User:Boris Tsirelson/Sandbox1: Difference between revisions

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===Consistent or inconsistent===
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The [[Heisenberg Uncertainty Principle|Heisenberg uncertainty principle]] for a particle does not allow a state in which the particle is simultaneously at a definite location and has also a definite momentum. Instead the particle has a range of momentum and spread in location attributable to quantum fluctuations.


If a theory states that 2+2=5, it is a paradox but not yet a contradiction. By "paradox" people may mean
An uncertainty principle applies to most of quantum mechanical operators that do not commute (specifically, to every pair of operators whose commutator is a non-zero scalar operator).
*a contradiction;
*an apparent contradiction;
*something counterintuitive;
*something surprising;
*something ironic;
etc. In contrast, a contradiction (in a mathematical theory) is, by definition, a pair of theorems (of the given theory) such that one is the negation of the other. Thus, two theorems
: <math>2+2=4,</math>
: <math>2+2=5</math>
are still not a contradiction. Two theorems
: <math>2+2=4,</math>
: <math>2+2\ne4</math>
are a contradiction.
 
If a contradiction exists in a given theory, this theory is called inconsistent. Otherwise, if no contradiction exist (rather than merely not found for now), the theory is called consistent.
 
An inconsistent theory is completely useless. Some philosophers disagree:
 
<blockquote>Superstitious dread and veneration by mathematicians in face of a contradiction (Ludwig Wittgenstein)</blockquote>
 
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[http://en.wikipedia.org/wiki/Strict_conditional wp:Strict conditional]
 
[http://en.wikipedia.org/wiki/Paradoxes_of_material_implication wp:Paradoxes of material implication]
 
[http://en.wikipedia.org/wiki/Relevance_logic wp:Relevance logic]

Latest revision as of 03:25, 22 November 2023


The account of this former contributor was not re-activated after the server upgrade of March 2022.


The Heisenberg uncertainty principle for a particle does not allow a state in which the particle is simultaneously at a definite location and has also a definite momentum. Instead the particle has a range of momentum and spread in location attributable to quantum fluctuations.

An uncertainty principle applies to most of quantum mechanical operators that do not commute (specifically, to every pair of operators whose commutator is a non-zero scalar operator).

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