Dirkman wrote:"If there are counterfactual outcomes at various measurement settings, what are they? In other words: if there is objective realism a la EPR, one should be able to identify the hypothetical values that would have been obtained if a different measurement pair had been chosen."
If you can identify the flaw in the following argument, you will be able to answer your own question:
A photon A is heading toward Alice's detector on a distant galaxy. It will interact with the detector tomorrow to produce an outcome of +1 or -1. But the 'laws' of the excluded middle (no third truth-value) and of non-contradiction (not both truth-values), mandate that one of the propositions "Alice's will get +1", "Alice's will get -1", is true (always has been and ever will be) and the other is false (always has been and ever will be).
Suppose 'Alice's will get +1' is true today. Then whatever Alice does (or fails to do) before the photon hits her detector will make no difference: the outcome is already settled. Similarly if 'Alice's will get +1' is false today, no matter what Alice does (or fails to do), it will make no difference: the outcome is already settled.
Therefore, the future will be what it will be, irrespective of Alice's planning, choices or, intentions.Consider the following statements:
a) If I look at the moon, I will see it.
b) Had I looked at the moon yesterday, I would have seen it.
(a) is a True statement. In this case, it is implicit that the possibility of either looking at the moon or not looking at the moon still exists.
(b) is a counterfactual statement. Statement (b) will be valid even if it is impossible for me to look at the moon now (perhaps I was blinded overnight). Accepting (b) as a valid/true statement does not mean: (c) "Seeing the moon" exists prior to me looking at the moon.
Most confusion about the meaning of counterfactual outcomes originates from sloppy use of the concepts of "Truth", "Possibilities" "Existence", "Actualities". EPR/Bell discussions are often exhibitions of serious misunderstandings of those concepts.
Dirkman wrote:"If there are counterfactual outcomes at various measurement settings, what are they?"
The counterfactual outcomes are the outcomes she could have gotten had she chosen any other settings than the one she actually chose. The result which Alice will get when she tilts her detector to angle
a, could not possibly
exist before Alice actually makes a measurement!!! However, the statement "
If Alice turns her detector to angle a she will obtain the result A." is a
True statement, which will continue to be
True even if Alice had her detector to angle
b, instead.
Consider the EPRB example:
Let us denote observable "
what Alice observes when she tilts her device to angle a" as A, and "
what Alice observes when she tilts her device to angle b" as B and "
what Alice observes when she tilts her device to angle c" as C. For a single photon, All three observables A, B, C are
possible, however if Alice never measures anything, none of them
exist as actual outcomes. Therefore although A,B,C are all "possible", only the one which Alice actually measures, will
exist. The other two will be counterfactual. For the specific particle, once Alice measures at "a", it is now impossible to measure the other two, therefore, the counterfactual outcomes B and C can not possibly exist at the same time as A. Let's look at it another way by rephrasing the statements:
A: if Alice measures the photon at angle "a" she will obtain "A"
B: If Alice measures the photon at angle "b" she will obtain "B"
C: If Alice measures the photon at angle "c" she will obtain "C"
All three statements can be
True simultaneously. However, outcomes A, B, C can't
exist simultaneously because of a contradiction: If Alice measures the photon at angle "a", then certainly she did not measure the photon at angles "b" or "c". In other words, all three are
possibilities are simultaneously true, but only one of them can and will
exist. The others will be counterfactual.
Bell's problem was that he did mathematics by mixing and combining A,B and C in the same expression. At best, he can tell you about mathematical relationships between
possibilities. Drawing any inference from such relationships about what
exists, or
actual results of experiments is utter stupidity.
Dirkman wrote:In other words: if there is objective realism a la EPR, one should be able to identify the hypothetical values that would have been obtained if a different measurement pair had been chosen.
Do you agree that if Alice had picked a setting different from the one she actually picked she would have obtained a result? That result, whatever it is, is the counterfactual result.
[quote="Dirkman"]"If there are counterfactual outcomes at various measurement settings, what are they? In other words: if there is objective realism a la EPR, one should be able to identify the hypothetical values that would have been obtained if a different measurement pair had been chosen."[/quote]
If you can identify the flaw in the following argument, you will be able to answer your own question:
[b]A photon A is heading toward Alice's detector on a distant galaxy. It will interact with the detector tomorrow to produce an outcome of +1 or -1. But the 'laws' of the excluded middle (no third truth-value) and of non-contradiction (not both truth-values), mandate that one of the propositions "Alice's will get +1", "Alice's will get -1", is true (always has been and ever will be) and the other is false (always has been and ever will be).
Suppose 'Alice's will get +1' is true today. Then whatever Alice does (or fails to do) before the photon hits her detector will make no difference: the outcome is already settled. Similarly if 'Alice's will get +1' is false today, no matter what Alice does (or fails to do), it will make no difference: the outcome is already settled.
Therefore, the future will be what it will be, irrespective of Alice's planning, choices or, intentions.[/b]
Consider the following statements:
a) If I look at the moon, I will see it.
b) Had I looked at the moon yesterday, I would have seen it.
(a) is a True statement. In this case, it is implicit that the possibility of either looking at the moon or not looking at the moon still exists.
(b) is a counterfactual statement. Statement (b) will be valid even if it is impossible for me to look at the moon now (perhaps I was blinded overnight). Accepting (b) as a valid/true statement does not mean: (c) "Seeing the moon" exists prior to me looking at the moon.
Most confusion about the meaning of counterfactual outcomes originates from sloppy use of the concepts of "Truth", "Possibilities" "Existence", "Actualities". EPR/Bell discussions are often exhibitions of serious misunderstandings of those concepts.
[quote="Dirkman"]"If [u]there are[/u] [u]counterfactual outcomes[/u] at various measurement settings, what are they?"[/quote]
The counterfactual outcomes are the outcomes she could have gotten had she chosen any other settings than the one she actually chose. The result which Alice will get when she tilts her detector to angle [b]a[/b], could not possibly [i]exist[/i] before Alice actually makes a measurement!!! However, the statement "[i]If Alice turns her detector to angle [b]a[/b] she will obtain the result A.[/i]" is a [i]True[/i] statement, which will continue to be [i]True[/i] even if Alice had her detector to angle [b]b[/b], instead.
Consider the EPRB example:
Let us denote observable "[i]what Alice observes when she tilts her device to angle a[/i]" as A, and "[i]what Alice observes when she tilts her device to angle b[/i]" as B and "[i]what Alice observes when she tilts her device to angle c[/i]" as C. For a single photon, All three observables A, B, C are [i]possible[/i], however if Alice never measures anything, none of them [i]exist[/i] as actual outcomes. Therefore although A,B,C are all "possible", only the one which Alice actually measures, will [i]exist[/i]. The other two will be counterfactual. For the specific particle, once Alice measures at "a", it is now impossible to measure the other two, therefore, the counterfactual outcomes B and C can not possibly exist at the same time as A. Let's look at it another way by rephrasing the statements:
A: if Alice measures the photon at angle "a" she will obtain "A"
B: If Alice measures the photon at angle "b" she will obtain "B"
C: If Alice measures the photon at angle "c" she will obtain "C"
All three statements can be [i]True[/i] simultaneously. However, outcomes A, B, C can't [i]exist[/i] simultaneously because of a contradiction: If Alice measures the photon at angle "a", then certainly she did not measure the photon at angles "b" or "c". In other words, all three are [i]possibilities[/i] are simultaneously true, but only one of them can and will [i]exist[/i]. The others will be counterfactual.
Bell's problem was that he did mathematics by mixing and combining A,B and C in the same expression. At best, he can tell you about mathematical relationships between [i]possibilities[/i]. Drawing any inference from such relationships about what [i]exists[/i], or [i]actual[/i] results of experiments is utter stupidity.
[quote="Dirkman"]In other words: if there is objective realism a la EPR, one should be able to identify the hypothetical values that would have been obtained if a different measurement pair had been chosen.[/quote]
Do you agree that if Alice had picked a setting different from the one she actually picked she would have obtained a result? That result, whatever it is, is the counterfactual result.