Comments about "Probability amplitude" in Wikipedia
This document contains comments about the article Probability amplitude 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.
Contents
Reflection
Introduction
The article starts with the following sentence.

In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems

The problem is that in the physical world all what exist can only be represented by a positif number. Even the number of zero does not exist.

The modulus squared of this quantity represents a probability density.

The biggest problem is how to measure this probability density function.

Probability amplitudes provide a relationship between the wave function (or, more generally, of a quantum state vector) of a system and the results of observations of that system, a link first proposed by Max Born,

The wave function is a mathematical description of a system or process, based on physical measurements.





These probabilistic concepts, namely the probability density and quantum measurements, were vigorously contested at the time by the original physicists working on the theory, such as Schrödinger and Einstein.
The physical problem behind the debate is that at any moment each particle will have a specific position but that the sequence of sequentieel positions is unknown. What is known that certain positions are more probable than others.


It is the source of the mysterious consequences and philosophical difficulties in the interpretations of quantum mechanics—topics that continue to be debated even today.

1 Overview

Neglecting some technical complexities, the problem of quantum measurement is the behaviour of a quantum state, for which the value of the observable Q to be measured is uncertain.

This sentence is 'uncertain'.

Such a state is thought to be a coherent superposition of the observable's eigenstates, states on which the value of the observable is uniquely defined, for different possible values of the observable.

Idem.

When a measurement of Q is made, the system (under the Copenhagen interpretation) jumps to one of the eigenstates, returning the eigenvalue belonging to that eigenstate.

Idem.




1.1 Physical










1.2 Mathematical










2 Wave functions and probabilities










3 Discrete amplitudes










4 Examples

Take the simplest meaningful example of the discrete case: a quantum system that can be in two possible states: for example, the polarization of a photon.

What are the two states of a photon? IMO a photon is described by two parameters: The 'frequency' of rotation and the direction of the axis of rotation.








5 Normalization










6 The laws of calculating probabilities of events

Provided a system evolves naturally (which under the Copenhagen interpretation means that the system is not subjected to measurement), the following laws apply:

This puts you in a type of Catch 22 situation. If you are not allowed to make any measurement or observation how is it possible to understand that certain laws apply?
This is even more tricky: Laws are usefull to study almost identical processes and specific relevant for the parts that are 'identical'. For example: Newton's Law can be used when two or more objects are involved.








7 In the context of the doubleslit experiment



For example, in the classic doubleslit experiment, electrons are fired randomly at two slits, and the probability distribution of detecting electrons at all parts on a large screen placed behind the slits, is questioned.

Why using the therminology 'classic doubleslit experiment'?
The structure of the article should be: First explain the experiment. That you can use one slit or two slits. Secondly to show the actual results. Thirdly to explain the results.
An important difference is if you fire electrons simultaneous or if the electrons are fired one after an other.

An intuitive answer is that P(through either slit) = P(through first slit) + P(through second slit), where P(event) is the probability of that event.

How are these probabilities measured?
What is clear is a sentence like this one: # of electrons going through the first slit + # of electrons going through the second slit = # of electrons going through the either slit.
The point is that you can count both seperately. But what is the physical significance of the addition?
IMO rather limited.

When nature does not have a way to distinguish which slit the electron has gone through (a much more stringent condition than simply "it is not observed"), the observed probability distribution on the screen reflects the interference pattern that is common with light waves.

This whole sentence seems obscure. The whole point is that with waterwaves, when there is an interference pattern the assumption is that the wave goes through both slits or holes. This means that both waves influence each other. In the case when single electrons are considered, and observations shown that there is an interference pattern only when there two slits the explanation must be physical implying that 'something' goes through both slits. 'Nature' has nothing to do with this.



However, one may choose to devise an experiment in which the experimenter observes which slit each electron goes through. Then case B of the above article applies, and the interference pattern is not observed on the screen.

IMO it is impossible (statistical relevent) that the outcome of 1000 experiments are different compared with a second group of identical experiments, with the only difference that there is one observer versus no observer. All identical group of experiments with different results must have a physical explanation.
The closing of one hole could be such a situation, but unfortunate is not mentioned.



One may go further in devising an experiment in which the experimenter gets rid of this "whichpath information" by a "quantum eraser". Then, according to the Copenhagen interpretation, the case A applies again and the interference pattern is restored.

What is a quantum eraser?
The Copenhage interpretation is not going to help the physical issues involved.






8 Conservation of probabilities and the continuity equation










9 Composite systems










10 Amplitudes in operators










11. See also
Following is a list with "Comments in Wikipedia" about related subjects
Reflection 1  Measurement.
When an observer performs a measurement he or she makes a physical change. It is like putting a thermometer into your mouth to measure your temperature. The same is involved when you want to measure something when elementary particles are involved. The main problem is when you want to do that the original state of the particle is changed, making it difficult to perform more experiments on that same particle.
You could also describe the issue as follow: It is impossible to repeat the same experiment with elementary particles, because the original state of the particles is not known.
This means that every time when you perform 'the same experiment' twice the outcome is different, because the experiment is not the same.
All of this seems 'physical' logical. The whole problem is that you cannot explain this by using mathematics. The only thing you can claim is that certain outcomes of the experiment are more probable than others and if you want to be more specific you have to perform the experiment 1000 times.
Reflection 2
Reflection 3
Feedback
If you want to give a comment you can use the following form Comment form
Created: 11 January 2022
Go Back to Wikipedia Comments in Wikipedia documents
Back to my home page Index