Dear Edwin,

Thanks indeed for the welcome, the very helpful guidance,* and the hopeful news that your forehead-slapping is behind us; just one small uppercut needed now -- under the chin -- "small" given my appreciation of your own views and engagement on these matters.

For I think it not good to refer to any particle by the unit vector -- "invoking the third particle c" -- associated with the relevant SGD. It gets quite messy and confusing in what, IMO, should really be a very simple matter. (Some, as you probably know, even refer to the particles as Alice and Bob -- the SGD operators -- such is the confusion greeting newcomers to this important subject.)

I know and appreciate what you mean but I like to make this subject as easy as possible for newcomers -- and to be especially free to discuss those interesting hypothetical cases where Alice and Bob freely and independently select the same or antiparallel orientations.

* I should also explain that I'm working my way into FQXi via a new and troublesome internet upgrade, so your advice should soon be reflected in my expanded involvement here. (AND, playing safe, I might go with a series of short replies for a while.) PS: While I'm at it: every sentence of mine comes with an implicit IMO!

So, on the subject of particle identification, I suggest we stick with selections from the pwn+i family -- introduced at equation (22) but with lambda not used in this text here for convenience -- it being understood that each particle carries a unique lambda, correspondingly identified: NO two particles the same!

That is: particle p'wn+i carries a lambda' (lambda-prime) antiparallel to the lambda of its twin pwn+i -- that antiparallel relation here a consequence of the symmetry associated with the conservation of total angular momentum in the production of each pair.

Note in passing: In this way, pwn+i brings Joe Fisher's primary theme (the uniqueness of Reality) into mathematical form -- and hence into the best logic -- and hence into the Bell story.

Following your suggestion: Let's now expand upon the meaning of the Bellian lambda that is introduced into the maths at equation (3): Let's follow the clue -- "Bell's hint" -- in equation (1) and see how far we can take it.

So, since Bell's 1964:(1) and our (1) allow that 'a' is a unit vector, let lambda be one too. And, since we are working with spin and SGDs -- and always subject to Bell's (1964) boundary conditions -- let lambda be the most general unit vector in the space of 'a' -- a unit vector in 3-space.

Then, since lambda is beyond our control -- a truly random variable in 3-space -- and recognising that no two can be the same: we must label them accordingly. NB: Not here (yet) relating the lambda label to a particle label.

Equations (3)-(7) thus follow, and the source of Bell's famous inequality is revealed:

In general: Bell's 1964:(14b) IS NOT EQUAL TO Bell's 1964:(14a)! QED.

Noting that any difficulties for newcomers probably reside in the common but rigorous notation, which is soon easily grasped; especially if they ask questions.

THUS: The first IT from BIT!

For we started with BIT (information, essentially provided by Bell and his boundary conditions) and we discover a fairly sensational IT (one missed by the whole Bellian community, as far as I know).

That IT is particle pn+i!

NB: pn+i is a crucially different particle because, carrying a crucially different lambda, it cannot POSSIBLY be paired with particle pi in the manner of Bell's maths -- 1964:(14b) = 1964:(14a) -- as Bell and many others would have us believe.

Hence the IMPOSSIBILITY of Bell's manoeuvre. And hence the downfall -- per that equation (22) -- of all CHSH-style inequalities: here simply, theoretically; and (importantly), as confirmed experimentally -- as you yourself stress.

AND hence the wonder -- given the conclusions drawn (and so forcefully promulgated) re nonlocality and the impossibility of common-sense local realism -- that not one of Bell's supporters critically revisited his maths posthaste.

To be continued:

With my thanks again; please don't hesitate to interpose remarks -- even swift uppercuts -- at any stage; Gordon

Edwin, continuing: Let's next talk about "any fine points" before returning to the central section of your response.

A - Fine points: The essay is intended to be error-free and typo-free so that any "puzzles" may be addressed confidently by the Reader -- with minimum fear that there's a bug in the system, so to speak. Consequently, to anyone, finding something that halts or niggles or grates or jars, etc, it's, "Please let me know; I'm from down-under and I'm here to help."

Perhaps the "finest point" is that the underlying theory is extremely comprehensive YET based on what is essentially high-school maths and logic. That is, from such simplicity we arrive at a goal that I associate with both Planck and Einstein (even Bell): "The quantum is classical" -- a view that I understand is akin to your own.

Now: It seems this above point is not popular -- to the extent that making comments on the theory is evidently considered to be "beneath their dignity" by most of my supposed critics over the years -- to the extent that the theory is not worthy of even one word to explain why their promised reviews are not forth-coming.

Even here, at FQXi, there are those who allocate low ratings without one word of criticism -- despite my earnest requests for such!

So, to illustrate some of that simplicity, let's turn to:

B - the central section of your response:

Starting at -- as you understand the problem -- but in my terms: Yes, Bell is clumsy with his lambda in that the lambdas in the particle duo pi and p'i are most certainly NOT the same as those in ANY OTHER pair!

So we can slightly tighten your understanding: "Unless and until someone shows how a second particle-pair can be produced, with exactly the same generalised, unconstrained hidden variables that applied to the first particle-pair, then this is, as we say, unphysical, i.e., impossible."

We then come to this; me trusting that I've edited it correctly -- in line with your thinking -- re which particles are involved:

"Consider, as an example only, that lambda is a 'phase angle' of the wave function common to the first particle-pair. There may, of course exist an analogous phase angle in another entangled particle-pair. But there is no way to measure these phase angles (except statistically via 'weak' measurement) and no grounds to assume that they are equal from one particle-pair to the next."

Yes! Thank you; though phase-angles of wave functions, per your example, are not here required per note (**) below.

Then, with some editing, we have:

"But this is implied by Bell's PAIRING of lambdas in 14(a) and 14(b) while -- clearly and correctly -- such lambdas -- specifically lambdai and lambdan+i -- CANNOT be so paired."

Yes, with my thanks again. **BUT please be critical of my changes to your phrasings BECAUSE you appear to be rightly bridging my theory to QM -- a job I'm happy to leave to others -- and my understanding in that area will be improved via any valid amendments or criticism that you might make.

With my thanks again; Gordon

Gordon,

You are correct, I shouldn't have called the settings particles, even though it is the fact that there are different particles that is the source of Bell's mistake. So I'll try to be very clear in my statements, and let's take it slow and easy. If you've reviewed Joy's blogs you know that the same equations gave rise to literally hundreds of comments. Very frustrating. Let's avoid that if possible. I also think at this point it's best not to confuse the discussion of Bell's math with Its and Bits. That can be pointed out later. Finally I don't want to jump to equation (22) and CHSH. I actually believe that if we do this carefully and correctly, you can nail Bell here. Let's try to establish one thing at a time without getting sidetracked and without bringing in anything other than necessary information.

Let's establish first that Bell's (14b) is not equal to Bell's (14a).

Unfortunately, to follow this, one must read your essay with a copy of Bell's paper on hand. But I think we can talk it through despite this awkward fact.

We begin by noting that a and b are settings of the Stern Gerlach device (SGD) chosen by Alice and Bob respectively. Bell then pulls c out of a hat and uses it in place of b, and then subtracts P(a,b) - P(a,c), where P is the probability or expectation value of two variables, expressed as an integral over the hidden variable lambda. The difference of these two values is two integrals which he combines into one.

For any experimental run only two settings are possible therefore this expression with three settings represents more than one run. But in Bell's (14a) representing the difference P(a,b) - P(a,c) he subtracts the integral forms of these using the same lambda for both the first and second experimental runs. This is generically valid in that lambda represents the 'hidden variable' of a candidate theory, but it is specifically invalid as there is no reason to believe that the specific lambda that determines P(a,b) in the first run is the same as the lambda that determines P(a,c) in the second run. Bell's integration variable lambda assumes they are the same in both runs.

His earlier definition of the measurement A(a,lambda) representing the SGD setting a and parameter lambda defines A to always be plus or minus one. Thus the product A(x,lambda) A(x,lambda) is always +1 and Bell uses the fact that one can insert a factor of plus one into an equation without changing the equation. He uses this to go from (14a) to (14b). This is an incorrect step, as is made clear when you label the lambdas according to which run they represent.

Bell claims that (14b) is equal to (14a). You point out that this is actually a new Bell inequality. QED.

This is where I'd like to stop. Do you agree with the above? If so, I can put the equations in a .pdf file and link it to the comment. Then we can go on to further questions.

If I've made a mistake, or stated something poorly, please correct me but please keep it as simple as possible.

Edwin Eugene Klingman

My last comment was to your previous one. In your last comment you note that Bell's pairing of lambdas is incorrect. Please confirm that the error occurs when he tries to use factor of +1 into (14a). That is, he assumes that

A(x,lambda) A(x,lambda) = +1

but he really has

A(x,lambda) A(x,lambda') = ?

Edwin Eugene Klingman

Brief comments attached to extracts from yours:

1. "Finally I don't want to jump to equation (22) and CHSH."

No problem; my reference back to (22) simply returned us to the source of the particle family pwn+i that we called upon.

2. "I actually believe that if we do this carefully and correctly, you can nail Bell here."

Indeed and for sure: Bell falls here.

3. "Unfortunately, to follow this, one must read your essay with a copy of Bell's paper on hand."

Note that a copy of Bell (1964) is available via hyperlink from my references.

4. "This is generically valid in that lambda represents the 'hidden variable' of a candidate theory, but it is specifically invalid as there is no reason to believe that the specific lambda that determines P(a,b) in the first run is the same as the lambda that determines P(a,c) in the second run. Bell's integration variable lambda assumes they are the same in both runs."

In my terms: "This is specifically valid if one assumes naive realism but is generically invalid as we can find examples in reality where a lambda that determines P(a,b) in the first run is NOT the same as the lambda that determines P(a,c) in the second run."

5. "In your last comment you note that Bell's pairing of lambdas is incorrect. Please confirm that the error occurs when he tries to use factor of +1 into (14a). That is, he assumes that

A(x,lambda) A(x,lambda) = +1 but he really has A(x,lambda) A(x,lambda') = ?"

....

NB: The error occurs as you say: when he tries to use a factor of +1 into (14a).

BUT your notation and reasoning is not quite correct:

Bell correctly knows that A(b,lambdai) A(b,lambdai) = +1 is a truism.

But in (14b) he has placed this truism between A(a,lambdai) and A(c,lambdan+i).

Many questions now arise. Chief amongst them:

(a) What's happened to A(a,lambdan+i)?

(b) How can he reduce the mess that remains?

Clearly (a) is unphysical, and (b) -- reduction of the mess -- requires these impossibilities:

A(b,lambdai) A(c,lambdan+i) = A(b,lambdai) A(c,lambdai).

OR:

A(b,lambdai) A(c,lambdan+i)) = A(b,lambdan+i) A(c,lambdan+i).

Both are IMPOSSIBLE! QED.

Please check this carefully against the better (fuller) picture given in (3)-(7). Many thanks; Gordon

Ed, Here's a PS re my last post and

item (a) -- What's happened to A(a,lambdan+i)? --

(a) can also be treated (and is no doubt best treated) as the impossibility:

A(a,lambdan+i) = A(a,lambdai)

which is the approach taken in (3)-(7). See (7) specifically where this requirement appears as another impossibility for Bell's analysis to survive.

All Bell's troubles being solved, in short, per (7)

IFF: lambdan+i = lambdai ... ... !

Gordon

Gordon,

Act1

I rank your essay one of the best and thoughtful that I've read so far; surely a special commendation prize can be awarded for your Bio.

In response to your request for critical comments, I suspect your lengthy Abstract and your humorous Bio is putting off people reading your essay, but encouraging them to rank it anyway. You have now have 8 member ratings and 4 public ratings but only 5 (including me) that left comments, after they discovered the hidden quality of your essay - so what did the other eight rate?

It is admirable that you bring humour to research but the humour in your Bio is far more subtle than that in your correspondence with Peter. Yet I wonder how many will decode and see that no tWo draGons is replying in kind to ProJect snake.

Joking aside, Act 2 follows.

Gordon,

Act 2:

You ask in your title: Is this description of physical reality complete?

Heisenberg, Bohr, et al defined the Copenhagen interpretation of QM by 1927. In 1931 Gödel presented his incompleteness theorems for mathematics. Thus, the 1935 EPR dream "If, without any way disturbing a system, we can predict with certainty (ie, with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity)" can only be valid if our mathematics is complete, which it never can be.

With our incomplete knowledge of mathematics and physics, any description (present or future) of QM processes will always be incomplete - that is the stark reality of Gödel's incompleteness theorems.

    Gordon,

    You were correct tthat my terminology confused particles and settings. Now you state:

    "The error occurs as you say: when he tries to use a factor of +1 in (14 a)."

    Please confirm that you mean:

    "Bell's error occurs as I say..."

    not

    "I make an error when I say..."

    Then you say "but your notation and reasoning is not quite correct." I believe my notation is correct, but inconsistent with yours. And I should have followed through, so I would say my reasoning, as presented, is incomplete. As you note, it is when he does this insertion that the error pops up between A(a,Li) and A(c,Ln+i), [where I am now using 'L' for 'lambda', as was done in comments on Joy's blogs]. And it is not just because he cannot guarantee the result is +1, but because of what results after the insertion.

    My notation was inconsistent because your readers may still be confused by the i and n+i and I wanted to show that in general A(x,L) A(x,L') won't be equivalent to +1 for any setting x but different parameters (L, L') if L and L' characterize different runs. And I left the details incomplete because my next comments were to discuss the fact that Bell has four A's but you have six A's, and this is the area where his problem shows up. I felt it was too much detail for one comment.

    I'm usually not such a stickler for words, but I know from Joy's experience that 1.) every word counts, and 2.) every word must be correct.

    Thank you for pointing out the link to Bell's paper in your references. I've been using "Unspeakable..." [pages 14 to 19] but many do not have that book.

    As I noted, I do not normally make such a fuss over words, but this "disproof" has got to be perfectly correct. After we beat these points into the ground I plan to clean up the above notes, with both your equations and Bell's equations in proper format, but only after all "incorrect" or "incomplete" reasoning has been straightened out. My final writeup will not have all of these if's, and's, and but's.

    Are we having fun yet?

    Edwin Eugene Klingman

    Hi Gordon,

    Continuing with your work I wish to compare Bell's equation (14b) with your equation (4). The astute reader will note the presence of six A's in your expression versus four A's in Bell's equation, and this is sure to cause you a headache if we do not explain the extra terms.

    What Bell has done is to insert A(b,L) A(b,L) = +1 between A(a,L) and A(c,L) which allows him to factor out a common term A(a,L) A(b,L) from the resultant expression. Because you distinguish between A(a,Li) and A(a,Ln+i) in order for you to arrive at the desired common factor, it is necessary for you to insert four terms:

    A(a,Li) A(a,Li) A(b,Li) A(b,Li) = (+1)(+1) = (+1)

    and then rearrange terms as given in your equation (4). This leaves the resultant in brackets:

    [A(a,Li) A(b,Li) A(a,Ln+i) A(c,Ln+i) - 1].

    At this point, as you noted in a comment above, to progress from here requires either

    A(b,Li) A(c,Ln+i) = A(b,Li) A(c,Li)

    or

    A(b,Li) A(c,Ln+i) = A(b,Ln+i) A(c,Ln+i).

    As you say, when one considers what these physically represent, it is impossible to achieve either one of these expressions.

    Do you agree that the above symbols and reasoning are correct? If so then I agree with you that the equality between (14a) and (14b) is *not* an equality as Bell claimed. We can then go on to look at what you claim is Bell's next misstep.

    I'm having fun!

    Edwin Eugene Klingman

    Hi Gordon,

    Reading your essay a second time after refreshing myself on the EPR paradox, etc, All in all, I get the flavor of the message in your essay. I agree essentially with virtually all the conclusions you itemized, in particular that physics at the quantum level is understandable without too much mathematical maneuvering and renormalizations.

    You say, 'The hopes of Einstein and Bell prevailing, wm does not conflict with Lorentz invariance'. Tread softly here, Lorentz invariance is a much dishonestly used term and there may be evidence for situations where it is violated, so depends what you take it to mean.

    Then if 'the quantum is classical, Planck and Einstein were right', why cant things be as easy as when Alice measures her sock and finds it is for the Left foot, she can without any signalling infer that Bob has the Right foot'. Why is so much mathematical equation required to express this. Pardon my naivety.

    Regards,

    Akinbo

    Ed. Your penultimate post is pasted here, my replies inserted. I'll do the same, in a new post, with your last post. NB: I'm now attempting to practice precision; putting a temporary halt to our easy (yet understandable) colloquialisms. Alas, I'm sure to sin; which I'm thinking is maybe OK: For you're sure to improve things in review; as is your custom.

    EK: = ""Gordon, You were correct that my terminology confused particles and settings. Now you state:

    "The error occurs as you say: when he tries to use a factor of +1 in (14 a)."

    Please confirm that you mean: "Bell's error occurs as I say..."

    not "I make an error when I say..." ..""

    GW: Ed (EK) is correct when he says that Bell's errors begin as Bell moves from his (14a) to (14b).

    EK: = ""Then you say "but your notation and reasoning is not quite correct." I believe my notation is correct, but inconsistent with yours. And I should have followed through, so I would say my reasoning, as presented, is incomplete. As you note, it is when he does this insertion that the error pops up between A(a,Li) and A(c,Ln+i), [where I am now using 'L' for 'lambda', as was done in comments on Joy's blogs]. And it is not just because he cannot guarantee the result is +1, but because of what results after the insertion.""

    GW: I agree with your last sentence, but it is now out-of-order - "insertion" in BT contexts now banned! So:

    In the interest of total precision, let's make Bell's (14a) physically significant. Let's represent the (signed) core [.] of his integral in (14a) as follows:

    - [A(a,L1)A(b,L1) - A(a,L2)A(c,L2)]. ---(14a*)

    Where the numbered Ls (= lambdas; L1 and L2) come from odd and even numbered particle-pairs respectively; ie, we do NOT follow the Essay and run n AB tests over particle-pairs 1-n; then run n AC tests over particle-pairs (n+1)-2n.

    INSTEAD we do one AB test with particle-pair#1; then one AC test with particle-pair#2; then one AB test with particle-pair#3; etc.

    So we have, with precision:

    (14a*) = A(a,L1)A(b,L1)[A(a,L1)A(b,L1)A(a,L2)A(c,L2) - 1]. ---(14b*)

    Now the core of our (14b*) here should equal the core [.] of Bell's (14b). That is:

    (14b**) = [A(a,L1)A(b,L1)A(a,L2)A(c,L2) - 1] =?= [A(b,L?)A(c,L?) - 1]. ---(14b)

    NB: L? is in play here because we have (as yet) few clues as to what Bell's up to.

    But A(c,L?) must be A(c,L2) because setting L2 was only ever tested against 'c'.

    And so A(b,L?) must be A(b,L2)!

    BUT setting L2 was NEVER tested against 'b' -- so here's nonsense and Bell's 1st impossibility.

    WITH equally no escape in reverting to P(b,c) = A(b,L1)A(c,L1); since L1 was never tested against 'c'.

    It's crazy!

    YET: Via his introduction to his (15), Bell agrees that A(b,L?)A(c,L?) = P(b,c) in (14c); and so too in his (14b). So is it somehow possible to remove the =? from between our (14b**) and Bell's (14b) above? Can you and I agree with Bell; for all that we each require is:

    A(a,L1)A(b,L1)A(a,L2)A(c,L2) = crazy A(b,L2)A(c,L2) or crazy A(b,L1)A(c,L1); that is

    A(a,L1)A(b,L1)A(a,L2) = A(b,L2); or A(a,L1)A(a,L2)A(c,L2) = A(c,L1)---(X)

    Alas: You and I know IMPOSSIBLEs when we see them; Bell and his supporters do not. For, inadvertently requiring AND allowing the IMPOSSIBLE L1 = L2, they make the nonsense in (X) the norm. QED!

    EK: = ""My notation was inconsistent because your readers may still be confused by the i and n+i and I wanted to show that in general A(x,L) A(x,L') won't be equivalent to +1 for any setting x but different parameters (L, L') if L and L' characterize different runs.""

    GW: Sir, you trespass here on hallowed ground. That prime (') has been my little mate since day-one. So me, seeing A(x,L)A(x,L'), knows that it is ALWAYS -1.

    However, your thoughts so pure and well-intentioned, can we use "something like" that L1 and L2 that have served us so well above? (PS: But I'd like it to be close to the Essay.)

    NB: I'm a stickler for developing friendly intuitive natural efficient notations; one beautiful notation for all.

    EK: = ""And I left the details incomplete because my next comments were to discuss the fact that Bell has four A's but you have six A's, and this is the area where his problem shows up. I felt it was too much detail for one comment.""

    GW: Check and see if you'd be happy with Bell's four. (I suspect not; though it would be good to match Bell at every step.) I'm pretty sure that I need six to ensure absolute precision, beyond reproach (as above).

    EK: = ""I'm usually not such a stickler for words, but I know from Joy's experience that 1.) every word counts, and 2.) every word must be correct.

    Thank you for pointing out the link to Bell's paper in your references. I've been using "Unspeakable..." [pages 14 to 19] but many do not have that book.

    As I noted, I do not normally make such a fuss over words, but this "disproof" has got to be perfectly correct. After we beat these points into the ground I plan to clean up the above notes, with both your equations and Bell's equations in proper format, but only after all "incorrect" or "incomplete" reasoning has been straightened out. My final writeup will not have all of these if's, and's, and but's.""

    GW: You have my full support in these endeavours.

    With best regards; Gordon. E and OE! 1 post to follow: #

    Edwin; This is that other post that I foreshadowed, in response to your latest (above) post: BUT, having now read this latest post of yours, there is no need for me to copy and enter my comments in reply. For I can sum up my remarks like this:

    What you have written is in perfect accord with our colloquial discussions. But, under the terms of your sound advice, our friendly efficient colloquialisms must be put on hold for a while. So those colloquial "insert" remarks in "a BT context" must also be put on hold.

    Which is no problem because, by coincidence, I've roughed-out the "precise" case in my earlier reply above. Me hoping you'll come up with a neat physically-significant notation for L1 and L2.

    PS: Are you clear about the use of my little mate, the prime (')?

    Gordon

    Hello Gordon,

    I also prefer Euclid's work, which summarizes ancient Alexandrian mathematics. I am also an engineer, unfortunately on old one. I was 11 when I faced Soviet tanks in Eastern Berlin 60 years ago.

    May I ask you to explain as concisely as possible what is the essence and benefit of the "wholistic mechanics" you are suggesting? A search engine did not yet know this expression.

    Eckard

    Gordon,

    Your explanation keeps improving as you flesh out the details and the logic. When I go back and read your essay I see how concise and well stated it is, but I understand it better because of the above comments. I hope other readers will benefit as well.

    As soon as I get caught up on other commitments, I will return and we will then work through the next part of your essay in similar fashion. I now understand why 'insertion' is denigrated and you can have 'prime'.

    Have fun,

    Edwin Eugene Klingman

    Anton; thanks for your warm greetings and very welcome comments and ranking. It's also nice to know that you've questioned "that subtle Bio" and are having some fun seeing the light!

    PS: I'm planning to get into the detail of your own interesting essay over the next week.

    With thanks again, and best regards; Gordon

    • [deleted]

    • Post #36

    Dear Anton; such a warm Act I. So why do I now anticipate a chilling new experience in Act II? That is: Am I about to lose my first ever game of chess? Let's see:

    Your first 4 moves -- Heisenberg, Bohr, Copenhagen, EPR -- are anticipated and fairly well countered in the Essay. As to your 5th: Unfortunately, under the rules here, there was insufficient space to enter my reply in anticipation. So here it is in response:

    5. AV - Gödel !? --- 5. GW - My theory is consistent!

    6. AV - Your move. --- 6. GW - My move is sealed.

    With the fondest regards; Gordon

    Hello Eckard, and thanks for letting me know that we have some good things in common.

    As to the essence and benefit of wholistic mechanics: Concisely, its essence resides in its doubled abbreviation wm/WM, for therein lies its message of uniting the small/BIG in one unified theory. In this unifying sense, wm's essence is in the spirit of Planck, Einstein, and many others; even John Bell.

    Moreover, wm is wholly classical -- at a most fundamental level -- with consequent benefits when it is critically examined: for there are no mysteries here. Yet, despite its simplicity, wm takes us deeper than conventional QM into the underlying wholly-local-realistic dynamics of that important experiment, EPRB. WM boldly declares: The quantum is classical!

    As to your search -- "wholistic mechanics" -- it once, for me, registered a single site; but that's a long story. I just now received 101 google responses in 0.21 seconds; many being irrelevant, but not all. I see there a reference to my 1998/1999** article in Physics Essays. But the theory began in 1989, as mentioned in my FQXi2013 essay here; and that 1998/1999** combination is essentially subsumed in the essay before you.

    So, hopefully very clearly, you can see that your input -- at any level; but preferably critically -- would be very welcome here.

    Thus, if I may turn huckster for the moment: I'd suggest that we have on sale here today a ground-floor bargain-basement opportunity to be of service to the world: Quickly sink an emerging nonsense or find its valid limitations or correct its shortcomings or develop it further or just ask questions. For, with any of these activities, most here seem to be having some serious and productive fun. Which is surely no bad thing these days.

    So, Eckard, me here wanting to stay concise, please don't hesitate to probe further.

    With best regards; Gordon

    ** The double-date being essential as there were many printer-errors in the original article; it being very difficult to follow without the Erratum!

      No no - shrewdest players know exactly the right time to call

      6. AV - offer stalemate? --- 6. GW - ?

      Regards Anton

      Hi Akinbo; and thanks for the "naive" inputs, for I'm very much from the same school myself (as you've no doubt seen).

      Thus: my use of the term "Lorentz invariance" simply echoes Bell's desire to Bell's supporters. My own terminology is "a fully relativistically covariant formulation" so I'd be pleased if you could expand on your alert. Especially if you thought that there were situations where my own term failed.

      Now as to those socks. Can you access Bell's Bertlmann article and Bell's sock analogy therein? [Please let me know.] And can you be wary of that term "measurement"? For I'd like you to seriously analyse the sock case yourself; then get back to me.

      HINT-1: Do not subjugate your naivety! Consider, for example your statement above: "... Alice measures her sock." Does Alice know that it's a clean and present sock before "measurement"? Or before the post-person shoves its parcel into the letterbox?

      And what if the person who sent the sock to Alice had made it from the finest thread -- such that it's impossible to tell the inside of the sock from the outside? And what if -- in the post-person's haste to deliver, or in Alice's rough haste to unpack the parcel -- the sock was unwittingly turned inside out?

      HINT-2: For, reversing the analogy: I trust you can see that the interaction between a spin-half particle and an SGD is far more disorienting and lasting to the particle than an accidental turning-inside-out is to a special sock.

      Enjoy! And please stay in touch so that our shared naivety keeps flowing; Gordon