## Comments about "Quantum entanglement" in Wikipedia

This document contains comments about the article "Quantum entanglement" 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.
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 momemtum 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 counterclockwise, 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 behavior 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 a by product of the reaction inside the source, 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 of being correlated can only be established by performing a measurement on both particles.

### 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 hugh 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.
An entangled system contains at least one or more entangled particle pairs. In each entangled pair the two particles are negative correlated.
In entanglement, one constituent cannot be fully described without considering the other(s).
In entanglement the description (after being measured) of one particle, defines the description of the other particle based on 1000 experiments.
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.
See also: Reflection 3 - Quantum Entanglement Paradox - 22 May 2018
For instance, a spin-zero particle could decay into a pair of spin-½ 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 momemtum) 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 evnts. 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 important.
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 difference 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 everway, 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 hidding variables are required to explain the outcome of each experiment.

### 2.4 Violations of Bell's inequality

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 maybe true, but this is of no importance of what is physical happening.

### 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 something exists has nothing to do with quantum entanglement. This existing 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.
Carbage?
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 'relatif' 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 supperpositions.

### 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

Following is a list with "Comments in Wikipedia" about related subjects

### 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 vaqueness 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 eperiment 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 correleted.
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 exist an 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 can not 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 can not be measured properly.
This general rule is also valid incase 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?

### Feedback

If you want to give a comment you can use the following form Comment form
Created: 10 December 2016
Modified: 22 May 2018

Go Back to Wikipedia Comments in Wikipedia documents