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I watched this YouTube video by Sabine Hossenfelder to try and better understand superdeterminism:

https://www.youtube.com/watch?v=ytyjgIyegDI

(Note: Physics begins around 8:12, before that she's mostly talking about history and background information.)

At 12:11, she defines Superdeterminism as follows:

What a quantum particle does depends on what measurement will take place.

She then introduces this equation: $$ \rho(\lambda|ab)\neq \rho(\lambda) $$

She explains it as meaning that the probability distribution of the hidden variable changes, depending on the settings of the detector at the time of measurement.

Since the hidden variable exists before the time of measurement, it sounds like superdeterminism is nothing more than a retrocausal explanation, where the measurement retroactively alters the hidden variable. But I must be misinterpreting something, because retrocausality is (relativistically) equivalent to superluminal communication, and would therefore violate locality. At the beginning of the video (1:42), she explains that locality is a separate assumption from statistical independence (i.e. "no superdeterminism"), and at 17:05, she explicitly states that superdeterminism is local, and so a retrocausal explanation would seem to be ruled out.

The only other interpretation I can think of is that the hidden variable and the detector are correlated, not by some causal or physical connection, but as a brute fact, with no underlying physical mechanism connecting them. I find that interpretation difficult to accept, but I suppose it's not directly contrary to any law of physics. This is what I had believed superdeterminism to be before I watched the video, but now I'm confused.

Is superdeterminism a retrocausal explanation, or is there some other physical mechanism that could explain how this correlation arises?

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  • $\begingroup$ I do believe that QM will be shown in the end be a theory of superluminal connections in the sense that two entangled particles are at the two ends of some kind wormhole-like idea (gravitational or not), like ER=EPR. Once you allow for wormholes in a theory, you break causality or predictability from initial (t=0) conditions. You can have closed time like curves. May be QM is suffering from that. $\endgroup$
    – user338734
    Commented Jul 2, 2022 at 1:55
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    $\begingroup$ You've hit on the core reason most people don't take superdeterminism seriously... there's no clear mechanism. If you don't justify it with retrocausality, the mechanism has to be something like "God/the simulation writers/aliens set up the initial conditions of the universe to force you to only feel like doing experiments that happen to make QM look true by accident, even though it really isn't true". It's just one step above Descartes' demon. $\endgroup$
    – knzhou
    Commented Jul 2, 2022 at 4:59
  • $\begingroup$ I recommend reading Rethinking Superdeterminism and Superdeterminism: A Guide for the Perplexed. $\endgroup$
    – Galen
    Commented Aug 17, 2022 at 15:04

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Since the hidden variable exists before the time of measurement, it sounds like superdeterminism is nothing more than a retrocausal explanation, where the measurement retroactively alters the hidden variable

That's not how I'd put it. Assuming you're thinking of the standard two-party Bell scenario, "superdeterminism" means that you're describing state reaching the detectors (and/or whatever hidden variable describing it) and the measurement choices of Alice and Bob as not independent from each other. So it's not that measurement choices change retroactively the hidden variable. Rather, it's that measurement choices and hidden variables are correlated via some other hidden variable.

Bell's result relies on the assumption that you can write the output probability distribution as $$p(ab|xy)=\sum_\lambda p_\lambda p_\lambda(a|x) p_\lambda(b|y),$$ meaning that there is a hidden variable $\lambda$ explaining, for all measurement choices $x,y$, the probabilities of getting outcomes $a,b$. Most notably, this means that the measurement choices $x,y$ are thought of as independent. However, if $x$ and $y$ are also correlated, "explained" by some other hidden variable, nonlocality results might fail to hold.

In other words, if you trace back the causes of Alice's and Bob's decisions as well, talking about a conditional probability distribution $p(ab|xy)$ loses meaning. Rather, you'd have to talk about a joint probability distribution $p(abxy)$, meaning that both measurement choices and outcomes are "outcomes", possibly arbitrarily correlated and maybe "explained" by some third "cause" (a "superdeterministic hidden variable", if you will).

In this scenario, there's not possible Bell inequality to derive. Any distribution is possible. The problem is that these superdeterministic assumptions are too accommodating. They don't really explain anything. And an actual mechanism that would result in the observed correlations would seem rather involved and "conspiratorial".

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The point of superdeterminism is that it places a global constraint on the entirety of the universe. Retrocausality instead refers to causal chain of events linking backwards in time. Definitionally, these are different.

You may argue they are similar in spirit however, and someone might even argue that they are equivalent in some sense, but this is certainly not agreed upon.

From wikipedia (sadly this sentence doesn't have a citation),

Some authors consider retrocausality in quantum mechanics to be an example of superdeterminism, whereas other authors treat the two cases as distinct. No agreed-upon definition for distinguishing them exists.

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