Insights Why Is Quantum Mechanics So Difficult? - Comments

[microsansfil]

But the general axiomatisation of physics is beyond that.

But In the spécific of QM axiomatic is only your speech ? From the same axiomatic we can build different semantics. In mathematics is Model theory. The link between semantic and syntax is build by Gödel's completeness theorem.

Patrick

 

[atyy]

But In the spécific of QM axiomatic is only your speech ? From the same axiomatic we can build different semantics. In mathematics is Model theory. The link between semantic and syntax is build by Gödel's completeness theorem.

Yes, the derivations must put in some "semantics", or rather "physics". Semantics is the assignment of sets (and to use sets we have to have natural language) to meaningless symbols and grammar. Physics is the assignment of things we see and things we do to meaningless symbols and grammar. Even Euclidean geometry has different physical interpretations because of the duality between lines and points in the theory, so a physical line can correspond to a point in the theory. The derivations of Hardy or Chiribella et al start from the same physics background as standard Copenhagen - we assume a commonsense macroscopic world, and we know what a measurement (a little black box that takes an input and gives an output). They are alternative axioms for Copenhagen, in the same sense that the Hilbert action, the Palatini action and the Einstein field equations are different axioms for the same classical theory of gravity.

 

[bhobba]

he actually goes and claims Copenhagen is wrong?

Yes that's an error - one of its, fortunately, minor ones.

Why put yourself through such nonsense when you've got Landau, Dirac and Von Neumann sitting right there... I guess QM is so hard because people ignore the good books.

You mean Von-Neumann's thrashing of the Dirac Delta function that Ballentine rectifies? Things have moved on a lot since that classic was penned.

I am not going into the issues with the others, but will point out Ballentine is the only one of those that explains the true foundation of Schroedinger's equation etc - the symmetries of the POR.

Otherwise it looks basically like it's pulled out of a hat.

Dirac comes closest with his algebraic approach to Poisson Brackets but it doesn't explain why it holds. The POR is a general law applicable to all physics.

Thanks
Bill

 

[atyy]

Finally a bit of substance regarding this book. So Ballentine a) not only doesn't make the flaws explicit, b) he actually goes and claims Copenhagen is wrong? Mix that with c) You have to use a different system of probability (apparently equivalent after you do a ton of work and change your entire perspective of probability), d) you have to treat single particle systems in some weird way, & a potential e) your only benefit is fewer axioms at the expense of a less general form of QM, where as you say it's even questionable that he can achieve QM at all. I haven't read any of the guys bragging about Ballentine on here mention any of this stuff, these are such serious issues that I'm amazed tbh...

Why put yourself through such nonsense when you've got Landau, Dirac and Von Neumann sitting right there... I guess QM is so hard because people ignore the good books.

Thanks man

OK, maybe I was a bit hard on Ballentine claiming that Copenhagen is wrong. Strictly, speaking he only claims that his caricature of Copenhagen is wrong. But as you can see, even bhobba who likes the book makes far stronger criticisms of Ballentine's earlier interpretation - the claim that the earlier Ensemble Interpretation is secretly Bohmian is very strong criticism. Nothing wrong with being Bohmian of course, but the assumption should be stated clearly. Ballentine is vague enough, and doesn't even mention the Heisenberg cut, unlike Landau and Lifshitz or Weinberg, that I don't know if I agree with bhobba. But yes, if Ballentine is secretly Bohmian that would make a lot of sense, since one would then not need to add an assumption that proper and improper mixtures are equivalent, an assumption Ballentine makes in his book but fails to state. It also seems that Ballentine is secretly Many-Worlds, since he seems to want to have unitary evolution of the wave function and nothing else. Maybe he is secretly Bohmian Many-Worlds, which is possible, since Bohmian mechanics has unitary evolution of the wave function.

 

[bhobba]

Strictly, speaking he only claims that his caricature of Copenhagen is wrong. But as you can see, even bhobba who likes the book makes far stronger criticisms of Ballentine's earlier interpretation - the claim that the earlier Ensemble Interpretation is secretly Bohmian is very strong criticism.

Very true. BTW the BM thing is fixed in the book - but at a cost.

Don't get me wrong.

It has issues eg I think that propensity stuff is a crock of the proverbial - I wouldn't touch it with a barge pole.

But you have to look at it overall.

His explanation of the math, for example, is simply a cut above, even giving an overview of the important Rigged Hilbert Space formalism.

Thanks
Bill

 

[TrickyDicky]

On the other hand, the thing that is puzzling about QM as an incomplete theory is that there are no hints as to the limits of its applicability. There are no hints as to what more complete theory might replace it.

And if there were you couldn't mention them here anyway, so there are reasons to waffle on about beside the point interpretational debates.

 

[atyy]

Very true. BTW the BM thing is fixed in the book - but at a cost.

Don't get me wrong.

It has issues eg I think that propensity stuff is a crock of the proverbial - I wouldn't touch it with a barge pole.

But you have to look at it overall.

His explanation of the math, for example, is simply a cut above, even giving an overview of the important Rigged Hilbert Space formalism.

Thanks
Bill

Yes, I agree that Ballentine's presentation of the symmetries in the first few chapters is valuable, and hard to find elsewhere. So I would say use Ballentine for the "maths" (I put it in quotes because he presents it in a nice physicky way, which I don't know if strict mathematicians will like), but not so much for the interpretation, which is (at best) Copenhagen renamed.

 

[stevendaryl]

And if there were you couldn't mention them here anyway, so there are reasons to waffle on about beside the point interpretational debates.

Well, what I mean is this: People are pretty sure that General Relativity has to break down when it comes to conditions where both gravity and quantum mechanics are important. People knew that Schrodinger's equation wouldn't work relativistically. Fermi knew that his original model for weak interactions had to break down at high energy (because it wasn't renormalizable). Balmer knew that his formula for the energy spectrum of hydrogen can't possibly be the final theory, because it was clearly ad hoc. Einstein knew from early on that Special Relativity wouldn't work in cases where gravity was important. So a lot of theories of physics are provisional, and the people who create them already know that they aren't the final answer, and they often know the conditions under which their theories will turn out to be wrong. But QM is very different in this regard, in that nobody has a clue as to what conditions would cause it to break down.

 

[atyy]

Well, what I mean is this: People are pretty sure that General Relativity has to break down when it comes to conditions where both gravity and quantum mechanics are important. People knew that Schrodinger's equation wouldn't work relativistically. Fermi knew that his original model for weak interactions had to break down at high energy (because it wasn't renormalizable). Balmer knew that his formula for the energy spectrum of hydrogen can't possibly be the final theory, because it was clearly ad hoc. Einstein knew from early on that Special Relativity wouldn't work in cases where gravity was important. So a lot of theories of physics are provisional, and the people who create them already know that they aren't the final answer, and they often know the conditions under which their theories will turn out to be wrong. But QM is very different in this regard, in that nobody has a clue as to what conditions would cause it to break down.

Yes, there are two sorts of theories: those which can be a theory of some universe, and so experiment, and experiment alone tell us it must break down (eg. Newtonian gravity), while there are others where the theory itself tells us it must breakdown (eg. QED, if there is no asymptotic safety). Copenhagen itself suggests QM must breakdown, since Copenhagen typically does not acknowledge a wave function of the universe. Interpretations such as Bohmian Mechanics would place QM together with QED, and so far these are the only interpretations that are known to be without technical flaw (except maybe for chiral interactions). Bohmian Mechanics says that QM must break down, because it requires the quantum equilibrium condition, which is analogous to equilibrium in statistical mechanics. For the ensembles to emerge from a single reality, there has to be non-equilibrium in reality, but not detectable over the resolutions that we are able to access at the moment. If pure Many-Worlds works, then QM could conceivably be a theory of some universe, just like Newtonian gravity.

 

[TrickyDicky]

Well, what I mean is this: People are pretty sure that General Relativity has to break down when it comes to conditions where both gravity and quantum mechanics are important. People knew that Schrodinger's equation wouldn't work relativistically. Fermi knew that his original model for weak interactions had to break down at high energy (because it wasn't renormalizable). Balmer knew that his formula for the energy spectrum of hydrogen can't possibly be the final theory, because it was clearly ad hoc. Einstein knew from early on that Special Relativity wouldn't work in cases where gravity was important. So a lot of theories of physics are provisional, and the people who create them already know that they aren't the final answer, and they often know the conditions under which their theories will turn out to be wrong. But QM is very different in this regard, in that nobody has a clue as to what conditions would cause it to break down.

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 which we we know what it means to break down.

 

[stevendaryl]

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 which we we know what it means to break down.

I'm using QM in a more general sense than Schrodinger's equation. QFT is the quantum mechanics of fields.

 

[atto]

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.

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.

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.

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.

 

[Sugdub]

… 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...

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.”

 

[Sandalwood]

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.

 

[Rabin D Natha]

Author: ZapperZ
Originally posted on Jun16-14

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 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: ZapperZ
Originally posted on Jun16-14

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.

 

[Fredrik]

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.

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).

 

[bhobba]

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).

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.

Thanks
Bill

 

[vanhees71]

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).

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!

 

[bohm2]

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).

Even at a conceptual level QM is not complete as pointed out by Goldstein:

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.

And the solution does not eliminate the problem:

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.

 

[Fredrik]

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!

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).

 

[bhobba]

Even at a conceptual level QM is not complete as pointed out by Goldstein:

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.

And the solution does not eliminate the problem:

Some interpretations do, but raises others.

Thanks
Bill

 

[RUTA]

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).

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.

 

[exponent137]

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.

 

[ShayanJ]

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).

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!

 

[Fredrik]

QM says all things happen.

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.

Of course these are in the context of Copenhagen interpretation!

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.

 

[bhobba]

QM says all things happen.

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.pdf

What 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.

Thanks
Bill

 

[ShayanJ]

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.

 

[bhobba]

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.

The mathematical part is what is known as a generalised probability model or theory:
http://arxiv.org/pdf/1402.6562v3.pdf
http://www.mathematik.uni-wuerzburg.de/sommerschule2011/download/ln-janotta.pdf

The 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.

Thanks
Bill

 

[ShayanJ]

The physical part is, lust like probability theory where you have abstract events and apply it to various things, you apply it to observations.

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!

 

[Demystifier]

One of the reasons for quantum mechanics be so difficult is this:
https://www.physicsforums.com/threads/what-is-quantum-theory-about.767672/