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Re: astonishing correlations

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On September 18,  RichD wrote:
> This one is inspired by recent discussion of John Bell's 
> paper.  It's easy/hard;  non-obvious, yet simple once you see 
> the solution. 
> Given a pair of identical detectors, spaced far apart. 
> In between, a gun, which fires a pair of particles, one 
> at each detector.  Each detector holds a bulb, which 
> flashes red or green upon receiving a particle. 
> It also holds a switch, with 3 positions.  Prior to each 
> trial, the switch is set to an arbitrary position, randomly, 
> and independently of the other detector. 
> There exists no physical connection between the detectors. 
> You run 1000 trials, and observe the following: 
> I)  Considering each detector in isolation, the bulb 
> flashes red/green, 50/50, with no apparent pattern, 
> it appears completely random.  And no discernible 
> relation to the switch setting. 
> II)  Considering the pair, things become more interesting: 
> i)  When both switches are set to the same position, the 
> bulbs always flash the same color. 
> ii)  When they are set differently, there is no apparent relation 
> between the colors. 
> There is no communication channel between the 
> detectors. However, a particle constitutes a possible 
> channel, from gun to detector. 
> How do you explain the operation of this apparatus? 
> Does it seem plausible and practical, in principle? 

Assuming anyone is interested in this topic...

II (i) is the vital point. No connections between the detectors, how do 
they coordinate their outputs? There must be messages carried by the 
particles, that's the only reasonable hypothesis. 

So we postulate that the particles contain instructions. 
3 switch positions, and 2 colors  ==>  a particle contains 3 bits, 
one for each position.  A bit dictates the color, R/G, for the 
corresponding position.  Therefore 8 possible states, thus:
RRR
RRG
...
GGG

Each pair must carry identical states, in order to achieve II (i). 
The states are uniformly distributed, per the observations.

So far, so mundane, nothing interesting.  Now the trick: there's 
a vital piece of data missing from the original note, call it (III).  
The student must experience this insight, to see its relevance.  
Strictly speaking, it's unnecessary to provide this information, 
it's easily derived.  

III)  Considering only the pair of bulbs, ignoring the switches, 
there are 4 possible color states.  Obviously, from (I) and (II), 
these are uniformly distributed.

Put I, II, and III together, using freshman level combinatorics, 
one can discover something startling, Nobel worthy - 


--
Rich

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astonishing correlations RichD <r_delaney2001@yahoo.com> - 2023-09-18 11:21 -0700
  Re: astonishing correlations Sylvia Else <sylvia@email.invalid> - 2023-09-19 10:02 +1000
    Re: astonishing correlations RichD <r_delaney2001@yahoo.com> - 2023-09-18 20:11 -0700
      Re: astonishing correlations Sylvia Else <sylvia@email.invalid> - 2023-09-19 13:57 +1000
        Re: astonishing correlations RichD <r_delaney2001@yahoo.com> - 2023-09-19 11:25 -0700
          Re: astonishing correlations Sylvia Else <sylvia@email.invalid> - 2023-09-20 10:31 +1000
            Re: astonishing correlations Maciej Wozniak <maluwozniak@gmail.com> - 2023-09-19 23:40 -0700
            Re: astonishing correlations RichD <r_delaney2001@yahoo.com> - 2023-09-20 11:39 -0700
              Re: astonishing correlations Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-09-20 12:06 -0700
              Re: astonishing correlations Sylvia Else <sylvia@email.invalid> - 2023-09-21 09:45 +1000
                Re: astonishing correlations RichD <r_delaney2001@yahoo.com> - 2023-09-21 15:58 -0700
  Re: astonishing correlations Lou <noelturntive@live.co.uk> - 2023-09-20 02:54 -0700
  Re: astonishing correlations RichD <r_delaney2001@yahoo.com> - 2023-09-23 17:10 -0700
    Re: astonishing correlations Ken Hughes <kenhughes@aol.com> - 2023-09-25 05:48 -0700

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