This document contains comments about the article "Principle of locality" in Wikipedia
• The text in italics is copied from that url
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

### Introduction

The article starts with the following sentence.
In physics, the principle of locality states that an object is only directly influenced by its immediate surroundings. A theory which includes the principle of locality is said to be a "local theory".
The theory of locality does not add something to our understanding.
This is an alternative to the older concept of instantaneous "action at a distance".
In physics the concept of instantaneous "action at a distance" does not exist. Newton's law includes instantaneous action, but this is physical wrong.
The Special Theory of Relativity limits the speed at which such influences can travel to the speed of light, c.
Special Relativity has nothing to do with this
Therefore, the principle of locality implies that an event at one point cannot cause a simultaneous result at another point: that an event at point A cannot cause a result at point B in a time less than T = D / c , where D, is the distance between the points. The time between the cause (at point A) and the effect (at point B) is defined bij the intervening medium between the two points. For electromagnetic effects this is the speed of electromagnetic radition i.e the speed of light. The principle of locality has nothing to do with this.
In 1935 Albert Einstein, Boris Podolsky and Nathan Rosen (in their EPR paradox) theorised that quantum mechanics might not be a local theory, because a measurement made on one of a pair of separated but entangled particles causes a simultaneous effect, the collapse of the wavefunction, in the remote particle (i.e. an effect exceeding the speed of light).
Each measurement here does not cause any instantaneous physical effect there. In that sense also Newton's Law is wrong which supports that concept.
What happens in my mind is something different. Bassed on 1000 experiments I know that in certain experiments there is a clear 100% correlation between what is measured at both points A and B. When one side measures red always the other side measures red. When green the other side measures green.
If I now perform this same experiment and I measure green than instantaneous I know that the other side also will measure green. Nothing spooky. No collapse of a wave function. Only physics.
This is a paradox: in effect, under the laws of special relativity, the result occurs before the cause.
This has nothing to do with Special Relativity. There is no paradox.
Starting from the source, during the the whole path, each of two photons is in their own state. That means if they are entangled (negative correlation) as measured then this entanglement started as a result of the original reaction. That is all.
Experimental tests of the Bell inequality, beginning with Alain Aspect's 1972 experiments, show that quantum mechanics seems to violate the inequality, so it must violate either locality or realism.
How do we know that the Bell inequality is such a yardstick? What you can do using mathematics that in certain experiments the two particles are entangled and in others not.
However, critics have noted these experiments contained "loopholes", which prevented a definitive answer to this question.
This point is in some sense not important. What you should try to keep the experiment as simple as possible and explain the results. If there is faster than the speed of light involved than clearly demonstrate this.
This might now be resolved: in 2015 Dr Ronald Hanson at Delft University performed what has been called the first loophole-free experiment.
Accordingly to the wording "might" we are not sure. See allo Reflection 1: Loophole-free violation

### 2 Relativity

Locality is a key axiom of Einstein's relativistic quantum field theory, where it is essential to causality that effects do not propagate faster than the speed of light.
The only thing that is important that propagation takes time. With propagation we mean the transportation of physical effects as a result of an event towards its surroundings. These physical effects inturn can cause other events to happen. In case of electromagnetic caused events the speed involved is the speed of light.

### 3. Quantum mechanics

Einstein, Podolsky and Rosen (dubbed the "EPR" group) identified a paradox in the theory: quantum mechanics predicts non-locality (in breach of special relativity), unless position and momentum are simultaneously real properties of the particle.
The whole issue is that you have to agree upon that in case when two measurements reveal that the two particles are entangled, this entanglement is already established at the source and has nothing to do with the measurement it self. No tricky explanation.

### 3.2 Local realism

Einstein's principle of Local Realism is the combination of the principle of locality (limiting cause-and-effect to the speed of light) with the assumption that a particle must objectively have a pre-existing value (i.e. a real value) for any possible measurement, i.e. a value existing before that measurement is made.
What is important are the two concepts:
• Cause and effect does not happens instantaneous.
• Any measurement (a process in itself) reveals something what is already available before the event.
When you study the CDSH experiment the real measurement already happens at each of the two polarizers of Alice and Bob. It is not at the detectors. The detectors only detect a photon. The effect (at Bob) that caused the specific photon to be detected (by Bob) was the polarizer (of Bob).
Local realism is a feature of classical mechanics, and of classical electrodynamics; but quantum mechanics theories reject the principle, based on the experimental evidence of distant quantum entanglements: an interpretation which Einstein rejected (as being a paradox), but which is supported by a 1972 experiment based on Bell's 1964 inequality theorem.
The whole issue is: what is the physical difference betwee two random photons versus two entangled photons?
When two random photons are measured, for example the spin, the two measured values are completely independent, When two entangled photons are measured this is not the case. In fact the logical reasoning is different. When there exist a dependency, between two identical measured values of a photon pair, then the two photons are called entangled.
In the first case the correlation factor is zero. In the second case in principle the correlation factor is +1 or -1.
The explanation is the specific reaction in the source which emits either two random photons or two entangled photons.
If an experiment shows quantum mechanics to have violated Bell's theorem, then, by definition, QM must have violated either locality or realism. But it is unclear whether the 1972 experiment demonstrates a genuine violation, because it did not test the sub-class of inequalities, and because of experimental limitations in the test.
This whole argumentation does not hold. Each experiment demonstrates something and it is the challenge of the experimentor to explain the results. The first step is to do the experiment under more different conditions with the emphasis on simplicity.
There does not exist something like a wrong experiment. An experiment is not wrong because it is not in agreement with a certain mathematical model or equation. An experiment is only wrong because you try to repeat a certain experiment and you do not follow the "recipe" of the original experiment. This "recipe" can also be wrong.

### 3.3 Realism

Realism in the sense used in physics is the idea that nature exists independently of man's mind: that even if the result of a possible measurement does not exist before the act of measuring it, that does not mean it is a creation of the mind of the observer (contrary to the "consciousness causes collapse" theory in quantum mechanics).
It is one of the basics of physics that physical process have nothing to do with humans, nor what happens in the human mind .
What I know or what I have measured have nothing to do which all what happend before the measurement. The only thing what is important that when I perform a measurement I "destroy" something, I change something (locally). In that sense I can never perform exactly the same measurement twice.
A mind-independent property does not have to be a value of a physical variable, such as position or momentum. A property can be potential (i.e. can be a capacity): in the way that a glass object has the potential (or capacity) to break, if subjected to a particular force, but otherwise will not actually break.
This is a horrible sentence. mind-dependent or independent properties do not exist. Physics has nothing to do with the mind.
When dealing with an "entangled" pair of particles, what we are really dealing with is a pair which we know for certain to have a common origin. It is logical to make an assumption that because they have a common origin they will have properties in common, an assumption we cannot possibly make if we choose two particles entirely at random. So we should not be surprised to find that the laws of certainty, rather than of mere statistical probability, apply to entangled pairs.
The most important issue when we are dealing with "a pair of particles", that they have a common origin. There exist no law of certainty. One thing we know that if we measure only one particle, the outcome of that measurement is random. The other thing we also know that generally speaking when we measure the other particle, the outcome of that measurement is also random. Only in some special cases teh outcome is correlated. This depents about typical reaction that happend when the particle pair was created and has to be established by many tests.
Even though the result of striking a glass object with a hammer does not exist before the act of striking it, that does not mean the broken glass is a creation of the observer.
This is a very complicated sentence to write that the culprit of the broken glass and the observer, both, don't have to be the same person.
Such an outcome would be realistic in a metaphysical sense, without being realistic in the physicist's sense of local realism (which requires that a single value be produced with certainty).
The only values you can produce with certainty are situations where you can count something. This are dimension less quantities.

### 3.4 Copenhagen interpretation

In most of the conventional interpretations, such as the Copenhagen interpretation and the interpretation based on Consistent Histories, where the wavefunction is not assumed to physically exist in real spacetime, it is local realism that is rejected.
If the "Copenhage Interpretation" means that cause and effect can happen instantaneous than it is wrong.
These interpretations propose that actual definite properties of a physical system "do not exist" prior to the measurement; and the wavefunction is nothing more than a mathematical tool used to calculate the probabilities of experimental outcomes.
Even before you perform a measurement now the physical world was in a certain actual state before, except we do not know what that state was.
The problem is when you want to know this previous state you will "destroy" or change this state which makes it impossible to established the present state.
This is both true for photons and electrons. The main difference is that for electrons you can calculate a wave function. See Wikipedia Schr%C3%B6dinger_equation"
The issue is that in order to measure an electron you change actual position or state of the electron. Because the wave function is a type of description of the electron you can also say that the wave function is destroyed. But this is typical a local effect and not an global effect.

### 3.5 Bohm interpretation

The Bohm interpretation preserves realism, hence it needs to violate the principle of locality in order to achieve the required correlations
Of the two concepts realism and locality, the first is the least realistic.
Unfortunate the details are missing how to achieve the required correlations.
It does so by maintaining that both the position and momentum of a particle are determinate, in that they correspond to the definite trajectory of the particle, but that trajectory cannot be known without knowing the physical state of the entire universe.
The physical state of the entire universe is and cannot be know, As such this is a ridiculous "solution".
The physical issue that it is impossible to measure the speed of a particle. This implies that you have to know the position of the particle at two different positions. These measurements will influence the state of the particle implying that the true speed of a particle is engulfed in mist.

### 3.6 Many-worlds interpretation

In the many-worlds interpretation, both realism and locality are retained, but counterfactual definiteness is rejected by the extension of the notion of reality to allow the existence of parallel universes.
The concept of parallel universes is unrealistic. There exist only one universe which contains all that exists.

### 3.8 Loophole-free violation

In 2015, Dr. Ronald Hanson reported observing a loophole-free violation in an experimental test of Bell's theorem: in other words, a result which—for the first time—is free of any additional assumptions (previous experiments, going all the way back to 1972, had required that various assumptions be made in order to obtain an unambiguous contradiction of local realism)
The problem is that you can always perform a test which (claimed) is in contradiction of a certain theory. However that still means that you have to describe the full results of your experiments. The point is why in this case can you not use locality and realism in order to explain the results?
This result rules out large classes of local realism theories.
Which theories in particular. More detailed infomation is required.
The most important local theory is that instantantaneous action at a distance is impossible.

### Reflection 1: Loophole-free violation

See:Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km By B. Hensen
At page 1, left side we read:
The remarkable discovery made by Bell is that in any theory of physics that is both local (physical influences do not propagate faster than light) and realistic (physical properties are defined prior to and independent of observation) these correlations are bounded more strongly than in quantum theory.
My interpretation is that using the quantum theory either local and/or realism is wrong.
The problem with realism is that "physical properties" are not always as clear cut as we would like. It is impossible to calculate the speed of an individual photon.
In particular, if the input bits can be considered free random variables (condition of free will") and the boxes are suffciently separated such that locality prevents communication between the boxes during a trial, the following inequality holds under local realism: S = (0,0) + (0,1) + (1,0) - (1,1) <=2 (1) where (a,b) denotes the expectation value of the product of x and y for input bits a and b.
Equation (1) is a rather strange asymmetrical equation. Why not write that the sum of the 4 values is <=4?
At the bottom of page 1, right side, we read:
If the measurement outcomes are used as outputs of the boxes, quantum theory predicts a value of S = 2 sqrt(2), showing that the combination of locality and realism is fundamentally incompatible with the predictions of quantum mechanics.
Unfortunate the details are not supplied in this particular case for both the Bell inequality and with quantum mechanics.
Any way suppose that the outcome of an experiment S=2.4 what is the physical explanation? See page 6, Fig 4.
Figure 4 shows the 4 values
(0,0) = 0.75 (0,1) = 0.6 (1,0) = 0.5 (1,1) = -0.6
S = 0.75 + 0.6 + 0.5 - (-0.6) = 2.45
When you study this result the whole issue is: not all the boxes (in absolute sense) are equal to 0.5
When that is the case the relation:
S = 0.5 + 0.5 + 0.5 - (-0.5) = 2
would be true and "Bell's inequality" would not be violated.
It is this difference that the article should try to explain.

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Created: 16 December 2016
Updated: 13 June 2018

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