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by **FrediFizzx** » Sun Jun 30, 2019 7:25 am

FrediFizzx wrote:Hi Folks,

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

$A({\bf a},\, \lambda) := \lim_{{\bf s_A} \rightarrow\, -\text{sgn}({\bf a}\cdot{\bf s_A}){\bf a} }\Big[\langle\phi_{\bf n \text R}|\{ ({\boldsymbol\sigma}\cdot{\bf a}) \,(\lambda \,{\boldsymbol\sigma}\cdot (-{\bf s_A}))\}|\phi_{\bf n \text R}\rangle \Big] = \mp 1$
$B({\bf b};\, \lambda) :=\lim_{{\bf s_B} \rightarrow \, +\text{sgn}({\bf b}\cdot{\bf s_B}){\bf b}}\Big[\langle\chi_{\bf n \text R}|\{ (\lambda\,{\boldsymbol\sigma}\cdot (+{\bf s_B})) \,( {\boldsymbol\sigma}\cdot {\bf b})\}|\chi_{\bf n \text R}\rangle \Big]= \pm 1$

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

For Heine, keep in mind that from the paper $s_B = -s_A$ always.

by **gill1109** » Sun Jun 30, 2019 10:05 am

FrediFizzx wrote:
FrediFizzx wrote:Hi Folks,

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

$A({\bf a},\, \lambda) := \lim_{{\bf s_A} \rightarrow\, -\text{sgn}({\bf a}\cdot{\bf s_A}){\bf a} }\Big[\langle\phi_{\bf n \text R}|\{ ({\boldsymbol\sigma}\cdot{\bf a}) \,(\lambda \,{\boldsymbol\sigma}\cdot (-{\bf s_A}))\}|\phi_{\bf n \text R}\rangle \Big] = \mp 1$
$B({\bf b};\, \lambda) :=\lim_{{\bf s_B} \rightarrow \, +\text{sgn}({\bf b}\cdot{\bf s_B}){\bf b}}\Big[\langle\chi_{\bf n \text R}|\{ (\lambda\,{\boldsymbol\sigma}\cdot (+{\bf s_B})) \,( {\boldsymbol\sigma}\cdot {\bf b})\}|\chi_{\bf n \text R}\rangle \Big]= \pm 1$

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

For Heine, keep in mind that from the paper $s_B = -s_A$ always.

Please explain your notation.

by **FrediFizzx** » Sun Jun 30, 2019 10:13 am

gill1109 wrote:
FrediFizzx wrote:
FrediFizzx wrote:Hi Folks,

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

$A({\bf a},\, \lambda) := \lim_{{\bf s_A} \rightarrow\, -\text{sgn}({\bf a}\cdot{\bf s_A}){\bf a} }\Big[\langle\phi_{\bf n \text R}|\{ ({\boldsymbol\sigma}\cdot{\bf a}) \,(\lambda \,{\boldsymbol\sigma}\cdot (-{\bf s_A}))\}|\phi_{\bf n \text R}\rangle \Big] = \mp 1$
$B({\bf b};\, \lambda) :=\lim_{{\bf s_B} \rightarrow \, +\text{sgn}({\bf b}\cdot{\bf s_B}){\bf b}}\Big[\langle\chi_{\bf n \text R}|\{ (\lambda\,{\boldsymbol\sigma}\cdot (+{\bf s_B})) \,( {\boldsymbol\sigma}\cdot {\bf b})\}|\chi_{\bf n \text R}\rangle \Big]= \pm 1$

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

For Heine, keep in mind that from the paper $s_B = -s_A$ always.

Please explain your notation.

Which exact notation don't you understand and I will explain it? I'm sure that you understand some of it.
.

by **Yablon** » Sun Jun 30, 2019 11:34 am

gill1109 wrote:
FrediFizzx wrote:
FrediFizzx wrote:Hi Folks,

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

$A({\bf a},\, \lambda) := \lim_{{\bf s_A} \rightarrow\, -\text{sgn}({\bf a}\cdot{\bf s_A}){\bf a} }\Big[\langle\phi_{\bf n \text R}|\{ ({\boldsymbol\sigma}\cdot{\bf a}) \,(\lambda \,{\boldsymbol\sigma}\cdot (-{\bf s_A}))\}|\phi_{\bf n \text R}\rangle \Big] = \mp 1$
$B({\bf b};\, \lambda) :=\lim_{{\bf s_B} \rightarrow \, +\text{sgn}({\bf b}\cdot{\bf s_B}){\bf b}}\Big[\langle\chi_{\bf n \text R}|\{ (\lambda\,{\boldsymbol\sigma}\cdot (+{\bf s_B})) \,( {\boldsymbol\sigma}\cdot {\bf b})\}|\chi_{\bf n \text R}\rangle \Big]= \pm 1$

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

For Heine, keep in mind that from the paper $s_B = -s_A$ always.

Please explain your notation.

Let me explain my view of one part of the notation, namely, the limit function, and let me refer to https://jayryablon.files.wordpress.com/ ... e-4.3a.pdf which is the most recent draft of my pre-symposium paper which Richard and Joy and Fred have seen before.

Prior to one of the particles from the singlet being observed, let's call that t<0, that particle has a has a certain wavefunction, presumed to be a Schroedinger's Cat superposition of base eigenstates. When an observation occurs at t=0, that wavefunction is "collapsed" into one of the base eigenstates, in which it now exists thereafter for t>0.

Now, in section 5 of the file linked above, I have shown in my proposed "Alice experiment" how, if QM could "whisper" its counterfactually definite elements of reality to Alice while t<0, then she would be able to "predict with certainty" what she will soon measure at t=0. Of course the uncertainty principle is a sort of "white noise" which prevents such whispering. But QM itself still "knows" this data even if humans cannot.

So here is the point: when t<0, there is still a counterfactual element of reality $\bf a \cdot \bf s$ which is part of the eigenvalue of the t<0 wavefunction. And, if QM could whisper all of its elements of reality to Alice, then she could predict with certainty that she will end up observing a +1 if $\bf a \cdot \bf s >0$ , and a -1 if $\bf a \cdot \bf s <0$ . Same hemisphere versus opposite hemisphere orientations. So to be more precise, QM -- with all of the information it has in its possession -- can "predict with certainty" that Alice will measure $\text{sgn}(\bf a \cdot \bf s)$ . And it "knows" $\bf s$ .

Moreover, as I will show when I add the next few sections of the above paper, at t=0, the spin direction itself is "destroyed", and is forced by the simultaneous measurement constraints of uncertainty principle to align either parallel or antiparallel to $\bf a$ , depending upon the hemisphere toward which the spin was pointing before the collapse. This coincides precisely with what we know from Stern-Gerlach. Moreover, this "predictability with certainty" based on the elements of reality known to QM finally frees us from having to regard t<0 wavefunctions as being probabilistic Shroedinger's Cat superpositions, which is at the heart of the problem.

All of this means that at collapse, the spin is transformed such that:

$\bf s \rightarrow \bf{s'} = \text{sgn}(\bf a \cdot \bf s) \bf a$ (1)

So I suggested the above to Joy and Fred for use in the measurement functions. As I have said, however, I personally think that using "lim" is misleading, because there is a calculus meaning to that term which I really do not see here, at least when we are using QM rather than its isomorphic language GA. My personal preference would be to use "collapse" or "observe" in place of "lim." And here, I lean to "observe," because once we are able to dispense with the half-alive half-dead Cat, "collapse" is an artifact of the fact that humans do not have available to them, all of the real data that is known to QM. From the standpoint of QM, humans finally observe what QM knows with certainty the humans will observe.

Jay

by **gill1109** » Sun Jun 30, 2019 11:46 am

FrediFizzx wrote:
gill1109 wrote:
FrediFizzx wrote:
FrediFizzx wrote:Hi Folks,

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

$A({\bf a},\, \lambda) := \lim_{{\bf s_A} \rightarrow\, -\text{sgn}({\bf a}\cdot{\bf s_A}){\bf a} }\Big[\langle\phi_{\bf n \text R}|\{ ({\boldsymbol\sigma}\cdot{\bf a}) \,(\lambda \,{\boldsymbol\sigma}\cdot (-{\bf s_A}))\}|\phi_{\bf n \text R}\rangle \Big] = \mp 1$
$B({\bf b};\, \lambda) :=\lim_{{\bf s_B} \rightarrow \, +\text{sgn}({\bf b}\cdot{\bf s_B}){\bf b}}\Big[\langle\chi_{\bf n \text R}|\{ (\lambda\,{\boldsymbol\sigma}\cdot (+{\bf s_B})) \,( {\boldsymbol\sigma}\cdot {\bf b})\}|\chi_{\bf n \text R}\rangle \Big]= \pm 1$

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

For Heine, keep in mind that from the paper $s_B = -s_A$ always.

Please explain your notation.

Which exact notation don't you understand and I will explain it? I'm sure that you understand some of it.
.

I've told you lots of times exactly what notation I don't understand. In short: What is your *mathematical definition* of "lim"?

Clearly you are not using the standard epsilon-delta definition and I get the strong impression that neither you Fred nor Joy are familiar with it (the concept of bound and free variables also seems completely alien to you both). Yet you want to use standard calculus theorems about manipulations with limits. Those standard rules are a consequence of the standard definition. If you adopt a non-standard definition then you can't use the standard rules. I would just like to know what is *your* definition?

Actually I already have understood "from the horse's mouth" that he is using physical imagery, not a mathematical definition. This makes his whole theory "poetry". Very attractive poetry, there's no doubt about that. But it isn't mathematics and I suspect it isn't science. It might inspire scientists ...

by **Heinera** » Sun Jun 30, 2019 11:57 am

Yablon wrote:All of this means that at collapse, the spin is transformed such that:

$\bf s \rightarrow \bf{s'} = \text{sgn}(\bf a \cdot \bf s) \bf a$ (1)

[...]
Jay

This is basically equations (9) in Bell (1964).

Have you read Peres' "Quantum Theory: Concepts and Methods"? If not, you should certainly do so. A google search with keywords fisica quantum theory concepts will point you to a free pdf-version of the book.

by **FrediFizzx** » Sun Jun 30, 2019 1:34 pm

gill1109 wrote:
FrediFizzx wrote:
gill1109 wrote:...
Please explain your notation.

Which exact notation don't you understand and I will explain it? I'm sure that you understand some of it.
.

I've told you lots of times exactly what notation I don't understand. In short: What is your *mathematical definition* of "lim"? ...

It is exactly the same as the regular definition. Do you think there is a problem if the limit actually goes the value instead of just approaching it infinitesimally? There is no problem. Of course it does matter if you are trying to avoid an infinity but that is not the case here.
.

by **Heinera** » Sun Jun 30, 2019 2:02 pm

FrediFizzx wrote:It is exactly the same as the regular definition. Do you think there is a problem if the limit actually goes the value instead of just approaching it infinitesimally? There is no problem. Of course it does matter if you are trying to avoid an infinity but that is not the case here.
.

The typical use of a limit is when the expression is not uniquely defined for the value the limit goes to (or there is some other singularity for that value). E.g.,

$\lim_{x\rightarrow 0} \frac{f(x)}{x}$

since you can't divide by zero. If the limit can actually go to the value, the whole notation is superfluous, and no mathematician would use it. E.g.,

$\lim_{x\rightarrow 2} \frac{f(x)}{x}$

would simply be written as

$\frac{f(2)}{2}$ .

by **FrediFizzx** » Sun Jun 30, 2019 2:07 pm

Heinera wrote:
FrediFizzx wrote:It is exactly the same as the regular definition. Do you think there is a problem if the limit actually goes the value instead of just approaching it infinitesimally? There is no problem. Of course it does matter if you are trying to avoid an infinity but that is not the case here.
.

The typical use of a limit is when the expression is not defined for the value the limit goes to. E.g.,

$\lim_{x\rightarrow 0} \frac{f(x)}{x}$

since you can't divide by zero. If the limit can actually go to the value, the whole notation is superfluous, and no mathematician would use it. E.g.,

$\lim_{x\rightarrow 2} \frac{f(x)}{x}$

would simply be written as

$\frac{f(2)}{2}$ .

But that doesn't capture what is going on with the physics, does it? There is no problem with the limits going to an actual value if an infinity is not being avoided.
.

by **Heinera** » Sun Jun 30, 2019 2:18 pm

No, there's no problem. It's just confusing and unnecessary, and gives the impression that you don't understand the mathematical concept of limits.

by **FrediFizzx** » Sun Jun 30, 2019 2:21 pm

Heinera wrote:No, there's no problem. It's just confusing and unnecessary, and gives the impression that you don't understand the mathematical concept of limits.

And I can't believe we are spending all this time explaining how limits actually work. It is absolutely necessary to show the physics. Please demonstrate how you would show the physics without the use of limits.
.

by **FrediFizzx** » Sun Jun 30, 2019 2:29 pm

Ok, you Bell fans have no valid argument against the functions any more so stop with this obfuscation about the limits. There is absolutely no problem with the limits.
.

by **Heinera** » Sun Jun 30, 2019 2:31 pm

FrediFizzx wrote:
Heinera wrote:No, there's no problem. It's just confusing and unnecessary, and gives the impression that you don't understand the mathematical concept of limits.

And I can't believe we are spending all this time explaining how limits actually work. It is absolutely necessary to show the physics. Please demonstrate how you would show the physics without the use of limits.
.

I would write a couple of clear sentences to explain the formulas, and let it be with that.

by **Yablon** » Sun Jun 30, 2019 4:03 pm

Heinera wrote:
Yablon wrote:All of this means that at collapse, the spin is transformed such that:

$\bf s \rightarrow \bf{s'} = \text{sgn}(\bf a \cdot \bf s) \bf a$ (1)

[...]
Jay

This is basically equations (9) in Bell (1964).

Have you read Peres' "Quantum Theory: Concepts and Methods"? If not, you should certainly do so. A google search with keywords fisica quantum theory concepts will point you to a free pdf-version of the book.

Bell's equation (9) is at https://cds.cern.ch/record/111654/files ... 00_001.pdf. His equation (9) for Alice is:

$A\left( \vec{a},\vec{\lambda } \right)=\text{sign}\ \vec{a}\cdot \vec{\lambda }$ ,

and his $\vec{\lambda }$ is the same as $\bf{-s_A}$ which Fred has been using in his posts. The transformation:

$\bf s \rightarrow \bf{s'} = \text{sgn}(\bf a \cdot \bf s) \bf a$ (1)

which I posted has some similarities but it conveys different information. If the add the word "observe" to the right arrow which is my preference (and I reiterate that I do not think using "limit" is a good idea because that gives a misleading calculus connotation), then what this says is that when Alice observes a hemispheric direction of a spin $\bf s$ , the act of observing transforms the spin into an $\bf{s'}$ which is now aligned parallel or anti-parallel to $\bf a$ , dependent upon which hemisphere the original spin was pointing in relation to the vector $\bf a$ . So if (1) is now applied to a dot product $\bf a \cdot \bf s$ , that dot product itself, as a result of the "observe" act, will transform as:

$\mathbf{a}\cdot \mathbf{s}\to \mathbf{a}\cdot \mathbf{{s}'}=\mathbf{a}\cdot \left[ \sgn \left( \mathbf{a}\cdot \mathbf{s} \right)\mathbf{a} \right]=\sgn \left( \mathbf{a}\cdot \mathbf{s} \right)\left( \mathbf{a}\cdot \mathbf{a} \right)=\sgn \left( \mathbf{a}\cdot \mathbf{s} \right)1=\pm 1$ (2)

And all this is just one way of dressing up the Stern-Gerlach result, which as I said and will show in my next draft of https://jayryablon.files.wordpress.com/ ... e-4.3a.pdf, can be shown to be a direct consequence of the simultaneous measurement restrictions of the uncertainty principle.

I am headed off to my annual July 4 week at the beach. So while others are reading novels, I will try to take a good look at Peres. Thank you for that beach reading recommendation!

I may try from time to time to post a reply or two, but getting a post to go through from my iPhone is sometimes spotty. So in any event, to all, have a great week ahead as summer really kicks off!

Jay

by **FrediFizzx** » Sun Jun 30, 2019 5:06 pm

It is the calculus connotation exactly with the limit going to the actual value. There is no problem using limits that go to the actual value if not trying to avoid an infinity.

$\lim_{x \rightarrow c} x = c$

Does anyone disagree with that? I certainly hope not.
.

by **Yablon** » Sun Jun 30, 2019 7:13 pm

FrediFizzx wrote:It is the calculus connotation exactly with the limit going to the actual value. There is no problem using limits that go to the actual value if not trying to avoid an infinity.

$\lim_{x \rightarrow c} x = c$

Does anyone disagree with that? I certainly hope not.

Fred,

It is totally irrelevant whether someone agrees or disagrees; there is no need or reason in the present context to even have this discussion about calculus.

Physically, when you observe $\mathbf s$ it changes orientation into $\mathbf s'=\pm \mathbf a$ , and so wavefunctions and eigenvalues and functions with $\mathbf s$ in them have that replaced with $\pm \mathbf a$ . That is all you and Joy are really saying, and it is all you need to say.

If I am leaning against a wall at a 70 degree angle, and then I stand up straight at 90 degrees, I don't talk about the limit as my position approached upright and invoke calculus. Geez, that's make me an even bigger nerd!

I just say that earlier I was leaning and now I am standing upright. There is no need to make it any more complicated than that!

Jay

by **FrediFizzx** » Sun Jun 30, 2019 7:20 pm

We have to use some kind of math function and I can't think of anything better to use. What have you got to use?

by **Yablon** » Sun Jun 30, 2019 7:32 pm

FrediFizzx wrote:We have to use some kind of math function and I can't think of anything better to use. What have you got to use?

Setting a variable to some value. Specifically, in this context, set:

$\bf s \rightarrow \bf{s'} = \text{sgn}(\bf a \cdot \bf s) \bf a$

in pertinent functions in which it appears.

Jay

by **FrediFizzx** » Sun Jun 30, 2019 7:37 pm

Yablon wrote:
FrediFizzx wrote:We have to use some kind of math function and I can't think of anything better to use. What have you got to use?

Setting a variable to some value. Specifically, in this context, set:

$\bf s \rightarrow \bf{s'} = \text{sgn}(\bf a \cdot \bf s) \bf a$

in pertinent functions in which it appears.

Jay

Now put that in the A and B functions and see how silly it looks. Here is a couple of lists of functions. Pick a math function besides limits that might work.

https://en.wikipedia.org/wiki/List_of_m ... _functions

https://en.wikipedia.org/wiki/List_of_t ... _functions
.

by **Yablon** » Sun Jun 30, 2019 8:49 pm

FrediFizzx wrote:
Yablon wrote:
FrediFizzx wrote:We have to use some kind of math function and I can't think of anything better to use. What have you got to use?

Setting a variable to some value. Specifically, in this context, set:

$\bf s \rightarrow \bf{s'} = \text{sgn}(\bf a \cdot \bf s) \bf a$

in pertinent functions in which it appears.

Jay

Now put that in the A and B functions and see how silly it looks. Here is a couple of lists of functions. Pick a math function besides limits that might work.

https://en.wikipedia.org/wiki/List_of_m ... _functions

https://en.wikipedia.org/wiki/List_of_t ... _functions
.

Any function!

Set the domain to something specific. Therefore obtain something specific for the range.

Set x=2 in y=x^2. Find y=4.

Set x=5 in y=5x. Find y=5x5=25.

Set $\mathbf {s=\pm a}$ in $y=\mathbf{s \cdot a}$ . Find $y=\pm \mathbf {a \cdot a}=\pm 1$

Why make things way more opaque than they need to be?!

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