to show
how the mathematics of the continuum, as normally used in quantum
theory, can be applied to a model which is physically discrete and
finite. Infinite quantities appear from the misapplication of this
mathematics, not from the physical model. Using a finite number of
terms, the standard infinite perturbation expansion in qed is seen
to be an approximation to a finite expansion which does not have
the problem of the Landau pole or the Dyson instability.
The consequence is that, instead of trying to understand nature in
terms of quantum fields with inconsistent properties, and treating
Feynman diagrams as merely a calculational technique with no physical
meaning, we can fully justify Feynman?s conception that electrodynamics
is described by interactions between charged particles and photons.
Mathematically, Feynman diagrams are graphs. The configuration of
lines and vertices has meaning, but the paper on which a graph is
drawn does not. By representing possibilities for configurations
of particle interactions, Feynman diagrams give real insight into
the fundamental structure of matter.
This paper is certain to engender hostility from field theorists.
By showing that fields are virtual, particle theoretic qed undermines
the rationale for many of the developments of the last fifty years,
including string theory and the Higgs mechanism by which particles
in the standard model are thought to gain mass (this does not
preclude the existence of new particles). There is little value in
theories which have no empirical foundation, no mathematically
rigorous justification and which make no correct predictions. A
valid challenge to particle theoretic qed needs to be based in
mathematics or empirical physics, not in citing authority, accepted
wisdom, or half-baked philosophical argument. I don?t see that my
construction leaves scope for such a challenge.
preferably around 70, so that readers don't have to scroll horizontally
to read each line. I have manually reformatted this article. -- jt]]
Journal Ref: EJTP 10, No. 28 (2013) 27?80
http://www.ejtp.com/articles/ejtpv10i28p27.pdf
In QED, The Strange Theory of Light and Matter, Feynman describes
the electromagnetic force as transmitted by photons, or particles
of light. The photon carries momentum from one electron to the
other, pushing them apart and explaining the Coulomb force. Many
physicists reject this conception, claiming that the photon in the
diagram is ?virtual?, a device which does not really exist. My paper
demonstrates that Feynman?s view is correct; photons transmitting
a real force can be regarded as real, but quantum fields are virtual.
The debate on the fundamental nature of light has swung to and fro
for 350 years. Corpuscular theory, influenced by Epicurean atomism,
was proposed by Pierre Gassendi and published posthumously in the
1660s, but Hook published a wave theory also in the 1660s and Huygens
described waves in his Treatise on Light (written 1678, published
1690). The development of corpuscular theory in Newton?s Opticks,
published in 1705, made particles dominant, but the argument was
thought to have been resolved in favour of waves by Young?s experiment
in 1801. In 1905 Einstein explained the photoelectric effect in
terms of quanta of light, and Dirac and Feynman clearly favoured a
particulate interpretation of quantum phenomena, but the orthodoxy
over the last 50 years has been that quantum electrodynamics is a
quantum field theory, based on quantisation of the wave function
(second quantisation).
Since the late 1940s, quantum electrodynamics has given some of the
most accurate predictions known to science, but at the same time
it has been beset with problems of the infinite, meaning that it
is mathematically incorrect, at least in some details. Some infinities
have been removed by ad hoc procedures known as renormalisation.
But renormalisation has no proper mathematical justification and
was severely criticised by two of the founders of qed. Feynman
called it a ?shell-game? (i.e. a fraud), a ?dippy process? and
?hocus-pocus?. Dirac said ?This is just not sensible mathematics.
Sensible mathematics involves neglecting a quantity when it is small
? not neglecting it just because it is infinitely great and you do
not want it!?.
Many physicists embrace renormalisation. They argue that physics
consists of nothing more than rules for calculation, and are satisfied
if the results agree with observation. They claim that the photons
appearing in Feynman diagrams are ?virtual?, and cannot be regarded
as particles with the real effect of transmitting the electromagnetic
force.
But the historical purpose of physics has been to describe the
workings of nature. This requires a single comprehensive theory
applying to all phenomena, not one theory for non-relativistic
quantum mechanics, another for relativistic quantum theory, and a
third for classical electrodynamics. The Landau pole and the Dyson
instability show that, even after renormalisation, standard qed
does not make mathematical sense. It is at best a collection of
algorithms leading to a number of correct physical predictions. It
is thought of as a ?field theory?, and is not a consistent part of
a single theory incorporating either standard quantum mechanics or
classical electromagnetism.
My paper, published in the open access, peer reviewed, Electronic
Journal of Theoretical Physics seeks to change all of this. It is
a mathematically rigorous construction of full quantum electrodynamics
from first principles in foundations of quantum mechanics, avoiding
all infinite quantities, and yielding classical electrodynamics in
the appropriate correspondence. In this form, qed is mathematically
consistent and unified with other areas of physics. It is a theory
of particles, as conceived by Dirac and Feynman, not a theory of
fields as described in most ?modern? accounts.
I make explicit Von Neumann?s interpretation of quantum mechanics,
that quantum logic is a language which tells us what can be known
about the results of measurements, by showing that the language
makes statements in the subjunctive mood. The wave function, f(x),
is identified with the statement ?if we were to do a measurement,
we would find the particle at position x?. The superposition, f(x)
+ f(y), simply means ?we would find the particle at either x or y?.
We find where photons are created or annihilated, rather than where
they are, but the principle is the same. When we will do a measurement,
the subjunctive is replaced by the future tense and a probability
can be calculated. I show that the mathematical structure of formal
sentences in the subjunctive is precisely the structure of quantum
mechanics, and that consistency with probability theory requires
that Schr?dinger?s equation is obeyed. Waves are an illusion generated
by mathematical structure. Quantum fields appear in mathematical
structure, not in underlying physics. Space appears as an emergent
property from the interactions of many particles, not as a background
into which particles can be placed.
As with Einstein?s treatment of special relativity, My treatment
of quantum theory is formulated in terms of the results of measurement.
All physical properties arise from interactions, including the
property of position. It only makes sense to describe position
relative to other objects, not with respect to a prior space or
spacetime. Quantum uncertainty arises precisely because space is
not a fundamental physical concept.
Measurement necessarily has finite range and resolution. The only
physical processes are discrete particle interactions, which are
again finite. A key mathematical step in my treatment is to show
how the mathematics of the continuum, as normally used in quantum
theory, can be applied to a model which is physically discrete and
finite. Infinite quantities appear from the misapplication of this
mathematics, not from the physical model. Using a finite number of
terms, the standard infinite perturbation expansion in qed is seen
to be an approximation to a finite expansion which does not have
the problem of the Landau pole or the Dyson instability.
The consequence is that, instead of trying to understand nature in
terms of quantum fields with inconsistent properties, and treating
Feynman diagrams as merely a calculational technique with no physical
meaning, we can fully justify Feynman?s conception that electrodynamics
is described by interactions between charged particles and photons.
Mathematically, Feynman diagrams are graphs. The configuration of
lines and vertices has meaning, but the paper on which a graph is
drawn does not. By representing possibilities for configurations
of particle interactions, Feynman diagrams give real insight into
the fundamental structure of matter.
This paper is certain to engender hostility from field theorists.
By showing that fields are virtual, particle theoretic qed undermines
the rationale for many of the developments of the last fifty years,
including string theory and the Higgs mechanism by which particles
in the standard model are thought to gain mass (this does not
preclude the existence of new particles). There is little value in
theories which have no empirical foundation, no mathematically
rigorous justification and which make no correct predictions. A
valid challenge to particle theoretic qed needs to be based in
mathematics or empirical physics, not in citing authority, accepted
wisdom, or half-baked philosophical argument. I don?t see that my
construction leaves scope for such a challenge.