gill1109 wrote:By the way, I do not think we settled the question of what is a correlation. Theories talk about correlations. Experimenters gather date and calculate things which they call correlations. We have to discuss sooner or later what we take as axiom or definition, what we take as heuristic principle, what we mean by chance.
Well, lets go back to
viewtopic.php?f=6&t=383#p8702. I just want to know whether the calcuation
(1.17a)
with the standard deviations:
(1.17b)
to derive:
(1.19)
is a mathematically correct calculation? Yes or no? And if no, why?
Now, for want of better technical language I would call this a theoretical correlation. And I would agree that there is a second very important calculation to be done which goes event by event, emits a singlet at each event which then splits, which then has a binary value detected by Alice and another one by Bob, and which also arrives at
as an expectation value from an average as the number of events approaches infinity. And, if locality is to stand a chance, that second calculation would have show also, that there is no non-local signalling. But we have to walk before we run, so I all want right now is your agreement that there is nothing mathematically amiss in the above calculation.
gill1109 wrote:Yablon wrote:III: 8) Finally, with two of the three spherical coordinates
and
being observable but the third coordinate
being unobservable-in-principle, does everyone agree that there is a good discussion to be had regarding the EPR status of
as an "element of reality"? (We are not having that discussion yet, I just want to see if everyone can get this far on the same page).
...
Now here too something is being slipped in which we are going to have to grapple by the horns. Why should something be "unobservable-in-principle"? A theory may assert that there are no experiments which can directly access certain variables in the theoretical model. But if the theory itself is in question, we can't take that assertion and raise it to the level of dogma.
I recall that Inge Helland (he's a guy, from Norway) has attempted to rewrite and fuse quantum mechanics and statistics through introduction of a new kind of variables. He calls them e-variables ("epistemic conceptual variables"). Get his book, and read it:"Epistemic Processes (A Basis for Statistics and Quantum Theory)"
https://www.springer.com/gp/book/9783319950679 which came out very recently.
I took a look at whatever I could see from the online reference, and it does look interesting. But again, let keep the rubber on the road. So I have a few questions, and I will try to stay as mathematical as possible and not use words or phrases (such as "uncertainty principle") which carry too much weighty baggage:
1) From my question III: 4), Do you agree with Robertson that for constant non-commuting operators
and
, the standard deviations for those operators have an inequality with the commutator for those operators which is given by:
?
2) For the "same particle," do you agree that if
which means that two operators do not commute, that the equation of point 1) above simplifies to:
?
3) Do you agree that it is important to differentiate between whether
and
are operators for two different particles or for the same particle?
4) Do you agree that for the "same particle," when we actually observe a state value of
and therefore acquire a known result, that the
a priori non-zero standard deviation, after the observation, goes from
? "Before we know to after we know."
5) And here is the main point for critics of "uncertainty" which is really better called "impossibility of simultaneous measurement" (and this is what EPR confine themselves to). Do you agree with the following disproof-by-contradiction?
a) Postulate that
. So we have observed a result from the X operator, and the point 2 equation is now:
?
b) Also postulate that
. So we have also simultaneously observed a result from the Y operator.
c) Now the 5)a) equation becomes:
.
d) So as a result of 5)c) we have falsified the postulate 5)b) that we observed something from Y simultaneously with X. And so, we cannot simultaneously observe both.
Call it uncertainty, or don't. But unless you care to argue that Robertson's 1) is wrong, we are stuck with the fact that some quantities pertaining to the same particle or interacting system simply cannot be simultaneously measured, when there are non-commuting operators involved.
Anything else, or can we start to talk about how to best understand the "reality" of those quantities which cannot be observed because some other quantity for the same particle or system has already been observed and a second observation would raise a contradiction in the nature of 5)c)?
Jay