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Wednesday, February 7, 2018

Thinking about the origins of the Quantum Mechanics.

Since I am not a physicist, I have just a few publications on physics.
The latest was “The excitation energy spectrum for a system with electron pairs tunneling in a two-leg ladder has a doping depended gap” (https://arxiv.org/abs/1609.07981)
And now, this.
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, 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.
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” (se 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.
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.
Or we can 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.
Hence, 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?
Of course, mathematics behind this idea is way above my abilities. So, feel free to jump in!
Some 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 Quantum-Mechanical  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 non-commuting 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 un-disturbed 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 quantum-mechanical 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.

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