Randomness

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Re: Randomness

Postby FrediFizzx » Fri Jun 28, 2019 1:09 pm

FrediFizzx wrote:
Heinera wrote:
FrediFizzx wrote:That is not what the polarizer simulation says. Now, we have a spin vector for the original singlet that can point in any 3D direction. We call it s.

The only time that you will get AB = -1 always is when s = a = b or -s = a = b.
.

I don't care what the polarizer simulation says. QM predicts that the correlation is -1 when the two detector settings are equal. That is, -cos(0).

Hmm... there is something wrong with that prediction then as it seems to be contrary to experiment. Ok, let me take another look at the polarizer simulation.
.

You are right. The prediction is good. I missed in the polarizer simulation that the +/- on a and b in the limits are linked. So we need a refinement for the measurement functions.




Where
.
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Re: Randomness

Postby Heinera » Fri Jun 28, 2019 1:32 pm

This looks very non-local. How do the functions A and B synchronize their ?
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Re: Randomness

Postby FrediFizzx » Fri Jun 28, 2019 1:40 pm

Heinera wrote:This looks very non-local. How do the functions A and B synchronize their ?

It may look that way but it is local. comes from the fact that s_A or s_B can be +/- in the bra-ket. But s_A = -s_B always. So there is no randomness between A and B because of that. Probably could write the functions a bit better.
.
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Re: Randomness

Postby Joy Christian » Fri Jun 28, 2019 2:11 pm

Heinera wrote:
This looks very non-local. How do the functions A and B synchronize their ?

and are shared randomnesses. They are permissible hidden variables in the local-realistic framework proposed by Bell. To make this clear, I would write the measurement functions as




where and .

***
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Re: Randomness

Postby Gordon Watson » Fri Jun 28, 2019 2:32 pm

FrediFizzx wrote:
Heinera wrote:
FrediFizzx wrote:
Heinera wrote:The only way to get a correlation of -1 is that the results are always opposite.

:mrgreen: If the results are always opposite, then how do you get ++ and -- ?
.

For a=b, you obviously don't.

That is not what the polarizer simulation says. Now, we have a spin vector for the original singlet that can point in any 3D direction. We call it s.

The only time that you will get AB = -1 always is when s = a = b or -s = a = b.
.

Fred,

This is nothing like a polarizer-simulation. Please, where does this particular idea come from? Are you referring to a serious model?

Thanks.
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Re: Randomness

Postby FrediFizzx » Fri Jun 28, 2019 2:55 pm

Gordon,

We already cancelled that assertion.
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Re: Randomness

Postby FrediFizzx » Fri Jun 28, 2019 5:21 pm

Joy Christian wrote:
Heinera wrote:
This looks very non-local. How do the functions A and B synchronize their ?

and are shared randomnesses. They are permissible hidden variables in the local-realistic framework proposed by Bell. To make this clear, I would write the measurement functions as




where and .

***


We probably should have where it belongs so it doesn't look non-local.




where and .

This simply embodies the superposition.
.
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Re: Randomness

Postby gill1109 » Fri Jun 28, 2019 6:07 pm

Joy Christian wrote:
gill1109 wrote:Joy Christian introduces a dummy variable s in the definition of functions A(a , λ) etc as the limit as s converges to a of some complicated function involving s , a and λ

I will not bother to respond to your previous reply because it is just a tedious repetition of your claims of the past twelve years. But I will correct your claim that s in my model is a dummy variable. It is not. It is the vector direction of the spin bivector I.s. You should give up your habit of misrepresenting other people's work. That habit does not help science at all. It harms it.

Dear Joy, I am not misrepresenting you.
I read your formulas, supposing them to be written in the conventional language of mathematics.
You keep repeating your written words.
I keep saying that there is a mismatch between your English language utterances and your mathematical language utterances.
You disagree. OK. We are going to have a great symposium! We can ask a big audience including Bell critics as well as Bell supporters; mathematicians, physicists and philosophers; what they think about some of these formulas.
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Re: Randomness

Postby FrediFizzx » Fri Jun 28, 2019 6:33 pm

FrediFizzx wrote:We probably should have where it belongs so it doesn't look non-local.




where and .

This simply embodies the superposition.
.

In fact I think this looks better. We can pull lambda out to the front even though it is where it belongs.




where and .

simply embodies the superposition.
.
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Re: Randomness

Postby gill1109 » Fri Jun 28, 2019 6:35 pm

FrediFizzx wrote:We probably should have where it belongs so it doesn't look non-local.



where and .
This simply embodies the superposition.

Now you have to specify the joint probability distribution of and . Independent fair coin tosses? In that case, the model makes the pair depend deterministically on the two measurement settings and on a single hidden variable which takes on four different values each with probability 1/4.

So Fred, I need to ask you,
(1) when you write in mathematics "limit as ..." do you want us to understand the usual calculus epsilon-delta definition of limit, or do you, like Joy, have something else in mind?
(2) if indeed the limits are +1 or -1, then the pair (A,B) can take on at most our different values ++, +-, -+. -- too, with four probabilities which, listed in order of size, are a coarsening of (1, 1, 1, 1) divided by 4. Here are the only five possibilities
(4, 0, 0, 0)
(3, 1, 0, 0)
(2, 2, 0, 0)
(2, 1, 1, 0)
(1, 1, 1, 1)
each divided by 4.
This is all about *partitions* of a set of four elements. You could bring in some Young diagrams here! https://en.wikipedia.org/wiki/Young_tableau or Hasse diagrams https://en.wikipedia.org/wiki/Hasse_diagram
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Re: Randomness

Postby Joy Christian » Fri Jun 28, 2019 6:36 pm

FrediFizzx wrote:
We probably should have where it belongs so it doesn't look non-local.




where and .

This simply embodies the superposition.

Yes, that is better and unambiguous.

***
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Re: Randomness

Postby FrediFizzx » Fri Jun 28, 2019 6:45 pm

gill1109 wrote:
FrediFizzx wrote:We probably should have where it belongs so it doesn't look non-local.



where and .
This simply embodies the superposition.

Now you have to specify the joint probability distribution of and . Independent fair coin tosses? In that case, the model makes the pair depend deterministically on the two measurement settings and on a single hidden variable which takes on four different values each with probability 1/4.

So Fred, I need to ask you,
(1) when you write in mathematics "limit as ..." do you want us to understand the usual calculus epsilon-delta definition of limit, or do you, like Joy, have something else in mind?
(2) if indeed the limits are +1 or -1, then the pair (A,B) can take on at most our different values ++, +-, -+. -- too, with four probabilities which, listed in order of size, are a coarsening of (1, 1, 1, 1) divided by 4. Here are the only five possibilities
(4, 0, 0, 0)
(3, 1, 0, 0)
(2, 2, 0, 0)
(2, 1, 1, 0)
(1, 1, 1, 1)
each divided by 4.
This is all about *partitions* of a set of four elements. You could bring in some Young diagrams here! https://en.wikipedia.org/wiki/Young_tableau or Hasse diagrams https://en.wikipedia.org/wiki/Hasse_diagram

I don't consider to be a hidden variable. It simply embodies the superposition of the particles in the singlet.
.
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Re: Randomness

Postby Heinera » Fri Jun 28, 2019 11:15 pm

FrediFizzx wrote:In fact I think this looks better. We can pull lambda out to the front even though it is where it belongs.




where and .

simply embodies the superposition.
.


Great. We can also pull mu out to the front:




You see what happens here? If and are independent, the introduction of into the theory has no effect. The product is still a single binary random variable.
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Re: Randomness

Postby Joy Christian » Sat Jun 29, 2019 12:10 am

Heinera wrote:
FrediFizzx wrote:In fact I think this looks better. We can pull lambda out to the front even though it is where it belongs.




where and .

simply embodies the superposition.
.


Great. We can also pull mu out to the front:




You see what happens here? If and are independent, the introduction of into the theory has no effect. The product is still a single binary random variable.

That is your model, not ours. You have learned the strawman trick from Gill well. Strawman trick is often used in politics, and also, by some (as I have learned the hard way), in science.

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Re: Randomness

Postby Heinera » Sat Jun 29, 2019 12:28 am

Joy Christian wrote:That is your model, not ours. You have learned the strawman trick from Gill well. Strawman trick is often used in politics, and also, by some (as I have learned the hard way), in science.

***

Ok, you didn't understand that I made no changes to the model, but hopefully Fred will.
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Re: Randomness

Postby Joy Christian » Sat Jun 29, 2019 12:35 am

Heinera wrote:
Joy Christian wrote:That is your model, not ours. You have learned the strawman trick from Gill well. Strawman trick is often used in politics, and also, by some (as I have learned the hard way), in science.

***

Ok, you didn't understand that I made no changes to the model, but hopefully Fred will.

Oh... but you did, and you didn't understand that you did!

***
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Re: Randomness

Postby FrediFizzx » Sat Jun 29, 2019 12:44 am

Heinera wrote:
Joy Christian wrote:That is your model, not ours. You have learned the strawman trick from Gill well. Strawman trick is often used in politics, and also, by some (as I have learned the hard way), in science.

***

Ok, you didn't understand that I made no changes to the model, but hopefully Fred will.

I don't see any problem. It is no longer a single binary variable. If lambda is +1, mu can be +/- 1. If lambda = -1, mu can be +/-1. What does that give you? It gives you ++, +-, -+, --.
.
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Re: Randomness

Postby Heinera » Sat Jun 29, 2019 12:48 am

FrediFizzx wrote:I don't see any problem. It is no longer a single binary variable. If lambda is +1, mu can be +/- 1. If lambda = -1, mu can be +/-1. What does that give you? It gives you ++, +-, -+, --.
.

No, because lambda and mu only appear together as a product, and the product cannot take on 4 different values.
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Re: Randomness

Postby FrediFizzx » Sat Jun 29, 2019 12:54 am

Heinera wrote:
FrediFizzx wrote:I don't see any problem. It is no longer a single binary variable. If lambda is +1, mu can be +/- 1. If lambda = -1, mu can be +/-1. What does that give you? It gives you ++, +-, -+, --.
.

No, because lambda and mu only appear together as a product, and the product cannot take on 4 different values.

:D ??? I just proved you are wrong. If lambda is +1, mu can be +/- 1. If lambda = -1, mu can be +/-1. What does that give you? It gives you ++, +-, -+, --.
.
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Re: Randomness

Postby Heinera » Sat Jun 29, 2019 12:58 am

FrediFizzx wrote:
Heinera wrote:
FrediFizzx wrote:I don't see any problem. It is no longer a single binary variable. If lambda is +1, mu can be +/- 1. If lambda = -1, mu can be +/-1. What does that give you? It gives you ++, +-, -+, --.
.

No, because lambda and mu only appear together as a product, and the product cannot take on 4 different values.

:D ??? I just proved you are wrong. If lambda is +1, mu can be +/- 1. If lambda = -1, mu can be +/-1. What does that give you? It gives you ++, +-, -+, --.
.


Remember that it is the same lambda and mu in both functions A and B. So if in A, we must also have in B. And the same holds for . Only two possibilities.
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