[jackhalford]

you have it wrong, QM is the only physical theory that has randomness as an inherent part, as compared to e.g thermodynamics where randomness is due to lack of information. It is proven (see Bell inequalities) that randomness in QM isn't due to lack of information.

You can't just wave away the collapse mechanism, what do you make of the double alit experiment? isn't the target "real" enough?

[konschubert]

The problem with the double slit experiment is that the target isn't treated as a quantum system.

That's why the wave function "collapses": Because it collides with the non-quantum target.

It's a useful approximation, but of course in reality, there is no such thing as a non-quantum thing.

And if you evolve the target's wave function with the wave function of the particle, then there is no stochastic collapse.

[choeger]

What you are saying is that whenever we, the observer, leave the QM model we use the collapse as a computational trapdoor function? Sounds like an interesting point of view.

But would that not also imply that we should be able to measure the quantum world with quantum devices? Say we have a quantum property that is extremely close to p=0.5. If we could invent a device to replicate that property perfectly and measure it repetitively we could then estimate ever more accurate boundaries for the "true" value of p, no?

[Diggsey]

You can't "copy" data in QM: operations can neither destroy nor create information.

[H8crilA]

> QM is the only physical theory that has randomness as an inherent part

It's either inherent randomness or just a deep hole in the whole thing (similar to the alien chess thought experiment problem). Personally I choose to believe that the theory is just incomplete because nobody can even define what a "measurement" really is, meaning in which cases what we do is a "measurement" and in which cases it is not a "measurement". I also think that this is what people like Feynman refer to when they say things like "nobody understands QM", it's actually "nobody understands the wave function collapse", the rest is just maths.

[konschubert]

Agreed.

The measurement is the theoretical duct tape between the "quantum world" and the "classical world".

But there is no such thing as a "classical world", it's just a useful approximation.

And therefore, there is also no such thing as a "measurement", it's also an approximation.

(Maybe not even an approximation, but maybe more like a projection...)

[TeMPOraL]

I'm voting for a deep hole.

My layman feeling wrt. QM, and Copenhagen school in particular, is that we're searching for too computationally simple mental models. Most other areas of physics - like GR, SR, thermodynamics - can get away with aggregating matter into points, perfect spheres, etc. because they're working in macro scale, but QM is trying to deal with the smallest bits of our reality. Now the boundary between QM and "classical physics" is one where your quantum system will interact with 10^{double digit} amount of other quantum-relevant bits. I have a feeling that searching for what constitutes "a measurement" in such scenario is missing the point, and even talking about the macro system being entangled with the test system is pretty much skipping over all the interesting bits.

[the8472]

> nobody can even define what a "measurement" really is

Isn't that the observer becoming entangled with the measured system?

[TeMPOraL]

It is, but that's in interpretations that also don't have the concept of "wave function collapse" in them. WFC is a feature of interpretations that considers measurement as something ontologically special.

[Jweb_Guru]

If you don't consider measurement ontologically special, then you need to somehow derive a physically meaningful Born rule without reference to measurement, which so far is something that AFAIK has only been accomplished in theories with large amounts of nonlocality and extra assumptions. The idea that people cling to the obviously false projection postulate out of obstinance is really strange to me, there just aren't very good alternatives available (at least not with the math fully worked out).

[konschubert]

I would love to consider measurement something ontologically special, but it's not possible because there is no well-defined definition for what a measurement is.

The definitions I have found always invoke the presence of a "classical system"/"observer".

But that just kicks the can down the road, because there is no well-defined definition of a "classical system" either.

[Jweb_Guru]

Sure. Everyone agrees Copenhagen is just kicking the can down the road. I'm just saying, let's not act like we have a ton of viable theories to fill out the rest of the road; in the meanwhile, we still have to perform measurements and make predictions, and the projection postulate is handy for that.

(It would help tremendously if we ever measured quantum states that weren't "collapsed", but as we've never done this so far it makes most of the stochastic collapse stuff hard to justify, even if it seems intuitively like the right approach).

[8note]

Once you design a turing machine that can solve the halting problem, I'm sure it'll be able to break Bell's inequalities too

Bell's inequalities show that there isn't a local state that can be there.

[H8crilA]

Turing machine as an abstract concept is known to not hold a solution to the halting problem. There's no question about that, the only question is how the abstract concept assumptions pertain to the real world (infinite tape? maybe a problem, maybe not?; is the execution speed bounded? or maybe we can somehow count to infinity by exponentially increasing the speed? things like that).

On the other hand nobody has any clue what the quantum measurement / wave function collapse actually is. There are theories/interpretations but no truly satisfying answers in the same way as for example Newton's equations were a satisfying answer to the elliptical movement of planets, even though we later found out in the 20th century that F ~ 1/r^2 was actually an approximation.

We simply don't know, and we have no idea when shall we know.

[konschubert]

Bell's inequalities talk about "measurements". But measurement's aren't real.

[ibab]

In the Everett/Many Worlds interpretation the appearance of randomness can be explained as an emergent phenomenon resulting from not being able to predict which part of the wave function we will end up in before running an experiment.

[Jweb_Guru]

The Everett/Many Worlds interpretation cannot reproduce the predictions of quantum mechanics without extra assumptions (e.g. the Born rule) that don't have any physical basis within the context of MWI.

[ibab]

Yes, you are right to point this out. There are some important details that are still being debated. Personally my impression is that the debate has advanced enough to the point where MWI can’t be outright dismissed based on this argument. There are multiple plausible explanations and the remaining difficulties have more to do with philosophy than physics.

Edit: To give one example of an approach that I think is promising: We start by describing the observer and environment through a density matrix (a probability distribution over possible wave functions) and introduce an interaction with a quantum system (e.g. a spin). Given a reasonable interaction, you can show that the entanglement in the combined state (observer, environment and spin) leads to the system approaching a state that is a probability distribution of entangled states where each probability corresponds to the Born rule. Interestingly in this case the probabilities emerge from our lack of knowledge about the microstate of the observer/environment, so it’s actually thermodynamic uncertainty.

[Jweb_Guru]

I'm not dismissing MWI, I'm just saying that current formulations either don't reproduce quantum mechanics or don't really address the existence of randomness within quantum mechanics.

[Jweb_Guru]

While I intuitively like the statistical approach you mention, under it the Born rule holds only approximately, so it should be theoretically possible to observe entangled states which we have never done--i.e. it produces different predictions from the Copenhagen interpretation of quantum mechanics, which means it's not strictly a different interpretation, but its own falsifiable theory. Like I said in another comment, if we ever do observe entangled states directly, people will jump on board one of these alternate explanations like lightning. But until we do, the question of why we never ever observe anything that doesn't look like collapse still needs mathematical justification.

[eigenket]

I am not aware of any interpretation that has the Born rule without assuming something equivalent to it. For example de Broglie–Bohm theory requires you to assume the original distribution of the particles follows the Born rule. QBists just postulate it, consistent histories just postulates it etc.

I am not particularly a many-world proponent, but I do not think it is fair to level this accusation as an issue for many worlds without bringing up that every other interpretation has the same "flaw".

[Jweb_Guru]

AFAIK it can in fact be derived through Gleason's Theorem under the assumption of noncontextuality, so I don't think it's fair to say that nobody can derive the Born rule without assuming it (many people have issues with noncontextuality but that's very much a philosophical thing). The thing you have to demonstrate is that a probability measure actually connects to physical observables in some way, and this is the part that is difficult (and as far as I can tell MWI does nothing to resolve this conundrum).

[eigenket]

Gleason's theorem also makes a big assumption when you require that the measurement outcomes are associated with POVM elements (or projection operators if you don't like POVMs). I lumped that in with "assuming something equivalent to it" since Gleason's theorem (at least by my understanding) is exactly the statement that assuming non-contextuality+POVMs/POMs is equivalent to assuming Born's rule.

Although its really cool I don't think Gleason helps you tie any particular interpretation to the Born rule, since you still have to make a jump to tie your measurement outcome to a POM/POVM element.

As far as your last sentence goes, this is sort of what I was trying to argue in my comment above. The "part that is difficult" that you identify as being unresolved by MWI is also completely unresolved by pilot wave theory, or qbism or consistent histories or any other interpretation (as far as I am aware).

[Jweb_Guru]

I think we're in agreement there (though IMO it's highly nonobvious that noncontextuality+POVMs automatically get you the Born rule, so I don't think it's "cheating" to assume that--obviously any set of axioms that let you derive Born will have such a property!). I was mostly saying, I don't think MWI helps us understand where the probabilities come from any more than any other interpretation--you need something more. And if you can't identify where the probabilities come from, then saying your theory is "deterministic" rings fairly hollow to me.

[GistNoesis]

What is usually misunderstood about QM is that QM isn't a model of the world.

QM is a model of "what we can observe from the world" based on "what we can observe from the world".

QM is a model of "accessible" information.

What laymen usually wants is to understand how the world evolve.

What QM physicists tell them is there exist some inaccessible information, but using accessible information we have, we know how to predict all the accessible information (albeit stochastic-ally).

The typical example to help computer scientists to understand is the seed of a pseudo-random generator in an online casino. The players will never be able to access the seed, therefore the best they can do is make decision based on the value of the generated random numbers they observe and their probabilities.

Bell inequalities are a consequence of this modelisation. They are a refurbishing of Boole's inequalities, a theorem about probability which only bound those who use probability.

The usual fallacy forward is telling QM is a non-local theory, classical local theory can't violate Bell inequalities, Bell inequalities violations are observed in the real world, therefore the world is not local...