Just wanted to mention that Physics is not immune to this. Bell’s theorem requires only a first-year college math skill, yet it took 30 odd years after EPR to formulate it. Not even Einstein himself was able do it. Event horizons and inescapability of singularity required virtually no new math beyond 1917, yet it took some 50 years for the physicists to understand the picture. There are clearly some mental blocks people have which take decades and new generations to overcome.
The idea of an event horizon goes back to John Michell in 1783. The derivation of a black hole and event horizon from the equations of General Relativity were done by Schwarzschild mere months after the publication of GR in 1915 (get your dates right!).
(Cool tidbit: Schwarzschild was an artillery gunner during the Great War, and spent his time looking for solutions to the Einstein field equations when he wasn’t calculating trajectories. He published the math behind GR black holes in a letter to Einstein from the front.)
What shminux means is that, even though the Schwarzschild metric was derived early as you say, its physical interpretation as a black hole was not understood till much later. According to Wikipedia, it was not until 1958 that the Schwarzschild radius was identified as an event horizon, a surface which causal influences could only cross in one direction. It was also in the 1950s that the maximal extension analytic extension of the Schwarzschild metric was constructed, and it was not till the 1960s that these results became widely known and progress in black hole physics really took off (along with Wheeler coining the term “black hole” sometime around 1964).
What does that mean? (Not a rhetorical question, I really don’t know!)
In graphical model terms, Bell inequality violations mean there is no “hidden variable DAG model” underlying what we see. But maybe Tsirelson inequality points to some correct generalization of the “hidden variable DAG” concept to the quantum setting (???). To my knowledge, nobody knows what to make of this, although it doesn’t take much math background to understand Tsirelson inequalities.
To be a little more precise, I can imagine an object that does not posit anything ontologically beyond the four variables related by the graph:
A → B <-> C ← D
The distributions that live in this object will, in general, violate both Bell and Tsirelson inequalities. So this object is “not physical.” I can also posit a hidden variable DAG (in other words I posit in addition to A,B,C,D another variable H):
A → B ← H → C ← D
This will obey Bell inequality. So this is “classically physical, but not physical.”
The question is, what should I posit beyond A,B,C,D to violate Bell, but obey Tsirelson? Whatever it is, it cannot be a hidden variable H. But maybe I can posit something more complicated, or “weird”? But obvious in hindsight?
Just wanted to mention that you can trade the EPR-style non-locality for macroscopic many worlds. For all its failings, this approach pushes the strangeness of QM into a local event where the branches interact. In the EPR example, it is where you compare the measurement results from the two detectors. Thus it might be more productive to base any DAG model on an MWI picture, or at least on a setup where there are only a finite and small number of branches, not uncountably many of them, like in Schrodinger’s cat or EPR, maybe something like this quantum bomb tester.
Just wanted to mention that Physics is not immune to this. Bell’s theorem requires only a first-year college math skill, yet it took 30 odd years after EPR to formulate it. Not even Einstein himself was able do it. Event horizons and inescapability of singularity required virtually no new math beyond 1917, yet it took some 50 years for the physicists to understand the picture. There are clearly some mental blocks people have which take decades and new generations to overcome.
The idea of an event horizon goes back to John Michell in 1783. The derivation of a black hole and event horizon from the equations of General Relativity were done by Schwarzschild mere months after the publication of GR in 1915 (get your dates right!).
(Cool tidbit: Schwarzschild was an artillery gunner during the Great War, and spent his time looking for solutions to the Einstein field equations when he wasn’t calculating trajectories. He published the math behind GR black holes in a letter to Einstein from the front.)
What shminux means is that, even though the Schwarzschild metric was derived early as you say, its physical interpretation as a black hole was not understood till much later. According to Wikipedia, it was not until 1958 that the Schwarzschild radius was identified as an event horizon, a surface which causal influences could only cross in one direction. It was also in the 1950s that the maximal extension analytic extension of the Schwarzschild metric was constructed, and it was not till the 1960s that these results became widely known and progress in black hole physics really took off (along with Wheeler coining the term “black hole” sometime around 1964).
Here’s a test of hindsight bias:
QM violates Bell inequalities, but obeys Tsirelson inequalities (http://arxiv.org/pdf/1303.2849v1.pdf).
What does that mean? (Not a rhetorical question, I really don’t know!)
In graphical model terms, Bell inequality violations mean there is no “hidden variable DAG model” underlying what we see. But maybe Tsirelson inequality points to some correct generalization of the “hidden variable DAG” concept to the quantum setting (???). To my knowledge, nobody knows what to make of this, although it doesn’t take much math background to understand Tsirelson inequalities.
To be a little more precise, I can imagine an object that does not posit anything ontologically beyond the four variables related by the graph:
A → B <-> C ← D
The distributions that live in this object will, in general, violate both Bell and Tsirelson inequalities. So this object is “not physical.” I can also posit a hidden variable DAG (in other words I posit in addition to A,B,C,D another variable H):
A → B ← H → C ← D
This will obey Bell inequality. So this is “classically physical, but not physical.”
The question is, what should I posit beyond A,B,C,D to violate Bell, but obey Tsirelson? Whatever it is, it cannot be a hidden variable H. But maybe I can posit something more complicated, or “weird”? But obvious in hindsight?
I am not familiar with using DAG in QM, sorry.
Just wanted to mention that you can trade the EPR-style non-locality for macroscopic many worlds. For all its failings, this approach pushes the strangeness of QM into a local event where the branches interact. In the EPR example, it is where you compare the measurement results from the two detectors. Thus it might be more productive to base any DAG model on an MWI picture, or at least on a setup where there are only a finite and small number of branches, not uncountably many of them, like in Schrodinger’s cat or EPR, maybe something like this quantum bomb tester.
The “non-DAG jargon” question is: “what are the ontological implications of Tsirelson inequalities?”
My point is that this has the feel of one of those questions with an answer that will be very obvious (but only in hindsight).