## Good physics

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If, like me, you've heard about, and read up on, the famous Bell Inequality experiment, then my guess is, unless you're physics grad, that you won't understand it. I, too, don't understand it, but my understanding of it is now a little better than it was before listening to the presentation below.

OK, there's a challenge. I'll see if I can explain Bell's Theorem on an intuitive level. I'll use coins instead of particles.

Suppose Alice and Bob have one each of a pair of coins that have been prepared in an entangled state. Due to their entanglement, if the coins are measured by devices tilted at the same angle (say, 120 degrees) then Alice and Bob will observe the same outcome, i.e., they will both observe heads or they will both observe tails. Whereas if the coins are measured by devices tilted at different angles then, per the probabilities predicted by QM, they may or may not observe the same outcome.

What explains those correlations, even when the coins are separated by large distances? Perhaps the coins communicate instantly (Einstein's "spooky action at a distance"). Or perhaps the coins have definite orientations (i.e., heads or tails) for every possible measurement angle - which any actual measurement simply reveals.

Let's assume the latter (called local hidden variables) and test it. The experiments will involve a measuring device for each coin. Each measuring device can be tilted at an angle of 0, 120, or 240 degrees prior to measurement. Only experiments where the relative angle between the measuring devices is 120 or 240 degrees will be conducted (we already know that the outcomes will be the same when the relative angle is 0 degrees, i.e., when the devices are tilted at the same angle).

Now consider the possible coin orientations for each potential measurement angle. (1) They could be heads for all three angles. (2) Or tails for all three angles. (3) They could be heads for two of the angles and tails for the other angle. (4) Or tails for two of the angles and heads for the other angle. That exhausts all the possibilities.

For the initial two cases, measuring each coin at different angles will always return the same outcomes (e.g., both heads, or both tails). For the final two cases, measuring each coin at different angles will return the same outcome 1/3 of the time (e.g., for HTH the three possible combinations are HT, TH or HH).

Note how the measured coin orientations are the same either 100% of the time or 1/3 of the time. That's Bell's inequality - the measured coin orientations are the same for at least 1/3 of the times that the experiment is performed.

However QM predicts the same outcome 1/4 of the time (cos^2 120 = cos^2 240 = 0.25). Thus QM violates Bell's inequality.

When this is tested empirically, the same measurement outcomes are observed 1/4 of the time as QM predicts. Therefore the assumption of local hidden variables is mistaken.
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I get it. And with moderately careful reading, great job!
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:ok: Well said!
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I think the question of the nature of the wave-function is a metaphysical question, or even THE metaphysical question implied by modern physics. A lot of the controversies revolve around that point.

Nice. That's pretty much what I've come to think and I can see how this model can kickstart many a speculative journey.
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...per the probabilities predicted by QM...

So when you say the probabilities that QM predicts, do you mean via the Schrodinger wave function and/or matrix mechanics?

I think the question of the nature of the wave-function is a metaphysical question, or even THE metaphysical question implied by modern physics. A lot of the controversies revolve around that point.

My interest is piqued by the wave function also. From what I've learned, geometry of the wave function is analogous to drawing a smooth curve on a linear graph based on the averaging of standard deviations, a "continuous" approximation to what is essentially quantized or "lumpy" but in a very specific, replicable way that has some wavelike properties. Is that accurate?
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I think it's indisputable that the 'wave function' is not ACTUALLY a wave. It's a distribution of probabilities. When you ask the question, 'where is the object', then the wave function allows you to determine the probability of where it is, but it's not as if it's just hidden there, position undetermined. It's not in a particular place until it's measured. That's the 'collapse' function, the avoidance of which is what gives rise to the 'many worlds' interpretation.

Check out Nature Loves to Hide, Shimon Malin https://g.co/kgs/PXbiXG . Expensive book but definitely worth the \$.
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Incidentally apropos of physics both good and bad :naughty: , this Scientific American profile of Hugh Everett is a must read. It’s semi-paywalled i.e if you’ve visited the site recently it might ask for a log in but if not you should be able to access it, and it’s so worth reading; so Dr Strangelove.

One of the odd spin-offs of this, is that David Deutsch is Everett’s #1 fan. His first book, Fabric of Reality, or something, is an impassioned plea for the reality of many worlds, and an implicit condemnation of all the bone-headed dinosaurs who can’t accept it. And Deutsch, let us recall, is the main theorist behind quantum computers. Which makes me wonder if the feasibility of the quantum computer is bound to the validity of the Many World’s interpretation. Waaay beyond my paygrade, but I do wonder.
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Thanks!

BTW, it's worth noting that Bell's Theorem makes three assumptions - locality, counterfactual definiteness (i.e., hidden variables or classical realism) and freedom-of-choice (in what measurement to perform).

So rejecting hidden variables need not imply rejecting locality. For example, Copenhagen, RQM, QBism, Many Worlds and Consistent Histories are all local interpretations.

So when you say the probabilities that QM predicts, do you mean via the Schrodinger wave function and/or matrix mechanics?

Yes.
• 478

To those who might know, does the following interpretation of Schrodinger's wave function have any validity: predicted proportion of behavior within a reference frame at the quantum scale, whether construed in terms of position, momentum or whatever, essentially modeling the average amount of energy within that reference frame relative to the rest of the wave function. So wave function collapse is a kind of change in relative energy that can be induced by measurement etc., not a split into separate worlds.
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One of the odd spin-offs of this, is that David Deutsch is Everett’s #1 fan. His first book, Fabric of Reality, or something, is an impassioned plea for the reality of many worlds, and an implicit condemnation of all the bone-headed dinosaurs who can’t accept it.

Your comment reminded me of this quote:

I think the argument for Everett’s theory is incontrovertible now. It seems to me that there is as much evidence for the existence of parallel universes as there is for the existence of dinosaurs. The logic for the evidence in both cases is very similar. No-one has ever seen a dinosaur, we’ve only seen fossils, and similarly, no-one has ever seen a parallel universe, but we have seen interference phenomena. And just as there is no other explanation of dinosaurs, so there is no other explanation for interference phenomena. And what most physicists do nowadays is they adopt what is called the “shut up and calculate” interpretation. Which says just use the equations to predict the outcome of experiments but do not ask what brings about those outcomes. Which is just the same logic as saying, “Do not ask what brings about fossils.”

To those who might know, does the following interpretation of Schrodinger's wave function have any validity:

I don't know - are you referring to an objective collapse theory?
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Which is just the same logic as saying, “Do not ask what brings about fossils.”

No, it's not just the same. It's a false analogy. Fossilised remains are objectively real. The interpretation of observations in physics is inferential. I think there's something deeply, profoundly wrong about Deutsch's philosophy, although of course, who am I to question a wunderkind.

My philosophical interpretation follows Heisenberg's. He points out that sub-atomic objects neither exist, nor don't exist; their existence is described in terms of probabilities, so they have a degree of existence, which is actualised by measurement. When measured, what is potential becomes actual. And the act of observation is inextricably connected with that. This is what Deutsch cannot accept, because ultimately he's a materialist. So he'd rather accept sliding doors than idealism.
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So he'd rather accept sliding doors than the idealism.

How does either option there amount to a form of idealism?
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I watched that forever ago already. I just skimmed through it again. Ok quantum wave functions collapse when observed. Where is the idealism?
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And you still have to ask?
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Yup. The video hasn’t shown that “observer” has anything do with minds. Or what exactly is and isn’t an observer.
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Well, if you missed the part where he said 'JUST BY OBSERVING' then there's probably nothing to talk about.
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I think it's worth explaining the "stakes" in bell's inequality.

A fundamental rule of physics is locality, which just means information doesn't travel faster than the speed of light, which is another way of saying causes don't makes effects at faster than the speed of light. So "information travelling" is the same thing as "causes propagating" in these conversations.

Quantum correlations between distant events, such as a material, say a crystal, that produces pairs of particles going in different directions but when both are measured the pairs always have something correlated, such as opposite spin or polarization or what have you: measuring one particle allows a scientist at detector A predict with 100% certainty a measurement by another scientist at detector B, and A and B can be as far apart as the scientists can do.

So, we "know" something instantaneously about B from observations at A, which on first viewing seems to say information has traveled faster than light. Of course, if we inspect closer we don't "really know" anything about B because we're making the assumption that scientist at B makes a measurement, the device still works, a whole bunch of other assumptions. Rather, we're just predicting something at B based on our knowledge of A; but this isn't unusual. We predict things about other places and times regularly; that we predict the sun rises tomorrow does not mean information has traveled from tomorrow to today to allow us to make that predictions. So, already, with this more careful viewing, we're just predicting and not "exchanging information"; and these sorts of experiments can never be setup in such a way to allow the scientists to communicate faster than light. So locality isn't in trouble.

However, we are still left to wonder if the thing about particles at A and B is determined when the first scientists measures or whether it was "really set" at the crystal or whatever creating the particle pair. It's much simpler to imagine the incoming particle responsible for the key event, hits the crystal and two particles emerged with the correlated features and travel to scientists at A and B already with these values of interest. This intuitive way of looking at it is thus called "hidden variables", as the values we're interested in are there, just hidden from us until we measure them and so know about them.

Quantum mechanics is highly wound up in measurement uncertainty and the logical implications of this; however, for a while one could still wonder if the things being measured really become "definite" when they are measured or are already definite and we then just measure them to know something about this pre-existing definiteness. Just as on our normal human scale we measure a door to find out what it already is, not somehow to make nature take on some value at the same instant we measure it.

If the door is "already a meter" wide before we measure it, then there's some variable of definite value that is hidden from us but revealed to us when we measure it. For doors, this makes sense. However, for particles, quantum mechanics strongly suggests things really are uncertain until measured, that nature only takes on the definite value we are trying uncover in our act of uncovering it, but, if so, then correlated events must somehow "talk" to each other instantaneously; since particle at B cannot know ahead of time what scientist at A will measure and so prepare itself to be measured in the expected way; it is equally uncertain as perhaps scientist B will measure it first and so making B a clear value then forces A to take on the corresponding value when it's measured. Quantum mechanics (for a while) only "suggested" this instantaneous resolution of values at faster than light travel, because the "hidden variables" weren't needed to do quantum mechanics, so if they can be thrown out anyway and quantum mechanics is already quite bizarre, then, once you're "in it", it becomes intuitive to just not care about locality in this case (as it can't be used to communicate anyways, so who cares).

But people did care!

However, for a while, how to resolve the debate of whether there are hidden variables -- which seems question setup to be something in principle that can't be resolved by experiment, similar to resolving if there are ghosts we can't see or ever detect ever around or not by experiment -- had no experimental resolution.

Bells inequality is a proposed way to resolve the debate with experiment and prove the quantum entanglement realm is non-local and correlations are "made to exist" instantaneously without the cause needed for the correlation to happen travelling at slower than the speed of light (as opposed to if the values of the particle are set when the particles are created in an entangled state, then the information travels with them, since they already have the values to be discovered later, slower than light, to the detectors and so our usual visualization of cause remains local). Of course, we can change our intuition of cause to basically exclude these correlations, because scientist A is not able to use this effect to cause anything different to happen at B faster than the speed of light; so if cause is effecting events, then cause remains local and we just don't think about it more than this (the "shutup and calculate" view of physics).

I say "proposed way" because the experiments can involve crazy loopholes if not setup super carefully, and it get crazy complicated, and I'm not sure if there's consensus about what all the loopholes even are and if experiments have closed them all. Generally, new bell inequality experiments aim to close one loophole. If there's a proof about whether all the loopholes are for sure known about, I'm not aware of it. It's not like we're doing something like math and proofs in physics, obviously not: that would be crazy talk.
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what exactly counts as an observation?

If I rig a bomb to explode if and only if the electron goes through the right slit, will the bomb explode? Will it only explode if a conscious agent could hear the explosion if it happened or is affected by it in some way? Etc

It talks specifically about consciousness at 16:38

The idea that consciousness plays any role is one of countless interpretations. It is not implied by anything you’ve said here. And it’s not even popular.

To take a bit from the video:

“What was happening in the universe before conscious observers evolved?”

“What exactly counts as a conscious observer?”

“According to Einstein’s theory of relativity, different events can seem to have happened at different times depending on observer. If the events were quantum wave collapse, which observer collapsed the wave functions?”

And many more issues.

Put another way: There is probably a reason most quantum mechanics interpretations that bring in consciousness are dismissed as pseudoscience nowadays by most experts. That being that it’s an unnecessary, problematic and poorly defined assumption.
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Put another way: There is probably a reason most quantum mechanics interpretations that bring in consciousness are dismissed as pseudoscience nowadays by most experts.

Ah, but do you have a non-pseudoscientific definition of expert.

Aie, there's the rub. But don't worry! I nominate myself to fill this power vacuum.
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Ah, but do you have a non-pseudoscientific definition of expert.

Someone with a Phd or doctorate at least.

And it’s not the domain of science to define what “expert” means. So there is no scientific or pseudoscientific definition. But that’s what I have in mind when I say “expert”.
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Someone with a Phd or doctorate at least.

We can devise an experiment to resolve who likely has these socially constructed tittles, but to propose an "experiment" that bestows the claims to knowledge we desire, in our version our science today, means we need an experiment and it needs to be done multiple times and be peer-reviewed by existing experts ... but we don't know who's an expert yet, so the experiments cannot be done and pass into our version of science.

And it’s not the domain of science to define what “expert” means. So there is no scientific or pseudoscientific definition. But that’s what I have in mind when I say “expert”.

If it's a claimed fact about the world, then it's clearly psuedoscience. That proposed empirical facts about the world (we can observe this PhD degree on the wall of this university and agree this person is an expert) can be a state of knowledge neither scientific nor psuedoscientific is itself pseudoscience gobblediegook.
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There is probably a reason most quantum mechanics interpretations that bring in consciousness are dismissed as pseudoscience nowadays by most experts.

Results of a straw poll taken at a conference of physicists at a Quantum Foundations meeting (by Anton Zelliger et al):

The Copenhagen Interpretation, associated with Bohr and Heisenberg, is shown to be the most accepted. It doesn't mention consciousness as such, but says that the observer has a role in the experimental outcome, which calls into question the purported 'mind-independent' nature of the result.

“What was happening in the universe before conscious observers evolved?”

See this post.
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but says that the observer has a role in the experimental outcome

Sure. But doesn’t say “conscious observer” does it? I’m sure if you asked those same physicists of consciousness was required to collapse wave functions you’d get an overwhelming “no”.

which calls into question the purported 'mind-independent' nature of the result.

If only conscious observers were able to collapse wave functions, it would. But again, the theory says nothing like that. Only that an observer is required.

It is analogous to wearing a pair of spectacles, without which nothing can be seen, and then looking through them, and demanding 'show me where in this picture there are spectacles'.

No what’s being asked is “What would the world look like without spectacles”. The answer is “nothing can be seen” and that’s a problem. I’m not demanding you show me consciousness, I’m asking what the world would look like absent of it. The common answer is: same as it always has been. If some apocalyptic event killed every conscious agent in existence, would all quantum states remain forever unresolved?

In your theory, consciousness is required to collapse wave functions. So what happens when no consciousness has evolved yet? Well, no wave functions have collapsed. What does that even look like? When everything is everywhere.
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We can devise an experiment to resolve who likely has these socially constructed tittles

You mean looking at their resumes?

If it's a claimed fact about the world

No, it’s a definition. An expert is someone with a PhD or doctorate. We can confirm whether or not someone has this by looking at their resume. What’s so difficult here?
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You mean looking at their resumes?

You don't seem to be able to extricate yourself from your pseudoscientific beliefs about the world.

We can look at their resumes, I agree. Whether there is some difference between expert and layperson about our empirical world, relating to our state of knowledge as such and not features of society we are told about without experimental evidence, is what I disagree with.

No, it’s a definition. An expert is someone with a PhD or doctorate. We can confirm whether or not someone has this by looking at their resume. What’s so difficult here?

So much difficulty. See above.

You can't just define experts into existence in any meaningful sense.
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The video hasn’t shown that “observer” has anything do with minds. Or what exactly is and isn’t an observer.

A physical observer is an objective instrumental observer not a person. Mathematical or plain language interpretation of the observations translates objective observation into a public hypothesis. Interpretation requires not one mind but the agreement of expert minds, which takes it from private opinion or belief into a public factoid.
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not features of society we are told about without experimental evidence, is what I disagree with.

Seeing the resume is experimental evidence.

And how do you think they got said features? If not by actually knowing what they're talking about (with maybe a few rare exceptions)?

You can't just define experts into existence in any meaningful sense.

So no experts exist I guess.....

Have a good one.
• 478
are you referring to an objective collapse theory?

Those theories make sense to me. As the article says, "the absolute square of the wave function is interpreted as an actual matter density". I'd be inclined based on what I've read to interpret it as a multifaceted energy density that models waves and wavicles, and this makes it more intuitive to comprehend how degrees of freedom (variable rates) for both local and nonlocal motion of many types simultaneously obtain. According to the web: "quantum tunneling seems to happen instantaneously - or at least, so incredibly quickly that it's essentially instantaneous": measurable in attoseconds, or quintillionths of a second. So quantum nonlocality is probably never absolutely instantaneous, but in many contexts the measuring devices are not sensitive enough to register time elapsed. This doesn't mean that quantum processes aren't local - interactively correlated - in some sense, but its a completely different sort of physical interaction.
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A physical observer is an objective instrumental observer not a person

Bingo!

As the article says, "the absolute square of the wave function is interpreted as an actual matter density"

Really?

"The square of the wave function, Ψ^2, however, does have physical significance: the probability of finding the particle described by a specific wave function Ψ at a given point and time is proportional to the value of Ψ^2." (Britannica)
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