Comments about the article in Nature: The 'Spookiness'of quantum physics could be incalculable

Following is a discussion about this article in Nature Vol 577 23 January 2020, by Davide Castelvecchi
To read the real article selects: Open access.
In the last paragraph I explain my own opinion.



Albert Einstein famously said that quantum mechanics should allow two objects to affect each other’s behaviour instantly across vast distances, something he dubbed “spooky action at a distance”
See for general comments: wikipedia EPR paradox Quantum mechanics should not allow anything. Quantum mechanics should not disagree with the results of any experiment.
Decades after his death, experiments confirmed this.
The only thing that experiments confirm is that there are correlations between distant objects.
not that there is: spooky (instantaneous) action at a distance
But, to this day, it remains unclear exactly how much coordination nature allows between distant objects.
The only way to solve this issue is by performing multiple experiments, at different distances.
To solve the issue 'exactly' by means of methematics is impossible.
Now, five researchers say they have solved a theoretical problem that shows that the answer is, in principle, unknowable.
This is what I call: 'common sense'.
The team’s proof, presented in a 165-page paper, was posted on on the arXiv preprint repository on 14 January, and has yet to be peer reviewed.
See: by: Ji. Z. Natarajan, A. Vidick, T. Wright and J. & Yuen, H.
For more detail: Reflection 2 - Article: MIP* = RE
At the heart of the paper is a proof of a theorem in complexity theory, which is concerned with efficiency of algorithms.
The efficiency of what? I expect that the efficiency of an algorithm to solve a mathematical problem is very much problem dependent. The efficiency to solve a physical problem even more.
Earlier studies had shown this problem to be mathematically equivalent to the question of spooky action at a distance — also known as quantum entanglement.
At first approach, quantum entanglement in physics (i.e that distant objects are correlated) is a physical issue and has nothing to do with mathematics.

"Quantum game theory"

The theorem concerns a game-theory problem, with a team of two players who are able to coordinate their actions through quantum entanglement, even though they are not allowed to talk to each other.
How can the two players coordinate their actions through quantum entanglement?
If this is not know in detail, the whole discussion leads to nothing.
For a more detailed discussion see: Reflection 1 - Quantum game theory
This enables both players to ‘win’ much more often than they would without quantum entanglement.
I expect that they play against two players that don't use quantum entanglement.
But it is intrinsically impossible for the two players to calculate an optimal strategy, the authors show.
It is very important to get more detail, how this quantum entanglement works.

"Observable properties"

In a 1976 paper, using the language of operators, Connes asked whether quantum systems with infinitely many measurable variables could be approximated by simpler systems that have a finite number.
Any system described by a certain number of variables can be described by a system with less variables but that introduces an error.
The problem is to what extend a quantum system i.e. a system which evolution can be studied at elementary particle level can be described in the first place i.e. accurately. IMO it can not.
For example any reaction which creates two particles (instantaneous) the position of these particles cannot be monitored continuously.
This is the physical part of the problem. Mathematical (theoretical considerations) are different.
But the paper by Vidick and his collaborators shows that the answer is no: there are, in principle, quantum systems that cannot be approximated by ‘finite’ ones.
To study quantum systems as a 'type of thought experiment' (i.e. in principle) is wrong.
To approximate quantum systems by 'finite' ones (what ever that means) introduces errors.

Disparate fields

But researchers have barely begun to grasp the implications of the results.
I doubt if the results are clear in the sense that qauntum entanglement can be used in practical applications.
In particular, measuring the amount of correlation between entangled objects in a communication system can provide proof that it is safe from eavesdropping.
The first quality of any communication system should be that it should operate as designed (in a simple way). The second quality is that it should warn the users if there is eavesdropping involved.
The confluence of complexity theory, quantum information and mathematics means that there are very few researchers who say that they are able to grasp all the facets of this paper.
That says it all.
Connes himself told Nature that he was not qualified to comment.
Then who does?

Reflection 1 - Quantum game theory

The theorem concerns a game-theory problem, with a team of two players who are able to coordinate their actions through quantum entanglement, even though they are not allowed to talk to each other. What is such a game?

The whole question is to what extend quantum entanglement can be used in order to communicate between the two players. Personally I have doubts and I have no idea how this is realised

In many entanglement experiments the information that both sides receive is correlated. Normally there is a source which emits two particles. That means when one side receives a side receives a "0" the other side always receives a "1". Or the opposite. What this means in order to transmit information that in some way or an other you must be able to manipulate the source. How to do that is the big question.

Reflection 2 - Article: MIP* = RE

To read the article: "MIP* = RE" by Z Ji, A Natarajan, T Vidick, J Wright and H Yuen select this link:
This reflection only gives a general impression about the article.


We show that the class MIP of languages that can be decided by a classical verifier interacting with multiple all-powerful quantum provers sharing entanglement is equal to the class RE of recursively enumerable languages.

7 Classical and Quantum Low-degree Tests - page 60

7.1 The classical low-degree test - page 60

7.1.1 The game - page 60

We first provide a high-level description of the game for k = 1. etc
Then a winning strategy is the following: etc
Why to discuss the winning strategy. If there exists a winning strategy there is no game.

7.2 The Magic Square game - page 65

7.3 The Pauli basis test - page 65

Informally, the quantum low-degree test asks the players to measure a large number of qubits and return a highly compressed version of the measurement outcome.

7.3.1 The game - page 65

8 Introspection Games - page 80

8.1 Overview -page 80

Consider a normal form verifier V = (S,D). In this section we design a normal form verifier VINTRO = (SINTRO,DINTRO) such that in the n-th game VINTRO(n) the verifier expects the players to sample for themselves questions x and y distributed as their questions in the game VN for index N = 2^n. This is the “introspection” step.
The reason of this text is to give an impression what is involved.

9 Oracularization 109

9.1 Overview

In this section we introduce the oracularization transformation. At a high level, the oracularization GORAC of a nonlocal game G is intended to implement the following: one player (called the oracle player) is supposed to receive questions (x, y) meant for both players in the original game G, and the other player (called the isolated player) only receives either x or y (but not both), along with a label indicating which player in the original game the question is associated with (we refer to such players as the original players, e.g. “original A player” and “original B player”).
The reason of this text is to give an impression what type of article this is. IMO very theoretical.

Reflection 3 - Article: An Introduction to Quantum Game Theory

To read the article An "Introduction to Quantum Game Theory" select:
This essay gives a self-contained introduction to quantum game theory, and is primarily oriented to economists with little or no acquaintance with quantum mechanics. It assumes little more than a basic knowledge of vector algebra. Quantum mechanical notation and results are introduced as needed. It is also shown that some fundamental problems of quantum mechanics can be formulated as games.
No comments

Page 4

Meanwhile, in quantum mechanics, the reactionary forces of determinism were at work.
The concept of determinism has nothing to do with forces.
In a 1935 paper Einstein-Podolsky-Rosen (EPR) attempted to prove the incompleteness of quantum mechanics by considering entangled pairs of particles which go off in different directions.
If it is possible by means of an experiment to demonstrate that two particles are correlated i.e. meaning that they are correlated then that becomes a fact. There is nothing wrong if before 1935 'quantum mechanics' did not mention this.
The particles may become separated by light-years.
The same type of experiments should demonstrate that.
Nevertheless a measurement of one particle will instantly affect the state of the other particle, an example of quantum mechanics’ ‘spooky action at a distance’.
That is not true. . The fact that there are correlations can only be established by performing hundreds of experiments which all should show the same result i.e. showing that both particles, created by this specific experiment, are correlated. It is no indication that the measuring of one affects the other.

Page 5

(We will discuss entanglement later, in the body of this essay, but essentially two particles are entangled if their wave functions cannot be written as tensor products.)
That may be mathematical true, no argument, but if this is also physical true is a whole different question.
This instantaneous effect is sometimes called the ‘EPR channel’, though properly speaking it should be called the Bohr channel because Bohr argued for its existence, while EPR argued against it.
John Bell formulated a set of inequalities that would distinguish experimentally whether quantum mechanics was incomplete, or whether physics is non-local, permitting instantaneous propagation of some effects of some causes.
It is difficult if not impossible by means of mathematical inequalities to demonstrate if certain physical processes can affect each other instantaneous.
Fortunately Bohr was right and EPR were wrong, as experimental evidence has decisively demonstrated.
To summarize: Bohr believed in instantaneous propagation and EPR did not.
As a matter of fact the most simple explanation is at the moment that the particles are emitted, immediate after the reaction, they are already correlated. No propagation of any sort takes place. Neither between the particle that is measured first (towards the other) or the particle that is measured second.
That is the whole explanation.
The Bohr channel is now the basis of quantum teleportation, and, indeed, every quantum computer is in some sense a demonstration of the Bohr effect.
Neither the Bohr channel nor quantum teleportation are real physical effects.
The ‘killer app’ that created a storm of interest in quantum computation came when Peter Shor showed that a quantum mechanical algorithm could factor numbers in polynomial time.
Peter Shor never really demonstrated this feature. What Peter Shor showed that you can perform certain calculations much faster on a quantum computer than on a classical based on certain assumptions. In reality these assumptions can not be realised. Specific when the number of parallel processors part of a classical computer is more than the number of QUbits of a Quantum Computer.
Shor’s algorithm relies mainly on superposition and an ingenious application of the quantum Fourier transform.
The central issue of Shor's algorithm is to calculate the periocity. This can easily be done on a classical computer.

Page 6

Quantum game theory seems to have crystallized when David Meyer gave a talk on the subject at Microsoft Corporation (see [46] for an account). Of the twelve quantum games considered in this essay, three are due to Meyer (the Spin Flip game, and Guess a Number games I and II).
The 12 quantum games are not 12 games which can be played in the normal sense. They are much more mathematical thought experiments which describe what will happen when the game is played on a quantum computer, following the rules of quantum mechanics. They are much more mathematical abstractions.
One may conversely note that some may similarly object to mixing economic concepts with those of quantum mechanics, but such objections are at least premature.
Econonomics, the study of producing products and the trade of these products versus physics, the study chemical processes and quantum mechanis are two complete different endavours
Indeed, the human brain is arguably a quantum computer though the mind may be more than that, so to ignore quantum mechanics in questions of psychology, much less economics, is folly indeed.
The human brain can de considered a quantum mechanical process but is not a quantum computer.
In the reverse direction, the role of the human mind in the quantum measurement problem has been a subject of contention since it was first clearly delineated by von Neumann.
The human mind nor anything human is involved in the evolution of an process at the level of elementary particles i.e. quantum mechanics.

The Grover Search Algorithm - page 27

Escaping prisoner’s dilemma in a quantum game - page 32

We now have enough background to tentatively define a quantum game.

page 33

The object of the game is that of endogenously determining the strategies that maximize the payoffs to player j.
This means this is a mathematical chalenge, much more than an ordinary game which the intention to play against each other.

Quantum game theory - page 34

Entangled states act as a single whole without reference to space or time
What this text indicates that entangled states operate as one unit.
Any operation performed on one entangled qubit instantly affects the states of the qubits with which it is entangled.
This indicate physical the same the same
Entanglement generates ‘spooky action at a distance’.
Physical changes between entangled states act instantaneous.

Reflection 4 - Quantum Mechanics versus Mathematics

Quantum mechanics is the area to study the behaviour of elementary particles.
One of the most important tools is the standard model which shows that the elementary particles like protons, electrons and neutrons are not elementary particles in the strict sense, but are made out of quarks and anti-quarks.

In order to understand quantum mechanics two tools are available: Visible observations and physical observations. Visible observations are measurements directly done by the human eye. They are human centered. Physical observations are performed by a measurement device. Both have their limitations. A clear division line between the two does not exist.
One important tool to count elementary particles is by means of a geiger muller counter. The problem is that counting particles in this way will also effect the state of the particle measured. What that means is that of an original elementary particle only one parameter can be measured.

At elementary particle level the predictive power of mathematics is limited. The definition of what means that two particles are correlated is almost the same as the question. Correlation means that two identical parameters (for example spin) measured from two elementary particles are opposite (for example opposite direction, N-S versus S-N). What the definition does not say that in order to measure correlation 1000 identical experiments have to performed and that both correlated particles have to be created at the same time. They are the by products of a reaction, part of the experiment. The whole process, in which two correlated particles are created is called entanglement.
The predictive power of any entanglement process is limited because nothing can be said about the direction of the spin of the particle which is measured at the left side of the experiment. This assumes that there are two measurement devices: one which the particle going left and a second for the particle going right.
Consider a reaction, where two particles are created simultaneous and where the spin of both particles are measured. In these reactions nothing can be said about the direction of the spin of the particle that is measured first. My understanding is that the spin of a such a particle can have any direction in space. For the particle that measured second a different situation exists. In many cases the direction can also be completely random but that is no absolute fact. The difference is that in some reactions the spin of the second particle can be opposite the particle measured first. The accuracy is a function of distance and can be influenced by other external sources.
Assume that in the above experiment the particle which travels to the left detector, is measured first. However this does not matter. There is no difference when the particle which travels to the right detector, is measured first. The bottom line is that measuring the state of a particle is a local human activity, which changes the state of the measured particle locally but does not change the state of any particle globaly, at a distance instantaneous.

There are two important remarks.

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Created: 30 March 2018
Modified: 18 January 2021

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