I Quantum mechanics is not weird, unless presented as such

[Dadface]

Popular quantum magicians are at the same time very experienced specialist QM practitioners in quantum optics. They at least like to create for their audience the impression that parts of quantum mechanics is weird. This is common to magicians in any field, and not specific to quantum mechanics.

But since they understand their profession, I don't think any of our quantum magicians thinks that quantum mechanics is truly weird. It is fully rational to the mind sufficiently trained in mathematics and theoretical physics. This is why I think (and expressed in the title of the thread) that it is only the presentation that makes quantum mechanics appear weird.

Forgive me if I am wrong about this but I have the impression that the main target audience for your book are the expert QM practitioners and teachers. I think your book might have much wider appeal if you included a brief opening section summarising those aspects of the subject which may appear to be weird.

 

[A. Neumaier]

Forgive me if I am wrong about this but I have the impression that the main target audience for your book are the expert QM practitioners and teachers. I think your book might have much wider appeal if you included a brief opening section summarizing those aspects of the subject which may appear to be weird.

My book is for those who (perhaps do not yet but) want to understand quantum mechanics on a serious level and have sufficient background in linear algebra and analysis. The course the book is based on was for mathematics master students. But most physics students can probably read it too after they mastered a course on classical mechanics covering the Lagrangian and Hamiltonian approach and the Poisson bracket.

In the book, I don't even mention weirdness! Thus people can see that one can set up everything of theoretical and practical interest in quantum mechanics without encountering anything weird. Opening the book with a chapter on quantum weirdness would defeat that purpose.

The book is a blueprint for possible courses on weirdless quantum mechanics. But it would be far more work than I can presently afford to actually turn it into a textbook that could replace a standard introduction to quantum mechanics. Thus it is explicitly designed as complementary reading for a standard textbook on quantum mechanics. But those prepared to invest some serious effort can study the book by itself. I even had feedback from several 16 years old self-learners who profited from the book.

 

[ddd123]

Neumaier: would you consider the Copenhagen interpretation weird? After all you propose your own thermal interpretation. If so, it may not just be a matter of exposition but of mathematical interpretation (collapse is pretty weird for example).

 

[Dadface]

My book is for those who (perhaps do not yet but) want to understand quantum mechanics on a serious level and have sufficient background in linear algebra and analysis. The course the book is based on was for mathematics master students. But most physics students can probably read it too after they mastered a course on classical mechanics covering the Lagrangian and Hamiltonian approach and the Poisson bracket.

In the book, I don't even mention weirdness! Thus people can see that one can set up everything of theoretical and practical interest in quantum mechanics without encountering anything weird. Opening the book with a chapter on quantum weirdness would defeat that purpose.

The book is a blueprint for possible courses on weirdless quantum mechanics. But it would be far more work than I can presently afford to actually turn it into a textbook that could replace a standard introduction to quantum mechanics. Thus it is explicitly designed as complementary reading for a standard textbook on quantum mechanics. But those prepared to invest some serious effort can study the book by itself. I even had feedback from several 16 years old self-learners who profited from the book.

I understand. Thank you and good luck with your book.

 

[A. Neumaier]

Neumaier: would you consider the Copenhagen interpretation weird? After all you propose your own thermal interpretation. If so, it may not just be a matter of exposition but of mathematical interpretation (collapse is pretty weird for example).

Yes, the Copenhagen interpretation is weird. Not because of Bell-type experiments but for much more elementary reasons. A particle has no properties unless measured; in particular it has no position and no momentum. Then how can a particle emitted from a source in a particular direction know that it has to appear some roughly predictable time later on the screen on the other side of the room in this direction? How can we analyze any experiment if we do not assume that the particles we prepare in our laboratory are indeed in the laboratory and stay there, so that position makes at least approximately sense? The Copenhagen interpretation is nothing-or-all, which is completely incompatible with how we think about quantum mechanics in actual experiments. It is valid only in very special circumstances where attention is focused exclusively on a few discrete quantum degrees of freedom. The collapse, an integral part of the Copenhagen interpretation, is provably invalid for position measurement. Upon a position measurement, the state of a system never goes into an eigenstate of the position operator since such eigenstates don't exist. And lots of similar things are wrong with the Copenhagen interpretation. It is a can of worms if you open it...

Thus in my view, the Copenhagen interpretation in the form of the traditional textbooks postulates is a very idealized approximation to a description relating quantum mechanics and reality. It is a relic of the early days where quantum experiments were restricted to very simple systems and a theory for realistic measurements didn't exist. It survives only because it is in so many textbooks, since it allows writers and teachers to spell out the foundations of quantum mechanics in 3-5 axioms (depending on who formulates the details) together with two standard experiments to make the axioms look plausible - and then never return to it but to practice shut-up-and-calculate. The price for this apparent simplicity is that all those who want to have a better understanding of quantum mechanics are haunted for the rest of their lives by the resulting quantum weirdness.

 

[dextercioby]

But prof. Neumaier or Arnold, however you prefer (I know that German is much more polite language), we have the concept of the so-called unsharp measurements, that is a way to circumvent strict collapse for observables with (partially) continuous spectrum. The only international (text)book that I know that briefly discusses this is "Quantum Mechanics" by Claude Cohen-Tannoudji, Bernard Diu and Frederic Laloë, p. 263 till 266 of the 1st edition of the English translation.

 

[A. Neumaier]

we have the concept of the so-called unsharp measurements, that is a way to circumvent strict collapse for observables with (partially) continuous spectrum.

Yes, that's why I called the Copenhagen interpretation

a relic of the early days where quantum experiments were restricted to very simple systems and a theory for realistic measurements didn't exist.

Unsharp measurements model realistic measurements in a much better way and can account for particles having an unsharp position and momentum. But such measurements flatly contradict the Copenhagen interpretation and at least some formulations of the Born rule, for example the version stated in Wikipedia's article on Born's rule:

The Born rule states that if an observable corresponding to a Hermitian operator

with discrete spectrum is measured in a system with normalized wave function

(see bra–ket notation), then

• the measured result will be one of the eigenvalues
  
  of [PLAIN]https://upload.wikimedia.org/math/7/f/c/7fc56270e7a70fa81a5935b72eacbe29.png, and
• the probability of measuring a given eigenvalue
  
  will equal
  

In the case where the spectrum of

is not wholly discrete, the spectral theorem proves the existence of a certain projection-valued measure [PLAIN]https://upload.wikimedia.org/math/f/0/9/f09564c9ca56850d4cd6b3319e541aee.png, the spectral measure of [PLAIN]https://upload.wikimedia.org/math/7/f/c/7fc56270e7a70fa81a5935b72eacbe29.png. In this case,

• the probability that the result of the measurement lies in a measurable set
  
  will be given by [PLAIN]https://upload.wikimedia.org/math/5/f/f/5ff5270179153c7fa9ac6a55fbb6f551.png.

In fact, once one allows for unsharp measurements one is already very close to my thermal interpretation - where position and momentum always exist independent of measurement, except that they are always unsharp. Infinitely precise position and momentum is a classical idealization, convenient when it applies but nowhere needed in physical practice.

 

[adeborts]

together with two standard experiments to make the axioms look plausible

Which are those?
Are the experiments replicable?
Are the attendant axioms provably untenable?
Are the observations of the experiments' outcome unexplainable?
Are all these, after all, still considered part and parcel of the QM?
If they are, do you have an explanation for the conundrum they pose?
If they are not, can you articulately dismiss them?
If you don't have a cogent explanatus for the above, would this turn any theory that doesn't have it - including yours - into just another Zeitvertreib?

Can you elucidate why in this, or a related thread, you qualify some conjectures/theories, constitutive of your panorama, as out-of-date - but imperturbably proceed to proffer some new ones?
Wouldn't the above Kunststück, coupled with the awareness of its occurrence, generate some hesitation in your pronouncements?

I am merely asking ...

 

[vanhees71]

First you have to be clear about which flavor of "Copenhagen" you mean. I think that flavors of Copenhagen interpretations that don't envoke the collapse postulate are the lest weird interpretations. Among them is the minimal interpretation, taking Born's rule simply as additional postulate and just take the meaning of the state as probabilistic, and that's just the vital core of interpretations necessary to use the formalism to real-world observations.

It's also of course an empty phrase to state that you don't know anything about a particle if nothing about its state is given. Quantum theory as physics is a whole is about observations of specific situations in nature. In an experiment, e.g., in particle physics, you pretty carefully prepare particles using an accelerator with a pretty well determined momentum. In fact in an accelerator like the LHC particles run in 2808 packets (bunches) per beam, each bunch containing about $10^{11}$ protons. Each beam is some cm long and about a mm wide. At the collision point it's squeezed to $\mu\mathrm{m}$ size. At each bunch crossing up to 20 collisions occur. So you have a pretty good determination of the protons' location with a pretty well determined momentum at the interaction point. Without that you'd not be able to get proton collisions in a collider with a sufficiently well defined collision (center of momentum) energy to be meaningful for particle physics. All this is, of course, fully consistent with quantum theory, and for sure it's nothing weird about it, although just remarkable and amazing to which precision one can construct accelerators and detectors testing the predictions of quantum theory (in this case the Standard Model of elementary particles, i.e., relativistic quantum field theory).

So what's done is indeed to prepare particles (protons) in a well defined state so that they can collide and then one measures the outcome of such a collision, and you do that many times to "collect statistics". It's precisely what's reflected in the formalism of QT without any weird assumptions on collapses, many worlds, de Broglie-Bohm trajectories (btw. the trajectories of the protons in the acclerator are calculated at an accuracy, enabling the accelerator physicists to design such high-precision machines, with good old classical physics which principles you learn in your E&M lecture in the 3rd-4th semester at the university, although of course much refined!), Qbism and what do I know other more or less esoteric ideas on the socalled "meaning of quantum mechanics", which in the popular culture sometimes even takes features of a kind of religion rather than good science!

 

[quantumgeography]

Does quantum mechanics have to be weird?

.

,,It is safe to say that nobody understands quantum mechanics.'' Richard Feynman.
I think QM will not be so weird, if it will be as usual as history lessons in a school programs. The only problem here is that a lot of people are not ready for this.

 

[ddd123]

So you have a pretty good determination of the protons' location with a pretty well determined momentum at the interaction point. Without that you'd not be able to get proton collisions in a collider with a sufficiently well defined collision (center of momentum) energy to be meaningful for particle physics. All this is, of course, fully consistent with quantum theory, and for sure it's nothing weird about it, although just remarkable and amazing to which precision one can construct accelerators and detectors testing the predictions of quantum theory (in this case the Standard Model of elementary particles, i.e., relativistic quantum field theory).

Are you referring to the HUP?

 

[vanhees71]

Of course science is embedded in social acitivity, but it is independent of a "worldview" since the only thing that counts is the success or failure to describe what's objectively and reproducibly observable. Of course, that limits its purpose to a subset of human experience but it cannot contradict any religion, and it's always possible that one day a reproducible observation invalidates the today "valid" theories and models. That happens astonishingly rarely but it happens. Famous examples are relativity which lead to abondaning the hitherto "valid" Newtonian theory about space and time. It also explained, why Newtonian mechanics is so successful in its realm of applicability. Even more extreme was the discovery of quantum theory, which lead to a total reconception of what "reality" itself means.

That's a great difference to religion, where you have to believe some basic principles without questioning them. This is contrary to any good practice in science. Although being better conservative and trying to understand any "new" phenomenon first with the so far considered valid models, one has to be open to the possibility that these models may be not always valid and observations and experiments may lead to a revision of the models. There's no "worldview" that supersedes this basic principle of how science works. You can argue as much as you like that, e.g., QT is incompatible with your worldview. From a scientific point of view this is fully irrelevant to the progress of science. Here only observable objective facts rule about the validity of models!

 

[vanhees71]

Are you referring to the HUP?

Among other things yes. I referred to the claim that due to quantum theory you don't know any property if you don't measure it. Of course, if you don't have any knowledge about whether there are protons or not, you don't know anything, but that's a tautology. I took as an extreme example to the contrary a modern accelerator, where one knows a lot about the protons accelerated by it, because it is obviously possible to prepare protons quite accurately, and all this is of course in accordance with quantum theory. If it were not, we'd have to give up quantum theory and look for a better model, but to the contrary QT is fully compatible with all observations so far, and it's simply not true that we don't know anything about particles only because quantum theory provides "only" probabilistic information about observables.

To put it in another, even more simple, way: Over all the mathematically sophisticated formalism, which is necessary because it's the only way to describe our observations and theoretical understanding adequately and unambiguously, one must not forget, what's really observed in the labs concerned with QT. Then the theory looses much if not all of its weirdness!

 

[ddd123]

Unless they're Bell tests or quantum erasers etc :)

 

[vanhees71]

Well, if you accept quantum theory (in the minimal interpretation), there's nothing weird anymore about Bell tests (to the contrary they confirm with high precision the predictions of quantum theory, violating the Bell inequality with a very high confidence level) or quantum erasers (you just choose different partial ensembles using a fixed measurement protocol). The very fact that such "postselection" works is also a strong confirmation for the principles of quantum theory.

Admittedly, from the point of view of our classically trained everyday experience these findings are quite weird, but not from the point of view of QT :-).

 

[vanhees71]

I don't know, how science should apply to single events like this story about G. W. Bush. It's a single event and most likely a coincidence that somebody could predict this. Is it clear that somebody really "predicted" this outcome of G. W. Bush's predidency and events concerning China or is this made up on some conspiracy web page?

I don't understand what you mean with this assertion concerning light. What's the context of this?

The objective observer of facts nowadays can be an electronic device providing measurement results at high accuracy (as used in all kinds of experiments in all kinds of labs across the world) and finally physicists evaluating these fixed facts about nature.

 

[A. Neumaier]

I think that flavors of Copenhagen interpretations that don't envoke the collapse postulate are the lest weird interpretations. Among them is the minimal interpretation

The minimal interpretation is significantly different from any version that deserves (in my view) to be called Copenhagen. In the Copenhagen interpetation (prevailing until the 1970es), each single object is in a well-defined (though possibly unknown) pure state, which collapses to a different state upon measurement. In contrast, in the (much later sensibly defined) minimal, statistical interpretation, the state is a property of the source (i.e., preparation procedure), not of the single quantum object. If you call the minimal interpretation a flavor of Copenhagen then the term ''Copenhagen interpretation'' loses its discriminating meaning.

At the collision point it's squeezed to μm size. At each bunch crossing up to 20 collisions occur. So you have a pretty good determination of the protons' location with a pretty well determined momentum at the interaction point.

I fully agree. My point is just that this is in flat contradiction to what one reads in the highly idealized presentations and discussions of axioms/postulates concerning the interpretation of quantum mechanics.

Both preparation and measurement are complex procedures with nontrivial qualifications of what it means to have prepared something and what counds as a measurement result, and to which accuracy something is prepared and measured. This is simply pushed aside by simplistic, strictly speaking invalid, statements given the status of postulates or axioms, and it is pretended that these are the ''foundations'' on which uantum mechanics rests. In reality, quantum mechanics rests on much stronger - and a bit more complicated - pillars that have almost nothing to do with complicated measurement processes (which are only used to verify the validity of the theory). The traditional foundations are but a caricature of the real thing.

 

[A. Neumaier]

Over all the mathematically sophisticated formalism, which is necessary because it's the only way to describe our observations and theoretical understanding adequately and unambiguously, one must not forget, what's really observed in the labs concerned with QT. Then the theory loses much if not all of its weirdness!

This is indeed the ostensible purpose of an interpretation. To relate shut-up-and-calculate to what's really observed in the labs. if it is done well, it proves the title of the present thread. But the textbook interpretations idealize far too much, so that if their postulates are taken too seriously, one ends up with lots of weirdness.

 

[ddd123]

Just to be sure, the minimal interpretation is the ensemble interpretation, right? As presented in Ballentine for example.

 

[A. Neumaier]

Just to be sure, the minimal interpretation is the ensemble interpretation, right? As presented in Ballentine for example.

Yes, minimal = ensemble = statistical interpretation, as in Ballentine and Peres. I prefer Peres, since he discusses it in a context that makes sense for real measurements.

 

[ddd123]

Okay I was wondering about this article on the HUP: http://plato.stanford.edu/entries/qt-uncertainty/ :

it is not straightforward to relate the spread in a statistical distribution of measurement results with the inaccuracy of this measurement, such as, e.g. the resolving power of a microscope. Moreover, the minimal interpretation does not address the question whether one can make simultaneous accurate measurements of position and momentum. As a matter of fact, one can show that the standard formalism of quantum mechanics does not allow such simultaneous measurements. But this is not a consequence of relation $\Delta_\psi p \Delta_\psi q \geq \hbar / 2$.

If one feels that statements about inaccuracy of measurement, or the possibility of simultaneous measurements, belong to any satisfactory formulation of the uncertainty principle, the minimal interpretation may thus be too minimal.

1) if it's not a consequence of that inequality, what is it a consequence of in orthodox quantum theory?
2) is the minimal interpretation too minimal as the article says?

 

[vanhees71]

The Heisenberg uncertainty relation, as proven in any modern textbook on QM, does not describe the disturbance of the system by measurement but a constraint on the accuracy with which position and momentum of a particle can be determined, i.e., it tells you that in any state of a particle, the standard deviations fulfill this inequality, and that's it.

I also disagree with the statement that the minimal interpretation is too minimal (at least in this context), since before you make statements about accuracy disturbance relations you have to define precisely what you mean by this. This is, by the way, an ongoing debate in the literature, but not a severe obstacle of quantum theory in my opinion, since this disturbance is defined by the kind of measurements you do on the particle and must be analyzed taking into account the mechanism behind the measurement apparatus for each experimental setup case by case.

 

[ddd123]

What about statements on the accuracy of simultaneous measurements of noncommuting observables on a single system? Could it be too minimal for that?

 

[vanhees71]

As I said, you have to define "simultaneous measurements of noncommuting observables on a single system" by giving a concrete description of the measurement apparatus. The usual Heisenberg uncertainty relation refers to measurements of each single observable on the single system with an accuracy much larger than the expected uncertainty of the single observables. The probabilistic nature of the physical meaning of the quantum state means that you have to measure each variable on an ensemble of independently but equally prepared systems (that's the definition of an ensemble).

There are of course much more general ideas on measuring procedures, i.e., you don't measure the observables accurately but minimize the influence on the system. This is quantified by defining accuracy-disturbance uncertainty relation, and it is still an open debate about them in the literature. Here are some (arbitrary) examples, I collected randomly when finding them on the web. Perhaps one of the other posters can provide a more systematic collection:

http://arxiv.org/abs/1201.1833
http://arxiv.org/abs/1504.04200
https://www.osapublishing.org/viewmedia.cfm?uri=QIM-2013-W6.10&seq=0
http://arxiv.org/abs/1007.3076
http://arxiv.org/abs/quant-ph/0307057
http://arxiv.org/abs/1306.1565

Here's an old posting of mine, nobody ever found interesting, but it summarizes the first citation above:

https://www.physicsforums.com/threa...elation-vs-noise-disturbance-measures.664972/

 

[naima]

The measuring device is a complex system in a metastable "neutral state", which then makes a transition into a stable pointer state through interaction with the microscopic quantity that is being measured. That's understandable. It's exactly what happens in classical mechanics, and is the reason that we can get discrete outcomes ("heads" or "tails") from continuous Newtonian dynamics.

But it's the pairing of distant measurement results in a correlated pair such as EPR that is mysterious. Alice's device is in a metastable state, and when it interacts with a spin-1/2 particle, it falls into a stable pointer state. Similarly for Bob's device. But to describe the transition using statistical mechanics seems to make the fact that Alice's and Bob's results are perfectly anti-correlated even more mysterious. If the measurement process is inherently statistical, then how does perfect anti-correlation come about?

I read this old question about weirdness.
When a system is prepared in a given state it is often in an eigenvector of an observable. if you re-measure the system to get this observable you get the same value. A measurement for something else give a random output.
There are devices which prepares pairs of particles with a global null spin along all directions. You can verify it even if they are separated. take any direction and ask Alice and Bob to locally measure the spin along it. Ask their results and add them. If you get 0 you have verified the preparation. Il the local directions are not the same you have a random result. It is not surprising because you have measured something else.
Weirdness is not absent but it is somewhere else.

 

[stevendaryl]

I read this old question about weirdness.
When a system is prepared in a given state it is often in an eigenvector of an observable. if you re-measure the system to get this observable you get the same value. A measurement for something else give a random output.
There are devices which prepares pairs of particles with a global null spin along all directions. You can verify it even if they are separated. take any direction and ask Alice and Bob to locally measure the spin along it. Ask their results and add them. If you get 0 you have verified the preparation. Il the local directions are not the same you have a random result. It is not surprising because you have measured something else.
Weirdness is not absent but it is somewhere else.

The weird thing is that (apparently) Alice's result is completely random, and so is Bob's, but they manage to always get the opposite result (when they measure using the same axis). That would not be surprising if their results were predetermined from the moment that the twin pair is created, but that isn't the case.

 

[naima]

Nature is only weird if you believe that it can abswer all YOUR questions.
Nature is a patient good teacher. It comes with datas, with answers. The problem is that the pupil does not understand what the teacher is talking about. It is like in Jeopardy. If you find the question the teacher will always give you as an answer the initial answer.
You know how to compute the spin density matrix as a linear combination of Pauli matrices and the identity matrix. the coefficient are the mean values of the yes/no "random" answers natures gives you. At the end although you never asked the good question your are able to win Jeopardy.
If the good question was about a number of particles (2 here) and a global property measuring a local thing of one of them is not rhe good question but nature does not refuse to help you.

 

[ddd123]

The weird thing is that (apparently) Alice's result is completely random, and so is Bob's, but they manage to always get the opposite result (when they measure using the same axis). That would not be surprising if their results were predetermined from the moment that the twin pair is created, but that isn't the case.

At the cost of sounding polemic, I think we should do either of the following:

1) admit it's weird and suspend judgement until a breakthrough comes, or at most say "I understand why it's weird for you but it doesn't bother me since I have the shut up and calculate framework, which is all I wanted";
2) explain what is missing in the intuitive picture that removes the weirdness in a clear straightforward manner.

I think so far we've seen either 1) or a moral statement that it shouldn't seem weird, then grasping at straws to justify that moral statement. 2) seems to be an unattainable goal at this moment.

 

[vanhees71]

The weird thing is that (apparently) Alice's result is completely random, and so is Bob's, but they manage to always get the opposite result (when they measure using the same axis). That would not be surprising if their results were predetermined from the moment that the twin pair is created, but that isn't the case.

The single results are not predetermined, but the correlation is. So what's surprising or even weird?

 

[vanhees71]

At the cost of sounding polemic, I think we should do either of the following:

1) admit it's weird and suspend judgement until a breakthrough comes, or at most say "I understand why it's weird for you but it doesn't bother me since I have the shut up and calculate framework, which is all I wanted";
2) explain what is missing in the intuitive picture that removes the weirdness in a clear straightforward manner.

I think so far we've seen either 1) or a moral statement that it shouldn't seem weird, then grasping at straws to justify that moral statement. 2) seems to be an unattainable goal at this moment.

My problem is indeed question 2). What's missing? Nothing (yet). We have quantum theory that works very well in describing everything we've observed so far. What else can you wish for and expect to get from the natural sciences?