It's funny that world-leading physicists were arguing about these questions in the 40s (even if briefly), because I feel like nowadays, everyone who has played Civilization would've intuitively known Whittaker's argument to be flawed (at least those of us that like to savescum). A photon with hidden variables is essentially like playing a game of Civilization with the "preserve random seed" option enabled: if you reload a save and then take the same action (e.g. order unit X to attack unit Y) 100 times, you'll get 100 times the same result (e.g. unit X wins) — just like a deterministic photon would always take the same path. But if you load that same save and then take a different action (e.g. first order unit A to attack unit B, and then order unit X to attack unit Y) you may get a different outcome (e.g. unit X might die), because the PRNG from that same random seed is fed operations in a different order. The result can still be absolutely deterministic, but nevertheless dependent on external inputs. Same for the photon that could start acting differently in a way that is still tied to its hidden variable state when the environment it is confronted with changes (as if each quantum particle was seeded with its own little PRNG).
Of course Bell later proved by experiment that quantum state cannot be explained as simply as a local hidden variable, no matter how it looks like. But these guys didn't know that yet.
The premise isn't just determinism, which is already a huge reach, but determinism which just happens to correlate observer choices with experimental results in exactly the way that casts doubt on the meaning of Bell experiments.
Superdeterminism is local actually, although accepting non-locality is another way to satisfy Bell's theorem that's compatible with hidden variables (Bohmian mechanics/pilot wave theory).
Schrödinger's fix to Whittaker's photon argument was to let the hidden variable take any value between zero and one, instead of just two. It's funny that such a small change was enough to rebuild the quantum probabilities.
It is not surprising that Schrödinger did this, what is surprising that a competent physicist, as Whittaker should have been, could ever write such an obviously weak "proof".
If there are hidden variables, it is pretty obvious that they cannot be binary variables, but their nature must be that of spins, i.e. rotation movements, where the probability of interaction depends on the instantaneous values of the rotation angles of the interacting particles (which correspond to the phases of the "wave" functions describing the system).
To give some nuance on the quote "Experimental evidence + logical deduction can never prove that either the deterministic or the indeterministic view is impossible": We can indeed rule out a local hidden variable model [1].
So if the deterministic view is true, then it has to be a holistic theory. The hidden variables must be global, i.e. "accessible" throughout the universe. They cannot be attached to a particle as in Whittaker's model or Schrödinger's modification.
The CHSH or Bell inequalities are based on quite dubious assumptions that seem a poor match for how real hidden variables should behave and the current quantum mechanics is still full of inconsistencies.
Much of the classic quantum mechanics, e.g. based on the Schrödinger or Dirac equations, is compatible with local hidden variables and I have not seen yet a precise account of which are the more recent axioms/assumptions that introduce an incompatibility with local hidden variables.
Thus I do not believe that the non-existence of local hidden variables has been proven beyond any reasonable doubt.
The GHZ/Mermin experiment refined the Bell argument into an "all-or-nothing" experiment with three parties. In that scenario, there are no probabilistic tests. Alice, Bob and Charlie each receive one particle (entangled, of course) and make a local decision to measure one of two quantities of that particle: x or y, each with a binary outcome. The decision to measure x or y is local and beyond the light cone of influence of each.
No matter what they chose to measure, the results are strongly correlated. So much so, that it is clear that you cannot predict every outcome of what the three parties measure. There just isn't a single pre-determined logically consistent assignment of outcomes before the actual measurement (there is a parity restriction of the outcomes).
But the measurements are consistent anyway. So, either there is faster-than-light communication which enforces the consistency, or indeed the outcomes cannot be decided until one of them measures something. It just isn't mathematically possible.
This is also independent of the physical theory by the way. You don't need Schroedinger, Dirac, or anything. Any physical theory that predicts measurements just like QM would will have this restriction. So hidden variables are incompatible with locality (no faster-than-light communication).
There is another out, Bell assumes markovianity(The sum across conditional probabilities requires divisibility), the discrepancy disappears if the particle trajectories while unmeasured are non-markovian/indivisible. See the work of Jacob Barandes. This view allows for determinism just fine and does not require ftl communication or global constraints.
If indeterminism gives us free will, it's like making a decision by rolling dice. I wouldn't call that free will.
One explanation that I heard of free will is that it depends on the complexity of a system. A simpler being might think it had free will while it is predictable to us because we see how it works. A much more complex being might be able to predict what we will do.
Just think of it intuitively: we don't hold babies or the insane responsible for their choices partly because they act randomly with no rhyme or reason, but you become responsible for your choices as you grow and your choices become more understandable and predictable in a way; in some real sense, you're more responsible the more deterministic you are!
In a sense, "Indeterminism" implied by probabilities at the quantum level can be said to give rise to "Free Will" as the strict chain of cause and effect is broken at the fundamental level. Since there are multiple possible outcomes from the same starting conditions, "Consciousness" may be the causal agent (Observer?) which selects one of the possible outcomes i.e. "choice due to free will". Think of it as Physics leaving all options open for an event (within bounds) and Consciousness selecting one among the set. Since the probabilities must add up to one, at the aggregate macro level it is predictable and deterministic while being unpredictable and indeterministic at the quantum micro level.
This makes sense and is self-consistent. But you speak of one single item in the range [0.0,1.0]. Might one speak of thousands - of millions - even of multitudes ? The "aggregate macro level" can be a combinatorial explosion of beauties and horrors.
You also imply (I think) that there is a finite space (bounded) for a variable to range in. Analogous to an LLM spanning and recombining its training materials. But what of the infinite - the unknown ? Of course one might say that we as hoominz are similarly bounded - that we are a variety of wetware LLM, limited by our own training materials (i.e. genes + sensory inputs + generated mental experiences).
But being of a spiritual bent myself, I ask: Where is the foot in the door for the divine ? Knocking at the door of fundamental unknowability - as you say, "unpredictable and indeterministic at the quantum micro level". If there is an intangible, immaterial element to our existence - call it a "soul" - then we might have identified the interface where "the rubber meets the road".
Obv others have considered this question at great length and in great depth.
Any human may have contradictory and uncorrelated aspects of personality, but nonetheless I find too difficult to believe such accusations.
Besides physics texts, Schrödinger has also written some more philosophical texts, which are very good and which show much more common sense than for many other physicists, past or present. The qualities of those texts seem quite incompatible with a deviant personality, like that of a paedophile.
In the absence of any concrete evidence, with all accusations based just on vague hearsay, I believe that it is much more likely that an accuser who has never done anything worthwhile is wrong, either non-intentionally or intentionally, than that the accused person, with a lifetime of great achievements, is guilty.
Moreover, even if the accusations of relations with young girls had been true, calling him a "paedophile" would not have been necessarily correct. What is classified as a paedophile in modern USA was not necessarily classified as such in other countries one century ago. In the past most European countries had much lower ages of consent than today, typically as low as 14 years.
"The guy was a paedophile and justified it" is a false sentence, because he certainly never admitted such a thing. The accusations were made post-mortem, based on hearsay, when he was no longer able to defend himself.
it was never proven in a court of law, nor have there been accusations of any kind in this regard in his lifetime. it seems that Moore couldn't read Schrödinger's shorthand and he had to rely on other sources [0] [0]https://science.orf.at/stories/3237287/
I had never heard that and just had a look at the Wikipedia article and those claims seem to be primarily based on one biography. Other research based on his journals disputes the image portrayed in the Moore biography.
He moved to Ireland in 1939. I am sure you are aware of certain events going on in Europe at that time that might have pushed him to leave Austria, as so many other famous scientists did...
It is crazy how readily people believe wild accusations with little credible evidence though. Not addressed at you specifically, just this whole subthread is wild.
The article mentions the great Physicist, Prof. S.N.Bose's take in a lecture delivered to the Indian Science Congress in 1944. It is titled "The Classical Determinism and The Quantum Theory".
The corresponding pdf can be found at Prof.S.N.Bose archive under Section 6 "Documents" titled "Presidential address at the Indian Science Congress, Delhi,1944 [Current Science, Vol XIII, No. 1]" - https://www.bose.res.in/Prof.S.N.Bose-Archive/
Prof. S.N.Bose is the Physics great after whom "Bosons", "Bose-Einstein Statistics", "Bose-Einstein Condensate" and even "Higgs Boson" are named - https://en.wikipedia.org/wiki/Satyendra_Nath_Bose
I find SN Bose's derivation of quantized distribution of energy levels so much more elegant than Plank's which reads more like a desperate hack to force a predetermined answer.
Planck admitted it himself that it was a hack he just postulated that there had to be quants. It was Einstein when he explained 1905 the photoelectric effect that quanta were accepted as "real"
Prof. Partha Ghose in his paper The Story of Bose, Photon Spin and Indistinguishability does a nice walkthrough of Bose's derivation - https://news.ycombinator.com/item?id=50195940
Wikipedia has a telling quote from the Physicist, Prof. Partha Ghose;
Bose's work stood at the transition between the 'old quantum theory' of Planck, Bohr and Einstein and the new quantum mechanics of Schrödinger, Heisenberg, Born, Dirac and others.
I have always felt that Prof.S.N.Bose never got full credit and acclaim for his achievements maybe because there were so many other greats at that time though Einstein recognized his originality.
Of course Bell later proved by experiment that quantum state cannot be explained as simply as a local hidden variable, no matter how it looks like. But these guys didn't know that yet.
Bell's theorem does not prove that. An alternative explanation is superdeterminism:
> https://en.wikipedia.org/wiki/Superdeterminism
"Weird" is underselling it.
If there are hidden variables, it is pretty obvious that they cannot be binary variables, but their nature must be that of spins, i.e. rotation movements, where the probability of interaction depends on the instantaneous values of the rotation angles of the interacting particles (which correspond to the phases of the "wave" functions describing the system).
So if the deterministic view is true, then it has to be a holistic theory. The hidden variables must be global, i.e. "accessible" throughout the universe. They cannot be attached to a particle as in Whittaker's model or Schrödinger's modification.
[1] https://en.wikipedia.org/wiki/CHSH_inequality
Much of the classic quantum mechanics, e.g. based on the Schrödinger or Dirac equations, is compatible with local hidden variables and I have not seen yet a precise account of which are the more recent axioms/assumptions that introduce an incompatibility with local hidden variables.
Thus I do not believe that the non-existence of local hidden variables has been proven beyond any reasonable doubt.
The GHZ/Mermin experiment refined the Bell argument into an "all-or-nothing" experiment with three parties. In that scenario, there are no probabilistic tests. Alice, Bob and Charlie each receive one particle (entangled, of course) and make a local decision to measure one of two quantities of that particle: x or y, each with a binary outcome. The decision to measure x or y is local and beyond the light cone of influence of each.
No matter what they chose to measure, the results are strongly correlated. So much so, that it is clear that you cannot predict every outcome of what the three parties measure. There just isn't a single pre-determined logically consistent assignment of outcomes before the actual measurement (there is a parity restriction of the outcomes).
But the measurements are consistent anyway. So, either there is faster-than-light communication which enforces the consistency, or indeed the outcomes cannot be decided until one of them measures something. It just isn't mathematically possible.
This is also independent of the physical theory by the way. You don't need Schroedinger, Dirac, or anything. Any physical theory that predicts measurements just like QM would will have this restriction. So hidden variables are incompatible with locality (no faster-than-light communication).
(my gut feeling was: it works till it does not work)
"In defense of the epistemic view of quantum states: a toy theory"
https://arxiv.org/abs/quant-ph/0401052
One explanation that I heard of free will is that it depends on the complexity of a system. A simpler being might think it had free will while it is predictable to us because we see how it works. A much more complex being might be able to predict what we will do.
In a sense, "Indeterminism" implied by probabilities at the quantum level can be said to give rise to "Free Will" as the strict chain of cause and effect is broken at the fundamental level. Since there are multiple possible outcomes from the same starting conditions, "Consciousness" may be the causal agent (Observer?) which selects one of the possible outcomes i.e. "choice due to free will". Think of it as Physics leaving all options open for an event (within bounds) and Consciousness selecting one among the set. Since the probabilities must add up to one, at the aggregate macro level it is predictable and deterministic while being unpredictable and indeterministic at the quantum micro level.
You also imply (I think) that there is a finite space (bounded) for a variable to range in. Analogous to an LLM spanning and recombining its training materials. But what of the infinite - the unknown ? Of course one might say that we as hoominz are similarly bounded - that we are a variety of wetware LLM, limited by our own training materials (i.e. genes + sensory inputs + generated mental experiences).
But being of a spiritual bent myself, I ask: Where is the foot in the door for the divine ? Knocking at the door of fundamental unknowability - as you say, "unpredictable and indeterministic at the quantum micro level". If there is an intangible, immaterial element to our existence - call it a "soul" - then we might have identified the interface where "the rubber meets the road".
Obv others have considered this question at great length and in great depth.
-I'll get my coat...
Worth the cost? I'd say not, but I'm generally an optimist.
Besides physics texts, Schrödinger has also written some more philosophical texts, which are very good and which show much more common sense than for many other physicists, past or present. The qualities of those texts seem quite incompatible with a deviant personality, like that of a paedophile.
In the absence of any concrete evidence, with all accusations based just on vague hearsay, I believe that it is much more likely that an accuser who has never done anything worthwhile is wrong, either non-intentionally or intentionally, than that the accused person, with a lifetime of great achievements, is guilty.
Moreover, even if the accusations of relations with young girls had been true, calling him a "paedophile" would not have been necessarily correct. What is classified as a paedophile in modern USA was not necessarily classified as such in other countries one century ago. In the past most European countries had much lower ages of consent than today, typically as low as 14 years.
"The guy was a paedophile and justified it" is a false sentence, because he certainly never admitted such a thing. The accusations were made post-mortem, based on hearsay, when he was no longer able to defend himself.
They must be based on identified witness testimonies, to have any kind of validity.
The article mentions the great Physicist, Prof. S.N.Bose's take in a lecture delivered to the Indian Science Congress in 1944. It is titled "The Classical Determinism and The Quantum Theory".
The corresponding pdf can be found at Prof.S.N.Bose archive under Section 6 "Documents" titled "Presidential address at the Indian Science Congress, Delhi,1944 [Current Science, Vol XIII, No. 1]" - https://www.bose.res.in/Prof.S.N.Bose-Archive/
Prof. S.N.Bose is the Physics great after whom "Bosons", "Bose-Einstein Statistics", "Bose-Einstein Condensate" and even "Higgs Boson" are named - https://en.wikipedia.org/wiki/Satyendra_Nath_Bose
Bose's work stood at the transition between the 'old quantum theory' of Planck, Bohr and Einstein and the new quantum mechanics of Schrödinger, Heisenberg, Born, Dirac and others.
I have always felt that Prof.S.N.Bose never got full credit and acclaim for his achievements maybe because there were so many other greats at that time though Einstein recognized his originality.