The
latest was “The excitation energy spectrum for a system with electron pairs
tunneling in a twoleg ladder has a doping depended gap” (https://arxiv.org/abs/1609.07981); also
"The Uncertainty Principle: a contemporary formulation".
Thinking about the origins
of the Quantum Mechanics.
Yesterday I attended a
seminar where the speaker presented a talk on quantum entanglement (and
more).
Quantum
entanglement has been known for decades (quantum entanglement has been known for the
same amount of time the uncertainty principle is known), but fairly recently
the interest to this property of the quantum world has exploded. One reason is
because quantum entanglement promises potential breakthroughs in technologies
(e.g. quantum computing, information security). The second reason is that
quantum mechanics is fundamentally different from classical physics, and that
difference may be the reason for physicists not being able to develop the
theory of quantum gravitation.
One of the interpretation of quantum
entanglement is that quantum objects can “feel” each other even if they are far
away apart from each other. In order to be able to “feel” each other those
particles have to be specifically prepared, i.e. entangled. We all know,
however, that all existing particles have been specifically prepared – that
happened at the “Big Bang”. Hence, we can assume, that all quantum particles
“feel” each other all the time. This can “explain” how quantum particles “know”
that they will interact with a macroscopic world, because, essentially, they
constantly “feel” the whole world, which is huge.
Of course, this interpretation of quantum
entanglement also can be used to “explain” telepathy, telekinesis, and all
known and yet unknown “psychic phenomena”.
Maybe,
that was one of the reasons that Albert Einstein claimed that quantum theory
was not complete. However, it is clear from his work, that when Einstein says a
“complete theory” he actually means “classical theory” (see some quotes below).
And his work proves that – yeas – quantum theory is NOT equal to classical
theory of natural phenomena. He didn’t like it. He was not alone in not liking
it. Many physicists tried to “fix” the quantum mechanics by using various
approaches (usually stochastic theories of hidden variables). But so far, all experiments
show that those theories are wrong.
The core
of the whole debate is not about whether quantum theory is
complete or incomplete.
The core
of the debate is about
what does “complete” mean!
At this
point we have a fork.
We can
just accept the fact that – yeas – quantum theory is NOT equal to classical
theory of natural phenomena, and just like it the way it is. That means we reject the
Einstein’s demand that a “complete” theory has to be an equivalent of the
“classical” theory.
Or we can
agree with the Einstein’s definition of “complete” theory and keep trying to
“fix” quantum mechanics.
In the
latter approach, one may try to search for a theory which has something new,
something which all previous theories did not have (maybe that was the reason
for their failure).
If trying
to find a “hidden” agent acting on the particle from the outside did
not succeed, maybe the agent is inside?
There is
some work where a charged particle “feels” a “recoil” when
emits a photon (radiative force). But the theory should work even for a
free particle.
The best approach in that venue has been offered by the "pilot wave theory" (but the wave which guides particles should be quantized as well). Let's take a look at a free particle. It disturbs the space around it. That disturbance propagates in space away from the particle in form of a wave, hits other objects, reflects back to the particle and affects its motion. For an electron, that wave may be described in terms of virtual photons (maybe).
As a mechanical model, one can try to see the particle as a tiny “ball” submerged into “liquid” (quantum vacuum); the “liquid” has no viscosity, but can generate a force on a particle due to “pressure” difference around the “ball”; the “pressure” in the “liquid” can randomly fluctuate; AND, the particle itself may “vibrate” making pulses acting on the “liquid” (which may be random, or harmonic, or both, or else). In other words, the particle can “make waves” in the “liquid”. Those waves change the “pressure” in the liquid, they may reach some other objects (screens, slits, other particles) and reflect of them, and interfere, and when the particle travels in this “wave field”, it “feels” the force due to local “pressure” difference. And who knows, maybe those waves can travel faster than light?
As a mechanical model, one can try to see the particle as a tiny “ball” submerged into “liquid” (quantum vacuum); the “liquid” has no viscosity, but can generate a force on a particle due to “pressure” difference around the “ball”; the “pressure” in the “liquid” can randomly fluctuate; AND, the particle itself may “vibrate” making pulses acting on the “liquid” (which may be random, or harmonic, or both, or else). In other words, the particle can “make waves” in the “liquid”. Those waves change the “pressure” in the liquid, they may reach some other objects (screens, slits, other particles) and reflect of them, and interfere, and when the particle travels in this “wave field”, it “feels” the force due to local “pressure” difference. And who knows, maybe those waves can travel faster than light?
Each
charge (electric, gravitational, ...) can be responsible for its own
"pulsing" in its own "liquid". And who knows, maybe
"gravitational" "pulsing" will help to quantize
gravitation?
Another
possibility comes from the fact that a classical particle not just has a
coordinate and a momentum at the same time, but has only ONE value of each.
Maybe quantum particles can have many values of a momentum and
(I know it sounds weird) a coordinate at the same time? If quantum particles
have to lose some of the attributes of classical particles, why not ALL of
them? Maybe they are some threedimensional "shadows" of
multidimensional objects, and those shadows can reveal themselves only when a
quantum particle interacts with a macroscopic object which always has a certain
value? There
is another possible explanation, which may solve all the mysteries 
the matter we know also interacts via particles which cannot travel
slower than the speed of light (tachyons). However, there is no yet any model which could offer a reasonable mathematical description of that interaction.
Of
course, mathematics behind this idea is way above my abilities. So, feel free
to jump in!
Appendix I
The
picture has been “stolen” from https://www.quantamagazine.org/entanglementmadesimple20160428/,
where Nobel Prize Laureate Dr. Frank Wilczek offers his take on quantum
entanglement. He provides a very clear explanation, with only two things to
keep in mind.
1. He (as
many other people) often uses word “knowledge”. In principle, any explanation
of every physical phenomenon should not include an intelligent subject.
However, in this case there is a quick fix, i.e. when we read something like
“we know” we should understand the underlining meaning, which is “there is a
macroscopic system which has a certain set of states and the interaction of the
microscopic system with that macroscopic system leads to bringing the
macroscopic system in a single specific state”. Of course, saying “we know” is
just much faster.
2. He
should have stressed a little bit more the importance of the existence of the
procedure (action, interaction) for preparing an entangled
state. If we write a wave function for two electrons, one of which is on Venus
and another one is on Mars, does it make the entangled? I don’t think so.
Particles do not become entangled due to simple fact that someone writes an
equation which includes them. Particles become entangled due to a physical
process which happens to them – at the same time and at the same place (+ or )
– i.e. locally. What happens after is
described by the specific laws (classical or quantum), and basically, it is
what it is. And when Dr. Wilczek makes the transition from table 1 (independent
cons) to table 2 (entangled cons) he should have made it clearer that the
system has been prepared to behave in that way (it does what it does because it was made to
do that).
Physics has known several famous though experiments. The problem with thought experiments that human mind can imagine so many things which may feel natural but would never exist. Sometimes it may lead to a confusion. For example, in EPR experiment (or similar) there are two particles which assumed entangled  meaning, prepared as a system via a specific interaction. But in the microscopic world interactions may differ from interactions in the macroscopic world. If an author think of something which would work in a macroscopic world and use it as a preparation action for a microscopic system it may lead to wrong conclusions. That is why one cannot just say "let's assume particles are entangled". One must offer a specific potentially possible way for entangling particles. Then and only then one can discuss the evolution of a system.
Physics has known several famous though experiments. The problem with thought experiments that human mind can imagine so many things which may feel natural but would never exist. Sometimes it may lead to a confusion. For example, in EPR experiment (or similar) there are two particles which assumed entangled  meaning, prepared as a system via a specific interaction. But in the microscopic world interactions may differ from interactions in the macroscopic world. If an author think of something which would work in a macroscopic world and use it as a preparation action for a microscopic system it may lead to wrong conclusions. That is why one cannot just say "let's assume particles are entangled". One must offer a specific potentially possible way for entangling particles. Then and only then one can discuss the evolution of a system.
Appendix II
A very
common representation of the Heisenberg principle states that we cannot know
the momentum and the coordinate of a particle at the same time. However, in
this particular interpretation, how should we explain the work of a “simple”
mass spectrometer? Let’s say, we use a simple Crookes tube (or its contemporary
version, Cathode Ray tube used in physics to do e/m experiment). When electrons
travel through a velocity selector, they have the same speed. When they enter a
region with magnetic field, the speed remains not changed, so we know the
momentum (speed*mass). And then when electrons hit a screen we ALSO know the
coordinate! It looks like we can know both! This is the only
experiment I know which seems in the violation with the Heisenberg principle. I
am pretty sure the principle is correct (operators of momentum and
radiusvector are not commutative), but I am not sure who to reformulate the
principle or how to redescribe the experiment in order to make them to match.
Appendix
IIISome notes on the famous EPR paper.
M
A Y 15 , 19 3 5 P
H Y S I C A L R E V I E W V O L U M E
4.7
Can
QuantumMechanical Description of
Physical Reality Be Considered Complete?
A.
EINSTEIN, B. PODOLSKY AND N.
ROSEN, Institute for Advanced
Study, Princeton, New Jersey (Received March 25, 1935)
Quotes from the paper

The meaning

“In
a complete theory there is an element corresponding to each element of
reality. A sufficient condition for the reality of a physical quantity is the
possibility of predicting it with certainty, without disturbing the system.”

Statement
of what the authors think “a complete theory” is, which is essentially,
Newtonian mechanics.

“In
quantum mechanics in the case of two physical quantities described by
noncommuting operators, the knowledge of one precludes the knowledge of the
other.”

Statement
of the authors’ understanding of quantum mechanics; which includes reference
to “knowledge”, which automatically involves a human factor, which should not
be a part of any theory of natural phenomena.

“Consideration
of the problem of making predictions concerning a system on the basis of
measurements made on another system that had previously interacted with it
leads to the result that if (1) is false then (2) is also false. One is thus
led to conclude that the description of reality as given by a wave function
is not complete.”

The
statement about “complete description of a system” is based on what type of
predictions is possible, hence, shows a belief (a definition) of what type of
predictions should be possible (from
the author’s point of view) to consider the description of a system; and again
we see that “complete” = “Newtonian”

“ANY
serious consideration of a physical theory
must take into
account the distinction
between the objective reality,
which is independent of
any theory, and
the physical concepts with
which the theory operates.”

The
definition (belief) of what is a “serious theory” – it must describe objective
reality.

“These
concepts are intended to correspond with the objective reality, and by means
of these concepts we picture this reality to ourselves.”

An
indicator of “serious theory”, the authors believe if that indicator is
missing – the theory is “not serious”. A “serious theory” must have concepts
which describe all elements of “objective reality”. But this leaves the room
for a discussion about what constructs “objective reality”.

“In
attempting to judge the success of a physical theory, we may ask ourselves
two questions: (1) "Is the theory correct ?" and (2) "Is the description given by the
theory complete ?" It is only in the case in which positive answers may
be given to both of these questions, that the concepts of the theory may be
said to be satisfactory. The correctness of the theory is judged by the degree
of agreement between the conclusions of the theory and human experience. This
experience, which alone enables us to make inferences about reality, in
physics takes the form of experiment and measurement.”

Stressing
the importance of being “complete”.

“Whatever
the meaning assigned to the term complete, the following requirement for a
complete theory seems to be a necessary one: every element of the physical
reality must have a counterpart in the physical theory. We shall call this
the condition of completeness.”

Giving
their definition of “complete”

“The
second question is thus easily answered, as soon as we are able to decide
what are the elements of the physical reality.”

“we
are able to decide” means that all scientist will come up to a common belief
about the elements of the physical reality. Hence, if someone has a different
picture of the physical reality, that one automatically excluded from this
particular discussion.

“The
elements of the physical reality cannot be determined by a priori philosophical
considerations, but must be found by an appeal to results of experiments and measurements.”

Another
postulate of what should be a correct theory – based on experiments.

“We
shall be satisfied with the following criterion, which we regard as
reasonable.”

The
authors make a statement about how will they decided if the description of
reality is sufficient. People who reject their criterion are automatically excluded
from this particular discussion.

“If,
without in any way disturbing a system, we can predict with certainty (i.e.,
with probability equal to unity) the value of a physical quantity, then there
exists an element of physical reality corresponding to this physical quantity.”

The
most important statement; the authors present the criterion of how they
decide what is a part of reality, and what is not. According to this
criterion, if the system cannot by undisturbed during a measurement, that
system will not be a part of reality.

“It
seems to us that this criterion, while far from exhausting all possible ways of
recognizing a physical reality, at least provides us with one such way,
whenever the conditions set down in it occur. Regarded not as a necessary,
but merely as a sufficient, condition of reality, this criterion is in
agreement with classical as well as quantummechanical ideas of reality.”

Making
a statement that from the authors point of view this criterion must describe
the classical and quantum world. Which is again basically stating that
quantum mechanics must behave the same way the classical mechanics does.

“The
fundamental concept of the theory is the concept of state, which is supposed
to be completely characterized by the wave function, which is a function of
the variables chosen to describe the particle's behavior.”

The
description of their interpretation of QM; wave function must completely describe
a state of the system, but leaves out the definition of a “sate”, which may
have various interpretations.

“Thus,
in the state given by Eq. (2), the momentum has certainly the value Po. It
thus has meaning to say that the momentum of the particle in the state given
by Eq. (2) is real.”

The
mathematical definite of what is real – from their point of view; real means
“having 100 % probability” to have a certain value.

“On
the other hand if Eq. (1) does not hold, we can no longer speak of the
physical quantity as having a particular value.”

“physical
quantity” may have or have no
“particular value”, hence may be “real” or “not real”.

“We
see that all values of the coordinate are equally probable. A definite value
of the coordinate, for a particle in the state given by Eq. (2), is thus not
predictable, but may be obtained only by a direct measurement.”

It
something is not predictable, the measurement can provide various values. But
an open question is left – did the particle have a certain value before the measurement?

“After
the coordinate is determined, the particle will no longer be in the state
given by Eq. (2). The usual conclusion from this in quantum mechanics is that
when the momentum of a particle is known, its coordinate has no physical
reality.”

Again,
the authors interpretation of what is not a part of a physical reality – it is
when a particle in a state in which physical quantity does not have a single
value, but has a value distribution.

“if
the operators corresponding to two physical quantities, say A and B, do not
commute, that is, if AB is different from BA, then the precise knowledge of
one of them precludes such a knowledge of the other.”

Reference
to “knowledge”, which leaves open the question about “existence”; can
something exist but be unknown?

“if
both of them had simultaneous reality  and thus definite values  these
values would enter into the complete description, according to the condition
of completeness.”

The
authors impose their definition of “reality”; “reality” is being equated with
“having definite values”; and to be complete, a theory must provide those
values.

“In
quantum mechanics it is usually assumed that the wave function does contain a
complete description of the physical reality of the system in the state to which
it corresponds.”

The
meaning of “complete theory” with which authors disagree by providing their
own meaning.

"The Uncertainty Principle: a contemporary formulation"
An example of the interconnection between micro and macro worlds: “Dark matter, dark energy and lightvacuum interactions.”
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