• 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.
Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot be described independently of the others, even when the particles are separated by a large distance—instead, a quantum state must be described for the system as a whole.
In all processes where there is quantum entanglement involved the pairs of particles that are entangled are created by a common source. This common source is the cause that certain parameters of particles are not random but are correlated. This is the explanation.
Measurements of physical properties such as position, momentum, spin, and polarization, performed on entangled particles are found to be appropriately correlated.
This sentence should be modified as such:
Measurements etc, performed on pairs of particles are found to be correlated. This correlation is called entanglement.
It should be mentioned that to measure momentum of a particle is tricky.
For example, if a pair of particles are generated in such a way that their total spin is known to be zero, and one particle is found to have clockwise spin on a certain axis, the spin of the other particle, measured on the same axis, will be found to be counter clockwise, as to be expected due to their entanglement.
This text is not very accurate. IMO try this proposed text: For example: Consider a source S which creates a pair of particles transmitted into two different directions "L" and "R". At both sides the particle spin is measured along the same axis. The results of the measurements show each time that when at "L" the spin is measured clockwise the spin at "R" is counter clockwise or vice versa. What the results mean that the results are correlated. This correlation is called entanglement.
(From a mathematical point of view this means that the total spin is zero, but from a physical point of view this is of no importance.)
However, this behaviour gives rise to paradoxical effects: any measurement of a property of a particle can be seen as acting on that particle (e.g., by collapsing a number of superposed states) and will change the original quantum property by some unknown amount; and in the case of entangled particles, such a measurement will be on the entangled system as a whole.
See Reflection 3 - Quantum Entanglement Paradox
It thus appears that one particle of an entangled pair "knows" what measurement has been performed on the other, and with what outcome, even though there is no known means for such information to be communicated between the particles, which at the time of measurement may be separated by arbitrarily large distances.
Immediate, as an inherent part of the reaction, when the two particles were "created", the two particles were already correlated or entangled. This entanglement has nothing to do if the particles are measured or not. The fact that both particles are correlated, can only be established, when the same parameter of both particles are measured.

### 1. History

The counterintuitive predictions of quantum mechanics about strongly correlated systems were first discussed by Albert Einstein in 1935, in a joint paper with Boris Podolsky and Nathan Rosen. In this study, the three formulated the EPR paradox, a thought experiment that attempted to show that quantum mechanical theory was incomplete.
It is always tricky to challenge physics of the behaviour of individual particles by means of a thought experiment.
Schrödinger shortly thereafter published a seminal paper defining and discussing the notion of "entanglement." In the paper he recognized the importance of the concept, and stated: "I would not call [entanglement] one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought."
The actual demonstration, for the first time, that certain particles are entangled i.e., are correlated by means of an experiment, is a huge performance.
Like Einstein, Schrödinger was dissatisfied with the concept of entanglement, because it seemed to violate the speed limit on the transmission of information implicit in the theory of relativity.
IMO the cause that particles are correlated has nothing to do with the speed of light. See also Reflection 3 - Quantum Entanglement Paradox

### 2.1 Meaning of entanglement

An entangled system is defined to be one whose quantum state cannot be factored as a product of states of its local constituents; that is to say, they are not individual particles but are an inseparable whole.
Entanglement can only be demonstrated by performing an experiment. The result of the experiment should demonstrate that the (two) particles involved are negative correlated.
But those two particles can only be considered as an entangled system, when the experiment is repeated only before, any measurement is performed.
In entanglement, one constituent cannot be fully described without considering the other(s).
In entanglement the description of one particle (after being measured), defines the description of the other particle only after 1000 experiments are performed. These 1000 experiments give the statistical data (correlation) between the two particles involved.
The state of a composite system is always expressible as a sum, or superposition, of products of states of local constituents; it is entangled if this sum cannot be written as a single product term.
What is the definition of a composite system?
I doubt if the concept composite system has any relevance. The only way to understand any system is by performing experiments.
Quantum systems can become entangled through various types of interactions.
The fact that reactions can create entangled particles, is an intrinsic capability of the reaction.
As an example of entanglement: a subatomic particle decays into an entangled pair of other particles. .
This is correct and this process or reaction happens in what is called "the source" of each experiment. After that the two particles travel in opposite directions and stay entangled (correlated) at (almost) infinitum.
The decay events obey the various conservation laws, and as a result, the measurement outcomes of one daughter particle must be highly correlated with the measurement outcomes of the other daughter particle (so that the total momenta, angular momenta, energy, and so forth remains roughly the same before and after this process).
The logic of the sentence is wrong. First you have to demonstrate by means of many tests and experiments that there are conservation laws. Secondly when you have established the laws and you repeat one of the experiments than you know what the outcome is. You then also know that in certain experiments, which create entangled particle pairs when you measure one what the result should be when the other is measured.
For instance, a spin-zero particle could decay into a pair of spin-˝ particles. Since the total spin before and after this decay must be zero (conservation of angular momentum), whenever the first particle is measured to be spin up on some axis, the other, when measured on the same axis, is always found to be spin down.
This is 100% correct. It is important to remember that the decay happens in the source and that the measurement process happens at far distance. It is also important to remember that in order to establish the conservation law (angular momentum) you have to perform this experiment a 1000 times and measure both particles.
The special property of entanglement can be better observed if we separate the said two particles. Let's put one of them in the White House in Washington and the other in UC Berkeley (think about this as a thought experiment, not an actual one). Now, if we measure a particular characteristic of one of these particles, get a result, and then measure the other particle using the same criterion, we find that the result of the measurement of the second particle will match the result of the measurement of the first particle, in that they will be opposite in their values.
There is nothing wrong with the above text. The only problem: don't do it as a thought experiment. Do it as an actual experiment. You can only learn something from actual experiments. One thing you can learn from this experiment is that you can learn if the correlation is a function of distance. The expectation is in general that the correlation will diminish as a function of distance.
The above result may or may not be perceived as surprising.
There is nothing surprising in this experiment. If you first demonstrate the "spin-zero particle decay process" at a short distance than there is nothing surprising that it also works the same at a large distance.

The paradox is that a measurement made on either of the particles apparently collapses the state of the entire entangled system – and does so instantaneously, before any information about the measurement result could have been communicated to the other particle and hence assured the "proper" outcome of the measurement of the other part of the entangled pair.
Performing measurements is generally speaking a physical process, specific a human action. During this process no information is transmitted to the other particle. Such an action has nothing to do with the state before this action. The point is that the correlation between certain parameters of the particle pairs is already established direct at the place where the reaction takes place.
In the quantum formalism, the result of a spin measurement on one of the particles is a collapse into a state in which each particle has a definite spin (either up or down) along the axis of measurement.
When you measure something nothing collapses. As explained before any measurement involves some change. This implies from a physical point of view that you can never perform the same measurement twice.
The outcome is taken to be random, with each possibility having a probability of 50%.
That is only true for the first test performed. When you know the outcome and when you know that the state of the particles is correlated than you know the state of the other particle.
However, if both spins are measured along the same axis, they are found to be anti-correlated. This means that the random outcome of the measurement made on one particle seems to have been transmitted to the other, so that it can make the "right choice" when it too is measured.
No transmission takes place as part of any measurement between the two particles.
The distance and timing of the measurements can be chosen so as to make the interval between the two measurements spacelike, hence, a message connecting the events would have to travel faster than light.
The two particles are correlated. To demonstrate that does require two measurements, but these measurements itself do not require any communication. The cause is in the original reaction when the two particles where created.
According to the principles of special relativity, it is not possible for any information to travel between two such measuring events.
There is no communication between the two measuring events. Period. To explain that you do not need Special Relativity.
It is not even possible to unambiguously say which of the measurements came first.
Also, that is of no importance.
The whole issue is to measure the spin of each particle in the same direction in as many experiments as possible. When you make the distant different, you can also experimental test if that makes a difference.
Therefore, the correlation between the two measurements cannot appropriately be explained as one measurement determining the other.
That is correct. The action of one measurement has no physical connection with the other.
Different observers would disagree about the role of cause and effect.
The cause of the correlation is in the original reaction who caused the two particles. Humans, in what ever way, have nothing to do with this.

### 2.3 Hidden variables theory

A possible resolution to the paradox might be to assume that the state of the particles contains some hidden variables, whose values effectively determine, right from the moment of separation, what the outcomes of the spin measurements are going to be.
No hidden variables are required to explain the outcome of any experiment.
The whole point is that if repetitions of the same experiment don't always show the same results, there must be a cause. The first point is to follow the script in exact the same order and accuracy.
Ofcourse it is also possible that it is impossible to repeat an experiment, because of physical limitations. It is impossible to repeat the result of a pin ball machine. (2023)

### 2.4 Violations of Bell's inequality

Local hidden variable theories fail, however, when measurements of the spin of entangled particles along different axes are considered.
The most important issue is: how the spin of a particle is measured. Observe that the word entangled is not used.
This is important because actual experiments are the basis of our understanding. (2023)
If a large number of pairs of such measurements are made (on a large number of pairs of entangled particles), then statistically, if the local realist or hidden variables view were correct, the results would always satisfy Bell's inequality.
That may be true, but this is of no importance of what is physical happening.
Consider the "two-channel" Bell test: https://en.wikipedia.org/wiki/CHSH_inequality#Experiments also see: https://en.wikipedia.org/wiki/Bell_test#Conduct_of_optical_Bell_test_experiments
The experiments involves 4 channels, which I identify at the left side as A+ and A-, and at the right side as B+ and B-. Those 4 channels are input to coincidence monitor CM where all the signals can be compared. That means on run 1 you get an A+B+ signal. On run 2 an A-B- signal etc. A complete pattern could look something like: A+B+, A-B-, A+B-, A-B-, A+B+, A-B+, etc. In total you could get A+B+: 22 times, A+B-: 24 times, A-B+: 28 times and A-B-: 26 times.
Consider an experiment with only alpha=0.
• Perform first a random selected experiment A which produces 2 photons. Perform this same experiment 1000 times. My expectation is that the number of A+B+, A+B-, A-B+ and A-B- signals received will be almost the same. Something like 245, 253, 255 and 247.
• Now perform a special experiment B which produces also 2 photons. Perform this experiment also 1000 times. The results are completely different 1, 496, 501, and 2 What that means that the photons are highly correlated. When one channel measures a + signal, the other channel measures a - signal.
The question to ask is, what have the direct results of these measurements, assuming it can be physical repeated in an actual experiment, have to do with the Bell inequality?
The question is much more: what is the physical explanation of this result, as measured by the CM. (2023)
The other angles could also be measured, in both experiment A and B. But if there is already one angle special in experiment B it requires a physical explanation of experiment B.

### 2.7 Mystery of time

There have been suggestions to look at the concept of time as an emergent phenomenon that is a side effect of quantum entanglement.
The fact that entities can be observed and have properties has nothing to do with quantum entanglement. This implies the concept of time
In other words, time is an entanglement phenomenon, which places all equal clock readings (of correctly prepared clocks, or of any objects usable as clocks) into the same history.
Garbage?
The Wheeler–DeWitt equation that combines general relativity and quantum mechanics – by leaving out time altogether – was introduced in the 1960s and it was taken up again in 1983, when the theorists Don Page and William Wootters made a solution based on the quantum phenomenon of entanglement.
Eureka?
Their result has been interpreted to confirm that time is an emergent phenomenon for internal observers but absent for external observers of the universe just as the Wheeler-DeWitt equation predicts.
Interesting?

### 2.8 Source for the arrow of time

Physicist Seth Lloyd says that quantum uncertainty gives rise to entanglement, the putative source of the arrow of time.
Quantum uncertainty and entanglement have nothing to do with each other, in the sense that one causes the other or vice versa.
The concept of "arrow of time" has nothing to do with both.

### 4.1 Pure states

If the former occurs, then any subsequent measurement performed by Bob, in the same basis, will always return 1. If the latter occurs, (Alice measures 1) then Bob's measurement will return 0 with certainty.
That means when Alice measures 0, Bob will always measure a 1 and when when Alice measures 1, Bob will always measure a 0.
That is maybe mathematical correct (I have no doubt) but that does not mean what physical happens (which is maybe approximate the same) and what is more important it does not explain the cause.

### 4.5 Entropy

In this section, the entropy of a mixed state is discussed as well as how it can be viewed as a measure of quantum entanglement.
IMO entropy has nothing to do with quantum entanglement i.e., as an explanation that there exists a correlation between certain parameters of individual particles as a result of a process reaction.

### 5 Applications

Entanglement has many applications in quantum information theory. With the aid of entanglement, otherwise impossible tasks may be achieved.
More detail is required to validate this claim. In theory it is 'relative' easy to describe mathematically certain processes which involve quantum entanglement (Shor's Algorithm). In reality this is difficult to do.
Most researchers believe that entanglement is necessary to realize quantum computing (although this is disputed by some)
IMO the whole concept of quantum computers is based on entanglement and superpositions.

### 5.3 Testing a system for entanglement

Systems which contain no entanglement are said to be separable.
This claim does not make sense. The reverse is unquestionable true. Why would you separate such a system?

### 6 Naturally entangled systems

The electron shells of multi-electron atoms always consist of entangled electrons.
It is the question of this belongs to the standard concept of entanglement. Electrons can be studied as part of an atom, together with neutrons and protons. If each electron is supposed to have a spin, the individual spins cannot be studied.
Entangled electrons are supposed to be 'far away' from the source where they were created. These individual electrons can be studied i.e., their spin can be measured and the result can be that they are correlated.
The correct ionization energy can be calculated only by consideration of electron entanglement.
The ionization energy can be calculated assuming that they each are in a specific shell i.e., specific "fixed" average distance from the core. That does not mean that the induvidual spins can be measured and established if they are correlated.

### Reflection 1 - Measurement

One very important issue of entanglement is the measurement process. I specific write here process because it involves in many cases an action by an observer. The purpose of a measurement is to collect numerical values about the state of the process. Each measurement involves changes. This is what you can expect. To define each change as a collapse of a wave function does not add anything. What is worse it introduces vagueness and adds complexity, what is not necessary.
What is also important that as part of the measurement process no communication with other parts of the system occurs. Communication in the sense that as a result additional changes somewhere else take place.

### Reflection 2 - Testing entanglement

Testing for entanglement is a tricky issue. In some sense the whole issue of entanglement is based to perform the same experiment 1000 times and to test the state of the parameter (polarization) that is supposed to be entangled. The result of each test should be when in one particle the state is 1 the other should be 0 and vice versa. This negative correlation should exist in 99.5% of the cases and even more.
That means when you perform the same experiment the next time you assume that the particles involved are entangled without any test.

### Reflection 3 - Quantum Entanglement Paradox - 22 May 2018

The Introduction paragraph explains that certain parameters of pairs of particles can be correlated.
The same paragraph also explains that certain measurements have to be performed at that such measurements will be on the entangled system as a whole.
This raises the question: Does any measurement on any such particle (of a pair) causes any change on the other particle?
Before answering this question, it is important to answer the following question: What exactly is a measurement? I do not know, if there exists a uniform answer. The most general answer is that a measurement is a process or reaction which the intention of calculating certain parameters of the system before the measurement.
The problem is that if that is the case and that process or reaction causes also any change on the other particle the same parameters cannot be measured any more, because the particle is disturbed.

This creates the following general rule:
The measurement of any parameter of a particle (in general: any disturbance) created after a reaction, should not have any influence on any of the other particles created. Because if it does these particles cannot be measured properly.
This general rule is also valid in case entangled particles are created after a reaction.

In 2.1 Meaning of entanglement the importance of 'various conservation laws' is mentioned. All these conservations laws are based on experiments. These experiments involve different experiments, which try to measure all what is created during a reaction. One of the underlying rules of these measurements, which can be all sorts of parameters, is, that they should be independent of each other (as much as possible). That means they should not influence each other. The problem is, if they are not, how can you establish that the total energy is constant?

### Reflection 4 - Quantum Conformance Test - 19 Jan 2022

The first time I read about the subject "Quantum Conformance Test" was in this article: https://physicsworld.com/a/quantum-entanglement-boosts-accuracy-of-industrial-quality-inspections/ In the paragraph "Entanglement does the trick" they describe how photon entanglement is used in this experiment.
The entangled photons are then sent down different paths, with one photon passing through the sample being tested and the other following a reference path.
The importance is that the entangled photons are created simultaneous at a common source. After that there is no physical link anymore between the two photons.

For more detail about the Quantum Conformance Test see this link: https://arxiv.org/abs/2012.15282 "Quantum Conformance Test" by Giuseppe Ortolano et all.