Difference between revisions of "Double-slit logic experiment"

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(Simple case: This tends to confirm that logic and uncertainty -- not waves -- require the surprising result of the double-slit experiment.)
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A '''double-slit logic experiment''' is the use of [[probability]] to determine of there is an underlying logical basis for the surprising effect observed in the [[double-slit experiment]] in [[physics]].
 
A '''double-slit logic experiment''' is the use of [[probability]] to determine of there is an underlying logical basis for the surprising effect observed in the [[double-slit experiment]] in [[physics]].
  
The logical essence of the double-slit experiment is to have two levels of uncertainty in sequence.  First, there is uncertainty about which of the two slits a "particle" passes through, and then there is uncertainty about where it lands on the distant screen.  Resolving the uncertainty at the first level through observation then effects the outcome at the second level.
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The logical essence of the double-slit experiment is to have two levels of uncertainty in sequence.  First, there is uncertainty about which of the two slits a "particle" passes through, and then there is uncertainty about where it lands on the distant screen.  Resolving the uncertainty at the first level through observation then affects the outcome at the second level.
  
A logic or thought experiment could model this phenonemon by setting up a [[random variable]] at the first level, and then another random variable at the second level that is a function of the first random variable.
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A logic or thought experiment could model this phenomenon by setting up a [[random variable]] at the first level, and then another random variable at the second level that is a function of the first random variable.
  
 
== Simple case ==
 
== Simple case ==
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'''''Answer''''':  The five locations on the distant screen have these probabilities:
 
'''''Answer''''':  The five locations on the distant screen have these probabilities:
  
:far left1/2 * 1/3 = 1/6
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{| class="wikitable"
:center left1/2 * 1/3 = 1/6
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|-
:center1/2 * 1/3 * 2 = 1/3
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! position
:center right1/2 * 1/3 = 1/6
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! probability
:far right1/2 * 1/3 = 1/6
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|-
 
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| far left
:Total = 1
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| <math>\frac{1}{2} \cdot \frac{1}{3} = \frac{1}{6}</math>
 
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|-
'''''Does the answer change if there is observation of the double slits, to remove the uncertainty at that level, as in advanced forms of the [[double-slit experiment]] using particles?'''''
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| center left
 
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| <math>\frac{1}{2} \cdot \frac{1}{3} = \frac{1}{6}</math>
'''''Answer''''': yes, arguably.  The pattern on the distant screen is never perfectly symmetric if there is observation of which particles pass through the double slits.  This tends to confirm that logic and uncertainty -- not waves -- require the surprising result of the [[double-slit experiment]].
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|-
 +
| center
 +
| <math>\frac{1}{2} \cdot \frac{1}{3} \cdot 2= \frac{1}{3}</math>
 +
|-
 +
| center right
 +
| <math>\frac{1}{2} \cdot \frac{1}{3} = \frac{1}{6}</math>
 +
|-
 +
| far right
 +
| <math>\frac{1}{2} \cdot \frac{1}{3} = \frac{1}{6}</math>
 +
|-
 +
| total
 +
| 1
 +
|}
  
 
==See also==
 
==See also==
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*[[Bayes' theorem]]
 
*[[Bayes' theorem]]
 
*[[Law of total probability]]
 
*[[Law of total probability]]
[[Category:mathematics]]
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[[Category:physics]]
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[[Category:Mathematics]]
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[[Category:Physics experiments]]

Latest revision as of 08:46, 7 April 2017

A double-slit logic experiment is the use of probability to determine of there is an underlying logical basis for the surprising effect observed in the double-slit experiment in physics.

The logical essence of the double-slit experiment is to have two levels of uncertainty in sequence. First, there is uncertainty about which of the two slits a "particle" passes through, and then there is uncertainty about where it lands on the distant screen. Resolving the uncertainty at the first level through observation then affects the outcome at the second level.

A logic or thought experiment could model this phenomenon by setting up a random variable at the first level, and then another random variable at the second level that is a function of the first random variable.

Simple case

Consider a double-slit experiment where a particle has a 50% chance of being found, if observed, to be passing through one of the slits. When it ends up on a distant background screen could then be one of three places for each slit: further left, straight ahead, or further right, each with a probability of one third. Assume that the placement on the distant screen of "further right" for the left slit is the same as "further left" for the right slit. 'What is the pattern observed on the distant screen when the double slits remain unobserved?

Answer: The five locations on the distant screen have these probabilities:

position probability
far left
center left
center
center right
far right
total 1

See also