Comments about "Uncertainty principle" in Wikipedia

This document contains comments about the article "Uncertainty principle" in Wikipedia
In the last paragraph I explain my own opinion.

Contents

Header

The article starts with the following sentence.
In quantum mechanics, the uncertainty principle, also known as Heisenberg's uncertainty principle, is any of a variety of mathematical inequalities[1] asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p, can be known
The real problem is the total error in all the measured physical parameters in any equation or set of related values. See also Reflection 1: Uncertainty principle

1. Introduction

1.1 Wave mechanics interpretation

According to the de Broglie hypothesis, every object in the universe is a wave, i.e., a situation which gives rise to this phenomenon.
You have to demonstrate this with real examples, otherwise it is more speculation.

1.2 Matrix mechanics interpretation

2 Robertson–Schrödinger uncertainty relations

3. Examples

4. Additional uncertainty relations

7 Critical reactions

Albert Einstein believed that randomness is a reflection of our ignorance of some fundamental property of reality, while
The first assumption should be that at each moment there exist a reality, which changes partly in some orderly way.
The second issue what is this reality and which are the laws that describe the changes.
The problem is that we humans have a limited way to describe (measure) the reality.
while Niels Bohr believed that the probability distributions are fundamental and irreducible, and depend on which measurements we choose to perform.
The probability distribution depends exactly how we perform the measurements. Each measurement has its own probability function.
Einstein and Bohr debated the uncertainty principle for many years.
It is much more important to understand that the uncertainty principle is not a physical law.

7.1 Einstein's slit

The first of Einstein's thought experiments challenging the uncertainty principle went as follows:
You cannot perform this thought experiment. What you can do is describe the mathematics based on the results of the experiment.
Consider a particle passing through a slit of width d. The slit introduces an uncertainty in momentum of approximately h/d because the particle passes through the wall.
How do you know all of this? Only by performing a real experiment
In fact the distance d already introduces a probability distribution.
But let us determine the momentum of the particle by measuring the recoil of the wall. In doing so, we find the momentum of the particle to arbitrary accuracy by conservation of momentum.
The first thing that you have to do is prove the law: conservation of momentum. This requires a clear description of how this momemtum is calculated for particles.
Bohr's response was that the wall is quantum mechanical as well, and that to measure the recoil
The wall is not quantum mechanical. What is important that all measurements can not be performed with 100% accuracy including the distance from the slit to the screen.

7.2 Einstein's box

Bohr was present when Einstein proposed the thought experiment which has become known as Einstein's box.
Thought Experiments to explain the physical reality are always tricky
Einstein argued that "Heisenberg's uncertainty equation implied that the uncertainty in time was related to the uncertainty in energy, the product of the two being related to Planck's constant."
It is important to know which specific reaction Einstein has in his mind. General speaking the time (moment) of a reaction and the reaction itself are completely independent of each other.
Secondly this is a complex sentence because it requires to understand Planck's constant.
The box could be weighed before a clockwork mechanism opened an ideal shutter at a chosen instant to allow one single photon to escape. "We now know, explained Einstein, precisely the time at which the photon left the box
We do not know the start time precisely. There is always an error marge.
"Now, weigh the box again. The change of mass tells the energy of the emitted light. In this manner, said Einstein, one could measure the energy emitted and the time it was released with any desired precision, in contradiction to the uncertainty principle.
You can also not measure the energy emitted precisely. There is always an error marge.
The problem specific in this case the two error marges are completely indepent of each other There is a different issue if you want to measure the duration.
"Through this chain of uncertainties, Bohr showed that Einstein's light box experiment could not simultaneously measure exactly both the energy of the photon and the time of its escape."
The issue is the (measurement of) start time of the escape and the energy of the photon are two completely independent processes. That is the problem.

7.3 EPR paradox for entangled particles

Bohr was compelled to modify his understanding of the uncertainty principle after another thought experiment by Einstein.
Again here: Why a thought experiment?
Measuring one particle, Einstein realized, would alter the probability distribution of the other, yet here the other particle could not possibly be disturbed.
Measuring one has no physical implication for the other one.
The EPR paradox when for example photon's are involved has nothing to do with the "uncertainty principle" in so far photons are counted.
In the EPR paradox there exist uncertainty within the experiment setup itself, when polarised photons are seperated based on polarisation angle.
He believed the "natural basic assumption" that a complete description of reality, would have to predict the results of experiments from "locally changing deterministic quantities", and therefore, would have to include more information than the maximum possible allowed by the uncertainty principle.
It is important to know the understanding of Einstein about the "uncertainty principle".
While it is possible to assume that quantum mechanical predictions are due to nonlocal, hidden variables, and in fact David Bohm invented such a formulation, this resolution is not satisfactory to the vast majority of physicists.
This sentence would be much clearer if it should read:
"While it is possible to assume that the explanation of certain experiments are due to nonlocal, hidden variables, and in fact David Bohm invented such a formulation, this resolution is not satisfactory to the vast majority of physicists."
The issue is that you cannot discus this issue in general. You have to specify the particular experiment.
The question of whether a random outcome is predetermined by a nonlocal theory can be philosophical, and it can be potentially intractable.
Again: The issue is that you cannot discus this issue in general. You have to specify the particular experiment.
The issue is definitly not phylosophical.

7.4 Popper's criticism

He disagreed with the application of the uncertainty relations to individual particles rather than to ensembles of identically prepared particles, referring to them as "statistical scatter relations". In this statistical interpretation, a particular measurement may be made to arbitrary precision without invalidating the quantum theory.
The problem with this sentence is that I need evidence if the sentence reflects a correct interpretation of the opinion of Karl Popper. For example if you want to understand the sentence you must know the definition Karl Popper uses for: Quantum Theory.
From a physical point of view there exists almost no uncertainty in the physical/chemical world.
Chemical reactions can often go into two directions. That means A + B can form C + D but also C + D can form A + B. In which direction the reaction goes depents about other external influences.
At the same time from a human perspective there is more uncertainty involved, because we do not know all the actual values of the parameters.
The problem with Popper's criticism is that IMO never a clear experiment was performed with either agreed or disagreed with Popper. See also Popper's experiment Comments

7.5 Many-worlds uncertainty

The many-worlds interpretation originally outlined by Hugh Everett III in 1957 is partly meant to reconcile the differences between Einstein's and Bohr's views by replacing Bohr's wave function collapse with an ensemble of deterministic and independent universes whose distribution is governed by wave functions and the Schrödinger equation.
It is tricky to explain something that is not clear i.e. the concept of 'wave function collapse' by something that is also not clear i.e. 'independent universes'. See also the comments: De Broglie-Bohm theory
Thus, uncertainty in the many-worlds interpretation follows from each observer within any universe having no knowledge of what goes on in the other universes.
Our knowledge of not knowing if the many-worlds interpretation is right or wrong (which is impossible to answer, because the question is not clear) has nothing to do with the uncertainty principle.

7.6 Free will

Some scientists including Arthur Compton and Martin Heisenberg have suggested that the uncertainty principle, or at least the general probabilistic nature of quantum mechanics, could be evidence for the two-stage model of free will.
Human behaviour (in casu free will) can not explained by using the uncertainty principle. The only thing that is true that humans can be uncertain, meaning that they have difficulties making choices, but that is for a large part caused by the society in which we live.

8. See also

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

11. External links

Following is a list of additional information:

Reflection 1: Uncertainty principle

The Uncertainty principle is not a physical law, because the law does not describe any physical phenomena.
The law reflects the limits of human knowledge, in the sense how accurate we can measure physical parameters. The main reason is the act of measuring is a physical process which in some sense always disturbs what you want to measure, thereby disturbing what you want to measure.

Reflection 2: Einstein versus Bohr

In both paragraphs 7.1 Einstein's slit and 7.2 Einstein's box different opions of both Einstein and Bohr are discussed. The problem is not so much who is right or who is wrong but more what is the correct answer.
The first issue is that as explained above the uncertainty principle is not a physical law, but an acknowledgment of our human incapability of the measurement process. The second issue that the uncertainty principle describes the measurement of dependent parameters. Specific if you want to know the speed of a particle you have to measure the position twice. That raises physical problems. The third issue is Planck's constant.

When you read both paragraph's you have no idea to want extend Einstein and Bohr agree with each other.
For example: suppose you perform an experiment as a thought experiment. The results Einstein has in mind can be different from Bohr's. Who is right and who is wrong?
In a thought experiment Einstein could assume that the speed of light is exactly: 299792,458000 km/sec and 1 meter is 1 meter. All the parameters are measured complete exact. This implies no error marge or uncertainty. Ofcourse in reality that is not realistic. Also here Einstein and Bohr can have a different opinion.

IMO I cannot imagine that Einstein would claim that you can measure the length of a rod exactly and that Bohr should claim that this is not true and at the same time not convince Einstein that his (Bohr's) opinion is the right one. I cannot imagine that. I think their disagreement is more about the physical details of the uncertainty principle.

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Created: 8 January 2017
Modified 13 December 2021

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