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 9:05 am

gill1109 wrote:
FrediFizzx wrote:I doubt very much that 3D space itself has a handedness. It is matter or forms of energy transport that can have a handedness. But sure, you can have left or right handed basis definitions for defining cartesian coordinates. Usually that is for defining objects via vectors that exist in the 3D space. Right hand rule or left hand rule. Most people are "locked" into the right hand rule and don't think about the left hand rule much. But anyways, yeah we have that 3D space is the cause of the 50-50 "fair" coin toss definition. No problem there.
.

OK

But you still haven’t responded to this, Fred:

gill1109 wrote:Trouble is, as you go down, randomness *has* to become more fine-grained. More precisely, it can’t ever be *less* fine-grained. In the lab, when we measure spins of two particles, there are four *joint* outcomes, not two. And they typically have probabilities different from zero, one half, or one. The deeper level has to have at least as many “atoms” of probability, and their sizes have to add up in groups to the sizes of atoms at the top level.

Now I’m happy to believe that at some deep level the handed-ness of space is responsible for the randomness of spin measurements. But I cannot believe it works through a single binary fair coin toss λ.

A real fair coin toss provides an excellent example. An idealised coin is launched vertically into the air with a rotation speed around a horizontal axis X > 0 and a vertical velocity Y > 0. It rises and then falls and hits a flat surface which instantly absorbs all energy and leaves the coin lying flat. In suitable units this could result in the binary outcome Parity(IntegerPart(XY)). If X and Y have a joint smooth probability distribution which extends in both directions far enough, the outcome is almost a fair coin toss. This has been studied long ago by Persi Diaconis. Who is both a great mathematician and a great conjuror. He can toss a coin and have it land heads 95% of the time.

I believe I took care of the middle sentence and the last paragraph with 3D space as the "cause". I don't get your point for the first paragraph. If we have a "cause" for the randomness then it stops there.
.
FrediFizzx
Independent Physics Researcher
 
Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

Re: Randomness

Postby gill1109 » Fri Jun 28, 2019 9:58 am

Fred, you still didn't respond to this:
gill1109 wrote:Trouble is, as you go down, randomness *has* to become more fine-grained. More precisely, it can’t ever be *less* fine-grained. In the lab, when we measure spins of two particles, there are four *joint* outcomes, not two. And they typically have probabilities different from zero, one half, or one. The deeper level has to have at least as many “atoms” of probability, and their sizes have to add up in groups to the sizes of the atoms of probability at the top level. Now I’m happy to believe that at some deep level the handed-ness of space is responsible for the randomness of spin measurements. But I cannot believe it works through a single binary fair coin toss λ.
.

You can't get the four probabilities of the joint outcomes ++, +-, -+ and --, which we see in real experiments and which QM predicts, which are all different from zero, one half, and one, as "coarse-grained" result of deterministic functions of the setting and of a hidden variable λ which only takes on two different values and does that each with probability one half. Please think about it!

Heinera has brought it up a number of times. So have I. Neither you nor Joy have given any response beyond repeating the statement that Joy's maths is right. Well, this is a mathematical contradiction.

Speaking of mathematical contradictions: Han Geurdes, Alexandre de Castro, and others believe that Bell's theorem is correct, *and* that they have a counterexample to Bell's theorem, and that therefore the logical foundations of mathematics need to be rewritten. Ilija Barukcik is another scientist who believes that the usual logical foundations of mathematics need to be rewritten - he finds inequalities like "S <= 2" meaningless since it stands 'for "S < 2" *and* "S = 2" are both possible', which is self-evidently false (I hope I have reproduced his published arguments correctly).

You can find these researchers and their work on ResearchGate; and moreover their papers are published in many journals.

All that's of course a possibility. But I would put my money elsewhere.
gill1109
Mathematical Statistician
 
Posts: 2812
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

Re: Randomness

Postby FrediFizzx » Fri Jun 28, 2019 10:29 am

gill1109 wrote:Fred, you still didn't respond to this:
gill1109 wrote:Trouble is, as you go down, randomness *has* to become more fine-grained. More precisely, it can’t ever be *less* fine-grained. In the lab, when we measure spins of two particles, there are four *joint* outcomes, not two. And they typically have probabilities different from zero, one half, or one. The deeper level has to have at least as many “atoms” of probability, and their sizes have to add up in groups to the sizes of the atoms of probability at the top level. Now I’m happy to believe that at some deep level the handed-ness of space is responsible for the randomness of spin measurements. But I cannot believe it works through a single binary fair coin toss λ.
.

You can't get the four probabilities of the joint outcomes ++, +-, -+ and --, which we see in real experiments and which QM predicts, which are all different from zero, one half, and one, as "coarse-grained" result of deterministic functions of the setting and of a hidden variable λ which only takes on two different values and does that each with probability one half. Please think about it!

Heinera has brought it up a number of times. So have I. Neither you nor Joy have given any response beyond repeating the statement that Joy's maths is right. Well, this is a mathematical contradiction.

Oh, you missed the new measurement functions.

The conclusion from this Stern-Gerlach polarizer simulation,

https://phet.colorado.edu/sims/stern-ge ... ch_en.html

Is that when a = b you will not get AB = -1 always if the angle between the particle spin vector and a is random in the actual experiment. So these functions are correct in that case.



.
FrediFizzx
Independent Physics Researcher
 
Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

Re: Randomness

Postby Joy Christian » Fri Jun 28, 2019 10:37 am

gill1109 wrote:You can't get the four probabilities of the joint outcomes ++, +-, -+ and --, which we see in real experiments and which QM predicts, which are all different from zero, one half, and one, as "coarse-grained" result of deterministic functions of the setting and of a hidden variable λ which only takes on two different values and does that each with probability one half. Please think about it!

This is wrong. The 3-sphere model does "get the four probabilities of the joint outcomes ++, +-, -+ and -- which we see in real experiments and which QM predicts", from "a hidden variable λ which only takes on two different values and does that each with probability one half."

I am not going to explain again how that is possible for the 3-sphere model because I have done so literally thousands of times during the past twelve years with no avail. But here is a Hint:

The measurement function A(a, λ) in the 3-sphere model is a point of the 3-sphere; thus it embodies all of the geometrical and topological properties of the 3-sphere in addition to λ.

***
Last edited by Joy Christian on Fri Jun 28, 2019 11:05 am, edited 1 time in total.
Joy Christian
Research Physicist
 
Posts: 2793
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

Re: Randomness

Postby Heinera » Fri Jun 28, 2019 10:59 am

FrediFizzx wrote:Oh, you missed the new measurement functions.

The conclusion from this Stern-Gerlach polarizer simulation,

https://phet.colorado.edu/sims/stern-ge ... ch_en.html

Is that when a = b you will not get AB = -1 always if the angle between the particle spin vector and a is random in the actual experiment.
.

That is against the prediction of QM, so there is clearly something you don't understand about the simulation. (Also, there are no entangled particle pairs in that simulation, so I dont see how you think it is relevant).
Heinera
 
Posts: 917
Joined: Thu Feb 06, 2014 1:50 am

Re: Randomness

Postby gill1109 » Fri Jun 28, 2019 11:10 am

Joy Christian wrote:
gill1109 wrote:You can't get the four probabilities of the joint outcomes ++, +-, -+ and --, which we see in real experiments and which QM predicts, which are all different from zero, one half, and one, as "coarse-grained" result of deterministic functions of the setting and of a hidden variable λ which only takes on two different values and does that each with probability one half. Please think about it!

This is wrong. The 3-sphere model does "get the four probabilities of the joint outcomes ++, +-, -+ and -- which we see in real experiments and which QM predicts", from "a hidden variable λ which only takes on two different values and does that each with probability one half."

I am not going to explain again how that is possible for the 3-sphere model because I have done so literally thousands of times during the past twelve years with no avail. But here is a Hint:

The measurement function A(a, λ) in the 3-sphere model is a point of the 3-sphere; thus it embodies all of the geometrical and topological properties of the 3-sphere in addition to λ.

***

Indeed you tried to explain thousands of times but I am not sure that anyone at all understood you. Maybe a few "believed you", but that is something different.

You say that the measurement *function* is a *point* of the 3-sphere????

The measurement function is A. It's a function.

A(a, λ) is the evaluation of the function A in the point (a, λ) and is the number -1 or the number +1.

You can think of these two numbers as being two rather special particular points on the 3-sphere.

But there is no way that the numbers -1 and +1 thereby "embody" geometrical and topological properties of the 3-sphere!

One might as well say that because the number 2 sqrt 2 is a real number hence a complex number, that it thereby "embodies" the geometrical and topological properties of the complex plane.
Last edited by gill1109 on Fri Jun 28, 2019 11:12 am, edited 1 time in total.
gill1109
Mathematical Statistician
 
Posts: 2812
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

Re: Randomness

Postby FrediFizzx » Fri Jun 28, 2019 11:12 am

Heinera wrote:
FrediFizzx wrote:Oh, you missed the new measurement functions.

The conclusion from this Stern-Gerlach polarizer simulation,

https://phet.colorado.edu/sims/stern-ge ... ch_en.html

Is that when a = b you will not get AB = -1 always if the angle between the particle spin vector and a is random in the actual experiment.
.

That is against the prediction of QM, so there is clearly something you don't understand about the simulation. (Also, there are no entangled particle pairs in that simulation, so I dont see how you think it is relevant).

Sorry, but it is not against the prediction of QM when s is pointing in a random 3D direction. We are specifying that s_A and s_B are entangled by the fact that s_A = -s_B. And the +/- on a and b in the limits automatically takes care of the superposition. Perhaps not ideal but it works.
.
FrediFizzx
Independent Physics Researcher
 
Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

Re: Randomness

Postby FrediFizzx » Fri Jun 28, 2019 11:13 am

gill1109 wrote:
Joy Christian wrote:
gill1109 wrote:You can't get the four probabilities of the joint outcomes ++, +-, -+ and --, which we see in real experiments and which QM predicts, which are all different from zero, one half, and one, as "coarse-grained" result of deterministic functions of the setting and of a hidden variable λ which only takes on two different values and does that each with probability one half. Please think about it!

This is wrong. The 3-sphere model does "get the four probabilities of the joint outcomes ++, +-, -+ and -- which we see in real experiments and which QM predicts", from "a hidden variable λ which only takes on two different values and does that each with probability one half."

I am not going to explain again how that is possible for the 3-sphere model because I have done so literally thousands of times during the past twelve years with no avail. But here is a Hint:

The measurement function A(a, λ) in the 3-sphere model is a point of the 3-sphere; thus it embodies all of the geometrical and topological properties of the 3-sphere in addition to λ.

***

Indeed you tried to explain thousands of times but I am not sure that anyone at all understood you. Maybe a few "believed you", but that is something different.

You say that the measurement *function* is a *point* of the 3-sphere????

The measurement function is A. It's a function.

A(a, λ) is the evaluation of the function A in the point (a, λ) and is the number -1 or the number +1.

You can think of these two numbers as being two rather special particular points on the 3-sphere.

But there is no way that the numbers -1 and +1 thereby "embody" geometrical and topological properties of the 3-sphere!

One might as well say that because the number 2 sqrt 2 is a real number hence a complex number, that it thereby "embodies" the geometrical and topological properties of the complex plane.

You will probably never understand it so let's stick to what the actual experiment is telling us.
.
FrediFizzx
Independent Physics Researcher
 
Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

Re: Randomness

Postby gill1109 » Fri Jun 28, 2019 11:21 am

FrediFizzx wrote:
Heinera wrote:
FrediFizzx wrote:Oh, you missed the new measurement functions.

The conclusion from this Stern-Gerlach polarizer simulation,

https://phet.colorado.edu/sims/stern-ge ... ch_en.html

Is that when a = b you will not get AB = -1 always if the angle between the particle spin vector and a is random in the actual experiment.
.

That is against the prediction of QM, so there is clearly something you don't understand about the simulation. (Also, there are no entangled particle pairs in that simulation, so I don't see how you think it is relevant).

Sorry, but it is not against the prediction of QM when s is pointing in a random 3D direction. We are specifying that s_A and s_B are entangled by the fact that s_A = -s_B. And the +/- on a and b in the limits automatically takes care of the superposition. Perhaps not ideal but it works.
.

QM doesn't say anything about spin vectors pointing in a random 3D direction s. QM talks about states (vectors in Hilbert spaces) and measurements of observables (Hermitean operators) and so on...

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 . He pictures this in a charming way as a real spinning thing approaching the dector and aligning itself with the detector. I don't object to the picture as long as it doesn't interfere with the mathematics.
gill1109
Mathematical Statistician
 
Posts: 2812
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

Re: Randomness

Postby Joy Christian » Fri Jun 28, 2019 11:31 am

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.

***
Joy Christian
Research Physicist
 
Posts: 2793
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

Re: Randomness

Postby Heinera » Fri Jun 28, 2019 11:49 am

FrediFizzx wrote:Sorry, but it is not against the prediction of QM when s is pointing in a random 3D direction.
.

There is no s in QM. The prediction of QM is that the measurement outcomes for an entangled particle pair will always have opposite values when the detector settings are the same for Alice and Bob. It is the only way to get a correlation of -1.
Last edited by Heinera on Fri Jun 28, 2019 11:56 am, edited 1 time in total.
Heinera
 
Posts: 917
Joined: Thu Feb 06, 2014 1:50 am

Re: Randomness

Postby FrediFizzx » Fri Jun 28, 2019 11:55 am

Heinera wrote:
FrediFizzx wrote:Sorry, but it is not against the prediction of QM when s is pointing in a random 3D direction.
.

There is no s in QM. The prediction of QM is that the measurement outcomes for an entangled particle pair will always have opposite values when the detector settings are the same for Alice and Bob.

What do you think <Psi_nR|...|Psi_nR> is? It is the singlet state for the s_A and -s_B particles.
.
FrediFizzx
Independent Physics Researcher
 
Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

Re: Randomness

Postby Heinera » Fri Jun 28, 2019 11:57 am

FrediFizzx wrote:What do you think <Psi_nR|...|Psi_nR> is? It is the singlet state for the s_A and -s_B particles.
.

I am talking about QM, not your model. If the results are not always opposite for a=b, then it is trivial to show that the correlation will not be -1.
Heinera
 
Posts: 917
Joined: Thu Feb 06, 2014 1:50 am

Re: Randomness

Postby FrediFizzx » Fri Jun 28, 2019 12:02 pm

Heinera wrote:
FrediFizzx wrote:What do you think <Psi_nR|...|Psi_nR> is? It is the singlet state for the s_A and -s_B particles.
.

I am talking about QM, not your model.

That is QM. Ok, take the R off. <Psi_n|...|Psi_n> What do you think the "n's" are? They are s_A and -s_B for the two particles.
.
FrediFizzx
Independent Physics Researcher
 
Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

Re: Randomness

Postby Heinera » Fri Jun 28, 2019 12:15 pm

The only way to get a correlation of -1 is that the results are always opposite.
Heinera
 
Posts: 917
Joined: Thu Feb 06, 2014 1:50 am

Re: Randomness

Postby FrediFizzx » Fri Jun 28, 2019 12:18 pm

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 -- ?
.
FrediFizzx
Independent Physics Researcher
 
Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

Re: Randomness

Postby Heinera » Fri Jun 28, 2019 12:22 pm

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.
Heinera
 
Posts: 917
Joined: Thu Feb 06, 2014 1:50 am

Re: Randomness

Postby FrediFizzx » Fri Jun 28, 2019 12:27 pm

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.
.
FrediFizzx
Independent Physics Researcher
 
Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

Re: Randomness

Postby Heinera » Fri Jun 28, 2019 12:32 pm

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).
Heinera
 
Posts: 917
Joined: Thu Feb 06, 2014 1:50 am

Re: Randomness

Postby FrediFizzx » Fri Jun 28, 2019 12:37 pm

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.
.
FrediFizzx
Independent Physics Researcher
 
Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

PreviousNext

Return to Sci.Physics.Foundations

Who is online

Users browsing this forum: No registered users and 73 guests

cron
CodeCogs - An Open Source Scientific Library