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FOUNDATIONS OF QUANTUM PHYSICS
Clarifying some muddled terms
MECHANICS encompasses models based upon the fundamental CD
polarity (Continuum/Discreteness), applying in its context
the equations of motion for singular points and differential
equations for the vector field,
STATISTICAL MECHANICS is the application of probability theory
to study the behavior of systems of a large number of particles.
It provides a framework for relating the microscopic properties
of individual particles to observable bulk properties of the
macroscopic system.
QUANTUM PHYSICS will encompass all Continuum/Discreteness polarity
based, field quantizing models, such as Plank's blackbody,
Einstein's photons, and the QFT.
QUANTUM MECHANICS (QM) is a catch-all term used indiscriminately
for any conjecture having really or apparently (see Bohr's model
below) anything to do with QUANTUM PHYSICS. We shall designate
with it exclusively the "Rudimental QM", the - ill founded in
discreteness - short interlude within the continual progress of
the Quantum Physics.
INCEPTION OF QUANTUM PHYSICS
Primacy of Continuum.
Comparing the QFT with the rudimental QM one usually contrasts
the relativistic versus non-relativistic approach. We shall use
a deeper and more general criterion founded in the basic CD
(Continuum/Discreteness) polarity and shall contrast the
foundational primacy of continuum versus that of discreteness.
Quantum Physics was born with Planck's study of the blackbody
radiation which formulated the concept of EM energy quanta
(E = hf) and with Einstein applying the quantum concept to the
fotoelectric effect and discovering photons.
Inception of the Quantum Physics is thus a clear case of
continuum primacy, of discretizing the EM field continuum
into quantum packets.
BOHR'S MODEL.
Primacy of discreteness.
In 1913 Bohr proposed his orbital model of atom, an entirely
discrete analogy of macroscopic planetary systems, where electrons
radiate or absorb energy quanta when changing their orbits.
It had the merit of supporting the Mendeleiev elements table,
the chemical valence and the hydrogen spectrum.
It had the demerit of neglecting the primacy of continuous field
as support of quantum discretization and of representing
infinitesimal events with a crude and naive macroscopic analogy.
Let's note that, similarly to Einstein's theory of the
photoelectric effect, Bohr assumed discrete amount of energy
being radiated by quantum jumps. However, he explained it by
the discreteness of the orbital energy levels and did not
believe in the existence of photons.
RUDIMENTAL QM.
Primacy of discreteness.
Physicists, excited by the discovery of quanta, confused
discretization of continuum with autonomous discreteness and,
with the zeal of neophytes, rushed to create new, absolutely
discrete physics - the rudimental QM formulated by Dirac,
Heisenberg and Schroedinger. It did not deal with continuous EM
field radiation, but with discrete atomic spectra of Bohr's
orbital model. Founded in naked discreteness, the rudimental QM
was necessarily acausal and its events occurred out of a blue sky,
randomly and magically.
Trying to tone down this magic, Einstein asserted:
***
On the basis of quantum theory there was obtained a surprisingly
good representation of an immense variety of facts which otherwise
appeared entirely incomprehensible. But on one point, curiously
enough, there was failure: it proved impossible to associate with
these Schroedinger waves definite motions of the mass points - and
that, after all, had been the original purpose of the whole
construction. The difficulty appeared insurmountable until it was
overcome by Born in a way as simple as it was unexpected.
The de Broglie-Schroedinger wave fields were not to be interpreted
as a mathematical description of how an event actually takes place
in time and space, though, of course, they have reference to such
an event. Rather they are a mathematical description of what we
can actually know about the system. They serve only to make
statistical statements and predictions of the results of all
measurements which we can carry out upon the system.
It seems to be clear, therefore, that Born's statistical interpretation
of quantum theory is the only possible one. The wave function does not
in any way describe a state which could be that of a single system;
it relates rather to many systems, to an 'ensemble of systems' in the
sense of statistical mechanics. (Einstein, 1936)
***
It hardly tones down anything. "On the basis of quantum theory"
sounds ambiguous. If it designates the rudimental QM "of these
Schroedinger waves", one hardly sees the immensity of "represented
facts". After all the objective of quantum physics consists in
defining and detecting particles, but none has been detected
by the rudimental QM. All were discovered by field quantizing
methods having nothing to do with Schroedinger wave. Born's
statistical interpretation simply confirms that Schroedinger
wave cannot represent and coordinate mechanical events. And Born's
interpretation of the Schroedinger wave as probability of finding
a particle in a SPACE location was not quite rigorous, because
the rudimental QM did not posit any particular SPACE.
Schroedinger played a major and rather unusual role in the
development of quantum physics. One could call him "eternally
dissatisfied".
He was dissatisfied with the discreteness of Bohr's model and
computed the spectral lines for hydrogen by treating a hydrogen
atom's single electron as a wave. This wave function elevated
him to principal founder of the QM, bestowing on him celebrity,
nay, immortality - in 2010 the Wikipedia writes:
"In physics, specifically quantum mechanics, the Schroedinger
equation is ... as central to quantum mechanics as Newton's
laws are to classical mechanics."
Enough to gratify anybody, one would say. And yet, Schroedinger
was dissatisfied. Dissatisfied with the statistical character of
his equation. Like Einstein, he believed that the statistical
approach of the QM was an approximation to an underlying eventtual,
causal theory. This dissatisfaction motivated him to conceive - with
help of the relativistic energy momentum relation - what is now
known as the Klein-Gordon equation and thus to decry the QM and to
anticipate the QFT. However, dissatisfied with his relativistic
corrections disagreeing with Sommerfeld's formula, he secluded
himself in a mountain bungalow with a lover and did not follow up
his anticipation of the QFT.
Failing to posit and to discover particles, extremist partisans of
the rudimental QM concentrated on contesting the causal view of
physics fending for the acausal randomness inherent in autonomous
discreteness. They did it mainly with the help of Bell's inequalities
and related experiments headed by that of Aspect, which failed for
numerous reasons, of which we shall mention a few:
-According to Franson the timing constraints of Aspect experiment
prohibit conclusive results. Aspect measured the time delays between
detections of photon pairs. The critical time delay is that between
the change of a polarizer angle and the detection of photon pairs.
Aspect estimated this time based on the speed of a photon and the
distance between the polarizers and the detectors.
However, Quantum Physics and the rudimental QM itself do not allow
making assumptions about particle's location between detections.
We cannot know when a particle traverses a polarizer unless we detect
the particle at the polarizer, which of course is not the case.
Photons are detected at detectors (BTW with inacceptable fuzziness
due to Heisenberg's uncertainty and to simple technological problems.)
-Actually, the uncertainty of the time of traversing the polarizer
is still larger, due to light propagating not as photon, but as wave
and to the vagueness of the very concept of position of a wave.
Photons are observed at birth and at death (here detection).
In between, light propagates as wave. And polarizing clearly applies
to waves and has no sense with respect to particles.
-Another timing problem consists in the difficulty in establishing
the time of detection. The process starts as a microscopic event like
the atom decay that determines the fate of Schroedinger's cat. While
few believe the cat's fate remains undecided until one opens the box
the exact time at which that fate has become certain is unclear.
Timing in a test of Bell's inequality to be conclusive requires that
we time the occurrence of a microscopic event. The trouble is there
is no clear definition of when that microscopic event occurs. Franson
observed the following:
The time interval over which the concerned probability amplitudes
may simultaneously exist and interact could conceivably be comparable
to the 89-nsec lifetime of the excited atomic state which produces
the pair of photons. If the photon emission time remains indeterminate
for this length of time then it is plausible that the final outcome
of the event may remain indeterminate for a comparable amount of time.
-Even if by some miracle an experiment demonstrated rigorously
the violation of Bell's inequalities, it would in no way refute
causality. Bell's inequalities have been derived upon the false
assumption of continuum based, causal models claiming to be certain
and exact. But causal field models are as fuzzy and uncertain as
the allegations of the QM. (see "CAUSALITY AND IMPLICATION").
Bell's inequalities derived for hypothetical, ideal, exact causality,
are violated by the real, fuzzy causality just as they would be by
the alleged acausality.
Another angle of attack against the causal view of physics was
Bohr's metaphysical "Copenhagen Interpretation". It can hardly
be ignored, due to its outrageous impact on vulgarization and
on pseudo-philosophy. Yet, the present chapter dealing with
foundations of physics and not with shamanism, we relegate it
to appendix.
QUANTUM FIELD THEORY (QFT)
Primacy of continuum
QM's speculations about "reality" - read "transcendency" -
being or not "deterministic", were metaphysical and had nothing
to do with physics. That concerns as well the ill founded Bell's
inequalities, as the experiments, impressing technologically,
but trapped in the incompatibility of infinitesimal events
with discrete macroscopic devices.
One understands and sympathizes with the zeal of neophyte
manifested by many physicists who saw behind the newly
revealed quanta a new, exciting world and embarked on its
discovery. It was like a charming reverie, but to stay nice
a reverie should not hang on too long, nor encroach upon
the wakening. Most woke up soon to the unchanged world and
went back to work on physics, which stayed what it had been,
to wit gathering events and constructing models fit to
coordinate them.
But some refused to wake up and obstinate themselves to daydream
about magic, random wonderland, blind to the innumerable
accomplishments of the QFT supported by the continuum based,
causal foundations of physics.
Indeed, admitting for the sake of argument that Bell's inequalities
and Aspect type experiments have some physical significance, it
could only be marginal with respect to the objective of quantum
physics, to wit to positing and discovering particles. In fact,
one does not see how they could possibly contribute to this objective
and, anyway, not a single particle has been posited, let alone
discovered by the rudimental QM.
On the other side, that of continuum based QFT we find innumerable
new particles, particle types and fields:
neutrons, positrons, baryons, bosons, fermions, leptons, muons,
mesons, pions, kaons, neutrinos, partons, hadrons, quarks, gluons,
antiprotons, ...
The number of known fields is increased to four: electro-magnetism,
weak and strong fields and gravity. Einstein's dream of a unified
field theory got realized in "three-quarters", the first three fields
having been unified. Gravity being by far the weakest, still escapes
the trials of unification and of quantization. The postulated gravity
quanta or gravitons escape all existing experimental devices. The
strength of the QFT consists inter alia in its capacity to postulate
and to predict. Dirac postulated the positron, discovered years
afterwards. Gravitons, whether discovered or not, embody with the
Higgs Boson and the string theory the intuitive postulating power
of the QFT. Let's recall that QFT sees its constructs explicitly or
implicitly as manifestations of the Continuum/Discreteness polarity.
For instance the Higgs boson in its capacity of "giving mass to the
gauge bosons" is envisaged more as field, than as particle.
The Klein-Gordon equation, anticipated by Schroedinger, sounded the
death knell of the rudimental QM. None of its basic and failed
concepts has been taken over to the QFT. There is there no
Schroedinger equation, let alone its "collapse", no "quantum
entanglement", no teleportation, no instantaneous communication,
no ufo flying photons coming to the double slit from unknown worlds.
This being said, QFT experiences its own serious problems, but
they are of mathematical nature, not physical or foundational.
Field quanta take the mathematical form of singularities, but current
mathematics cannot deal with singularities and the involved infinities.
It would need some new non-linear algebra, which for the moment nobody
knows how to tackle. QFT tries to escape - not to solve - the problem
of involved infinities with the help of "normalization", procedure
no less than dubious in Dirac's opinion:
"When you get a number turning out to be infinite which ought to be
finite, you should admit that there is something wrong with your
equations, and not hope that you can get a good theory just by
doctoring up that number."
In spite of its mind boggling achievements - or perhaps because
of them - the QFT appears to us more as a challenge, than an
accomplishment and that's what makes it so exciting.
APPENDIX
THE COPENHAGEN INTERPRETATION
Heisenberg Uncertainty Principle (HUP)
The position of a body can be judged by looking at it, i.e.
by observing the photons bounced off the object and arrived
at our eyes. The position of a car is not much altered by
the photons bouncing off it. But if photons are bounced off
an electron to determine its position, its velocity will be
altered and uncertain. Photons with shorter wavelength and
higher energy have less diffraction and determine electron's
position more precisely, but in doing so they alter the
electron's velocity more radically.
Observing an aspect of a particle we necessarily use some
physical detector whose action affects and blurs its other
aspects. It's a drawback of our physical perception which
restricts its certainty, but in no way determines the
intrinsic characteristics of the particle prior to the
measurement. Heisenberg elevated this simple measurement
problem to the metaphysical intrinsic quality of particles,
whose properties don't exist before an observation creates
them as precise/blurred couples. This implies that particles
being structures of properties don't exist, unless observed.
Thus, CI began to deny the very existence of an unobserved
electron. From the positivist idea that it is meaningless
to discuss the existence of something unobservable, came the
idea that the electron is an unreal, causeless "possibility"
which only achieves existence upon observation. Thus,
positivism became twisted into a sort of creationist solipsism
claiming that the observer somehow creates "reality" by the
act of conscious observation.
HUP holds for direct observations, but has been falsified by
deferred ones, such as photography. A photographic plate
containing the track of an electron can be used to determine
position and velocity within less than the uncertainty limit.
In a rather strange bit of reasoning Heisenberg denied the
evidence of the photographic plate by asserting that his
uncertainty principle is only relevant to predicting the
future, and that "this knowledge of the past is of a purely
speculative character", adding "It is a matter of personal
belief whether such a calculation concerning the past history
of the electron can be ascribed any physical reality or not."
(The Physical Principles of the Quantum Theory (1930))
For some reason, most physicists chose this personal belief
which denied physical reality of the past and conformed to
Heisenberg's and CI's reality of the future, without noticing
the intrinsic contradiction: HUP is supposed to concern
observation, but observation, once performed, slips into the
past, thus quitting the "future reality" and the alleged
relevance of HUP.
And yet, it's obvious to anybody having a slightest notion of
ontology that whatever "existence" or "reality" may mean,
they may be ascribed only to the past, while future is the
domain of possibility, of expectance and of project. Even the
most idealist philosopher, Hegel, stated it in one of nicest
and never contested assertion of philosophy:
"Wesen ist, was gewesen ist".
In this light, and in spite of his mathematical brilliance,
Heisenberg appears as a mediocre physicist and as a fatuous
philosopher, tainting the whole CI with amateurish solipsism.
Schroedinger's Equation (SE)
SE provides a statistical interpretation of the QM, just as
the Boltzmann equation, that of thermodynamics. Yet, nobody
pretended that a gas particle did not exist untill an
observation collapsed the Boltzmann equation. And if he did
he would be certified. That would be enough to put the fatuity
of SE's collapses in a nutshell, but some of their details are
too savory to be disposed of.
SE describes the probability of observing a particle in a
particular location, like the airline timetable describes
the probability of the plane from Paris to arrive in London.
Probability refers to future expectation. Conscious
observation "collapses", in terms of QM, the SE, switching
probability to knowledge. Waiting at the airport we expect
the plane as predicted by the timetable, but we know that it
arrived only after its observed landing. CI would claim
that the conscious observation of the landing "collapses"
the timetable and switches the flight from a "possibility"
to an existing plane, which did not exist prior to its
landing being observed. However, simple people awaiting
it and ignoring the intricacies of CI, don't question its
existence, but, when it is belated, worry about what may
have happened to it en route, observed or not.
And yet, great mathematicians affirm that the plane is just
an unreal, causeless "possibility" projected by the timetable
and achieving existence only by an observation "collapsing"
the timetable. Or, at least, that's exactly what they assert
with respect to a particle achieving existence only through
a conscious observation collapsing the SE. With the only
excuse that the expertly handled QM's equations cover from
them the gist of physics, as so decently admitted Feynman.
Talking about SE we have to mention how Schroedinger himself
evaluated its epistemological and physical sense. He created
the famous cat in order to reduce ad absurdum the "dogmatic
QM" with its "consciousness created reality" and to keep
probability at its due place.
Yet, amazingly, CI protagonists turned the Cat upside down,
elevated the symbol of their ridiculosity to their motto and
kept on asserting that the cat does not exist as long as nobody
looks into the box and comes to (alive or dead) existence only
by virtue of somebody peering at it. Or, alternatively, that
prior to the peering act it exists as both, alive and dead.
And such is the power of Nobel Prizes and of mathematical
celebrity, that none got certified.
To descend a bit deeper into the abyss of the SE collapse we
shall recall that quantal experiments use technological
detectors, whose records are subsequently investigated. That
raises the question: will SE collapse and the observed object
start existing at the moment of recorded detection, or at the
deferred conscious perception of the record by the experimenter.
Supposing that the cat in the box has been X-rayed at time T,
alive and kicking. The conscious observation takes place a year
afterwards, when the experimenter finally looks at the film.
Was the cat brought to existence at T by the X-ray device, or
by the experimenter looking at the film a year afterwards,
but always calling it to existence at T, instantaneously,
via retroactive, backwards bouncing time. CI favored this
latter case, as the X-ray device is not conscious and it's
consciousness that collapses SE and creates "reality".
So, a fellow looking at a X ray film calls a cat into
existence a year ago. What, if the cat reveals himself as
big and uncharitable, jumps out of the box and devours the
fellow, always a year ago? Who would then look at the film
and call the cat to existence? And supposing that the fellow
gets amnesia and forgets all about ever having seen the film?
Does the cat, after being called to ephemeral existence, fall
back to nothingness, both instantaneously, a year ago?
The reason wobbles a bit, but perhaps it may be restored to
stability by the Many-Worlds-Interpretation (MWI), a version
of CI. According to it, Schroedinger's cat is alive in some
"Worlds" and dead in others. The fellow, doubtless as well.
BTW, the "mystery" of electron's doppelganger of the Double
Slit experiment simply explicable by electron's interaction
with slit's physical matrix, is explained by CI's MWI as
apparition from another "World".
For readers who might not believe their eyes, we recall that
MWI has been embraced by such celebrities as Hawking and
Weinberg.
Quantum entanglement
Einstein believed that quantum entanglement could be used to
reveal a flaw in quantum theory, because he thought that quantum
entanglement could determine physical reality before observation
- at odds with the principles of CI. Consider two entangled
photons emitted by decay of a pion, one of which is sent to
observer Alice, and the other to observer Bob. Both observers
could be a considerable distance apart. Now, due to the pion being
neutral and by virtue of momentum preservation, the emitted photons
have opposite spins, say "+" and "-". So when Alice measures
the spin of her photon and finds for instance "+", we instantly
know that Bob's photon will have "-" spin - even though Bob has
not yet measured it!
But CI says that before Bob measures his photon it can have no
defined value for its spin property - it is in a superposition
state. Only when Bob measures it does its value become physically
real. How then can we know the result Bob will obtain before
Bob measures it? The solution according to CI is that it is
the measurement of Alice which collapses the wavefunction of
both Alice's and Bob's photons. It is the observation of the
spin of one of the photons as being, say, "+" that instantaneously
collapses both photons, resulting in Bob's photon becoming real
and having "-" spin.
Yet, the photons emitted by the splitted nuclei at Hiroshima, whether
in "superposition state" or not, did burn the city without waiting
to be called to existence by observations of Bob, John or Jack.
They seemed to exist independently of any observations, as causal
effects of the nucleus splitting.
But let's return from Hiroshima to Copenhagen and admit for argument's
sake that Alice - by observing it - has created her photon with "+"
spin. Having accomplished this godlike genesis she pretends to know
instantaneously that she has also created Bob's photon and endowed it
with the "-" spin. Yet, it's a false pretence. She can only guess it,
but not know. Indeed, both photons originating from a neutral pion, had
at the separation instant opposite spins, by virtue of momentum
conservation. But the photon aiming at Bob could experience on its way
all sorts of adventures, which might have modified its spin and its
other properties, including its very existence. So Alice will have her
guess confirmed, or infirmed, will KNOW what happened with Bob's photon
only after Bob sends her his observation report, which he can do only
at the maximum speed C. Thus, information speed does not exceed C,
in Copenhagen or elsewhere.
Consequently, the fundamental CI's claim of instantaneous transfer
of information may be supported, if at all, then only by direct
communication between Alice's and Bob's photons.
Transfer between photons
Instantaneous transfer of Information and the involved collapse
of the SE imply, as we have seen, conscious observers associated,
by definition, with some referentials. Now, may a photon be
considered as a referential and what would that imply? An observer
may be a human being or a technical detector, both physical bodies
having some rest mass. Now, this mass moving at C would become
infinite. Thus, photons may only be considered as events in Alice's
and Bob's feferentials, but not themselves as referentials and the
last support of instantaneous transfer of information vanishes.
Unless we assume that photons carry "immaterial" consciousness,
i.e. that we postulate a conscious photon, as did several advocates
of the CI. Not always in so many words. After all one has some
sense of prudishness and shirks the eventuality of making an ass
of oneself in public. Yet, the assertions of Neumann, Wigner,
London and Bauer boil down to "conscious particles" and thus to
Panpsychism.
Shelving it for the moment, let's consider the implications of
Alice's (A) and Bob's (B) photons considered as referentials.
With respect to A, B moves at C, so that, by virtue of Lorentz
Transformation, its time stops. Whatever their spatial distance,
A stays with B for eternity at the moment of their separation.
Timewise they appear as identical. On the other hand, the distance
measuring rods contract to zero for the distance expanding at C,
so that at the moment of separation the A/B distance instantly
becomes infinity by virtue of Einstein's Covering Principle
("NATURAL MODEL"). The timewise identical couple of photons
embraces instantly the infinite Cosmos. One reads the words, but
not getting their gist wonders what they may possibly mean.
Well, nothing at all, else than Lorentz Transformations being
valid for relative referentials' speed V smaller than C,
become for V=C meaningless fiddling with infinity.
In other terms, no referential can move at C, so that a photon
cannot be a referential i.e. carry and communicate knowledge.
Thus, the last hypothetical support of instantaneous transfer
of information vanishes and Alice is expelled from her Wonderland
together with the rest of the Copenhagen Interpretation.
It is commonly admitted, that Bohr triumphed in his controversy
with Einstein about the CI. It's true. When reason accepts to
discuss with obstinate magic, it throws in the towel in advance.
Who tried to discuss with a Jesuit the immaculate conception
from the point of view of biology, will know what we mean.
But there is another criterion of comparing their views, to wit
their underlying respective contributions to physics.
Bohr is credited with Bohr's Model, with the Copenhagen
Interpretation and with the Complementarity Principle.
We saw that Copenhagen Interpretation, whatever its merits,
falls within the province of metaphysics and not of physics.
The Complementarity Principle, aka the duality wave/particle
amounts to inventing boiling water, as it has been encompassed
in Einstein's discovery of quanta of EM waves, aka photons.
So, Bohr's contribution to quantum physics boils down to his Model.
However, as we saw, it contributed mainly to ill-founding of QM
in autonomous discreteness and may even be considered as staying
outside of Quantum Physics.
Indeed, Dirac said: (We need) "some fundamental change in our ideas,
probably a change just as fundamental as the passage from Bohr's
orbit theory to quantum mechanics (meaning the QFT)", which clearly
indicates that he did not consider Bohr's orbit theory as part of
Quantum Physics.
So Bohr hardly contributed anything to physics and confined himself
to shamanic metaphysics of the Copenhagen Interpretation.
Einstein, on the contrary, has determined the entire new physics
by creating the extended relativity, as well as the particle
physics with the discovery of photons. And the development of the
quantum physics, to wit the QFT, follows in his steps quantizing
fields and aiming at his dream of the unified theory.
