• 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.
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
That is not correct.
Probability is the branch of physics concerning a physical description of a process of how likely a certain outcome is to occur.
The mathematical counterpart is called: Probability Theory. See https://en.wikipedia.org/wiki/Probability_theory
A simple example is the tossing of a fair (unbiased) coin.
This is typical a physical process. For an unbiased coin the chance of a certain outcome is 1 out of 6. For a biased coin the outcome of outcome will be different.
Probability theory is also used to describe the underlying mechanics and regularities of complex systems.
It is interesting what the definition of a complex system is.

7 Relation to randomness and probability in quantum mechanics

In a deterministic universe, based on Newtonian concepts, there would be no probability if all conditions were known (Laplace's demon),
The problem is that the 'state' of the universe is not known, the therminology deterministic is not clear nor are all the initial conditions known. summing-up: this sentence is not clear
(but there are situations in which sensitivity to initial conditions exceeds our ability to measure them, i.e. know them)
This part is not clear and should be removed.
In the case of a roulette wheel, if the force of the hand and the period of that force are known, the number on which the ball will stop would be a certainty (though as a practical matter, this would likely be true only of a roulette wheel that had not been exactly levelled – as Thomas A. Bass' Newtonian Casino revealed).
Also this sentence defines an idealistic world concept and should be modified. The reality is that the result of a roulette depents about the force of throwing the ball, the force of moving the wheel and the positions of each relatif to the position of the wheel.
A probabilistic description can thus be more useful than Newtonian mechanics for analyzing the pattern of outcomes of repeated rolls of a roulette wheel.
What is required is a physical description of the operation of a roulette wheel. A mathematical description is very difficult because the surface is not flat. There are many obstacles which cause the direction of the ball to change. The only thing we know is, that when you throw 3700 times, the number of times you get each result should be approximate the same and equal to 100.
Probability theory is required to describe quantum phenomena.
That depents what exactly you want to describe. The numbers in the periodictable don't depend on Probability theory.
A revolutionary discovery of early 20th century physics was the random character of all physical processes that occur at sub-atomic scales and are governed by the laws of quantum mechanics
That is also not true. First of all you have to identify which particular physical process you want to discuss. The major problem is that the parameters of the induvidual elementary particles, which are part of an atom, are difficult to measure.
The objective wave function evolves deterministically but, according to the Copenhagen interpretation, it deals with probabilities of observing, the outcome being explained by a wave function collapse when an observation is made.
The whole question is to what extend the wave function is a physical reality as part of the behavior of elementary particles or is more a mathematical concept.
However, the loss of determinism for the sake of instrumentalism did not meet with universal approval.
This is a tricky sentence because neither the words determinism nor instrumentalism are clear.
Albert Einstein famously remarked in a letter to Max Born: "I am convinced that God does not play dice".
The real question to ask which particular processes depend on chance. and which particular processes follow strict rules.
You can also rewrite this as: Which process are indeterministic versus deterministic.

If this an either or question than all processes depend on chance and are indeterministic. However I prefer the first.
This is also the case for every digital computer program, even when you excute the same program twice. However from the user point of view, the results are always the same.
For a Quantum Computer the answer should be the same, however I doubt if the results are always the same. For more detial see: Reflection 1 - Probablity

Like Einstein, Erwin Schrödinger, who discovered the wave function, believed quantum mechanics is a statistical approximation of an underlying deterministic reality.
The word deterministic should be removed. The outcome of all observations unravels an underlying reality. It are the details of identical observations that improve our understanding and the interrelations between different processes.

Reflection 1 - Probablity

To answer the question if a process involves chance or is deterministic both concepts used should be clearly defined. This is also true in a more general context.
One common observation is: that no physical process can ever completly be repeated. That implies the initial conditions, nor the way the process evolves nor the result nor outcomes. All these stages are always different. This is the most probable, for any process in which elementary particles are involved.
What this means that each process always involves with a certain element of probability.
However that does not mean that in each and every process a wave function has to be included except if the process studied involves the behaviour of individual elementary particles.

Reflection 2 - Deterministic

From an historical perspectif Isaac Newton is the founder of determinism. The reason is that he discovered the laws that describe the movements of the planets around the Sun. The real question is are these laws in any way involved with the movement of the planets? Are these laws governing these movements? The answer is no. The movement is controlled by a force, by gravity, and is a physical concept.
A different question is the world deterministic?
Accordingly to Webster, Determinism is the theory that all occurences in nature are determined by antecedent causes or take place in accordance with natural laws . This is called cosmological determinism.
I have a problem with this definition. Determinism could be defined as that each event, each physical change, is caused by different events

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Created: 24 January 2022

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