Why Is Quantum Mechanics So Difficult?
Table of Contents
Key points:
- Quantum mechanics (QM) is often perceived as difficult, especially by non-physicists.
- The difficulty lies in the conceptual foundation of QM, as it doesn’t connect well with classical understanding.
- Unlike other areas of physics, there’s no direct continuity between classical concepts and QM.
- While the conceptual understanding is challenging, the mathematical formulation of QM is familiar and follows from existing knowledge.
- Mathematical formalism is crucial in QM, as it provides a bridge between classical and quantum worlds.
- QM’s mathematical formalism is the foundation on which our understanding is built.
- Disagreements often arise in the interpretation of QM, but the source, mathematical formalism, remains consistent.
- The mathematical aspect of QM is a means of conveying ideas and principles accurately, akin to musical notes conveying music.
- In QM, mathematics is a form of communication that accurately describes our universe.
- Quantum mechanics doesn’t fully make “sense” without embracing its mathematical continuity.
QM’s formalism
Strangely enough, QM’s formalism isn’t any more difficult than other areas of physics. The mathematics of the “standard” QM isn’t any worse than, let’s say, electromagnetism. Yet, to many people, especially non-physicists, QM presents a very daunting effort to understand.
I strongly believe that it all comes down to how we understand things and how we expand our knowledge. Typically, when we teach students new things, what we do is build upon their existing understanding. We hope that a student already has a foundation of knowledge in certain areas, such as basic mathematics, etc. so that we can use that to teach them about forces, motion, energy, and other fun stuff in intro physics. Then, after they understand the basic ideas, we show them the same thing, but with more complications added to it.
The same thing occurs when we try to help a student doing a homework problem. We always try to ask what the student knows already, such as the basic principle being tested in that question. Does the student know where to start? What about the most general form of the equation that is relevant to the problem? Once we know a starting point, we then build on that to tackle that problem.
The common thread in both cases is that there exists a STARTING point as a reference foundation on which, other “new” stuff is built upon. We learn new and unknown subjects based upon what we have already understood. This is something crucial to keep in mind because, in the study of QM, this part is missing! I am certain that for most non-physicists, this is the most common reason why QM is puzzling, and why quacks and other people who are trying to use QM in other areas such as “metaphysics” or mysticism, are using it in a completely hilarious fashion.
The Disconnect
There is a complete disconnect between our “existing” understanding of the universe based on classical understanding and QM. There is nothing about our understanding of classical mechanics that we can build on to understand QM. We use identical words such as particle, wave, spin, energy, position, momentum, etc… but in QM, they attain a very different nature. You can’t explain these using existing classical concepts. The line between these two is not continuous, at least, not as of now. How does one use the classical idea of a “spin” to explain a spin 1/2 particle in which one only regains the identical symmetry only upon two complete revolutions? We simply have to accept that we use the same word, but to ONLY mean that it produces a magnetic moment. It has nothing to do with anything that’s spinning classically. We can’t build the understanding of the QM spin using the existing classical spin that we have already understood.
Now interestingly enough, the MATHEMATICAL FORMULATION of QM is quite familiar! The time-dependent Schrodinger equation has the same structure as a standard wave equation. We call the energy operator as the Hamiltonian not for nothing since it looks very familiar with the Hamiltonian approach to classical mechanics. The matrix formulation isn’t anything new. What this means is that while the conceptual foundation of QM is completely disconnected from our traditional conceptual understanding, the mathematical formulation of QM completely follows from our existing understanding! Mathematically, there is no discontinuity. We build the formalism of QM based on our existing understanding!
Mathematical formulation
This is why, in previous threads in PF, I disagree that we should teach students the concepts of QM FIRST, rather than the mathematical formulation straightaway. There is nothing to “build on” in terms of conceptual understanding. We end up telling the students what they are out of thin air. The postulates of QM did not come out of our classical understanding of our world. Instead, mathematical formalism is the only thing that saves us from dangling in mid-air. It is the only thing on which our existing understanding can be built on.
What this implies clearly is that, if one lacks the understanding of the mathematical formalism of QM, one really hasn’t understood QM at all! One ends up with all these weird, unexplained, unfamiliar, and frankly, rather strange ideas on how the world works. These conceptual descriptions of QM may even appear “mystical”. It is not surprising that such connections are being made between QM and various forms of mysticism. One lacks any connection with the existing reality that one has understood. So somehow, since QM can do this, it seems as if it’s a license to simply invent stuff weely neely.
The mathematical formalism of QM is what defines the QM description. The “conceptual description” is secondary, and is only present because we desire some physical description based on what we already have classically. It is why people can disagree on the interpretation of QM, yet they all agree on the source, the mathematical formalism of QM.
QM as musical notes
This, however, does not mean that QM is nothing more than “just mathematics”. This is no more true than saying the musical notes on a sheet of paper are just scribbles. The notes are not the important object. Rather, it is the sound that it represents that’s the main point. The musical notes are simply a means to convey that point clearly and unambiguously. Similarly, the mathematics that is inherent in QM and in all of physics, is a means to convey an idea or principle. It is a form of communication, and so far it is the ONLY form of communication accurate and unambiguous enough to describe our universe. It reflects completely our understanding of phenomena. So a mathematical formulation isn’t “just math”.
You cannot use your existing understanding of the universe to try to understand the various concepts of QM. There is a discontinuity between the two. It is only via the mathematical continuity of the description can there be a smooth transition to build upon. Without this, QM will not make “sense”.
PhD Physics
Accelerator physics, photocathodes, field-enhancement. tunneling spectroscopy, superconductivity
[QUOTE="houlahound, post: 5551417, member: 551046"]What about predicting the result after something happened?[/QUOTE]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).
What about predicting the result after something happened?
[QUOTE="houlahound, post: 5551393, member: 551046"]This sort of thing;https://en.m.wikipedia.org/wiki/Teleology[/QUOTE]In physics, this can be achieved by specifying initial conditions in the future. :biggrin:
This sort of thing;https://en.m.wikipedia.org/wiki/Teleology
[QUOTE="houlahound, post: 5551388, member: 551046"]No[/QUOTE]Then what do you mean by "meaning"?
No
[QUOTE="houlahound, post: 5551374, member: 551046"]I have a different meaning of "meaning".[/QUOTE]Like the ultimate meaning of life according to some dogmatic religion? I don't need that kind of meaning in physics.
[QUOTE="Demystifier, post: 5551371, member: 61953"]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.[/QUOTE]I have a different meaning of "meaning".
[QUOTE="houlahound, post: 5551369, member: 551046"]Check last sentence above.[/QUOTE]Thanks, I've corrected the error.
[QUOTE="houlahound, post: 5551364, member: 551046"]There is meaning we create and belief there is a meaning beyond our own creation, which are you referring to?[/QUOTE]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.
Check last sentence above.
[QUOTE="vanhees71, post: 5551360, member: 260864"]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)![/QUOTE]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?
There is meaning we create and belief there is a meaning beyond our own creation, which are you referring to?
[QUOTE="houlahound, post: 5551357, member: 551046"]Demystifier what justification do you have that nature has to have a meaning?[/QUOTE]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.
[QUOTE="Demystifier, post: 5551353, member: 61953"]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.[/QUOTE]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 what justification do you have that nature has to have a meaning?
[QUOTE="vanhees71, post: 5551342, member: 260864"]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.[/QUOTE]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.
I for one go not turn to physics
[QUOTE="Demystifier, post: 5551338, member: 61953"]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. [/QUOTE]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.
[QUOTE="vanhees71, post: 5551317, member: 260864"]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 ;-)).[/QUOTE]As you certainly know by now, I disagree. I will not repeat my reasons because you have already seen them several times.[QUOTE="vanhees71, post: 5551317, member: 260864"]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?[/QUOTE]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.[QUOTE="vanhees71, post: 5551317, member: 260864"]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.[/QUOTE]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.[QUOTE="vanhees71, post: 5551317, member: 260864"]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.[/QUOTE]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.[QUOTE="vanhees71, post: 5551317, member: 260864"]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.[/QUOTE]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?)
When
[QUOTE="houlahound, post: 5551118, member: 551046"]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 text books 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.[/QUOTE]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 effecthttps://en.wikipedia.org/wiki/Hong–Ou–Mandel_effect
[QUOTE="Demystifier, post: 5550801, member: 61953"]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.[/QUOTE]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 ;-)).[QUOTE]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.)[/QUOTE]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?[QUOTE]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.[/QUOTE]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.
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 text books 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.
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 :/=================================I learnt 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".
[QUOTE="bhobba, post: 4824339, member: 366323"]But every now and then you have these aha moments of insight that helps enormously.[/QUOTE]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 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.
[QUOTE="Stephen Tashi, post: 5550765, member: 186655"]Introductory classical physics courses usually have an associated lab course. Is there a good lab course for introductory QM ?[/QUOTE]Er.. introductory GENERAL physics courses usually have labs. Those are not just intro classical physics. In many schools, the photoelectric effect and blackbody radiation is often included in these intro physics lab sequence, and thus, are often part of the labs.Zz.
[QUOTE="vanhees71, post: 4825535, member: 260864"]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.[/QUOTE]Introductory classical physics courses usually have an associated lab course. Is there a good lab course for introductory QM ?
[QUOTE="carllooper, post: 4904073, member: 218390"]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.[/QUOTE]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.pdfhttp://arxiv.org/pdf/1402.6562v3.pdfDoes such really resolve quantum weirdness? Who knows – but it does feel like progress has been made.ThanksBill
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
One of the reasons for quantum mechanics be so difficult is this:https://www.physicsforums.com/threads/what-is-quantum-theory-about.767672/
[QUOTE="bhobba, post: 4900996, member: 366323"]The physical part is, lust like probability theory where you have abstract events and apply it to various things, you apply it to observations.[/QUOTE]I know what you mean. I meant QFT is built upon QM with the assumption that QM is a completely physical theory. So when you say QM is actually a mathematical theory applied to universe, you have to modify QFT somehow that the distinction between the generalized probability theory part and the physics part become apparent. The same about string theory, LQG, etc.But that paper only deals with non-relativistic QM and even doesn't analyse continuous bases!
[QUOTE="Shyan, post: 4900978, member: 160907"]But it seems to me, it means the whole structure of QM and theories following it(standard model, its extensions, String theory, etc.), are not actually fully physical, but consist of a mathematics part(the probability theory part) and a physical part( I'm sure you can't say all of those are just mathematics, there should be some physical things attached to that probability theory to make it about universe). So there remains a lot of work for separating these parts which means this idea that QM is a new probability theory is still incomplete.[/QUOTE]The mathematical part is what is known as a generalised probability model or theory:http://arxiv.org/pdf/1402.6562v3.pdfhttp://www.mathematik.uni-wuerzburg.de/sommerschule2011/download/ln-janotta.pdfThe simplest is bog standard probability theory as defined by the Kolmogorov axioms – but it can be extended in all sorts of ways.What the paper I linked to shows is with some reasonable physical assumptions you end up with either standard probability theory or QM – with continuous transformations between pure states being the difference. And if you think about it physically that's what you want – if a state transforms to another state in say one second it transforms to something in half a second ie time is continuous.The physical part is, just like probability theory where you have abstract events and apply it to various things, you apply it to observations.ThanksBill
Well, I wasn't careful in saying that. I meant in classical physics, we just allowed phenomena we had a reason for. But in QM, we allow phenomena we don't have a reason against. This way QM allows everything to happen from the beginning until something wrong is found in allowing those phenomena.As examples, I can mention Einstein who allowed stimulated emission which seems non-sense from a classical point of view. Or allowing the wave function to have a probability for reflection when it reaches a potential step having a lower energy than the wave function's. So in QM, we allow everything we have no reason against(these reasons are chosen from a minimal set of laws i.e. a set of laws from which we removed any assumption that seems to be too much of assuming about nature and so only things remain in the set without which we should just forget about usefulness or consistency of physics), even things that seem very non-sense, and just give them probabilities to happen. So in QM we're trying to reduce the assumptions we have about nature as much as possible and allow as general evolutions as possible. This way we find that nature actually doesn't need to know the value of every quantity of every particle to handle its phenomena so we allow it to not know them!About that paper you linked to bhobba, I tried to read it but it seems I should learn more about QM so that I can fully appreciate it so I can't have a strong opinion about it now. But it seems to me, it means the whole structure of QM and theories following it(standard model, its extensions, String theory, etc.), are not actually fully physical, but consist of a mathematics part(the probability theory part) and a physical part( I'm sure you can't say all of those are just mathematics, there should be some physical things attached to that probability theory to make it about universe). So there remains a lot of work for separating these parts which means this idea that QM is a new probability theory is still incomplete.
[QUOTE="Shyan, post: 4900198, member: 160907"]QM says all things happen.[/QUOTE]Where you got that from has me beat.For me its simply the most reasonable extension of probability theory that allows continuous changes in systems:http://arxiv.org/pdf/quantph/0101012.pdfWhat QM says is when a system is not observed its up in the air what going on – your view of the state strongly influences the answer to that question. And yet there is no way to experimentally tell the difference.ThanksBill
[QUOTE="Shyan, post: 4900198, member: 160907"]QM says all things happen.[/quote]That would be the "both" option. QM doesn't say that both (or all) things happen. What it says is that what you call "all things" contribute to the probability of a detection event.To argue that QM says this, we have to assume something like "the wavefunction represents all the properties of the system", rather than just its preparation procedure. This is something that people tend to do automatically, almost always without realizing that they have added an unscientific assumption on top of the theory.[QUOTE="Shyan, post: 4900198, member: 160907"]Of course these are in the context of Copenhagen interpretation![/QUOTE]Yes, it's a claim made by an interpretation, not by the theory. I don't think it makes sense to call such an interpretation "Copenhagen", but I don't want to get into that very time consuming topic again.
[QUOTE="Fredrik, post: 4899682, member: 14944"]It explains a lot of complicated things, but fails to explain things that seem (to our intuition) that they should be much simpler. For example, it explains why the pattern on the screen in the double slit experiment looks the way it does (by predicting the probability of detection at each spot on the screen), but it doesn't tell us what the particles are doing between emission and detection. Does an individual particle go through one of the slits or both? Most people think it's "one" until they study QM and incorrectly concludes that QM says "both". (It really doesn't say anything about it).[/QUOTE]That's not a failure. Its not that QM just fails to say what happens in between. QM says all things happen. It says because nature doesn't need all the book-keeping required by classical physics to do what its going to do, so it doesn't do that book-keeping and whenever we ask her to give us a value of a quantity which she didn't care to give a value to, she just says:"who cares?!" and just hands a random value to us!That's actually like the situation where people just assumed the stationary action principle and it worked. There people said something is stationary in things that happen in nature because she does things the best way economically. Here we're assuming a minimum book-keeping principle where nature doesn't carry information that she doesn't need to handle its phenomena!Of course these are in the context of Copenhagen interpretation!
My opinion is that ontology of QM is important and it should be explained one day. Maybe quantum gravity and quantum consciousness will demand its explanation in calculations. I do not agree that "calculations" are enought. Isham writes, how times in QM and in GR disagree: http://arxiv.org/abs/gr-qc/9310031 Because those questions are not explained enought QM is also not explained enough. QM is only aproximation of quantum gravity! But, we can wait, and at first, formalism of QFT should be explained clearer. I disagree that its explanation is clear enough.
[QUOTE="Fredrik, post: 4899158, member: 14944"]QM doesn't explain a lot. It explains some things, like the energy levels in an atom. (They correspond to different solutions of the Schrödinger equation for the Coulomb potential). But mostly it just assigns probabilities to possible results of experiments. So what do you think that "good teacher" should explain, "in real, rational, physical language"? Should he explain what's actually happening in an experiment? It's unclear if QM even contains an answer to that. (I would be very surprised if it does). If you have heard an explanation in "real, rational, physical language", the person who gave it to you was either giving you a dumbed down version of how the calculations are made, or a non-scientific speculative answer based on a personal world view (an interpretation of QM).[/QUOTE]There are simple experiments with photon polarizations and neutron spins using interferometers that connect the QM formalism to properties of the experimental equipment directly, e.g., phase factors of phase plates, reflection and transmission coefficients of beam splitters, orientation of polarizers and SG magnets, locations and readings of detectors. I consider this to be "real, rational, physical language." Discussion of the "weirdness" can't take place until the analysis is done, so as the instructor you can choose whether or not to "Shut up and calculate," or point out the ontological mystery.
[QUOTE="bohm2, post: 4899655, member: 280368"]Even at a conceptual level QM is not complete as pointed out by Goldstein:[/QUOTE]As I have posted many times the real issue with QM is we have all these different interpretations. It doesn't matter what issue concerns you, and that includes the issue in the quote you gave (eg BM avoids it) there is an interpretation that avoids it. What we don't have is an interpretation that avoids all the criticisms.[QUOTE="bohm2, post: 4899655, member: 280368"]And the solution does not eliminate the problem:[/QUOTE]Some interpretations do, but raises others.ThanksBill
[QUOTE="vanhees71, post: 4899332, member: 260864"]This is a quite strange point of view since QM is the most comprehensive consistent theory about nature we have today, and it describes a lot.[…]Without quantum theory we couldn't even understand, why matter is stable. So if anything comes close to an "explanation" of why the world looks as we know it, it's quantum theory![/QUOTE]It explains a lot of complicated things, but fails to explain things that seem (to our intuition) that they should be much simpler. For example, it explains why the pattern on the screen in the double slit experiment looks the way it does (by predicting the probability of detection at each spot on the screen), but it doesn't tell us what the particles are doing between emission and detection. Does an individual particle go through one of the slits or both? Most people think it's "one" until they study QM and incorrectly concludes that QM says "both". (It really doesn't say anything about it).
[QUOTE="vanhees71, post: 4899332, member: 260864"]The accuracy with which this model works is embarrasing in some sense since we know that the Standard Model cannot be complete, because even within its range of applicability there are most probably problems at very high energies (Landau poles of a non-confining QFT).[/QUOTE]Even at a conceptual level QM is not complete as pointed out by Goldstein:[QUOTE]Suppose that the wave function of any individual system provides a complete description of that system. When we analyze the process of measurement in quantum mechanical terms, we find that the after-measurement wave function for system and apparatus that arises from Schrödinger's equation for the composite system typically involves a superposition over terms corresponding to what we would like to regard as the various possible results of the measurement -e.g., different pointer orientations. In this description of the after-measurement situation it is difficult to discern the actual result of the measurement -e.g., some specific pointer orientation. But the whole point of quantum theory, and the reason we should believe in it, is that it is supposed to provide a compelling, or at least an efficient, account of our observations, that is, of the outcomes of measurements. In short, the measurement problem is this: Quantum theory implies that measurements typically fail to have outcomes of the sort the theory was created to explain.[/QUOTE]And the solution does not eliminate the problem:[QUOTE]Textbook quantum theory provides two rules for the evolution of the wave function of a quantum system: A deterministic dynamics given by Schrödinger's equation when the system is not being “measured” or observed, and a random collapse of the wave function to an eigenstate of the “measured observable” when it is. However, the objection continues, textbook quantum theory does not explain how to reconcile these two apparently incompatible rules.[/QUOTE]
[QUOTE="Fredrik, post: 4899158, member: 14944"]QM doesn't explain a lot. It explains some things, like the energy levels in an atom. (They correspond to different solutions of the Schrödinger equation for the Coulomb potential). But mostly it just assigns probabilities to possible results of experiments. So what do you think that "good teacher" should explain, "in real, rational, physical language"? Should he explain what's actually happening in an experiment? It's unclear if QM even contains an answer to that. (I would be very surprised if it does). If you have heard an explanation in "real, rational, physical language", the person who gave it to you was either giving you a dumbed down version of how the calculations are made, or a non-scientific speculative answer based on a personal world view (an interpretation of QM).[/QUOTE]This is a quite strange point of view since QM is the most comprehensive consistent theory about nature we have today, and it describes a lot. Physics is not made to explain anything but first of all to observe nature, quantify the observations and find relationships between observed quantities. The results from the last ~400 years are astonishing. It turns out that there are pretty few fundamental laws that describe nature, most of them describable on the most fundamental level in terms of symmetry principles, starting from the symmetries of our description of space and time, going further to the fundamental (gauge) symmetries underlying the Standard model of Elementary particle physics.The latter is the most comprehensive theory ever created by mankind. It describes all of the hitherto known matter in terms of quarks and leptons as well as the fundamental interactions described in terms of a gauge theory which is partially "higgsed". The accuracy with which this model works is embarrasing in some sense since we know that the Standard Model cannot be complete, because even within its range of applicability there are most probably problems at very high energies (Landau poles of a non-confining QFT). In addition it doesn't describe gravitation and very likely there should be something called "dark matter" which is inferred from astronomical observations like the rotation curves of galaxies. For gravitation we have no really convincing quantum theory yet and rely on classical field theory (known as General Relativity).Without quantum theory we couldn't even understand, why matter is stable. So if anything comes close to an "explanation" of why the world looks as we know it, it's quantum theory!
[QUOTE="Fredrik, post: 4899158, member: 14944"]If you have heard an explanation in "real, rational, physical language", the person who gave it to you was either giving you a dumbed down version of how the calculations are made, or a non-scientific speculative answer based on a personal world view (an interpretation of QM).[/QUOTE]The interesting thing about QM is if you have studied some linear algebra, partial differential equations etc and you go through a book like Griffiths then you generally have no problems. You can do the problems and apply it. Basically that's what most physicists and applied mathematicians want. Mathematically its perfectly fine. Maybe that's simply because its written in the language of math and that's the only real way to explain it.ThanksBill
[QUOTE="Rabin D Natha, post: 4899121, member: 527652"]QM seeks to explain the real, rational physical universe. A good teacher can explain it in real, rational, physical language. Too often, specialists create their own unique worldview and lose touch with the ordinary uniververse. If you can't explain it, it has no value outside its unique community. In the ordinary world, Schrödinger's Cat is stuck in a poorly conceived experiment with a nonsensical hypothesis.[/QUOTE]QM doesn't explain a lot. It explains some things, like the energy levels in an atom. (They correspond to different solutions of the Schrödinger equation for the Coulomb potential). But mostly it just assigns probabilities to possible results of experiments. So what do you think that "good teacher" should explain, "in real, rational, physical language"? Should he explain what's actually happening in an experiment? It's unclear if QM even contains an answer to that. (I would be very surprised if it does). If you have heard an explanation in "real, rational, physical language", the person who gave it to you was either giving you a dumbed down version of how the calculations are made, or a non-scientific speculative answer based on a personal world view (an interpretation of QM).
[QUOTE="Greg Bernhardt, post: 4821250, member: 1"]Author: ZapperZOriginally posted on Jun16-14Strangely enough, QM's formalism isn't any more difficult than other areas of physics. The mathematics of the "standard" QM isn't any worse than, let's say, electromagnetism. Yet, to many people, especially non-physicists, QM presents a very daunting effort to understand.I strongly believe that it all comes down to how we understand things and how we expand our knowledge. Typically, when we teach students new things, what we do is build upon their existing understanding. We hope that a student already has a foundation of knowledge in certain areas, such as basic mathematics, etc., so that we can use that to teach them about forces, motion, energy, and other fun stuff in intro physics. Then, after they understand the basic ideas, we show them the same thing, but with more complications added to it.The same thing occurs when we try to help a student doing a homework problem. We always try to ask what the student know already, such as the basic principle being tested in that question. Does the student know where to start? What about the most general form of the equation that is relevant to the problem? Once we know a starting point, we then build on that to tackle that problem.The common thread in both cases is that there exists a STARTING point as a reference foundation on which, other "new" stuff are built upon. We learn new and unknown subject based upon what we have already understood. This is something crucial to keep in mind because in the study of QM, this part is missing! I am certain that for most non-physicists, this is the most common reason why QM is puzzling, and why quacks and other people who are trying to use QM into other areas such as "metaphysics" or mysticism, are using it in a completely hilarious fashion.There is a complete disconnect between our "existing" understanding of the universe based on classical understanding, and QM. There is nothing about our understanding of classical mechanics that we can build on to understand QM. We use the identical words such as particle, wave, spin, energy, position, momentum, etc… but in QM, they attain a very different nature. You can't explain these using existing classical concepts. The line between these two is not continuous, at least, not as of now. How does one use classical idea of a "spin" to explain a spin 1/2 particle in which one only regains the identical symmetry only upon two complete revolutions? We simply have to accept that we use the same word, but to ONLY mean that it produces a magnetic moment. It has nothing to do with anything that's spinning classically. We can't build the understanding of the QM spin using existing classical spin that we have already understood.Now interestingly enough, the MATHEMATICAL FORMULATION of QM is quite familiar! The time-dependent Schrodinger equation has the same structure as a standard wave equation. We call the energy operator as the Hamiltonian not for nothing since it looks very familiar with the hamiltonian approach to classical mechanics. The matrix formulation also isn't anything new. What this means is that while the conceptual foundation of QM is completely disconnected with our traditional conceptual understanding, the mathematical formulation of QM completely follows from our existing understanding! Mathematically, there is no discontinuity. We build the formalism of QM based on our existing understanding!This is why, in previous threads in PF, I disagree that we should teach students the concepts of QM FIRST, rather than the mathematical formulation straightaway. There is nothing to "build on" in terms of conceptual understanding. We end up telling the students what they are out of thin air. The postulates of QM did not come out of our classical understanding of our world. Instead, the mathematical formalism is the only thing that saves us from dangling in mid air. It is the only thing in which our existing understanding can be built on.What this implies clearly is that, if one lacks the understanding of the mathematical formalism of QM, one really hasn't understood QM at all! One ends up with all these weird, unexplained, unfamiliar, and frankly, rather strange ideas on how the world works. These conceptual description QM may even appear "mystical". It is not surprising that such connections are being made between QM and various forms of mysticism. One lacks any connection with the existing reality that one has understood. So somehow, since QM can do this, it seems as if it's a license to simply invent stuff weely neely.The mathematical formalism of QM is what defines the QM description. The "conceptual description" is secondary, and is only present because we desire some physical description based on what we already have classically. It is why people can disagree on the interpretation of QM, yet they all agree on the source, the mathematical formalism of QM.This, however, does not mean that QM is nothing more than "just mathematics". This is no more true than saying the musical notes on a sheet of paper are just scribbles. The notes are not the important object. Rather, it is the sound that it represents that's the main point. The musical notes are simply a means to convey that point clearly and unambiguously. Similarly, the mathematics that is inherent in QM and in all of physics, is a means to convey an idea or principle. It is a form of communication, and so far it is the ONLY form of communication accurate and unambiguous enough to describe our universe. It reflects completely our understanding of a phenomena. So a mathematical formulation isn't "just math".You cannot use your existing understanding of the universe to try to understand the various concepts of QM. There is a discontinuity between the two. It is only via the mathematical continuity of the description can there be a smooth transition to build upon. Without this, QM will not make "sense".Author: ZapperZOriginally posted on Jun16-14[/QUOTE]QM seeks to explain the real, rational physical universe. A good teacher can explain it in real, rational, physical language. Too often, specialists create their own unique worldview and lose touch with the ordinary uniververse. If you can't explain it, it has no value outside its unique community. In the ordinary world, Schrödinger's Cat is stuck in a poorly conceived experiment with a nonsensical hypothesis.
From my experience, undergraduate QM wasn't too difficult. Yes, there were things that weren't fully explained, but if you were willing to take them for granted and follow a few simple rules, it wasn't bad at all. The real hard stuff comes at the graduate level, and I think you need a really good grasp of classical mechanics to truly understand what's going on. Bohm's book Quantum Theory is quite possibly the best QM text I've come across. He highlights the parallels between CM and QM and also draws from what was known from experiments at the time. So it doesn't feel like you're learning QM by pulling random stuff out of thin air. Everything is explained very clearly. I highly recommend the book.
[quote="Greg Bernhardt, post: 4821250"]… I strongly believe that it all comes down to how we understand things and how we expand our knowledge…. One lacks any connection with the existing reality that one has understood… [/QUOTE]In case you wish to consider the view of a non-physicist, I would suggest to introduce QM to newcomers as a pure phenomenology, since it is nothing else in a first instance: 1- the mathematical formalism of QM deals with a range of experiments which have a “potential” for producing a flow of random discrete events amongst a well defined set, each experiment being characterised by: i) a reproducible statistical distribution, and ii) a continuous variation of this distribution in response to a continuous variation of a single operational parameter, for example the relative orientation or the distance between two devices in the experimental set-up.The “potential” (understood as a property of the experiment, not as a property of an hypothetical “system” located in the world) can be formally represented by the orientation of a unit vector in a Hilbert space (the list of cosines which define this orientation therefore corresponds to the list of coordinates of the usual “state vector”).2- one can infer the general form of the equation which predicts the evolution of the potential in response to a continuous change of the experimental context, namely when the variable parameter changes value in a continuous way, under the assumption that this evolution is independent of the initial state. 3- an extension of this formalism can be derived dealing with nested experimental setups such as the addition of new “analysers” in a series. These are typically non-continuous changes of the experimental set-up, and they naturally translate into discontinuous evolutions of the potential insofar it gets projected onto a different base of the same Hilbert space. It is essential to note that as long as it is not interpreted as a property of “something” located inside the experimental device, the potential is a-local. Therefore the famous “measurement problem” cannot arise (the “collapse” of the state vector is assumed to occur inside the experimental device).4- a further extension of the formalism deals with the combination of two contexts of the same family, leading to the combination of the contributing potentials into a new one. The distribution observed derives from the new combined potential, not from a direct combination of distributions.My recommendation would be to proceed through this purely phenomenological presentation of the QM formalism which never suggests that the “potential” might represent “something of the world”, and clearly refrains from promoting the belief that QM ought to be a “physics theory”, I mean a theory describing what there is in the world, how it works or what happens there inside the experimental device. This approach would be extremely concrete, directly connected to a series of well-known experiments. Emphasis would be made on clarifying which subset of the QM formalism can be derived on the basis of pure phenomenological considerations, taking due account of the symmetries within each context of the experimental setup and within the family of all contexts explored through varying the operational parameters: students should be taught the exemplary rationality of QM as a phenomenology before being prompted with the intricacies and paradoxes resulting from its interpretations as a physics theory. I think this approach could resolve the issue raised by the OP whereby: “One lacks any connection with the existing reality that one has understood.”
[quote="Greg Bernhardt, post: 4821250"]Strangely enough, QM's formalism isn't any more difficult than other areas of physics. The mathematics of the "standard" QM isn't any worse than, let's say, electromagnetism. Yet, to many people, especially non-physicists, QM presents a very daunting effort to understand.[/QUOTE]Probably there is nothing to understand for a man which expects some new, original knowledge.People want a new knowledge, but there is nothing new knowledge in the QM, but just a concept, convention, ie. a model with unrealistic ideas, entities like the half-spin, which is just a fundamental thing in this model.[quote="Greg Bernhardt, post: 4821250"]You can't explain these using existing classical concepts. The line between these two is not continuous, at least, not as of now. How does one use classical idea of a "spin" to explain a spin 1/2 particle in which one only regains the identical symmetry only upon two complete revolutions? We simply have to accept that we use the same word, but to ONLY mean that it produces a magnetic moment. It has nothing to do with anything that's spinning classically. We can't build the understanding of the QM spin using existing classical spin that we have already understood.[/QUOTE]That's the problem: the half-spin is just a mathematical sketch.It is no a coincidence the Sommerfeld solution is identical with the solutions of the Dirac equation for the hydrogen like atom, despite Sommerfeld doesn't used any intrinsic spin concept.The QM is just too much primitive, because completely artificial – numerical concept, thus this is unsatisfactory for people which are looking for a theory, ie. understanding, not a computational machine only.QM is good enough maybe for engineers, but not for the real scientists.
[quote="TrickyDicky, post: 4827164"]I'm not sure what you mean by saying that QM is very different in this regard, what are you calling QM exactly? Because the endless interpretational debates are mostly about "Schroedinger's QM", that you cite as an example of theory for wich we we know what it means to break down.[/QUOTE]I'm using QM in a more general sense than Schrodinger's equation. QFT is the quantum mechanics of fields.