Do electrons think? (1949)

Note that, contrary to popular understanding, it isn't even established that quantum mechanics is indeterminate or not subject to strict cause-and-effect.

It's indeterminate according to the mainstream Copenhagen interpretation, but de Broglie–Bohm theory [1] ("pilot wave theory") is an interpretation that is entirely deterministic, and its assumptions result in exactly the same final equations as the Copenhagen one. But every particle always has a definite position+momentum and there's no notion of wave collapse or philosophical trickiness of what constitutes an "observer". For more on the historical reasons why Copenhagen became mainstream and de Broglie-Bohm didn't, see [2].

[1] https://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory

[2] http://qr.ae/TUNXvC

Discussion here [0], also recommend this lecture[1]. I'm personally not a fan, but I like that people talk about it :) Dogma isn't good for anyone!

[0] https://news.ycombinator.com/item?id=13198025

[1] http://www.tcm.phy.cam.ac.uk/~mdt26/PWT/lectures/bohm7.pdf

In this instance, the popular understanding corresponds to the latest research better than realist theories like pilot-wave theory. Proponents of realist interpretations of QM have relied for decades on identifying possible classical channels of relativistic communication, or theorizing the existence of hidden variables.

The double slit experiment has been used in various forms to, over time, eliminate these channels. I'm not a physicist, but the language that they are using quite a few papers leads me to believe that these channels have been closed, and the realists are out of remaining options for maintaining realism.

For instance:

An experimental test of non-local realism, 2007

https://arxiv.org/abs/0704.2529

Wherein the authors show, using previously untested correlations between two entangled photons, that maintaining realist interpretations of quantum mechanics (such as pilot-wave theory) as a fundamental concept require the introduction of locality-defying 'action at a distance' actions.

Quantum erasure with causally disconnected choice, 2012

https://arxiv.org/abs/1206.6578

Wherein the authors, using an interferometric quantum eraser experiment, eliminate past and future communication channels by enforcing Einstein locality via a mechanism that I don't understand yet. They conclude that, "No naive realistic picture is compatible with our results because whether a quantum could be seen as showing particle- or wave-like behavior would depend on a causally disconnected choice. It is therefore suggestive to abandon such pictures altogether."

Experimental non-classicality of an indivisible quantum system, 2011

https://arxiv.org/abs/1106.4481

I understand even less of this one, looks like it has to do with performing the kinds of simultaneous measurements of various properties that one would expect to be able to, if realist interpretations were true. They conclude, "Not only is a single qutrit the simplest system in which such a contradiction is possible, but, even more importantly, the contradiction cannot result from entanglement, because such a system is indivisible, and it does not even allow the concept of entanglement between subsystems."

UPDATE:

Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km 2015

https://arxiv.org/abs/1508.05949v1

"For more than 80 years, the counterintuitive predictions of quantum theory have stimulated debate about the nature of reality. ... In the past decades, numerous ingenious Bell inequality tests have been reported. However, because of experimental limitations, all experiments to date required additional assumptions to obtain a contradiction with local realism, resulting in loopholes. Here we report on a Bell experiment that is free of any such additional assumption and thus directly tests the principles underlying Bell's inequality. ... This result rules out large classes of local realist theories, and paves the way for implementing device-independent quantum-secure communication and randomness certification."

I'm not aware of any significant challenges to these studies.

It would help if these weren't all from the same single source: Zeilinger's Vienna group and friends.

On the other hand formalism works seamlessly mathematically, which cannot be said of standard quantum mechanics. Even this year's Fields medalist Figalli has a paper on how good things are in Bohmian land.

Why do you think this disproves pilot wave theory?

> Physicists also compulsorily reject Bohm’s construction because it explicitly builds nonlocality into its framework—even though violations of Bell’s inequality have conclusively shown that the stage of our universe is nonlocal. This is perplexing. Nonlocality is unavoidable in any theory that recovers the predictions of quantum theory. Therefore, any criticism of a theory that displays Nature’s nonlocal feature in an obvious way is both unfounded and counterproductive. Despite this, Bohm’s inherent explication of nonlocality continues to be obnoxiously mistaken as a strike against it instead of for it.