by gill1109 » Tue Dec 28, 2021 1:19 pm
Joy Christian wrote: ↑Tue Dec 28, 2021 12:44 am
gill1109 wrote: ↑Tue Dec 28, 2021 12:32 am
Joy Christian wrote: ↑Tue Dec 28, 2021 12:14 am
If this is the claim of "superdeterminism", then it is completely false. There is never any selection of a subset of p(h) when experiments are done with a fixed set (a, b) of settings.
ALL of the hidden variables h in H play role in the experiment, without exception. The assumption p(h|a, b) =/= p(h) is false.
The assumption p(h|a, b) =/= p(h) can hold if and only if the hidden variables h influence the spontaneous choices of the random settings a and b.
p(h|a, b) =/= p(h) is not an *assumption* of superdeterminism, it's a *consequence* of superdeterminism. According to superdeterminism, the very notion of a spontaneous choice is misguided. No spontaneous choices exist. Not even in our brains, which are also subject to the laws of physics. Which are deterministic laws. Differential equations, according to Tim Palmer (of Jesus College / Oxford University, BTW) and his friends.
I think it is an interesting mathematical-physical model which might be adequate for cosmology but which I think breaks down at the level of real life, including real life Bell-type experiments.
Tim and I have known each other for 30 years. Michel wants to deny any metaphysical assumption behind the claim p(h|a, b) =/= p(h). He wants to claim that a selection of the subset p(h|a, b) =/= p(h) is necessitated by the very act of choosing (a, b). But that is pure baloney.
I largely agree with you, Joy (and with Fred). Though I wouldn't talk about selection of a subset. Tim and his friends Sabine and Jonte are talking about inequality of probability distributions.
We need to distinguish between values which might be taken by random variables, random variables themselves, and the sets in which those random variables must take values. I would use three different letter-types for these three different things. For instance: a possible setting of Alice is denoted by plain lower case
a, Alice's setting considered as a random variable is denoted by
A, and the set of all possible values of Alice's setting is
A. When Tim, Sabine, and Jonte write "p(h|a, b) =/= p(h)" they are talking about the inequality of conditional and unconditional probability distributions. They really mean that for (
a,
b) in a subset of
Ax
B of positive probability, in those experiments in which the pair of settings (
A,
B) happens to take on a value in that subset, the probability distribution of
H on
H is not the same as what it is overall.
Not surprisingly, they prefer to use a common lazy physicist's or lazy statistician's notation. If you are not used to it you might be puzzled. If you see what they really mean you might still be puzzled. You have to get used to it. Probability 101.
Now, how could this be? It is a general principle that there is no correlation without causation. But the causation may be in one direction or the other, or from the past, or from the future. If there is correlation between (
A, B) and
H, then either (
A, B) causes
H, or
H causes (
A, B), or there is a common cause
Z of both (
A, B) and of
H, or there is a common consequence
Z of (
A, B) and
H and we are *selecting* cases on the basis of outcomes of
Z.
Tim Palmer and his friends do argue that there is a common cause of *everything* hence all correlations which we see in the physical world are in some sense "spurious correlations". According to them, the correlations between settings and measurement outcomes in a Bell experiment is explained by "super hidden variables" which determine both the settings and the measurement outcomes and the hidden variables which physicists talk about. Super hidden variables behind the plain hidden variables.
I see that Joy and Fred more or less got the message but Michel is missing it.
Super-determinism can explain everything. But because it can explain everything, it really explains nothing. It is a religion, not a scientific hypothesis. No experiment can disprove it. It does not make any predictions.
[quote="Joy Christian" post_id=517 time=1640681040 user_id=63]
[quote=gill1109 post_id=515 time=1640680325 user_id=60]
[quote="Joy Christian" post_id=514 time=1640679298 user_id=63]
If this is the claim of "superdeterminism", then it is completely false. There is never any selection of a subset of p(h) when experiments are done with a fixed set (a, b) of settings. [color=#FF0000]ALL[/color] of the hidden variables h in H play role in the experiment, without exception. The assumption p(h|a, b) =/= p(h) is false.
The assumption p(h|a, b) =/= p(h) can hold if and only if the hidden variables h influence the spontaneous choices of the random settings a and b.
[/quote]
p(h|a, b) =/= p(h) is not an *assumption* of superdeterminism, it's a *consequence* of superdeterminism. According to superdeterminism, the very notion of a spontaneous choice is misguided. No spontaneous choices exist. Not even in our brains, which are also subject to the laws of physics. Which are deterministic laws. Differential equations, according to Tim Palmer (of Jesus College / Oxford University, BTW) and his friends.
I think it is an interesting mathematical-physical model which might be adequate for cosmology but which I think breaks down at the level of real life, including real life Bell-type experiments.
[/quote]
Tim and I have known each other for 30 years. Michel wants to deny any metaphysical assumption behind the claim p(h|a, b) =/= p(h). He wants to claim that a selection of the subset p(h|a, b) =/= p(h) is necessitated by the very act of choosing (a, b). But that is pure baloney.
[/quote]
I largely agree with you, Joy (and with Fred). Though I wouldn't talk about selection of a subset. Tim and his friends Sabine and Jonte are talking about inequality of probability distributions.
We need to distinguish between values which might be taken by random variables, random variables themselves, and the sets in which those random variables must take values. I would use three different letter-types for these three different things. For instance: a possible setting of Alice is denoted by plain lower case [i]a[/i], Alice's setting considered as a random variable is denoted by [i]A[/i], and the set of all possible values of Alice's setting is [b][u][i]A[/i][/u][/b]. When Tim, Sabine, and Jonte write "p(h|a, b) =/= p(h)" they are talking about the inequality of conditional and unconditional probability distributions. They really mean that for ([i]a[/i], [i]b[/i]) in a subset of [b][u][i]A[/i][/u][/b]x[b][u][i]B[/i][/u][/b] of positive probability, in those experiments in which the pair of settings ([i]A[/i], [i]B[/i]) happens to take on a value in that subset, the probability distribution of [i]H[/i] on [b][u][i]H[/i][/u][/b] is not the same as what it is overall.
Not surprisingly, they prefer to use a common lazy physicist's or lazy statistician's notation. If you are not used to it you might be puzzled. If you see what they really mean you might still be puzzled. You have to get used to it. Probability 101.
Now, how could this be? It is a general principle that there is no correlation without causation. But the causation may be in one direction or the other, or from the past, or from the future. If there is correlation between ([i]A, B[/i]) and [i]H[/i], then either ([i]A, B[/i]) causes [i]H[/i], or [i]H[/i] causes ([i]A, B[/i]), or there is a common cause [i]Z[/i] of both ([i]A, B[/i]) and of [i]H[/i], or there is a common consequence [i]Z[/i] of ([i]A, B[/i]) and [i]H[/i] and we are *selecting* cases on the basis of outcomes of [i]Z[/i].
Tim Palmer and his friends do argue that there is a common cause of *everything* hence all correlations which we see in the physical world are in some sense "spurious correlations". According to them, the correlations between settings and measurement outcomes in a Bell experiment is explained by "super hidden variables" which determine both the settings and the measurement outcomes and the hidden variables which physicists talk about. Super hidden variables behind the plain hidden variables.
I see that Joy and Fred more or less got the message but Michel is missing it.
Super-determinism can explain everything. But because it can explain everything, it really explains nothing. It is a religion, not a scientific hypothesis. No experiment can disprove it. It does not make any predictions.
