Why Is Quantum Mechanics So Difficult? - Comments

In summary: I like Landau and Lifshitz too. Their Mechanics book was a revelation; QM, while good and better than most, wasn't quite as impressive to me as Ballintine. But like all books in that series it's, how to put it, terse, and the problems are, again how to put it, challenging, but to compensate actually relevant.
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  • #2
Greg Bernhardt said:
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.

Agree entirely.

The mathematical formalism is required to understand the concepts.

That is exactly the process taken in my favourite QM book, Ballentine, and is much more rational than the semi historical approach usually taken.

The only problem with Ballentine is it is at graduate level.

I have always thought a book like Ballentine, but accessible to undergraduate students, would be the ideal introduction.

In particular it would have a 'watered' down version of the very important chapter 3 that explains the dynamics of QM from symmetry. Its a long hard slog even for math graduates like me - definitely not for undergraduates. But the key results and theorems can be stated, and their importance explained, without the proofs. I think its very important for beginning students to understand the correct foundation of Schroedinger's equation etc from the start - if the not the mathematical detail.

Thanks
Bill
 
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  • #3
I don't think there's one best way. Some learn better using the approach advocated here. Others learn better the other way around.
 
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  • #4
Honestly I think at the undergraduate level QM is the easiest physics class one has to take. It is just a cookbook on calculations. Every book is uninspired and my class was certainly uninspired. It is an incredibly boring subject at this level. So I don't think difficulty is the issue. It is simply the lack of physical concepts and a healthy dose of philosophy that is avoided when teaching QM at the undergraduate level. Indeed one of the professors I know basically called Griffiths' book a cookbook in differential equations. A good book can go a long way. For me the saving grace was Landau and Lifshitz. It is the sole reason I started liking QM. Seriously the way undergrad QM is taught really isn't fun for the students. Boredom from a lack of intellectusl stimulation really isn't how a physics class should be.
 
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  • #5
Hmmm, I still can't derive the Stefan-Boltzmann whatever - chills down my spine. How is that easy?
 
  • #6
atyy said:
Hmmm, I still can't derive the Stefan-Boltzmann whatever - chills down my spine. How is that easy?

What o_O
 
  • #7
WannabeNewton said:
What o_O

Is it easy?
 
  • #8
atyy said:
Is it easy?

Im actually not sure what youre referring to. Are you talking about the Stefan Boltzmann law of radiation? I am not sure what that has to do with undergrad QM apart from historical impetus but there is a particularly lucid derivation in section 9.13 of Reif if youre interested. It's more of a statistical mechanics derivation. Which is good because statistical mechanics, both classical and quantum, is actually extremely interesting at the undergrad level.
 
  • #9
WannabeNewton said:
Indeed one of the professors I know basically called Griffiths' book a cookbook in differential equations.

That I agree with.

I gave it away for health reasons no need to go into here. But I did enrol in a Masters in Applied Math at my old alma mater that included a good dose of QM. When mapping out the course structure with my adviser he said forget the intro QM course - since you have taken courses on advanced linear algebra, Hilbert spaces, partial differential equations etc it's completely redundant. Other students with a similar background to mine were totally bored. He suggested I start on the advanced course right away.

Really I think it points to doing a math of QM course before the actual QM course where you study the Dirac notation etc - basically the first and a bit of the second chapter of Ballentine. You can then get stuck into the actual QM.

And yes - I like Landau and Lifshitz too. Their Mechanics book was a revelation; QM, while good and better than most, wasn't quite as impressive to me as Ballintine. But like all books in that series it's, how to put it, terse, and the problems are, again how to put it, challenging, but to compensate actually relevant.

Thanks
Bill
 
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  • #10
WannabeNewton said:
Im actually not sure what youre referring to. Are you talking about the Stefan Boltzmann law of radiation? I am not sure what that has to do with undergrad QM apart from historical impetus but there is a particularly lucid derivation in section 9.13 of Reif if youre interested. It's more of a statistical mechanics derivation. Which is good because statistical mechanics, both classical and quantum, is actually extremely interesting at the undergrad level.

Actually, I only dimly remember what it is, although it was very exciting. It sounds right that it should be in a stat mech book, because the whole point IIRC was that classical thermodynamics was able to derive all sorts of completely correct things about blackbody radiation, yet classical stat mech could not. Then miraculously when one switched to quantum stat mech everything fell in place with classical thermo. I remember the narrative, but none of the calculations except Planck's. The text we used was Gasiorowicz, and I think his chapter 1 is all about this.

Apart from the Stefan-Boltzmann law, the other amazing derivation was Wien's displacement law. IIRC, these were all from classical thermodynamics, with no quantum mechanics, yet they are correct!
 
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  • #11
WannabeNewton said:
Honestly I think at the undergraduate level QM is the easiest physics class one has to take. It is just a cookbook on calculations. Every book is uninspired and my class was certainly uninspired. It is an incredibly boring subject at this level. So I don't think difficulty is the issue. It is simply the lack of physical concepts and a healthy dose of philosophy that is avoided when teaching QM at the undergraduate level. Indeed one of the professors I know basically called Griffiths' book a cookbook in differential equations. A good book can go a long way. For me the saving grace was Landau and Lifshitz. It is the sole reason I started liking QM. Seriously the way undergrad QM is taught really isn't fun for the students. Boredom from a lack of intellectusl stimulation really isn't how a physics class should be.
Well, the historic approach is bad. You are taught "old quantum mechanics" a la Einstein and Bohr only to be adviced to forget all this right away when doing "new quantum mechanics". I've never heard that it is a good didactical approach to teach something you want the students to forget. They always forget inevitably most important things you try to teach them anyway, but in a kind of Murphy's Law they remember all the wrong things being taught in the introductory QM lecture.

You see it in this forum: Most people remember the utmost wrong picture about photons, and it is very difficult to make them forget these ideas, because they are apparently simple. The only trouble is they are also very wrong. As Einstein said, you should explain things as simple as possible but not simpler.

Concerning philosophy, I think the healthy dose is 0! Nobody tends to introduce some philosophy in the introductory mechanics or electrodynamics lecture. Why should one need to do so in introdutory QM?

If you want to rise interpretational problems at all, you shouldn't do this in QM 1 or at least not too early. First you should understand the pure physics, and that's done with the minimal statistical interpretation. If you like Landau/Lifshits (all volumes are among the most excellent textbooks ever written, but they are for sure not for undergrads; this holds also true for the also very excellent Feynman lectures which are clearly not a freshmen course but benefit advanced students a lot), I don't understand why you like to introduce philosophy into a QM lecture. This book is totally void of it, and that's partially what it makes so good ;-)).
 
  • #12
vanhees71 said:
Well, the historic approach is bad. You are taught "old quantum mechanics" a la Einstein and Bohr only to be adviced to forget all this right away when doing "new quantum mechanics". I've never heard that it is a good didactical approach to teach something you want the students to forget. They always forget inevitably most important things you try to teach them anyway, but in a kind of Murphy's Law they remember all the wrong things being taught in the introductory QM lecture.

Abso-friggen-lutely.

And to make matters worse they do not go back and show exactly how the correct theory accounts for the historical stuff and students are left with a sort of hodge podge, not knowing what's been replaced and what changed or the why of things like the double slit experiment.

Thanks
Bill
 
  • #13
WannabeNewton said:
It is just a cookbook on calculations.
May be QM is primarily predictive. Quantum mechanics construed as a predictive structure. After we try to interpret it with épistemic or ontological human sense.

For example "The debate on the interpretation of quantum mechanics has been dominated by a lasting controversy between realists and empiricists" : http://michel.bitbol.pagesperso-orange.fr/transcendental.html

Patrick
 
  • #14
microsansfil said:
May be QM is primarily predictive. Quantum mechanics construed as a predictive structure. After we try to interpret it with épistemic or ontological human sense. For example "The debate on the interpretation of quantum mechanics has been dominated by a lasting controversy between realists and empiricists" : http://michel.bitbol.pagesperso-orange.fr/transcendental.html

I think philosophers worry more about that sort of thing more than physicists or mathematicians.

An axiomatic development similar to what Ballentine does is all that's really required, with perhaps a bit of interpretational stuff thrown in just to keep the key idea behind the principles clear.

And I really do mean IDEA - not ideas - see post 137:
https://www.physicsforums.com/showthread.php?t=763139&page=8

It always amazes me exactly the minimal assumptions that goes into QM and what needs 'interpreting'.

Thanks
Bill
 
  • #15
When discussing the best approach to teaching something like quantum mechanics, I think you really have to consider the purpose in teaching it. Some of the people studying quantum mechanics are going to go on to become physics researchers, but my guess is that that is a tiny, tiny fraction. A small fraction of those who learn QM go on to get undergrad physics degrees, and a small fraction of them go on to get postgraduate physics degrees, and a small fraction of them go on to get jobs as physics researchers. So for the majority (I'm pretty sure it's a majority) who are not going to become physics researchers, what do we want them to know about quantum mechanics?

I'm not asking these as rhetorical questions, I really don't know. But I think that if we want people to be able to solve problems in QM, there might be a best way to teach it to get them up to speed in solving problems. If we want them to understand the mathematical foundations, there might be a different way to teach it. If we want them to be able to apply QM to problems arising in other fields--say chemistry or biology or electronics--there might be another best way to teach it.

So when people say things like "You shouldn't bring up X, because that will just confuse the student" or "The historical approach, with all of its false starts and blunders, is just not relevant to today's students", they need to get clear what, exactly, they want the student to get out of their course in QM. And I think that the answer to that question isn't always the same for all students.
 
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  • #16
bhobba said:
And I really do mean IDEA - not ideas - see post 137:
https://www.physicsforums.com/showthread.php?t=763139&page=8

I assume you mean the idea expressed by the sentence:
An observation/measurement with possible outcomes i = 1, 2, 3 ... is described by a POVM Ei such that the probability of outcome i is determined by Ei, and only by Ei, in particular it does not depend on what POVM it is part of.

I would say that that's a single sentence, but I'm not sure I would call it a single idea. There are many other ideas involved in understanding why we would want basis-independence, why we are looking for probabilities in the first place, why we want the outcome probabilities to be determined by [itex]E_i[/itex] (as opposed to depending on both the system being measured and the device doing the measurement), what is an "observation" or "measurement", why should it have a discrete set of possible results, etc.
 
  • #17
bhobba said:
I think philosophers worry more about that sort of thing more than physicists or mathematicians.
probably not theory, but the people :

Erwin Schrodinger : Mind and matter - What Is Life? - My View of the World - ...
Werner Heisenberg : Physics and Philosophy: The Revolution in Modern Science - Mind and Matter - The physicist's conception of nature - ...
...


Patrick
 
  • #18
microsansfil said:
Erwin Schrodinger : Mind and matter - What Is Life? - My View of the World - ...Werner Heisenberg : Physics and Philosophy: The Revolution in Modern Science - Mind and Matter - The physicist's conception of nature - ...

Know both those books - but they are old mate.

These days the following is much better at that sort of level:
https://www.amazon.com/dp/0691004358/?tag=pfamazon01-20

But of relevance to this thread you will get a lot more out of that book if you know some of the real deal detail.

Thanks
Bill
 
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  • #19
bhobba said:
But of relevance to this thread you will get a lot more out of that book if you know some of the real deal detail.
To understand the quantum theory in terms of mathematical language, we have in "France" some good free lecture like this one from "Ecole polytechnique" : http://www.phys.ens.fr/~dalibard/Notes_de_cours/X_MQ_2003.pdf

on the other side there is not a unique look on its interpretation.

Patrick
 
  • #20
vanhees71 said:
If you want to rise interpretational problems at all, you shouldn't do this in QM 1 or at least not too early. First you should understand the pure physics, and that's done with the minimal statistical interpretation. If you like Landau/Lifshits (all volumes are among the most excellent textbooks ever written, but they are for sure not for undergrads; this holds also true for the also very excellent Feynman lectures which are clearly not a freshmen course but benefit advanced students a lot), I don't understand why you like to introduce philosophy into a QM lecture. This book is totally void of it, and that's partially what it makes so good ;-)).

In fact Landau and Lifshitz introduce philosophy early and correctly in their QM book, which is what makes it so wonderful.
 
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  • #21
stevendaryl said:
When discussing the best approach to teaching something like quantum mechanics, I think you really have to consider the purpose in teaching it...

I just wanted to add that, whether or not the student is going to go on to become a physicist, there are certain ways to teach quantum mechanics that I think are just bad. There might be ways to teach a little bit of the feel of what quantum mechanics is about without getting into the mathematics that would be necessary to solve actual problems. But what is worse than useless is to skip the actual facts about quantum mechanics and instead teach people sound bites about how "Quantum mechanics teaches us that the mind creates its own reality" or whatever Deepak Chopra might say about it. However, the goal of giving the layman a flavor of quantum mechanics without being misleading is very difficult to pull off.
 
  • #22
I start my undergrad QM course with Quantum Mechanics and Experience, David Z. Albert, Harvard Univ Press, 1992, ISBN 0-674-74113-7. It's not the dry math start that you find in, say, Principles of Quantum Mechanics, 2nd Ed., R. Shankar, Plenum Press, 1994, ISBN 0-306-44790-8. Don't get me wrong, I like Shankar and use it after the students do the calculations in Albert and some AJP papers cited below. I choose this intro because it involves some interesting phenomena that we can easily model mathematically. The phenomena is electron spin to include entanglement, so its "weirdness" tends to motivate the students to work on the matrix algebra needed to model it. And, the parameters in the matrix algebra correspond directly to Stern-Gerlach orientations and spatial locations of detector outcomes which are easy to visualize. Thus, while the outcomes are "mysterious," the modeling of the experiment is intuitive. I then have them reproduce the quantum calculations for each of Mermin's AJP papers on "no instruction sets":

"Bringing home the quantum world: Quantum mysteries for anybody," N.D. Mermin, Am. J. Phys. 49, Oct 1981, 940-943.
“Quantum mysteries revisited,” N.D. Mermin, Am. J. Phys. 58, Aug 1990, 731-734.
“Quantum mysteries refined,” N.D. Mermin, Am. J. Phys. 62, Oct 1994, 880-887.

Again, in each case, there is an easy-to-understand counterintuitive outcome that motivates the students to work with the simple, intuitive matrix modeling. We finish this intro by reproducing all the calculations in:

“Entangled photons, nonlocality, and Bell inequalities in the undergraduate laboratory,” D. Dehlinger and M.W. Mitchell, Am. J. Phys. 70, Sep 2002, 903-910

to include the error analysis. That gives them a grounding in an actual experiment. Only after all that do we proceed to Shankar.
 
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  • #23
Good comments!
However; There seems to be a Platonic trend among the "speculative" types including all the string theorists,
i.e.-no observables, no predictions...sounds like an elegant theory of pure mathematics.
Multiverses, "anthropic principle, demanding multiverses, Maldecena's conjecture ADS/cft also elegant
but lacking physical relevance. His holographic universe came about because he felt that information is
conserved in two dimensions inside black holes! Have these people no humility?
Q.M. requires more than analysis unless your limited to applied physics and just don't care.
The power of QM of course lies in its mathematical formalism but it is a physical theory and requires
interpretation. At this time, however (I'll say it again) all interpretation is premature. but even the
extraordinarily inelegant interpretations are better than a strictly analytical i.e.-Platonic approach.

Respectfully,

Barry911
 
  • #24
M

Barry911 said:
no observables, no predictions...sounds like an elegant theory of pure mathematics.

Pure math is the last thing QM is.

At the axiomatic level the primitive of the theory is an observation eg see post 137:
https://www.physicsforums.com/showthread.php?t=763139&page=8

The fundamental axiom is:
An observation/measurement with possible outcomes i = 1, 2, 3 ... is described by a POVM Ei such that the probability of outcome i is determined by Ei, and only by Ei, in particular it does not depend on what POVM it is part of.

When you get right down to it much of the difficulty of QM boils down to exactly what is an observation? Its generally taken to be something that occurs here in an assumed classical common-sense world. But QM is supposed to be the theory that explains that world - yet assumes its existence from the get-go.

Much of the modern research into the foundations of QM has been how to resolve that tricky issue - with decoherence playing a prominent role.

A lot of progress has been made - but issues still remain - although opinions vary as to how serious they are.

Thanks
Bill
 
  • #25
Problem:
The outcome of single quantun outcomes does not yield a meaningful outcome. Iteration of "identical
experiments" yields probability densities. P-densities do not predict where a quantum event will occur
only statistical weightings
 
  • #26
Barry911 said:
Problem:
The outcome of single quantun outcomes does not yield a meaningful outcome. Iteration of "identical
experiments" yields probability densities. P-densities do not predict where a quantum event will occur
only statistical weightings

There are problems with quantum mechanics, but you have not diagnosed them accurately. http://www.tau.ac.il/~quantum/Vaidman/IQM/BellAM.pdf
 
  • #27
Greg Bernhardt said:
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.

My 3rd year quantum prof explained this concept in his first lecture, and that was a very big "aha" moment for me. Up until then, all my teachers had tried to explain quantum mechanics in terms of classical mechanics, and it never quite made sense. When someone finally explained that you can't really understand quantum mechanics in terms of classical mechanics, I felt like I was finally able to start learning.
 
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  • #28
thegreenlaser said:
When someone finally explained that you can't really understand quantum mechanics in terms of classical mechanics, I felt like I was finally able to start learning.

"The paradox arises when using improper classical concepts to describe a quantum condition" dixit Serge Haroche

You don't perceive a elementary particle as you see an apple fall.

Patrick
 
  • #29
Barry911 said:
The outcome of single quantun outcomes does not yield a meaningful outcome. Iteration of "identicalexperiments" yields probability densities. P-densities do not predict where a quantum event will occur only statistical weightings

That QM is statistical is not one of its problems.

As Atty says - it has problems, but that aren't one of them.

Or rather, it would be more correct to say, whatever problem worries you, you can find an interpretation where is not an issue at all - the rub is you can't find an interpretation where all are fixed.

For example, at first sight it may seem that QM's statistical nature is a problem if you have some preconceived view of how nature works that it must be deterministic. However we have Bohmian Mechanics that is totally deterministic - but at a cost - non-locality and a preferred frame. Interpretations are all like that - 6 of one, half a dozen of the other, no easy answer.

Thanks
Bill
 
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  • #30
thegreenlaser said:
My 3rd year quantum prof explained this concept in his first lecture, and that was a very big "aha" moment for me. Up until then, all my teachers had tried to explain quantum mechanics in terms of classical mechanics, and it never quite made sense. When someone finally explained that you can't really understand quantum mechanics in terms of classical mechanics, I felt like I was finally able to start learning.

That's very common in QM.

I had read a lot of books on QM, including Ballentine's excellent text, and thought I had a pretty good grasp - but in my hubris I was mistaken.

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

A big one for me was this semantic use of the word - observation, that you think from everyday use means some kind of human observer. Books often don't state it clearly, but in QM observation does not mean that at all. It means something that occurs in our everyday common-sense classical world.

Another was the import of Gleason's theorem - the Born Rule is not pulled out of a hat - its actually required from what an observation in QM is. The key issue is non-contextuality.

Thanks
Bill
 
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  • #31
Hello bhobba:
Couple of questions...
1. Do you find a fundamental problem with the idea that the wave function represents a pure
probability description (Born) and yet represents all the information defining the "particle" of
interest?
2. I have a problem with the word "determinism" it seems to imply the cause-effect relation of Newton and
Laplace. I perhaps wrongly, assume you mean causality. Do you believe that the fundamental dynamics
of our universe is "statistical causality"? It certainly satisfies the requirement of effect following cause but
permits a limited variety of effects for an identical cause (identical in principle) and seems fundamental
to QM.
Also thanks for the recurring reference to Bellentine! I just bought the book. I've just finished the math chapter
and thought it excellent. It seems like a "superposition" of a textbook and an advanced popularizer.

Respectfully

Barry911
 
  • #32
Hi Barry

Barry911 said:
Do you find a fundamental problem with the idea that the wave function represents a pure probability description (Born) and yet represents all the information defining the "particle" of interest?

That's not what a wave-function is. Its simply a representation of the state. All a state is, is an aid to calculating the probabilities of outcomes. Those probabilities are all we can know.

To fully appreciate it you need to comes to grips with Gleason - see post 137:
https://www.physicsforums.com/showthread.php?t=763139&page=8

A state is simply a requirement of the basic axiom:
An observation/measurement with possible outcomes i = 1, 2, 3 ... is described by a POVM Ei such that the probability of outcome i is determined by Ei, and only by Ei, in particular it does not depend on what POVM it is part of.

Its something, that is required from that mapping, to aid us in calculating those probabilities.

To go even deeper in the why of Quantum Mechanics you need to understand the modern view that its simply the most reasonable probability model that allows continuous transformations between pure states, which physically is a very necessary requirement:
http://arxiv.org/pdf/quantph/0101012.pdf

At an even deeper level its what you get if you want entanglement:
http://arxiv.org/abs/0911.0695

In fact either the requirement of continuity or entanglement is enough to single out QM.

Barry911 said:
I have a problem with the word "determinism" it seems to imply the cause-effect relation of Newton

In this context it means are the outcomes of observations uniquely determined, or to be more specific defining a probability measure only of 0 and 1 is not possible under the Born Rule. Gleason shows this is impossible if you have non-contextuality. But in some interpretations, by means, for want of a better description, certain shenanigans, such as a pilot wave or many worlds, then the outcome is deterministic. However they all introduce extra stuff than the formalism either breaking non-contextuality, or a sneaky interpretation of decoherence like Many Worlds where you don't even really have an outcome. Consistent Histories is another sneaky way out as well by also not having an actual observation - but it is fundamentally stochastic, though in a conventional sense.

Barry911 said:
Also thanks for the recurring reference to Bellentine! I just bought the book. I've just finished the math chapterand thought it excellent. It seems like a "superposition" of a textbook and an advanced popularizer.

Its simply the finest book on QM I have ever studied.

Once you have gone through it you will have a thorough grasp of all the issues.

Its not perfect though eg you will notice in his discussion of Copenhagen he assumes the wave-function in the interpretation exists in a real sence. Very few versions of Copenhagen are like that - in nearly all of them its simply subjective nowledge:
http://motls.blogspot.com.au/2011/05/copenhagen-interpretation-of-quantum.html

Once you have gone through at least the first 3 chapters then you will have a good background to discuss what's going on in QM. For example you will understand Schroedinger's equation etc is simply a requirement of symmetry - the essence of QM lies in the two axioms Ballentine uses. Via Gleason that can be reduced to just one - all of quantum weirdness in just one axiom.

But that revelation awaits you.

Thanks
Bill
 
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  • #33
Regarding Ballentine, are these claims really true:

Among the traditional interpretations, the statistical interpretation discussed by
L.E. Ballentine,
The Statistical Interpretation of Quantum Mechanics,
Rev. Mod. Phys. 42, 358-381 (1970)
is the least demanding (it assumes less than the Copenhagen interpretation and the Many Worlds interpretation) and the most consistent one.

The statistical interpretation explains almost everything, and only has the disatvantage that it explicitly excludes the applicability of QM to single systems or very small ensembles (such as the few solar neutrinos or top quarks actually detected so far), and does not bridge the gulf between the classical domain (for the description of detectors) and the quantum domain (for the description of the microscopic system).

In particular, the statistical interpretation does not apply to systems that are so large that they are unique. Today no one disputes that the sun is governed by quantum mechanics. But one cannot apply statistical reasoning to the sun as a whole. Thus the statistical interpretation cannot be the last word on the matter.
http://arnold-neumaier.at/physfaq/topics/mostConsistent

Edit: I see on the wiki
http://en.wikipedia.org/wiki/Ensemble_interpretation#Single_particles
a rebuttal

&

I chose not to label the "ensemble interpretation" as correct because the ensemble interpretation makes the claim that only the statistics of the huge repetition of the very same experiment may be predicted by quantum mechanics. This is a very "restricted" or "modest" claim about the powers of quantum mechanics and this modesty is actually wrong. Even if I make 1 million completely different experiments, quantum physics may predict things with a great accuracy.

Imagine that you have 1 million different unstable nuclei (OK, I know that there are not this many isotopes: think about molecules if it's a problem for you) with the lifetime of 10 seconds (for each of them). You observe them for 1 second. Quantum mechanics predicts that 905,000 plus minus 1,000 or so nuclei will remain undecayed (it's not exactly 900,000 because the decrease is exponential, not linear). The relatively small error margin is possible despite the fact that no pair of the nuclei consisted of the same species!

So it's just wrong to say that you need to repeat exactly the same experiment many times. If you want to construct a "nearly certain" proposition – e.g. the proposition that the number of undecayed nuclei in the experiment above is between 900,000 and 910,000 – you may combine the probabilistically known propositions in many creative ways. That's why one shouldn't reduce the probabilistic knowledge just to some particular non-probabilistic one. You could think it's a "safe thing to do". However, you implicitly make statements that quantum mechanics can't achieve certain things – even though it can.
http://motls.blogspot.ie/2013/01/poll-about-foundations-of-qm-experts.html

They seem like pretty fatal flaws to me, or at least good reasons to choose Landau instead of this potentially shaky stuff...
 
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  • #34
bolbteppa said:
Regarding Ballentine, are these claims really true:

Ballentine is the most misleading book on quantum mechanics I have ever read. In every place where he deviates structurally (I'm not talking about minor accidental errors) from the textbook presentation, it is Ballentine who is wrong and not the textbook.

bolbteppa said:
They seem like pretty fatal flaws to me, or at least good reasons to choose Landau instead of this potentially shaky stuff...

I too would pick Landau and Lifshitz, or Weinberg for correct presentations of quantum mechanics.
 
  • #35
atyy said:
Ballentine is the most misleading book on quantum mechanics I have ever read.

That is very much a minority view.

Many regular posters around here, me, Strangerep, Vanhees and others rate it very highly.

That said Landau is up there as well. But watch it - its terse and the problems challenging to say the least.

Thanks
Bill
 
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<h2>1. Why is quantum mechanics considered to be difficult?</h2><p>Quantum mechanics is considered to be difficult because it involves concepts and principles that are not intuitive or easily understood based on our everyday experiences. It also requires advanced mathematical skills and abstract thinking.</p><h2>2. What are the main challenges in understanding quantum mechanics?</h2><p>The main challenges in understanding quantum mechanics include the abstract nature of the concepts, the use of complex mathematical equations, and the fact that it often contradicts our classical understanding of the world.</p><h2>3. Are there any real world applications of quantum mechanics?</h2><p>Yes, there are many real world applications of quantum mechanics, including the development of new technologies such as transistors, lasers, and computer memory. It also plays a crucial role in fields such as chemistry, material science, and cryptography.</p><h2>4. Can anyone understand quantum mechanics?</h2><p>While quantum mechanics may be difficult to grasp, anyone with a strong foundation in mathematics and physics can understand its basic principles. However, fully comprehending the intricacies of quantum mechanics requires years of study and research.</p><h2>5. Are there any simplified explanations of quantum mechanics?</h2><p>There are many simplified explanations of quantum mechanics available, but they often sacrifice accuracy for simplicity. It is important to have a basic understanding of the complex concepts and equations in order to fully understand the implications of quantum mechanics.</p>

1. Why is quantum mechanics considered to be difficult?

Quantum mechanics is considered to be difficult because it involves concepts and principles that are not intuitive or easily understood based on our everyday experiences. It also requires advanced mathematical skills and abstract thinking.

2. What are the main challenges in understanding quantum mechanics?

The main challenges in understanding quantum mechanics include the abstract nature of the concepts, the use of complex mathematical equations, and the fact that it often contradicts our classical understanding of the world.

3. Are there any real world applications of quantum mechanics?

Yes, there are many real world applications of quantum mechanics, including the development of new technologies such as transistors, lasers, and computer memory. It also plays a crucial role in fields such as chemistry, material science, and cryptography.

4. Can anyone understand quantum mechanics?

While quantum mechanics may be difficult to grasp, anyone with a strong foundation in mathematics and physics can understand its basic principles. However, fully comprehending the intricacies of quantum mechanics requires years of study and research.

5. Are there any simplified explanations of quantum mechanics?

There are many simplified explanations of quantum mechanics available, but they often sacrifice accuracy for simplicity. It is important to have a basic understanding of the complex concepts and equations in order to fully understand the implications of quantum mechanics.

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