Comments about "Hidden variable theory" in Wikipedia

This document contains comments about the article Hidden variable theory in Wikipedia
In the last paragraph I explain my own opinion.

Contents

Reflection

Introduction

The article starts with the following sentence.
Historically, in physics, hidden variable theories were espoused by some physicists who argued that the state of a physical system, as formulated by quantum mechanics, does not give a complete description for the system; i.e., that quantum mechanics is ultimately incomplete, and that a complete theory would provide descriptive categories to account for all observable behavior and thus avoid any indeterminism.
This sentence at the beginning of the article is wrong, because it does not explain what the concept of hidden variables mean. Instead it explains an (important) issue related with quantum mechanics.
Ofcourse in order to understand the argument you must understand the difference between complete versus incomplete
The existence of indeterminacy for some measurements is a characteristic of prevalent interpretations of quantum mechanics; moreover, bounds for indeterminacy can be expressed in a quantitative form by the Heisenberg uncertainty principle.
Also here no explanation about hidden variables.
The importance of this sentence is that indeterminism and the uncertainty principle are closely related.
Albert Einstein, the most famous proponent of hidden variables, objected to the fundamentally probabilistic nature of quantum mechanics, and famously declared "I am convinced God does not play dice".
Here the discussion starts. The question is: is this what Albert Einstein meant.
It is more clear if Einstein objected against: the probabilistic nature of nature i.e. the Universe IMO you cannot claim that the Universe is probabilistic. It means nothing.

1 Motivation

Under the Copenhagen interpretation, quantum mechanics is non-deterministic, meaning that it generally does not predict the outcome of any measurement with certainty.
The problem is: that any measurement involves a certain uncertainty. Part of the problem is to what extend you can make an exact copy of something. You cannot.
Instead, it indicates what the probabilities of the outcomes are, with the indeterminism of observable quantities constrained by the uncertainty principle.
This sentence is typical in many arguments: Too many different concepts are used in one sentence.
The question arises whether there might be some deeper reality hidden beneath quantum mechanics, to be described by a more fundamental theory that can always predict the outcome of each measurement with certainty: if the exact properties of every subatomic particle were known the entire system could be modeled exactly using deterministic physics similar to classical physics.
The problem is in classical physics there is also no absolute certainty. The two areas overlap.
Most people are satisfied and assume that all 1 Euro Coins are the same. At atomair level they are not.
The designation of variables as underlying "hidden" variables depends on the level of physical description (so, for example, "if a gas is described in terms of temperature, pressure, and volume, then the velocities of the individual atoms in the gas would be hidden variables"
That is correct. It would be better to write that the movement of the individual atoms are the hidden parameters.
It is also important to mention the accuracy of the description.
Physicists supporting De Broglie–Bohm theory maintain that underlying the observed probabilistic nature of the universe is a deterministic objective foundation/property—the hidden variable.
This is impossible to understand if you don't explain what the "probabilistic nature of the universe" is.
IMO it does not exist. The issue that in general physical parameters can not be measured accurate.
Others, however, believe that there is no deeper deterministic reality in quantum mechanics.
Yes. And what does this really means?

2 "God does not play dice"

In June 1926, Max Born published a paper, "Zur Quantenmechanik der Stoßvorgänge" ("Quantum Mechanics of Collision Phenomena") in the scientific journal Zeitschrift für Physik, in which he was the first to clearly enunciate the probabilistic interpretation of the quantum wavefunction, which had been introduced by Erwin Schrödinger earlier in the year.
Ofcourse you can define something of what you call a wavefunction. From a mathematical point there is nothing wrong with this. The issue is physical.
Born concluded the paper as follows:
I myself am inclined to give up determinism in the world of atoms.
It should be both: determinism and indeterminism. From a physical point of view it is impossible to describe the actual movement of atoms.
But that is a philosophical question for which physical arguments alone are not decisive.
The whole issue has nothing to do with philosophy. It is all in the area of physics.
Born's interpretation of the wavefunction was criticized by Schrödinger, who had previously attempted to interpret it in real physical terms.
If it is difficult to make the link between the wavefunction and the physical reality, than what is the purpose?

3 Early attempts at hidden variable theories

4 Declaration of completeness of quantum mechanics, and the Bohr–Einstein debates

5 EPR paradox

6 Bell's theorem

7 Bohm's hidden variable theory

8 Recent developments

9 Classes of Hidden Variables

10. See also

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Created: 12 December 2017

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