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Why Quantum Mechanics?

scottaaronson.blog

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Re: Why Quantum Mechanics?

#191

Post by kwhitefoot »

anon_123g987 wrote: post #172
stared wrote: post #135

> Why didn't God just make the universe classical and be done with it? What would've been wrong with that choice? I hear it over and over and still don't understand the premise. Classical mechanics is not something sacred. It is our first serious model of physics. Our first approximation is based on the scales at which we operate and our senses as humans. Furthermore, even "regular" quantum mechanics is a non-relativ…

> Classical mechanics is not something sacred. It is our first serious model of physics. Just a sidenote: it is at most our second serious model. Aristotle's Physics has a bad rap, but it's "a correct and non-intuitive approximation of Newtonian physics in the suitable domain (motion in fluids), in the same technical sense in which Newton theory is an approximation of Einstein's theory". See "Aristotle's Physics: a P…

You saved me the trouble of pointing out Rovelli's defence of Aristotle's physics.

I think it should be required reading for anyone interested in the development of physics.

Re: Why Quantum Mechanics?

#192

Post by PaulDavisThe1st »

platz wrote: post #183
breuleux wrote: post #165

Earlier quoted context omitted.

I mean, if QM wasn't true we would observe something else, wouldn't we? I don't understand how this is a meaningful question.

No, he's asking how to fit the data we do observe , and why QM is the obvious conclusion compared to other theories that fit the data that we do observe .

this is absolutely not what he is asking. his questions explicitly say to take QM as a given, but then move on to "why couldn't the universe be some other way?" He is not asking about other theories to explain the data we have; he is asking whether a substantively similar universe could have conceivably been built without QM.

Re: Why Quantum Mechanics?

#193

Post by naasking »

guerrilla wrote: post #189
naasking wrote: post #178

Earlier quoted context omitted.

It's definitive that you have to give up locality (Bohmian mechanics), counterfactual definiteness (Copenhagen and others), or statistical independence (Superdeterminism). It's not definitive at all about local hidden variables.

> It's not definitive at all about local hidden variables. What? > To date, Bell tests have found that the hypothesis of local hidden variables is inconsistent with the way that physical systems do, in fact, behave.

Bell's theorem assumes statistical independence in its proof that local hidden variables can't reproduce QM. Superdeterminism violates statistical independence, therefore Bell's theorem does not rule out a superdeterministic local hidden variables theory, like this one:

https://arxiv.org/abs/2010.01327v5

Re: Why Quantum Mechanics?

#194

Post by platz »

cannabis_sam wrote: post #152

>Why didn’t God just [MAKE THE PLANETS ORBIT AROUND EARTH] and be done with it? What would’ve been wrong with that choice? Okay then, can you explain the math behind that solution? How in the world does the words “God”, “just” and “be done with it” in anyway whatsoever help elucidate this issue…?

You're either getting caught up in the incidental religious reference, or failed to interpret Scott's conciseness. See this comment for elaboration on exactly what kind of counterfactual Scott is asking https://news.ycombinator.com/item?id=30117928 . He's asking about a hypothetical alternative in a very specific way, which is to see whether it sheds any light on the logical foundation of QM, not just to consider alternatives for the sake of considering them in themselves.

Scott's aim is to understand QM better.

Re: Why Quantum Mechanics?

#195

Post by guerrilla »

naasking wrote: post #193
guerrilla wrote: post #189

Earlier quoted context omitted.

> It's not definitive at all about local hidden variables. What? > To date, Bell tests have found that the hypothesis of local hidden variables is inconsistent with the way that physical systems do, in fact, behave.

Bell's theorem assumes statistical independence in its proof that local hidden variables can't reproduce QM. Superdeterminism violates statistical independence, therefore Bell's theorem does not rule out a superdeterministic local hidden variables theory, like this one: https://arxiv.org/abs/2010.01327v5

Oh, thank you. I've been meaning to check her blog on this.

Re: Why Quantum Mechanics?

#196

Post by Enginerrrd »

MichaelRazum wrote: post #80

Im just taking the easy course of QM by Suesskind. He had an example like you have two coins and give them randomy to your kids. The they move far away. Then one kid discovers what it got, it knows what the other has. So what I dont get is why QM you could argue that there is some hidden shared state. Guess this is a typical question. But anyway I‘m somehow not convinced that it is really random.

Others have provided good examples, but I'll put it in a way that might make more sense, albeit with a slightly less correct simplification.

>So what I dont get is why QM you could argue that there is some hidden shared state.

Because when you measure one of the coins in a particular way, there's an established probability that you'll change it some percentage of the time. (I.e. if you measure in this way 100 pre-prepared heads, you'll get some percentage of tails. [think of this as say measuring polarization of some photons after they've passed through a filter oriented to 0 degrees, by then placing a filter oriented at 45 degrees and seeing how many go through)

However, even after you do that measurement, you'll find that the other entangled photons are still correlated with the result of the ones you measured. So there's something "extra" going on, which is QM entanglement. I.e. that shared state.

You can actually see the effect of the "changing states" (not really what's going on, but if you were assuming the behavior was classical, it's what you'd start with. If you place two polarized filters at 90 degrees to each other and shine a light through it, you'll get basically zero photons out. Then, without changing anything else, you can put a third filter in-between the two but oriented 45 degrees from the others, and all of a sudden, about 25% of the light will pass all the way through the three filters! It's pretty cool. You could explain THAT part classically by saying that you are "changing the state of some of the photons by measuring them". But then... if you do that, you can't explain the correlation that happens when you do that with entangled photons, and classical explanations just don't really cut it unless you give up something like non-locality.

Re: Why Quantum Mechanics?

#197

Post by stared »

VirusNewbie wrote: post #187
stared wrote: post #145

Earlier quoted context omitted.

To elaborate on this a bit: One may argue that "a state" is a simpler concept than "a superposition of all state". Even in pure mathematics [1], I don't think that (say) real numbers are less fundamental than natural (unlike Kronecker in "Natural numbers were created by God, everything else is the work of men"). What's true for the set theory route, does not need to be true for any possible mathematics, including tho…

Really interesting to read your post, despite half of it being a bit over my head. That is quite cool you got to have a long conversation with Penrose! As to your statement about platonism or mathematical realism, I'm curious about something. Surely most axiomatic systems are a choice, so I can understand why we would say they're man made (euclidean geometry, ZFC, etc). However we also know about 'meta axioms', which…

I am not sure what is a "meta axiom". Could you give an example for one?

Re: Why Quantum Mechanics?

#198

Post by eigenket »

deltaonefour wrote: post #42
ketralnis wrote: post #13

Earlier quoted context omitted.

Why does a^2+b^2=c^2 for a right triangle? It's just axiomatic, right? Not exactly. It's only true in flat euclidean geometry. If General Relativity holds then we're only in a flat spacetime if the total energy content of the universe is in some range of values, otherwise the universe could be the 3d equivalent of a sphere or it could be a hyperbolic shape. In neither of these configurations do right triangles behave…

>Why does a^2+b^2=c^2 for a right triangle? It's just axiomatic, right? Pythagorean theorem is not an axiom. It's a theorem. >Not exactly. It's only true in flat euclidean geometry It's a theorem for Euclidean geometry. >So a^2+b^2=c^2 if and only if the big bang happened to have some particular initial conditions. It's not axiomatic, and studying _if it's even true_ tells you a lot more than you'd expect. For theore…

Slightly off topic but you can take the "Pythagorean theorem" as an axiom - given the first 4 Euclidean axioms it turns out that the 5th axiom is exactly equivalent to the Pythagorean theorem. You can equivalently start with the parallel postulate and derive Pythogoras or start with Pythagoras and derive the parallel postulate.

Re: Why Quantum Mechanics?

#199

Post by eigenket »

6gvONxR4sf7o wrote: post #40
sam-2727 wrote: post #18

Earlier quoted context omitted.

> Can you do QM with just the real valued probability distribution? You can't. The key fact is that other observables, such as momentum, depend on the complex part of the wave function.

But those have real valued probability distributions too, right? Does modeling the evolution of the joint distribution of all the observables not count?

There is not really a meaningful joint distribution. Some quantum observables are incompatible with each other which essentially means they can't be assigned simultaneous values.

More precisely a quantum observable is a map (a function) that takes in a quantum state and outputs a probability distribution, representing the probabilities of the various outcomes you could get if you measure that observable on that state. The equivalent statement is also true of classical observables and classical states.

Under classical rules it turns out that if you have many observables acting on the same system you can come up with a joint observable, that maps a state to a joint probability distribution for all the observables. For incompatible quantum observables this is emphatically not the case. Given two quantum observables there is generally not a joint observable representing simultaneous measurement of them.

Re: Why Quantum Mechanics?

#200

Post by platz »

PaulDavisThe1st wrote: post #192
platz wrote: post #183

Earlier quoted context omitted.

No, he's asking how to fit the data we do observe , and why QM is the obvious conclusion compared to other theories that fit the data that we do observe .

this is absolutely not what he is asking. his questions explicitly say to take QM as a given, but then move on to "why couldn't the universe be some other way?" He is not asking about other theories to explain the data we have; he is asking whether a substantively similar universe could have conceivably been built without QM.

> he is asking whether a substantively similar universe could have conceivably been built without QM.

thats what I wrote QM must be the obvious conclusion (compared to X)

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