Why Is Quantum Mechanics So Difficult? - Comments

[carllooper]

The fact that QM is formalised in terms of mathematical (and statistical) concepts does not mean such concepts are any less 'physical' than what they formalise. At the base of QM are still the actual physical observables, which, if truth be told, do not require of us that we express them in any other way.

But being the beasts that we are, we like to elaborate what we are seeing. To capture in some way what the observables may not immediately suggest. The concepts, in this sense, are an added bonus. A way of elaborating, in a different way, what we are otherwise seeing.

The concepts are, from an historical point of view, "weird" but that's only because the observables are weird. Not because the creators of the concepts are weird.

C

 

[bhobba]

The concepts are, from an historical point of view, "weird" but that's only because the observables are weird. Not because the creators of the concepts are weird.

You are correct.

But I don't think anyone seriously thought the creators of QM like Bohr, Heisenberg and Dirac were 'weird' (well Dirac actually was weird - but that's another story and the weirdness is in a different sense). Pretty much everyone understands they were driven to it out of desperation because of no other option.

But progress is inexorable and these days its understood to be an example of a generalised probability theory - the simplest that allows continuous transformations between pure states:
http://arxiv.org/pdf/quantph/0101012.pdf
http://arxiv.org/pdf/1402.6562v3.pdf

Does such really resolve quantum weirdness? Who knows - but it does feel like progress has been made.

Thanks
Bill

 

[Stephen Tashi]

The "ensemble" is not only conceptual, it's created all the time when physicists measure things in the lab. They perform the experiment many times with as independent realizations as possible and measure always the same quantities again and again, evaluate the outcome via statistical methods and give the result of the measurement.

Introductory classical physics courses usually have an associated lab course. Is there a good lab course for introductory QM ?

 

[ZapperZ]

Introductory classical physics courses usually have an associated lab course. Is there a good lab course for introductory QM ?

Er.. introductory GENERAL physics courses usually have labs. Those are not just intro classical physics. In many schools, the photoelectric effect and blackbody radiation are often included in these intro physics lab sequence, and thus, are often part of the labs.

Zz.

 

[Demystifier]

But every now and then you have these aha moments of insight that helps enormously.

I had 3 major phases in my learning of conceptual foundations of quantum theory.

1. First, learning standard QM. That included learning QFT in the spirit of high-energy physics. Unfortunately, it left some deep questions (like what is happening when we don't observe) unanswered.

2. Second, learning Bohmian QM. It gave a possible plausible answer to the question above, at least for non-relativistic QM. But it was still not entirely clear how to generalise it to relativistic QM and QFT. (I was still trying to use a high-energy spirit for relativistic QM and QFT.)

3. Third, learning how to reject the high-energy spirit of QFT and adopt the condensed-matter spirit instead. Using the concept of phonon as a prime example, I learned how to stop taking relativity, fields and known particles seriously. These can naturally be interpreted as emergent concepts, while the underlying unknown fundamental theory may have the form of non-relativistic QM. With such a view, Bohmian mechanics starts to make much more sense, at least conceptually. But also makes Bohmian machanics less relevant for explanations of phenomena that we actually see.

 

[andresB]

Initially I liked found the conversation about the best way to teach QM for undergrads but it quickly turns into interpretation of QM and if there is something that should be left out in undergrad courses of QM is that kind of things :/

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I learned Quantum theory in three courses of one semester (actually just 4 month) each. The first one was dedicated to the historical developments between black body radiation up to Schrödinger equation. the other two where proper QM courses.

After having some semesters learning all the stuff of classical physics, I can't see how you can not spend some time teaching the students necessity of developments of new concepts by showing the shortcomings of old physics to explain some observational things.

I agree that the mathematics should be teach first in a proper QM course, but Only after the student know that classical physics is not enough I would say "I will teach you these things about Bras and Kets and unitary operations, just bear with me for a while and I promise you than later on you will see how these formalism helps making predictions in real world and how it solved the problems that classical physics encountered".

 

[houlahound]

I don't know of any undergrad courses that teach QM by doing experiments. that would solve a lot of pedagogy and motivational problems. the only reason I can presume is that textbooks are easy teaching tools for course organisers - it is a no brainer (given a good proven book).

doing an experimental course takes more money, risk assessment, scheduling, maintenance, support staff, ordering stuff...

it's easier just to follow a good book.

 

[vanhees71]

I had 3 major phases in my learning of conceptual foundations of quantum theory.

1. First, learning standard QM. That included learning QFT in the spirit of high-energy physics. Unfortunately, it left some deep questions (like what is happening when we don't observe) unanswered.

The good news is that this is a question irrelvant to physics, because physics is all about reprducible objective phenomena in nature an nothing else. Religion, including philosophical speculation about "the meaning of it all", are not part of physics and can be left to a physicist's (spare) free time ;-)).

2. Second, learning Bohmian QM. It gave a possible plausible answer to the question above, at least for non-relativistic QM. But it was still not entirely clear how to generalise it to relativistic QM and QFT. (I was still trying to use a high-energy spirit for relativistic QM and QFT.)

I've never understood the hype about BM. You evaluate with more or less satisfaction some unobservable "trajectories" from a highly unintuitive non-local theory. So what?

3. Third, learning how to reject the high-energy spirit of QFT and adopt the condensed-matter spirit instead. Using the concept of phonon as a prime example, I learned how to stop taking relativity, fields and known particles seriously. These can naturally be interpreted as emergent concepts, while the underlying unknown fundamental theory may have the form of non-relativistic QM. With such a view, Bohmian mechanics starts to make much more sense, at least conceptually. But also makes Bohmian machanics less relevant for explanations of phenomena that we actually see.

There is no difference between the "high-energy and condensed-matter spirit of QFT". Since Kadanoff and K. Wilson it's pretty clear that all our relativistic QFTs are effective theories with validity up to some scale beyound which you don't resolve the physics anymore to get a description of the relevant and observable degrees of freedom. This is pretty much the same in condensed-matter physics, and only because often there are no divergences in non-relativistic QFT (used in condensed-matter physics) doesn't mean that you don't need to renormalize. Quite to the contrary the pertinent techniques like the functional renormalization-group approach become more and more important in both non-relativistic and relativistic many-body physics.

As I stressed above, the sensibility of implementing an artificial ad-hoc addition to the interpretation of QT in the spirit of BM has never become understandable to me, precisely for the reason you give yourself: It doesn't provide any deeper insight for the theoretical description of what we "actually see", and that's the only part of our perception of nature that's, by definition, relevant to the natural sciences.

 

[vanhees71]

I don't know of any undergrad courses that teach QM by doing experiments. that would solve a lot of pedagogy and motivational problems. the only reason I can presume is that textbooks are easy teaching tools for course organisers - it is a no brainer (given a good proven book).

doing an experimental course takes more money, risk assessment, scheduling, maintenance, support staff, ordering stuff...

it's easier just to follow a good book.

Well, in our mandatory lab (in Germany you have both the "Grundpraktikum" and the "Fortgeschrittenenpraktikum", consisting of a set of experiments you have to evaluate yourself, taking the data with more or less outdated equipment ;-)), there was a lot to learn about quantum theory. One of the most interesting experiments was the Stern-Gerlach experiment. Then we had some nuclear-physics experiments, helium at low temperatures, etc. For all of these you needed quantum theory to understand the very motivation of the experiment to begin with, and the "statistical nature" of quantum theory becomes a hands-on experience. Also these labs finally convinced me to become a theoretician, I think they are very valuable to get this experience to immunize you from many distractive philosophy (esoterics) concerning the "interpretation" of QT.

I guess nowadays, some 25 years later, it's even easy to provide very fascinating experiments with entangled photons to these labs. At a conference, I've seen in a little exhibition by educational-equipment companies ready setups of a laser to provide heralded single-photon states in terms of entangled photon pairs through parametric down conversion. I think that's a very good tool to debunk all the very misleading statements about photons as some kind of "massless particle" that you find even in otherwise good textbooks at the university level (let alone in high-school textbooks or even popular-science books). I think if there is anything to convince you from the correct picture provided by QED is an experiment like the demonstration of the HOM effect

https://en.wikipedia.org/wiki/Hong–Ou–Mandel_effect

 

[houlahound]

When I was an undergraduate I would hang out in the post grad research lab, they had an alarm system for when the professor (a respected theorist) walked toward the lab. He liked to touch the gadgets and was at risk of hurting himself or destroying weeks of data collection.

Nobody was game enough to tell him he was a liability in the lab so the post grads learned to manage him.

 

[Demystifier]

The good news is that this is a question irrelvant to physics, because physics is all about reprducible objective phenomena in nature an nothing else. Religion, including philosophical speculation about "the meaning of it all", are not part of physics and can be left to a physicist's (spare) free time ;-)).

As you certainly know by now, I disagree. I will not repeat my reasons because you have already seen them several times.

I've never understood the hype about BM. You evaluate with more or less satisfaction some unobservable "trajectories" from a highly unintuitive non-local theory. So what?

You cannot understand the hype about BM if you never seriously ask yourself (in spare time if you want) what is happening when we don't observe. As long as this question is irrelevant for you, BM is not something you should care about.

There is no difference between the "high-energy and condensed-matter spirit of QFT". Since Kadanoff and K. Wilson it's pretty clear that all our relativistic QFTs are effective theories with validity up to some scale beyound which you don't resolve the physics anymore to get a description of the relevant and observable degrees of freedom.

High-energy physicists know it, but many of them still don't accept it wholeheartedly. For instance, many of them still claim that we "don't know how to quantize gravity", forgetting that we do understand quantum gravity pretty well if effective theory is all we should really care about.

Another difference: For condensed-matter physicists, symmetry is nothing but a practical tool to simplify calculations. For high-energy physicists, symmetry may also be a deep fundamental principle which is a key for understanding physics at the deepest possible level.

This is pretty much the same in condensed-matter physics, and only because often there are no divergences in non-relativistic QFT (used in condensed-matter physics) doesn't mean that you don't need to renormalize. Quite to the contrary the pertinent techniques like the functional renormalization-group approach become more and more important in both non-relativistic and relativistic many-body physics.

Of course, techniques are the same. But I am not talking about techniques. I am talking about "spiritual" things which you might consider "irrelevant". Like "What does it all mean?", or "How to search for BSM theories when all LHC data are compatible with the SM?". The latter question is an important part of the mainstream research, even if, strictly speaking, should be considered irrelevant for physics.

As I stressed above, the sensibility of implementing an artificial ad-hoc addition to the interpretation of QT in the spirit of BM has never become understandable to me, precisely for the reason you give yourself: It doesn't provide any deeper insight for the theoretical description of what we "actually see", and that's the only part of our perception of nature that's, by definition, relevant to the natural sciences.

Perhaps you misunderstood me. I consider it less relevant than before because BM used to be about electrons and photons, while now, in my reinterpretation, it is about some more fundamental particles which we don't (yet) see in experiments. (If you will ask me what's the point of particles that we don't see in experiments, my answer is: What's the point of strings? What's the point of supersymmetric partners?)

 

[vanhees71]

Of course, techniques are the same. But I am not talking about techniques. I am talking about "spiritual" things which you might consider "irrelevant". Like "What does it all mean?", or "How to search for BSM theories when all LHC data are compatible with the SM?". The latter question is an important part of the mainstream research, even if, strictly speaking, should be considered irrelevant for physics.

These two questions are totally different concerning these epistemic questions. The first one "What does it all mean?" is indeed irrelevant for the natural sciences, because it's not the purpose of natural sciences to provide a "meaning". It's also a very unsharply posed question. There are tons of papers (and books since philosophers tend to write books rather than papers) written about it (and totally irrelevant to the natural sciences).

In contradistinction, the search for theories for physics beyond the Standard Model, is very relevant to physics. It's quite clear that the SM has severe problems at very high energies (Landau pole) and must break down at some point. Of course, the endeavor to find a more comprehensive model is almost hopeless, if there is no clear evidence for "new physics" from experiment. Also neutrino physics is clearly physics BSM. Another important question is also observational to a certain extent, and that's the question whether Dark Matter (in the astrophysical sense) really exists and if so what are its constituents.

 

[houlahound]

I for one do not turn to physics for meaning.

I derive my meaning from my relationships with people and nature and the honest attempt to leave them in better shape than I found them.

I don't need a physics equation or piece of scripture from an ancient book to fufil that.

 

[Demystifier]

These two questions are totally different concerning these epistemic questions. The first one "What does it all mean?" is indeed irrelevant for the natural sciences, because it's not the purpose of natural sciences to provide a "meaning". It's also a very unsharply posed question. There are tons of papers (and books since philosophers tend to write books rather than papers) written about it (and totally irrelevant to the natural sciences).

In contradistinction, the search for theories for physics beyond the Standard Model, is very relevant to physics. It's quite clear that the SM has severe problems at very high energies (Landau pole) and must break down at some point. Of course, the endeavor to find a more comprehensive model is almost hopeless, if there is no clear evidence for "new physics" from experiment. Also neutrino physics is clearly physics BSM. Another important question is also observational to a certain extent, and that's the question whether Dark Matter (in the astrophysical sense) really exists and if so what are its constituents.

Let me ask you a question. What do you think about string theory? Or about SUSY models in which SUSY partners can only be seen at energies that cannot be achieved by present technologies?

Another point. Some of the greatest physicists started with "what does it all mean" type of question, which eventually turned out to lead to something testable. For example, Bell inequalities.

 

[houlahound]

Demystifier what justification do you have that nature has to have a meaning?

 

[vanhees71]

Let me ask you a question. What do you think about string theory? Or about SUSY models in which SUSY partners can only be seen at energies that cannot be achieved by present technologies?

Another point. Some of the greatest physicists started with "what does it all mean" type of question, which eventually turned out to lead to something testable. For example, Bell inequalities.

Well, so far string theory hasn't provided anything to our understanding of nature. This doesn't mean that it is useless, because maybe one day an ingenious insight provides something observable. The same holds for SUSY models, which are however a bit closer to something having a chance to be observable.

The Bell example is a very good example for what distinguishes natural science from philosophical speculation. Bell provided a testable prediction concerning a wide class of deterministic local hidden-variable theories which contradicts QT. It brought question on validity of the non-classical aspects of QT to the level of a scientific question that could (first in principle and then beginning with the early 80ies also practically) be tested by experiments.

Of course, the heuristics is not necessarily scientific. Model and theory building has a lot to do with unscientific parts of our human experience. It's like art, if you wish. However, to make an idea a scientific model or theory it must necessarily provide objectively (quantitatively) testable predictions for observable phenomena. Otherwise it's no science. This makes it pretty difficult to consider string theory a natural science (I'd rather take it as part of mathematics, i.e., a "structural science"). SUSY models make scientific predictions, and that's why (a tiny subset of models) is testable and indeed tested at the LHC (unfortunately so far excluding more and more of these socalled minimal SUSY extensions).

Also, please don't get me wrong. I don't mean to devalue anything that I call "not scientific". E.g., math is not a natural science either, and there's a lot very relevant and important to us humans that is not covered by the natural sciences, including everything concerned with ethics (which is part of philosophy)!

 

[Demystifier]

Demystifier what justification do you have that nature has to have a meaning?

Well, humans have already found meanings for many things. Words have meanings. Romantic relationships have meanings. Classical physics has meaning. Perhaps even quantum mechanics has meaning.

 

[houlahound]

There is meaning we create and belief there is a meaning beyond our own creation, which are you referring to?

 

[Demystifier]

Also, please don't get me wrong. I don't mean to devalue anything that I call "not scientific". E.g., math is not a natural science either, and there's a lot very relevant and important to us humans that is not covered by the natural sciences, including everything concerned with ethics (which is part of philosophy)!

So, in your opinion, could Bohmian mechanics have some value, even if it is not science? After all, it has some non-trivial mathematical structure. In addition, similarly to ethics if you wish, it offers some meaning of QM for those human physicists who, for some personal reasons, need some meaning in physics for internal motivation. (After all, if physics does not have any meaning for you, then why do you do it?)

Or let me put it this way. Even if BM is not science, it is certainly a non-trivial intellectual discipline. So how should we classify it? Philosophy? Philosophy of science? Isn't philosophy of science a part of science as much as it is a part of philosophy?

 

[houlahound]

Check last sentence above.

 

[Demystifier]

There is meaning we create and belief there is a meaning beyond our own creation, which are you referring to?

I am talking about human creation. Physics, as a scientific discipline, is created by humans. Physics is a human way to describe and predict what we see. The "true reality" (whatever that means) may be entirely different.

 

[Demystifier]

Check last sentence above.

Thanks, I've corrected the error.

 

[houlahound]

I am talking about human creation. Physics, as a scientific discipline, is created by humans. Physics is a human way to describe and predict what we see. The "true reality" (whatever that means) may be entirely different.

I have a different meaning of "meaning".

 

[Demystifier]

I have a different meaning of "meaning".

Like the ultimate meaning of life according to some dogmatic religion? I don't need that kind of meaning in physics.

 

[houlahound]

No

 

[Demystifier]

No

Then what do you mean by "meaning"?

 

[houlahound]

This sort of thing;

https://en.m.wikipedia.org/wiki/Teleology

 

[Demystifier]

This sort of thing;
https://en.m.wikipedia.org/wiki/Teleology

In physics, this can be achieved by specifying initial conditions in the future.

 

[houlahound]

What about predicting the result after something happened?

 

[Demystifier]

What about predicting the result after something happened?

If "initial" condition is known at some arbitrary time $t_0$, the differential equation determines behavior for both $t>t_0$ and $t<t_0$ (if this is what you ask).