In what sense is QM "not understood"?

stevendaryl

I would say that there are aspects of the theory that are not understood, either. We have the recipe for using quantum mechanics, which is:

1. Between measurements, the system evolves according to Schrodinger's equation.
2. Measurement of any observable results in an eigenvalue of that observable, with probability computed from the wavefunction.
3. After a measurement, the system is in the eigenstate of the observable corresponding to the eigenvalue measured.

What's really not understood, at a theoretical level, is what constitutes a "measurement". We have a rule of thumb answer, which is that an interaction counts as a measurement if it leaves an irreversible record, such as a photograph, or a bubble in a bubble chamber, or a click in a Geiger counter, etc. But I wouldn't say that there is a very good theoretical understanding of what a measurement is.

harrylin

On this I agree with Doofy: I still would feel that SR is "magic" if I had not studied and understood its historical development. Regretfully I don't know much of the historical development of QM and its motivations (and it's still like magic to me).
Exactly.

krd

It depends on your learning style. I'm out of college a very long time. And I'm only coming back to my physics now. I find I'm learning much more, and having a much better understanding of the physics by studying the history. It's helping me re-learn my physics. And sometimes I find little tid bits that I would have missed otherwise. And it's sometimes just little tiny ideas, that link other pieces together.

Learning the formulas and learning how to execute them is not enough. I have seen a few instances where professional scientists - who can do all the fancy calculus - have had misunderstandings of the fundamental theory - or have had gaps in their understanding that shouldn't be there. It's bad science, to know all the names, know all the maths, but have misunderstandings of the underlying theory.

I don't know how much the interpretations may change - but physics and chemistry, the way those subjects are taught in schools, the teaching materials probably need to be completely gutted and rebuilt from the ground up. There might be better ways to describe physics and chemistry to make everything fit more coherently.

stevendaryl

But often theoretical developments happen when someone just starts "playing around" with ideas and with mathematical formalisms, and then noticing that something neat comes out of it. The context for the development of quantum mechanics was the observation that the energy levels of an electron in a hydrogen atom took only discrete values. So various people started looking at various ways that a discrete set of values can be produced.

Bohr's idea was just the ad-hoc rule that the angular momentum of an electron must be an integer multiple of h-bar. (This could be heuristically justified in terms of de Broglie's notion of matter/wave duality--only for certain values of angular momentum would the corresponding "matter wave" be a standing wave.)

Heisenberg noted that discrete eigenvalues pop up in matrix problems. So maybe operators like position, momentum, angular momentum, energy, etc., can be represented by matrices, or generalizations.

Schrodinger noted that discrete eigenvalues pop up in solutions to differential equations, so maybe there is some kind of function associated with the electron that satisfies a differential equation that produces eigenvalues corresponding to the observed energy levels.

These ideas were important, but they were really along the lines of guesses. It is really barking up the wrong tree to look to these founders for answers about the true meaning of quantum mechanics. Heisenberg had no more idea about the implications of noncommuting observables than anybody else did. Schrodinger had no more idea about the true meaning of the wave function than anybody else did. They were motivated by wanting to get discrete values for observables. I don't think that there was anything deeper involved. So that's the sense in which the historical point of view is of limited usefulness--the founders don't necessarily understand the theory any better than anybody else.

Fredrik

I don't share this view. Those questions are really about why things are happening, rather than about what is happening. When we solve the equation of motion of a two-body gravitational system, we find elliptical orbits, and no one doubts that it makes sense to say that an elliptical orbit is an approximate description of what the first object is "doing" near the other.

The way I see it, non-relativistic classical theories are all defined in a framework defined by Galilean spacetime. The Newtonian, Lagrangian and Hamiltonian approaches are just three different ways to consistently add matter to an empty spacetime. A specific theory in that framework is defined by its equations of motion. One way to find a new theory in this framework is to simply guess an equation of motion. (Actually, that is the Newtonian approach). The other approaches are just ways to eliminate the worst guesses. So I don't find it surprising that these approaches don't tell us anything about what's actually happening. They're not even part of the theories; they are just tools that help us eliminate the worst candidates for new theories.

In my opinion, it's that it assigns non-trivial probabilities (not always 0 or 1) to measurement results even when the state is pure (i.e. when we have maximal information about the preparation procedure). This inevitably raises questions like this: "If the state describes what's happening to the system, and assigns non-zero probabilities to two mutually exclusive measurement results, doesn't that mean that the system is actually doing both of those things?"

harrylin

Thanks for giving a summary - and I would appreciate to read a detailed, in-depth article superior to textbook summaries. Also thanks for preserving part of my original comment which I completely lost due to an editing mistake.
Likely so; still I expect that there is more to be found in a multitude of opinions and approaches of people who didn't really understand it, than in a single opinion of someone who also doesn't really understand it.

Fredrik

I agree. That's why I wrote "very well" instead of "completely". There are certainly mathematical theorems left to be proved, and I don't think we have a perfect understanding of how theories of interacting matter are to be defined in the framework of quantum mechanics. (I think it's perfectly understood in the case of non-interacting particle theories. I'm not sure about the case of interacting quantum field theories. I'm pretty sure that we don't have the answer when gravity is involved).

I don't know. I find that pretty satisfactory actually. Not in the sense that I wouldn't want to have a better understanding of it, but in the sense that I believe that this is the best we will ever be able to do without a better theory to replace QM.

harrylin

That shape was first proposed by Keppler who gave the correct equation first. However, if I correctly recall, I read somewhere that Keppler complained that he did not understand it. Later Newton's theory of gravitation gave a first feeling of understanding of the "why", not just due to equations but due to identifying a physical cause to which those equations relate. But perhaps that is what you meant?

stevendaryl

Yeah, I agree that the recipe for using quantum mechanics, using an informal notion of what counts as measurement, works pretty well, but I wouldn't say that the theory behind it is well understood. In particular, if measurements are themselves interactions (and what else would they be?) then they should themselves be described by quantum mechanics, rather than having a separate rule (wave function collapse to an eigenstate following a measurement).

Ken G

Yes, it is easier to describe what is happening in classical systems, but I would argue that even Kepler did that-- before there even was anything we could call classical mechanics. So we cannot argue that we understand the theory of classical mechanics simply because what we are trying to predict is easier to describe pictorially-- I think when we talk about understanding a theory, what we mean is, understand why that theory provides a good description of the behavior we see, even if the behavior seems weird. The classic example is relativity-- with a few fairly reasonable sounding postulates, we obtain an explanation of very weird behavior, so we say we understand relativity. The postulates don't seem to make any unbelievable claims.

But in the case of quantum mechanics, we have that rift built right into the postulates-- the rift between unitary evolution, and the Born rule. There's just no way to describe that rift without either asserting some physical structure that is completely not in evidence (like a pilot wave, or many worlds), or essentially saying "and then something we can never understand happens" (like Bohr did). So the what is not really that hard to describe (we get interference patterns, we get Bell correlations, etc.), it's just a bit more sophisticated than classical physics (and its elliptical orbits, as you say), and the why is inscrutable as usual-- nether the what or the why seem to be the crux of what is so hard to grasp about quantum mechanics. I think it is the measurement problem, that core inconsistency in the theory, which also spawns all the different interpretations. Those interpretations are weird not because they are different (we always see lots of different sounding interpretations of any theory, like Lorentz aethers and so on), but because of the basic disconnect they are grappling with.
Neither do I, because I don't think physics theories are supposed to tell us that. I don't think that's why we say we don't understand quantum mechanics.
Exactly, we are in agreement-- it is the measurement problem. Our theory is trying to tell us that multiple outcomes are in some sense "wrapped up" in the same state, yet we never actually see anything but one outcome.

nitsuj

I know very little about SR, and even less about QM. But from what I have learned from SR has me believing QM uncertainty roots into how we define & measure the dimensions (not to suggest there is a "solution").


Your comment above is well said and easy to understand. Tough thing to do for QM concepts.

Fredrik

I agree that we don't need a theory as sophisticated as Newton's to get this approximate description of what an object is "doing" while in orbit. I mentioned elliptical orbits as an example of when classical mechanics clearly tells us what an object is doing, to counter the suggestion that classical mechanics doesn't do that. (This was not an attempt to prove Ken G wrong, because it's clear that he and I mean different things by "describe what's happening", and "understand a theory". I only meant to illustrate what sort of thing I have in mind when I'm talking about descriptions of "what's happening").

A statement like "the orbits of planets are ellipses", is a theory by my definitions, because it makes testable predictions about results of experiments. This simple theory is already an approximate description about what's happening to an object in orbit. Newton's theory is a better theory, because it makes more accurate predictions about a wider range of phenomena.

Newton's theory explains why the simple theory works, but it raises a whole new set of "why?" questions. This illustrates another important idea: that the only thing that can explain why a theory works, is a better theory.

Ken G

There's probably a more general way to think about the issue of "what is a measurement" which cuts deeper into the heart of the problem-- and that is, "what is the role of the physicist in the physics." This is the element that Bohr was so focused on, and many take issue with him for raising such a philosophical issue, but I think his insight is still the crux of the matter. So in these terms, "what we don't understand" about quantum mechanics is "why can't we escape the role of the observer." In all other areas of physics, we can imagine that the observer is just a kind of "fly on the wall", and we don't have to attach any importance at all to the fact that an observation is being carried out. That's exactly what we cannot do in quantum mechanics, and we just don't know why. How we resolve that uncertainty is exactly the role of the various interpretations, but none can produce an unequivocally demonstrable answer-- to put it mildly.

Ken G

That's a key point I don't think a lot of people recognize about a physics theory, no matter how accurate or widely accepted it is: it never tells us "why" nature works the way she does, it only tells us why some previous theory worked as well as it did! To explain why we get the observations we do, we would actually need a theory that described what we are doing when we make an observation, which requires that we can model ourselves, modeling ourselves, and so on. That's why I hold it is never possible to use physics to say "why" we observe what we do, and we should not make that our goal for doing physics. But we'd still like to have theories that give a consistent and complete account that connects nature to the observed result, and that's just what quantum mechanics does not do, without invoking an interpretation that few agree on. I actually see this as a feature of QM, not a bug-- we aren't supposed to be able to map the complete connection between what nature is doing to our observation of it.

Fredrik

Yes, I agree about this part. (More details in my reply to harrylin above).

I'm not sure what you're saying here. Is it one of the following things? A) To understand the theory is to understand its mathematics and correspondence rules (the assumptions that tell us how to interpret the mathematics as predictions about results of experiments), or B) To understand the theory is to understand why its predictions are accurate.

If you meant A, then what we need to do before we can say that we understand the theory, is to prove the most relevant theorems, and convince ourselves that we have the right idea about how to perform measurements of the sort the theory makes predictions about. (I would say that we have accomplished this to a satisfactory degree already).

If you meant B, then what we need to do is to find a better theory. (If this is what you meant, then we have very different ideas about what it would mean to understand the theory. I would say that this is actually unrelated to "understanding the theory". It's an entirely different issue).

Hm, you probably meant neither. Maybe you meant C) To understand the theory is to know which things in the purely mathematical part of the theory correspond to things in the real world. This is of course the part that no one understands. So if we define "understand the theory" this way, then we don't understand it. But I don't use this definition. I'm using the one I labeled "A" above.

Fredrik

I have come to think about this role of the observer as an essential feature of the concept of "physics". Theories of physics are falsifiable statements about reality. To be falsifiable, a statement must have testable consequences. In other words, we must be able to use it to make predictions about results of measurements. And what is a measurement? It's an interaction between the system and its environment that puts some part of the environment into one of several states that a human observer can interpret as a result of the measurement. Such a state must last long enough for a human to observe it, and be distinguishable from states that correspond to other results. So that part of the environment, the "pointer" that indicates the result, has to behave in a way that will be perceived as classical.

A "classical" theory is a theory that only makes predictions that can be tested without significantly disturbing the system. So maybe we shouldn't be asking why QM is so weird, but instead be asking why there are classical theories that are actually pretty good.

Good post. No objections from me.

krd

Who says we're not supposed to?

We have to keep asking questions - reformulating things. Maybe, sometime in the future - a few thousand years from now we'll arrive at the end.

Dream.

We're no where near the end. Like at the minute we do not have 3d prints, that can shoot beams and create whatever matter we want - like pressing a button and making a chocolate cake appear out of nothing. I know it sounds like impossible magic. But so would mobile phones have sound to the ancients. Although they did believe their priests could talk to god.