Randomness

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

Re: Randomness

Postby Joy Christian » Sat Jun 29, 2019 1:06 am

***
You can avoid all that by sticking to the manifestly local functions I wrote down earlier:

Joy Christian wrote:
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 .

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

Re: Randomness

Postby FrediFizzx » Sat Jun 29, 2019 1:13 am

Heinera wrote:
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.

Well dang it. I thought I checked that. I will look at it all in the morning. Too sleepy right now.
FrediFizzx
Independent Physics Researcher
 
Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

Re: Randomness

Postby gill1109 » Sat Jun 29, 2019 5:53 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.

I object, your honour.

I do not use any strawman trick.

I read the formulas written by Joy Christian and take them seriously, and then I tell anyone who wants to hear what those formulas say to a mathematician who can read formulas.

What I find contradicts the words which Christian utters, and that's the reason he says that my "reading" of his work is a straw-man trick, as used by dirty politicians.

Please be charitable and honest, Joy. Don't slander me, either. We're civilized grown-ups and we're both scientists, right?

You've admitted that when you write down a formula which includes what looks like a mathematical limit, you never ever intended it to be read as a mathematical (epsilon-delta definition) limit. Since you don't use conventional mathematics and don't explain your unconventional "conventions", nobody can say whether your work is correct or incorrect. All one can say is that the English language is suggestive and poetical. Fine. Maybe it inspires some mathematician to look for a mathematical structure which reflects your poetry. That was indeed my original motivation for studying your work quite deeply. I had the feeling that there did have to be something in it, though maybe not exactly what the writer had in mind.
gill1109
Mathematical Statistician
 
Posts: 2812
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

Re: Randomness

Postby FrediFizzx » Sat Jun 29, 2019 6:56 pm

Hi Folks,

Thanks to your previous criticisms, we have arrived at the penultimate functions!




But don't give up now. Hammer them hard if you can. :D
.
FrediFizzx
Independent Physics Researcher
 
Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

Re: Randomness

Postby gill1109 » Sun Jun 30, 2019 1:44 am

FrediFizzx wrote:Hi Folks,

Thanks to your previous criticisms, we have arrived at the penultimate functions!




But don't give up now. Hammer them hard if you can. :D
.

Beautiful formulas, but mathematically, they make no sense. Remember what I keep saying about "bound variables" (aka dummy variables) and "free variables" and the epsilon-delta definition of limit? You can't have a limit as s converges to a function of s. At least, not in conventional mathematics. You are welcome to break with convention but then please tell us what you mean, precisely, with your unconventional notation.

You *can* take a limit as a difference between s and a function of s converges to zero. What it would exactly entail in the present case is just a question of writing out the epsilon-delta definition and seeing what it actually means.
gill1109
Mathematical Statistician
 
Posts: 2812
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

Re: Randomness

Postby Joy Christian » Sun Jun 30, 2019 2:13 am

***
The measurement functions, as defined, are perfectly valid functions. They are quite easy to understand in terms of the limits defined. We all know what "limit" means in mathematics.

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

Re: Randomness

Postby gill1109 » Sun Jun 30, 2019 4:39 am

Joy Christian wrote:The measurement functions, as defined, are perfectly valid functions. They are quite easy to understand in terms of the limits defined. We all know what "limit" means in mathematics.

We don't all know what limit means (or meant - it has changed over time) in mathematics.

Tell us what you think it means. I don't know. I'm only a statistician. What you told us before did not match what I learnt in undergraduate Cambridge mathematics 45 years ago. (First year courses on set theory and on analysis, and second year topology). And you told us you didn't know what bound and free variables were.
https://en.wikipedia.org/wiki/(%CE%B5,_%CE%B4)-definition_of_limit
https://en.wikipedia.org/wiki/Free_variables_and_bound_variables

But maybe physicists have a completely different mathematics. And nowadays the young people are taught category theory definitions
https://en.wikipedia.org/wiki/Limit_(category_theory)

https://ocw.mit.edu/courses/mathematics/18-s097-applied-category-theory-january-iap-2019/lecture-videos-and-readings/ MIT video course, Fong and Spivak

https://www.amazon.com/gp/product/1108482295 "An Invitation to Applied Category Theory: Seven Sketches in Compositionality"
by Brendan Fong, David I. Spivak
gill1109
Mathematical Statistician
 
Posts: 2812
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

Re: Randomness

Postby FrediFizzx » Sun Jun 30, 2019 7:49 am

gill1109 wrote:
Joy Christian wrote:The measurement functions, as defined, are perfectly valid functions. They are quite easy to understand in terms of the limits defined. We all know what "limit" means in mathematics.

We don't all know what limit means (or meant - it has changed over time) in mathematics.

I don't know how to explain it to you if you don't "get it". Maybe Heine can explain it to you as he seems to understand it.
.
FrediFizzx
Independent Physics Researcher
 
Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

Re: Randomness

Postby Heinera » Sun Jun 30, 2019 8:28 am

I have no idea what is supposed to mean. When one takes a limit, one of course does not have the same variable on both sides of the arrow. Maybe you could explain your intended meaning by giving us a worked-out numerical example of how this should be interpreted.
Heinera
 
Posts: 917
Joined: Thu Feb 06, 2014 1:50 am

Re: Randomness

Postby FrediFizzx » Sun Jun 30, 2019 8:34 am

Heinera wrote:I have no idea what is supposed to mean. When one takes a limit, one of course does not have the same variable on both sides of the arrow. Maybe you could explain your intended meaning by giving us a worked-out numerical example of how this should be interpreted.

sgn(n.s_N) just returns a sign +/- that depends on the angle between n and s_N via the cosine function. Pretty simple. And... that is the actual physics. Whether you get up or down out of the polarizer depends on the angle between n and s_N.
.
FrediFizzx
Independent Physics Researcher
 
Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

Re: Randomness

Postby Joy Christian » Sun Jun 30, 2019 8:52 am

Heinera wrote:When one takes a limit, one of course does not have the same variable on both sides of the arrow.

Well, one lives and learns. Here is your opportunity to learn. And the same goes for the other objectors. One can most certainly have the same variable on both sides of the arrow. :)

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

Re: Randomness

Postby Heinera » Sun Jun 30, 2019 9:44 am

FrediFizzx wrote:sgn(n.s_N) just returns a sign +/- that depends on the angle between n and s_N via the cosine function. Pretty simple. And... that is the actual physics. Whether you get up or down out of the polarizer depends on the angle between n and s_N.
.

But I guess that this s_N must change during the process, or else the lim notation is completely superfluous (even physically). So this angle between n and s_N should be taken exactly when?
Heinera
 
Posts: 917
Joined: Thu Feb 06, 2014 1:50 am

Re: Randomness

Postby FrediFizzx » Sun Jun 30, 2019 9:54 am

Heinera wrote:
FrediFizzx wrote:sgn(n.s_N) just returns a sign +/- that depends on the angle between n and s_N via the cosine function. Pretty simple. And... that is the actual physics. Whether you get up or down out of the polarizer depends on the angle between n and s_N.
.

But I guess that this s_N must change during the process, or else the lim notation is completely superfluous (even physically). So this angle between n and s_N should be taken exactly when?

It can be taken after n is set by the experimenter until the polarizer action.
FrediFizzx
Independent Physics Researcher
 
Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

Re: Randomness

Postby gill1109 » Sun Jun 30, 2019 9:56 am

Joy Christian wrote:
Heinera wrote:When one takes a limit, one of course does not have the same variable on both sides of the arrow.

Well, one lives and learns. Here is your opportunity to learn. And the same goes for the other objectors. One can most certainly have the same variable on both sides of the arrow. :)

We would love to learn. So please teach us! (None of us have ever seen anything like this before).

Let's make things as simple as possible. Let's think of real functions of real variables. What could you mean by writing lim_{x -> g(x)} f(x)? Well, one might interpret the arrow ("converges to") as "gets closer and closer to". Then we could rewrite the limit in conventional notation (with the intended conventional meaning) as lim_{x - g(x) -> 0} f(x). The limit would be the number y, say, if, for every epsilon > 0, there exists a delta > 0, such that if x is such that |x - g(x)| <= delta, then |f(x) - y| <= epsilon.

Well, if that is what you mean, then you can now start the work of figuring out whether or not the two expressions you have given do have limits in this sense, and if so, what they are. Also you can now start investigating whether or not the usual results about products of limits and the like will still be valid in your new notion of limit.

I understand that you furthermore want to couple the dummy variables in both limits to one another. I've never seen anything like that before in 50 years in the best university mathematics departments. Among my teachers were Stephen Hawking, John H . Conway, David Kendall, Peter Whittle; and I got a 1st class degree with distinction. So: please teach us! It is wonderful to see the envelope of what one can do in mathematics being pushed to dizzy new heights.
gill1109
Mathematical Statistician
 
Posts: 2812
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

Re: Randomness

Postby Heinera » Sun Jun 30, 2019 10:26 am

FrediFizzx wrote:
Heinera wrote:
FrediFizzx wrote:sgn(n.s_N) just returns a sign +/- that depends on the angle between n and s_N via the cosine function. Pretty simple. And... that is the actual physics. Whether you get up or down out of the polarizer depends on the angle between n and s_N.
.

But I guess that this s_N must change during the process, or else the lim notation is completely superfluous (even physically). So this angle between n and s_N should be taken exactly when?

It can be taken after n is set by the experimenter until the polarizer action.

Ok. I assume it will be constant during that period. So the initial (continuous) value of s_N can now be regarded as an extra hidden variable that influences the outcome via the signum function. Right?
Heinera
 
Posts: 917
Joined: Thu Feb 06, 2014 1:50 am

Re: Randomness

Postby FrediFizzx » Sun Jun 30, 2019 10:31 am

Heinera wrote:
FrediFizzx wrote:
Heinera wrote:
FrediFizzx wrote:sgn(n.s_N) just returns a sign +/- that depends on the angle between n and s_N via the cosine function. Pretty simple. And... that is the actual physics. Whether you get up or down out of the polarizer depends on the angle between n and s_N.
.

But I guess that this s_N must change during the process, or else the lim notation is completely superfluous (even physically). So this angle between n and s_N should be taken exactly when?

It can be taken after n is set by the experimenter until the polarizer action.

Ok. I assume it will be constant during that period. So the initial (continuous) value of s_N can now be regarded as an extra hidden variable that influences the outcome via the signum function. Right?

I don't think I would call it a hidden variable since we know that it is from the fact that s_N's spin vector can point in any random 3D direction. But whatever floats your boat. I suppose that once we know the "cause" then it is not really hidden any more is it? But for sure the fact remains that it is a variable.
FrediFizzx
Independent Physics Researcher
 
Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

Re: Randomness

Postby Joy Christian » Sun Jun 30, 2019 10:33 am

***
It is all quite easy to understand.

There are three ordinary vectors, , , and . All three vectors are given to set up the limit process. The vector approches either the vector or the vector , depending on the angle between and . What is so difficult in that to understand? If anyone has difficutly in understanding this, then they should draw a simple diagram of these three vectors.

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

Re: Randomness

Postby Heinera » Sun Jun 30, 2019 10:55 am

[quote="FrediFizzx"
I don't think I would call it a hidden variable since we know that it is from the fact that s_N's spin vector can point in any random 3D direction. But whatever floats your boat. I suppose that once we know the "cause" then it is not really hidden any more is it? But for sure the fact remains that it is a variable.[/quote]
In Bell's terminology a hidden variable is anything in the state that influences the outcome (no matter if we know it's cause), so this is definitely a hidden variable.

Now, in his original paper (1964) Bell gives some examples of classical models with initial spin vectors in section III. You model is now starting to look a lot like them. And without having dug any deeper in your latest version I would expect your correlations to be similar.
Heinera
 
Posts: 917
Joined: Thu Feb 06, 2014 1:50 am

Re: Randomness

Postby FrediFizzx » Sun Jun 30, 2019 10:56 am

Joy Christian wrote:***
It is all quite easy to understand.

There are three ordinary vectors, , , and . All three vectors are given to set up the limit process. The vector approches either the vector or the vector , depending on the angle between and . What is so difficult in that to understand? If anyone has difficutly in understanding this, then they should draw a simple diagram of these three vectors.

***

Yes, it is all pretty simple. Plus those three ordinary vectors are all random variables. Not hidden variables.
.
FrediFizzx
Independent Physics Researcher
 
Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

Re: Randomness

Postby FrediFizzx » Sun Jun 30, 2019 11:00 am

Heinera wrote:
FrediFizzx wrote:I don't think I would call it a hidden variable since we know that it is from the fact that s_N's spin vector can point in any random 3D direction. But whatever floats your boat. I suppose that once we know the "cause" then it is not really hidden any more is it? But for sure the fact remains that it is a variable.

In Bell's terminology a hidden variable is anything in the state that influences the outcome (no matter if we know it's cause), so this is definitely a hidden variable.

That is baloney. a and b influence the outcomes. So surely n relative to s is also going to influence the outcomes.
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: ahrefs [Bot] and 82 guests

cron
CodeCogs - An Open Source Scientific Library