Some people do not understand Counterfactual Definiteness

[minkwe]

Based on the discussion in the thread http://sciphysicsforums.com/spfbb1/view ... ?f=6&t=451

The following specific comments raised my brows:

By “realism” I mean counterfactual definiteness, which is a property classical mathematical physical models tend to have: they allow us to define, alongside of the outcomes of the experiments actually performed, also outcomes of experiments which could have been performed instead. Deterministic models have this property. Also non-deterministic, as long as any randomness is local.

Bell’s modelling of the EPR-B experiment, with functions A(a, lambda) and B(b, lambda), allows one to define outcomes of all possible spin measurements alongside of the measurements actually done. This model has the property of counterfactual definiteness. It is “local” because Bob’s measurement choice does not effect Alice’s outcome.

I think a discussion about the meaning of Counterfactual Definiteness (CFD) is badly needed. Like many other concepts such as "randomness", "locality", "realism". etc, the concept of "counterfactual definiteness" (CFD) has been bastardized by many in the quantum foundations community. One of the reasons nobody understands QM is because the meanings of words are free for all. It's the wild-wild west and don't even get me started about "virtual" particles.

A careful look at CFD will reveal that it does not mean what most people in the Bell community mistakenly think it means. First, let us start with a few definitions:

Realism: Realism means objects have properties independently of measurements. It does not mean measurements can't create some new properties, it only means something exists even if it is not being measured (cf. the moon exists even if nobody is looking).

Counterfactual: Counterfactual means contrary to actuality. Say Alice must make one measurement, for which she must pick one of two settings {x, y}. After the measurement, the actual setting is the one she picked and the counterfactual setting is the one she did not pick.

Counterfactual Definiteness: Now consider conditional statements of the form if Alice picks x she will obtain result -1. Although written out as a sentence, these types of statements are equivalent to statements of the form . These are statements made before the measurement -- a prediction of what will happen if the conditions are met. Such statements are not limited to any specific type of model (local, classical or quantum). Every model/theory that makes predictions, makes conditional statements similar to this before any experiments are performed. CFD only comes into the discussion when discussing the situation after the measurement has been made. Say Alice actually picked "y" instead of "x". In this case, "x" is the counterfactual setting. Counterfactual definiteness simply means the prediction made before the measurement remains valid even after the measurement has been made. In other words, it is still the case that had Alice picked "x", she would have obtained the -1 result. This is the meaning of CFD.

A little bit of common-sense will reveal that CFD is universally applicable in logic, and even QM makes use of CFD all the time. The truth value of conditional statements like "if X then Y", is not affected if the antecedent is false.

A prime example of the use of CFD in QM from Bell's paper is the following:

Consider a pair of spin one-half particles formed somehow in the singlet spin state and moving freely in opposite
directions. Measurements can be made, say by Stern-Gerlach magnets, on selected components of the
Spins and , If measurement Of the component , where is some unit vector, yields the value
+ 1 then, according to quantum mechanics, measurement of must yield the value -1 and vice versa.

In other words, Bell says, according to QM . This is a prediction (a conditional statement). Counterfactual definiteness simply means that the prediction is definite (still valid, not changed), even if Alice and Bob actually measured at settings instead of . QM says it must be so.

Therefore those who claim that CFD does not apply to QM are sorely mistaken. I'll leave it as an exercise for the reader to demonstrate from Bell's quote above how "realism" is used in QM. Another exercise for the astute reader, expand Bell's equation 14b using conditional statements, and see if you can figure out the logical contradiction [hint: viewtopic.php?f=6&t=292].

[Gordon Watson]

Thanks minkwe! HTH.

1. Bell (1964) is freely available online: http://cds.cern.ch/record/111654/files/vol1p195-200_001.pdf.

2. Let the three mathematical relations between Bell's equations (14) and (15) be, respectively: (14a), (14b), (14c).

3. Then Bell's error is his move from (14a) to (14b).

4. Using his equation (1) -- as Bell tells us -- there are several ways to make this move.

5. All such moves are false under QM:

6. For (14a) is true and (14b) leads to (15): which is false under QM.

7. On the subject of realism, some may find this interesting:

Clauser, J. F. & A. Shimony (1978). “Bell's theorem: experimental tests and implications.” Reports on Progress in Physics 41: 1881-1927:

http://www.science.oregonstate.edu/~ostroveo/COURSES/ph651/Supplements_Phys651/RPP1978_Bell.pdf

8. There are many and varied meanings attached to realism, including naive-realism.

9. In the context of math and physics, I choose to define my variant as true (non-naive) realism: some existents change interactively. That is, embracing all that "existence" means (and, I trust, denying none of it), I emphasise that "some existents change interactively".

10: I believe this emphasis is enough to expose much defective (even silly, as Bell half-expected) Bellian analysis

Thanks again, HTH; Gordon
.

[minkwe]

2. Let the three mathematical relations between Bell's equations (14) and (15) be, respectively: (14a), (14b), (14c).

3. Then Bell's error is his move from (14a) to (14b).

The contradiction is present even on the left-hand side of 14a.

P(a,b) - P(a,c) = "The correlation obtained if Alice and Bob measure at settings (a,b)" - "The correlation obtained if Alice and Bob measure at settings (a,c)"

The two terms contain contradictory premises. If Alice and Bob measured at (a,b) then they did not measure at (a,c). P(a,c) is counterfactual to P(a,b). The antecedents are contradictory therefore the combination of terms does not make physical sense since there is no universe in which True is False.

Here is an analogy I often use to illustrate the problem: Say a smart mathematician knows a thing or two about coins and probability theory, so he confidently derives and writes down an equality relationship that holds for all coins based on the assumptions that (1) coins have 2 sides, (2) Probabilities of mutually exclusive possibilities must add up to exactly 1. This relationship applies to all coins, no matter how biased

, where (H=head or T=tail).

He's not an experimentalist, thus to test this relationship in the lab, contacts his friend who has designed a coin-reading machine. The machine works by accepting one of two settings (H=head or T=tail). A coin is tossed into an opening above the machine, causing a bell to ring if the coin comes up the same side as the setting.

Together, they perform an experiment, with the machine set to H. After 50 tosses, they get 40 rings. . They repeat the experiment with the setting at T and after 50 tosses, they get 35 rings. .

But, based on their results, they get violating the mathematician's relation. Astounding -- one of the two assumptions must be wrong. Either the coin does not have two sides, or probability theory is wrong they conclude!!! Or maybe counterfactual definiteness is wrong, they ponder. The side of the coin that was not measured does not exist they surmise!!!!


What happened? Their machine is always biased towards the setting they picked to measure, with H being a bit more biased (0.8 vs 0.5) than T (0.7 vs 0.5). This can easily happen without anything being wrong with the realism of coins, probability theory, or counterfactual definiteness. Despite their combined skill in mathematics and experimentation, they do not understand the difference between actual and counterfactual measurements and what it implies when you add them in a mathematical expression. They should read Boole's Conditions of Possible Experience.

You see, the relationship was derived for joint measurements of H and T. You can't test that relationship by measuring H and T separately. You must measure them jointly. In other words. You must experience both jointly within the same experiment. Like:

or note subscripts!

Because we necessarily performed the experiment in two passes(1,2), since it was impossible for the machine to do both measurements simultaneously we arrived at a sum that is absurd when compared to the initial relationship. In fact, is the counterfactual result from experiment (1) and the counterfactual result from experiment (2). Therefore, although we obtained or , we could have inferred the counterfactual result or such that the original relationship or held as expected.

Thus, although the measured result for will always be correct in every experiment using the same coin. The counterfactual result when the machine was set to T, will always be different from the measured result.
Similarly, when Bell writes 1 + P(b,c) >= |P(a,b) - P(a,c)|, one of those terms is actual and the rest must be counterfactual. Therefore you can't use measurement expectations values from QM and experiments to compare directly. Rather you must infer the counterfactual values and use those instead.

The above analogy illustrates that the problem is not with counterfactual definiteness. The problem lies with failing to properly consider and take into account which terms in the expression must be counterfactual in a particular experimental context.

7. On the subject of realism, some may find this interesting:

Clauser, J. F. & A. Shimony (1978). “Bell's theorem: experimental tests and implications.” Reports on Progress in Physics 41: 1881-1927:

http://www.science.oregonstate.edu/~ostroveo/COURSES/ph651/Supplements_Phys651/RPP1978_Bell.pdf

From the above paper:

Realism is a philosophical view, according to which external reality is assumed to exist and have definite properties, whether or not they are observed by someone.

Do spin-1/2 particles exist before measurement according to QM? Do particles exist before measurement? Does the singlet state exist prior to measurement? Does the Stern-Gerlach magnet exist prior to measurement? How can you deny realism and still have a conversation about physics, even in QM? Those who claim to deny "realism" don't actually know what they are talking about.

[FrediFizzx]

"Those who claim to deny "realism" don't actually know what they are talking about." That is for sure. It is quite laughable. Quantum mechanics is about REAL probability factors for REAL physical events.
.

[gill1109]

2. Let the three mathematical relations between Bell's equations (14) and (15) be, respectively: (14a), (14b), (14c).

3. Then Bell's error is his move from (14a) to (14b).

The contradiction is present even on the left-hand side of 14a.

P(a,b) - P(a,c) = "The correlation obtained if Alice and Bob measure at settings (a,b)" - "The correlation obtained if Alice and Bob measure at settings (a,c)"

The two terms contain contradictory premises. If Alice and Bob measured at (a,b) then they did not measure at (a,c). P(a,c) is counterfactual to P(a,b). The antecedents are contradictory therefore the combination of terms does not make physical sense since there is no universe in which True is False.

Michel and Gordon:just read Bell’s own answer to this criticism. It’s as old the hills, often been repeated, and it’s wrong. Chapter 8 of “Speakable and Unspeakable” is a two page paper, and I wrote it out for you here: http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=441&start=20#p12423

[minkwe]

Michel and Gordon:just read Bell’s own answer to this criticism. It’s as old the hills, often been repeated, and it’s wrong. Chapter 8 of “Speakable and Unspeakable” is a two page paper, and I wrote it out for you here: http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=441&start=20#p12423

Wrong, you don't appear to understand the meaning of Counterfactual Definiteness. In your paper

https://arxiv.org/pdf/1207.5103.pdf "Statistics, Causality and Bell's theorem", you reveal this deficiency very cleary:

In a nut-shell, the inequality is an empirically verifiable consequence of the idea that the outcome of one measurement on one system cannot depend on which measurement is performed on the other. This idea, called locality or, more precisely, relativistic local causality, is just one of the three principles. Its formulation refers to outcomes of measurements which are not actually performed, so we have to assume their existence, alongside of the outcomes of those actually performed: the principle of realism, or more precisely, counterfactual definiteness.

How does a statement like this survive peer-review? There are several problems here:
1) Anything that is counterfactual can't be "empirically verified". "Empirical" means measured or experienced. "Counterfactual" means "not measured" or "not experienced"
2) Dependence does not mean causation. Dependence does not mean non-locality. The counterfactual outcome of the measurement not performed is not independent of the outcome of the measurement performed.
3) Measurements not performed (aka "Counterfactual measurements") by definition never exist and can never be experienced! This is simple modal logic. It is a contradiction/fallacy to suggest that they do. Suggesting that we should assume that they exist, suggests a lack of understanding of what "counterfactual" means. Existence means something very different in mathematics than in physics. A mathematician can simply conjure up a concept and it springs into existence on paper. Not so in physics. I've noticed a lot of mathematicians struggling with this, especially nowadays when everyone who can calculate thinks they are a physicist.
4) Counterfactual definiteness does not demand that we assume the absurdity of the existence of counterfactual outcomes. It only demands that we accept the validity of counterfactual predictions. That they remain valid even though they can't be experienced and will never be validated empirically (aka will never exist).
5) You admit in your paper that Bell's inequalities are formulated using outcomes of measurements which are not actually performed. Please can you point to which of the terms in the expression below are the ones actually performed, and which are those not performed?

[gill1109]

Michel and Gordon:just read Bell’s own answer to this criticism. It’s as old the hills, often been repeated, and it’s wrong. Chapter 8 of “Speakable and Unspeakable” is a two page paper, and I wrote it out for you here: http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=441&start=20#p12423

Wrong, you don't appear to understand the meaning of Counterfactual Definiteness. In your paper

https://arxiv.org/pdf/1207.5103.pdf "Statistics, Causality and Bell's theorem", you reveal this deficiency very cleary:

In a nut-shell, the inequality is an empirically verifiable consequence of the idea that the outcome of one measurement on one system cannot depend on which measurement is performed on the other. This idea, called locality or, more precisely, relativistic local causality, is just one of the three principles. Its formulation refers to outcomes of measurements which are not actually performed, so we have to assume their existence, alongside of the outcomes of those actually performed: the principle of realism, or more precisely, counterfactual definiteness.

How does a statement like this survive peer-review? There are several problems here:
1) Anything that is counterfactual can't be "empirically verified". "Empirical" means measured or experienced. "Counterfactual" means "not measured" or "not experienced"
2) Dependence does not mean causation. Dependence does not mean non-locality. The counterfactual outcome of the measurement not performed is not independent of the outcome of the measurement performed.
3) Measurements not performed (aka "Counterfactual measurements") by definition never exist and can never be experienced! This is simple modal logic. It is a contradiction/fallacy to suggest that they do. Suggesting that we should assume that they exist, suggests a lack of understanding of what "counterfactual" means. Existence means something very different in mathematics than in physics. A mathematician can simply conjure up a concept and it springs into existence on paper. Not so in physics. I've noticed a lot of mathematicians struggling with this, especially nowadays when everyone who can calculate thinks they are a physicist.
4) Counterfactual definiteness does not demand that we assume the absurdity of the existence of counterfactual outcomes. It only demands that we accept the validity of counterfactual predictions. That they remain valid even though they can't be experienced and will never be validated empirically (aka will never exist).
5) You admit in your paper that Bell's inequalities are formulated using outcomes of measurements which are not actually performed. Please can you point to which of the terms in the expression below are the ones actually performed, and which are those not performed?

Counterfactual definiteness (in this context, for me) means the mathematical existence within a mathematical model. It is not a meta-physical or philosophical statement about physical reality. It is totally irrelevant for the derivation of Bell’s inequality whether any experiments are performed at all.

“lambda” is an element of some set, assumed to mathematically exist in some mathematical model, under some metaphysical assumptions about reality. “a” is a number or an angle or a label on a device. “A” is a function. “A(a, lambda)” is a number. Within a mathematical framework it turns out that there must be some relations holding between some expectation values. In experiments it turns out that that relation was violated. Hence we learn that those model assumptions need to be abandoned.

Regarding your formula, separate procedures are performed in the lab to determine P(b, c), P(a, b) and P(a, c). One needs to take precautions such as the repeated rapid, local, random selection of settings, to ensure that each sample average is taken with respect to a random sample from the *same* population of elements “lambda”.

I’ve noticed a lot of physicists struggling with the distinction between model and reality.

The more recent martingale methods which I helped introduce use randomisation of settings in a more fundamental way, to take care of problems of time dependence, memory, time trends and jumps in physical parameters, in actual experiments.

Please read Bell’s “answer to critics”. We are repeating discussions which have been repeated again and again for 50 years. I typed it out, specially for you and Gordon. It’s only two pages in “Speakable and Unspeakable”, Chapter 8. http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=441&start=20#p12423. Fred found it for us. It’s a beautiful piece of writing.

You guys aren’t the first to raise this issue and you won’t be the last.

[Gordon Watson]

2. Let the three mathematical relations between Bell's equations (14) and (15) be, respectively: (14a), (14b), (14c).

3. Then Bell's error is his move from (14a) to (14b).

The contradiction is present even on the left-hand side of 14a.

P(a,b) - P(a,c) = "The correlation obtained if Alice and Bob measure at settings (a,b)" - "The correlation obtained if Alice and Bob measure at settings (a,c)"

The two terms contain contradictory premises. If Alice and Bob measured at (a,b) then they did not measure at (a,c). P(a,c) is counterfactual to P(a,b). The antecedents are contradictory therefore the combination of terms does not make physical sense since there is no universe in which True is False.

A: You are mistaken.

There is NO contradiction on LHS (14a): it is the simple difference between two expectations. And it holds, no matter how those expectations are obtained.

In the simplest case, under an idealised EPRB, and in my notation (since Bell's is often taken to be a probability):

(1) Alice and Bob obtain "the quantum mechanical expectation value" .

(2) Bob then resets his principal axis from to and they together obtain "the quantum mechanical expectation value" .

Further, as in my draft: the certain TRUTH of LHS (14a) — against the certain FALSITY of (14b) — is established via my irrefutable inequality.


B: Since I supplied the link to Clauser & Shimony (1978) — to make their "realism" available — I take it that your final questions are not addressed to me. Under true local realism (TLR), I provide the rider/clarifier: some existents change interactively. I thus explicitly reject naive-realism.


C: As for this from you: "Those who claim to deny "realism" don't actually know what they are talking about."

I'd say: Those who deny "realism" don't realise that there are many "unbranded" realisms on the market. And — until one identifies the contents — we don't know what they are talking about.
.

[gill1109]

2. Let the three mathematical relations between Bell's equations (14) and (15) be, respectively: (14a), (14b), (14c).

3. Then Bell's error is his move from (14a) to (14b).

The contradiction is present even on the left-hand side of 14a.

P(a,b) - P(a,c) = "The correlation obtained if Alice and Bob measure at settings (a,b)" - "The correlation obtained if Alice and Bob measure at settings (a,c)"

The two terms contain contradictory premises. If Alice and Bob measured at (a,b) then they did not measure at (a,c). P(a,c) is counterfactual to P(a,b). The antecedents are contradictory therefore the combination of terms does not make physical sense since there is no universe in which True is False.

A: You are mistaken.

There is NO contradiction on LHS (14a): it is the simple difference between two expectations. And it holds, no matter how those expectations are obtained.

In the simplest case, under an idealised EPRB, and in my notation (since Bell's is often taken to be a probability):

(1) Alice and Bob obtain "the quantum mechanical expectation value" .

(2) Bob then resets his principal axis from to and they together obtain "the quantum mechanical expectation value" .

Further, as in my draft: the certain TRUTH of LHS (14a) — against the certain FALSITY of (14b) — is established via my irrefutable inequality.


B: Since I supplied the link to Clauser & Shimony (1978) — to make their "realism" available — I take it that your final questions are not addressed to me. Under true local realism (TLR), I provide the rider/clarifier: some existents change interactively. I thus explicitly reject naive-realism.


C: As for this from you: "Those who claim to deny "realism" don't actually know what they are talking about."

I'd say: Those who deny "realism" don't realise that there are many "unbranded" realisms on the market. And — until one identifies the contents — we don't know what they are talking about.
.

Gordon,
“ Under true local realism (TLR), I provide the rider/clarifier: some existents change interactively. I thus explicitly reject naive-realism.”. You embrace non-locality!
Richard

[minkwe]

Counterfactual definiteness (in this context, for me) means the mathematical existence within a mathematical model.

Sorry, this is not how science works. You don't just conjure up new meanings and claim "for me" as a defense. Please provide the definition of "counterfactual definiteness".

It is not a meta-physical or philosophical statement about physical reality. It is totally irrelevant for the derivation of Bell’s inequality whether any experiments are performed at all.

It absolutely is a philosophical statement about previously mutually exclusive possibilities that do not exist because the alternates were realized. If you want I can show you multiple examples from your own writings that prove that you are making philosophical arguments on this subject, despite your denials. Perhaps you also do not understand what that means but first provide your definition of "counterfactual definiteness".

“lambda” is an element of some set, assumed to mathematically exist in some mathematical model, under some metaphysical assumptions about reality. “a” is a number or an angle or a label on a device. “A” is a function. “A(a, lambda)” is a number. Within a mathematical framework it turns out that there must be some relations holding between some expectation values. In experiments, it turns out that that relation was violated. Hence we learn that those model assumptions need to be abandoned.

There you go again claiming that A(a,lambda) is not a function. Here is what you said in the other thread yesterday (viewtopic.php?f=6&t=459):

Bell’s A(a, lambda) is an arbitrary function of the initial state of everything relevant in all of the physical systems involved - detectors, source, transmission lines - and of the setting “a”, which is later introduced into Alice’s detector, from outside. A dial on an apparatus is set to point at “a”. “lambda” is the context!

It has not gone un-noticed that you deny reference to experiments and insist it's all mathematics when it suits you then later invoke experiments when it suits you. This is not how physics is done. In physics, if you are modeling experiments, you must consider the experimental context throughout. This is the Bell problem. This is the reason we have stagnation in QM -- mathematicians think they are physicists because they know how to calculate. I gave a very simple coin-reading machine example above that illustrates this problem very clearly. Did you understand it? is a number, so what? My example above illustrates succinctly what happens when a mathematical relation is derived completely divorced from the experiment it is meant to model. It shows how invoking experiments later to exclaim "violation!" a fallacious. It shows why P(H) + P(T) = 1 in the context of empirically measured results from the experiment is wrong, even though it would be correct in an abstract mathematical exercise. It shows how applying the abstract mathematical relation to the experiment after-the-fact requires that one of the terms must be counterfactual and unmeasurable and must not simply be substituted for empirically measured counterparts. It is very clear, perhaps that's why you don't bother to address it.

Regarding your formula, separate procedures are performed in the lab to determine P(b, c), P(a, b) and P(a, c). One needs to take precautions such as the repeated rapid, local, random selection of settings, to ensure that each sample average is taken with respect to a random sample from the *same* population of elements “lambda”.

It's Bell's formula. Again, you invoke labs and experiments when it suits you. Didn't you just claim that this had nothing to do with labs and experiments? Didn't you claim it was all about mathematical models? If you engaged with my example for more than a minute, you won't make claims like this.

However, you have to answer just two questions
(1) What is your definition of counterfactual definiteness,
(2) You state in your paper that "Its formulation refers to outcomes of measurements which are not actually performed, so we have to assume their existence, alongside of the outcomes of those actually performed". So please again, which of the terms P(b, c), P(a, b) and P(a, c) result from measurements actually performed, and which result from measurements not actually performed?

I’ve noticed a lot of physicists struggling with the distinction between model and reality.

Me too, however almost all mathematicians struggle with modeling reality.

The more recent martingale methods which I helped introduce use randomisation of settings in a more fundamental way, to take care of problems of time dependence, memory, time trends and jumps in physical parameters, in actual experiments.

I think we established not too long ago that you probably don't understand the meaning of "randomness". viewtopic.php?f=6&t=400

Please read Bell’s “answer to critics”. We are repeating discussions which have been repeated again and again for 50 years.

I've read Bell's answer to critics many times he does not mention "Counterfactual definiteness". Feel free to explain here in this thread how his paper is relevant to the topic. In fact, please use whatever argument you like from Bell's paper to explain what my coin-tossing machine example is missing? Feel free to cite any paper that discusses counterfactual definiteness in a manner favorable to Bell and presents a counter-argument to what I explain in my coin-tossing machine example. To rebut an argument you first have to understand it.

[minkwe]

The contradiction is present even on the left-hand side of 14a.

P(a,b) - P(a,c) = "The correlation obtained if Alice and Bob measure at settings (a,b)" - "The correlation obtained if Alice and Bob measure at settings (a,c)"

The two terms contain contradictory premises. If Alice and Bob measured at (a,b) then they did not measure at (a,c). P(a,c) is counterfactual to P(a,b). The antecedents are contradictory therefore the combination of terms does not make physical sense since there is no universe in which True is False.

A: You are mistaken.

There is NO contradiction on LHS (14a): it is the simple difference between two expectations.

You say that because you did not understand the coin-tossing machine example I gave above. Please review it again.

Based on that example, do you agree that there is a contradiction on the LHS of P(H) + P(T) = 1? According to your argument, the LHS is simply a sum of probabilities.

[gill1109]

Counterfactual definiteness (in this context, for me) means the mathematical existence within a mathematical model.

Sorry, this is not how science works. You don't just conjure up new meanings and claim "for me" as a defense. Please provide the definition of "counterfactual definiteness".

Sorry, this *is* how science works. I may specify my own definition of a vague term like “counterfactual definiteness”, about which there is a huge literature stretching from philosophy, through the foundations of physics, into modern statistical science (“causality’). My definition is moreover commonly adopted in my field - statistics, AI, machine learning...I follow Boris Tsirelson, and recent writers on causality (Pearl, Peters, ...).

In the present case it it is not difficult. Suppose one imagines a deterministic physics in which the future evolution of detectors, transmission lines, source ... is determined by the state at some time t_0 of a myriad particles throughout Alice and Bob’s labs. Suppose settings a and b are inserted “from outside” into some measurement devices, and then later outcomes A(a, lambda) and B(b, lambda) get observed, for some functions A and B. Then we can define what every measurement outcome would have been, had a different setting a’ been inserted by Alice: she would have got the outcome A(a’, lambda). We suppose (locality) that it wouldn’t have made a difference if Bob had chosen b’ instead of b.

I refer to Tsirelson’s “citizendium” article on quantum entanglement, and to Jonas Peters’ book on causality, for further background.

*For me*, “counterfactual definiteness” is a property which classical physics certainly respects. Quantum mechanics does not. I have done a lot of work in forensic science. “Justice” is impossible without discussion of “what would have happened, if, counter to actual fact, suspect X had not taken a loaded gun with him on his way to the bank”. Personal morality is also meaningless without a concept of free will and hence the possibility of counterfactual reasoning. I’m pretty sure you feel that you are a free agent. You choose freely what you write on this forum. You imagine what would be the effect of writing different things, and you choose your words accordingly. In your mind you have a model of the world and this model allows you to envisage, simultaneously, different possible futures.

You seem a bit confused about mathematical notations. Let Theta be a set of directions (angles between minus pi and plus pi). Let Lambda be a set of initial configurations of the elementary particles making up the physical system detectors, source, transmission lines in an EPR-B experiment. Suppose that when Alice inserts setting “a” and Bob inserts setting “b” into their detectors, Alice’s detector produces outcome A(a, b, lambda) = +/-1; Bob similarly. Suppose the function A does not depend on setting b. Consider many independent repetitions whereby lambda is chosen according to a probability distribution rho. Then Alice and Bob’s outcomes are A(a, lambda) and B(b, lambda) and the expectation value of their product is int A(a, lambda)B(b, lambda) rho(d lambda).

A is a function; A(a, lambda) is a number. We consider a theory according to which lambda exists, with probability distribution rho. A(a, lambda) is the outcome which Alice *would* observe *if* she used setting “a”; lambda being chosen at random by nature according to the distribution rho.

With fancy philosophical terminology one says that A(a, .) is the counterfactual outcome observed by Alice if, contrary to fact, she chooses setting “a”, whatever setting she actually used. And maybe she just went home and switched her apparatus off. Still: if you have a deterministic theory in which lambda plays the role of initial state of the entire system, then you can say that the model satisfies “counterfactual definiteness’.

[minkwe]

Counterfactual definiteness (in this context, for me) means the mathematical existence within a mathematical model.

Sorry, this is not how science works. You don't just conjure up new meanings and claim "for me" as a defense. Please provide the definition of "counterfactual definiteness".

Sorry, this *is* how science works. I may specify my own definition of a vague term like “counterfactual definiteness”, about which there is a huge literature stretching from philosophy, through the foundations of physics, into modern statistical science (“causality’). My definition is moreover commonly adopted in my field - statistics, AI, machine learning...I follow Boris Tsirelson, and recent writers on causality (Pearl, Peters, ...).

And the definition is ...??? A lot of discussion of multiple unrelated things and no definition provided. If somebody asks you "What is counterfactual definiteness", they expect you to answer the question in a cogent manner and not ramble about a lot of things without answering the question. That's what politicians do, not scientists.

A is a function; A(a, lambda) is a number.

Bell’s A(a, lambda) is an arbitrary function of the initial state of everything relevant in all of the physical systems involved

viewtopic.php?f=6&t=459#p12472

[gill1109]

Counterfactual definiteness (in this context, for me) means the mathematical existence within a mathematical model.

Sorry, this is not how science works. You don't just conjure up new meanings and claim "for me" as a defense. Please provide the definition of "counterfactual definiteness".

Sorry, this *is* how science works. I may specify my own definition of a vague term like “counterfactual definiteness”, about which there is a huge literature stretching from philosophy, through the foundations of physics, into modern statistical science (“causality’). My definition is moreover commonly adopted in my field - statistics, AI, machine learning...I follow Boris Tsirelson, and recent writers on causality (Pearl, Peters, ...).

And the definition is ...??? A lot of discussion of multiple unrelated things and no definition provided. If somebody asks you "What is counterfactual definiteness", they expect you to answer the question in a cogent manner and not ramble about a lot of things without answering the question. That's what politicians do, not scientists.

I gave you the definition. Try reading what I wrote.

With respect to an EPR-B experiment: counterfactual definiteness means the existence of functions A, B and rho with the usual properties. Is that clear enough for you? It’s a property of a mathematical model.

The standard de Broglie-Bohm model for EPR-B also satisfies counterfactual definiteness. But it is not local. It defines functions A(a, b, lambda) and B(a, b, lambda). Bob’s setting has an influence on Alice’s outcome.

[minkwe]

I gave you the definition. Try reading what I wrote.

You explained the meaning of "counterfactual" in the following quote:

Suppose settings a and b are inserted “from outside” into some measurement devices, and then later outcomes A(a, lambda) and B(b, lambda) get observed, for some functions A and B. Then we can define what every measurement outcome would have been, had a different setting a’ been inserted by Alice: she would have got the outcome A(a’, lambda).

This is exactly the same definition of "Counterfactual" I provided in the first post. This means you agree that a "counterfactual" measurement is the measurement that could have been done but was not in fact done.

With respect to an EPR-B experiment: counterfactual definiteness means the existence of functions A, B, and rho with the usual properties. Is that clear enough for you? It’s a property of a mathematical model

But you haven't provided a clear answer about the meaning of "counterfactual definiteness" (to you). You keep talking about how different things satisfy counterfactual definiteness but you haven't defined it clearly. You now say counterfactual definiteness in EPRB means "the existence of functions A, B, and rho with the usual properties". That's as clear as mud. And appears completely unrelated to your agreed definition of "counterfactual" above. I've explained clearly what counterfactual definiteness means in the first post of this thread! Why is it so difficult for you to provide a clear definition? Perhaps that's on purpose.

[gill1109]

I gave you the definition. Try reading what I wrote.

You explained the meaning of "counterfactual" in the following quote:

Suppose settings a and b are inserted “from outside” into some measurement devices, and then later outcomes A(a, lambda) and B(b, lambda) get observed, for some functions A and B. Then we can define what every measurement outcome would have been, had a different setting a’ been inserted by Alice: she would have got the outcome A(a’, lambda).

This is exactly the same definition of "Counterfactual" I provided in the first post. This means you agree that a "counterfactual" measurement is the measurement that could have been done but was not in fact done.

With respect to an EPR-B experiment: counterfactual definiteness means the existence of functions A, B, and rho with the usual properties. Is that clear enough for you? It’s a property of a mathematical model

But you haven't provided a clear answer about the meaning of "counterfactual definiteness" (to you). You keep talking about how different things satisfy counterfactual definiteness but you haven't defined it clearly. You now say counterfactual definiteness in EPRB means "the existence of functions A, B, and rho with the usual properties". That's as clear as mud. And appears completely unrelated to your agreed definition of "counterfactual" above. I've explained clearly what counterfactual definiteness means in the first post of this thread! Why is it so difficult for you to provide a clear definition? Perhaps that's on purpose.

I have a clear definition. It means, within a mathematical model, of the existence of the outcomes of not actually performed measurements, alongside of the outcomes of actually performed measurements.

[minkwe]

I have a clear definition. It means, within a mathematical model, of the existence of the outcomes of not actually performed measurements, alongside of the outcomes of actually performed measurements.

Thus to you, counterfactual definiteness means the mathematical existence of outcomes of unperformed measurements alongside outcomes of actually performed measurements.

Then which of the terms P(a,b), P(a,c) and P(b,c) are counterfactual and which are not according to you? Going back to my coin-reading machine example, which of the terms P(H) and P(T) is counterfactual and which is not?

[gill1109]

Your question does not make any sense to me, sorry.

[minkwe]

Your question does not make any sense to me, sorry.

https://arxiv.org/pdf/1207.5103.pdf "Statistics, Causality and Bell's theorem", you reveal this deficiency very cleary:

In a nut-shell, the inequality is an empirically verifiable consequence of the idea that the outcome of one measurement on one system cannot depend on which measurement is performed on the other. This idea, called locality or, more precisely, relativistic local causality, is just one of the three principles. Its formulation refers to outcomes of measurements which are not actually performed, so we have to assume their existence, alongside of the outcomes of those actually performed: the principle of realism, or more precisely, counterfactual definiteness.

I think you understand the question very well, you just don't want to answer.

[FrediFizzx]

Your question does not make any sense to me, sorry.

https://arxiv.org/pdf/1207.5103.pdf "Statistics, Causality and Bell's theorem", you reveal this deficiency very cleary:

In a nut-shell, the inequality is an empirically verifiable consequence of the idea that the outcome of one measurement on one system cannot depend on which measurement is performed on the other. This idea, called locality or, more precisely, relativistic local causality, is just one of the three principles. Its formulation refers to outcomes of measurements which are not actually performed, so we have to assume their existence, alongside of the outcomes of those actually performed: the principle of realism, or more precisely, counterfactual definiteness.

I think you understand the question very well, you just don't want to answer.

Just continue on without his answer.
.