I Quantum mechanics is not weird, unless presented as such

[A. Neumaier]

But the space of all, say for definiteness, row vectors of finite dimension, is infinite dimensional,

But then it is already outside the scope of Hardy's ''derivation'' of QM.

By the way, one of the most important rigged Hilbert spaces is the Gelfand triple consisting of Schwartz space on $R$, the Hilbert space $L^2(R)$, and the space of tempered distributions. It is the rigged Hilbert spaces relevant for the discussion of the Fourier transform. Everything is intrinsically infinite-dimensional, Hardy's theory says nothing at all about it, and your feeble attempt to reduce rigged Hilbert spaces to finite dimensions doesn't apply in a natural way.

 

[bhobba]

But then it is already outside the scope of Hardy's ''derivation'' of QM..

How so? The test space is all finite dimensional

By the way, one of the most important rigged Hilbert spaces is the Gelfand triple consisting of Schwartz space on $R$, the Hilbert space $L^2(R)$, and the space of tempered distributions. It is the rigged Hilbert spaces relevant for the discussion of the Fourier transform. Everything is intrinsically infinite-dimensional, Hardy's theory says nothing at all about it, and your feeble attempt to reduce rigged Hilbert spaces to finite dimensions doesn't apply in a natural way.

Indeed. That's the dual of the space of open support test functions. As I said you enlarge the test space for mathematical convenience - but they can be viewed as approximations to the space of vectors with finite dimension.

Thanks
Bill

 

[A. Neumaier]

Buckyball field is rather weird thing IMO.

Only because you have a too limited concept of a field.

A field is anything that has values at every point in a region of space. Thus the density of water is a field featuring in hydromechanics, and the density of polyethylen fibers is a field featuring in rheology.
They are different fields, as one can see by trying to mix the two.

Polyethylen consists of much larger molecules than a buckyball. Double slit experiments show that buckyball fields are indeed very natural objects.

 

[A. Neumaier]

The test space is all finite dimensional

No. You need to test with all vectors of all dimensions, which form an infinite-dimensional space. (Well, you also need to give a rule for adding vectors of different lenghts, but this was implied throughout your arguments.)

 

[bhobba]

No. You need to test with all vectors of all dimensions, which form an infinite-dimensional space. (Well, you also need to give a rule for adding vectors of differwnt lenghts, but this was implied throughout your aguemnts.)

Yes - but each element of the space is finite dimensional so covered by Hardy's derivation.

Thanks
Bill

 

[A. Neumaier]

each element of the space is finite dimensional so covered by Hardy's derivation.

No. Each element of the space is a single point in the infinite-dimensional space. If it is considered to be a space, it is zero-dimensional, and Hardy's theory is vacuous in that case.

What you need to show given Hardy's theory is that everything persists in the limit of letting the dimension go to infinity. This is highly nontrivial, as one suddenly needs a lot of functional analysis to make the argument.

And you would have to explain why in this limit suddenly all the nice features of quantum mechanics appear that permit the application to atoms and molecules, etc.. Only after having explained these, you have explained QM.

 

[bhobba]

No. Each element of the space is a single point in the infinite-diemensional spac. If it is considered to be a space, it is zeero-diemnsional, and Hardy's theory is vacuous in that case.

Your logic escapes me. I am simply considering the space of all states covered by Hardys derivation. That's all.

Thanks
Bill

 

[A. Neumaier]

the space of all states covered by Hardys derivation.

The space you just named is not a vector space but a union of completely arbitrary finite-dimensional vector spaces that are apriori unrelated with each other.

if you want to relate them and create an infinite-dimensional vector space you need to define some sort of projective or inductive limit, and then equip this limit with the same structure as the one you had in the toy finite-dimensional case. Also you need to make sure that you don't use any other assumptions than Hardy's 5 axioms, and that the structure of the limiting object still has properties analogous to those assumed in finite dimensions in the axioms. Finally you need to relate the space you created to the infinite-dimensional spaces actually used in quantum mechanics and show that the intuition that quantum physicists have regading these infinite-dimensional spaces is compatible with the interpretation resulting from Hardy and your limiting construction. This is a tall order.

In particular, where do the canonical commutation relations come from in your amendment of Hardy's derivation? (He is silent about that.)

 

[bhobba]

The space you just named is not a vector space but a union of completely arbitrary finite-dimensional vector spaces that are apriori unrelated with each other.

What vector space axiom doesn't it have?

Thanks
Bill

 

[A. Neumaier]

What vector space axiom doesn't it have?

Addition is not even defined between the vectors of two different vector spaces. For example, what is $(1,2)+ (1,2,3)$? Or what is $|up\rangle + |up\rangle\otimes|down\rangle$? Unless you define it explicitly, neither of these expressions has a meaning.

 

[bhobba]

Addition is not even defined between the vectors of two different vector spaces. For example, what is $(1,2)+ (1,2,3)$?

Its obvious - (2,4,3).

Thanks
Bill

 

[A. Neumaier]

Its obvious - (2,4,3).

Why is it not (1,3,5), based on the rule ''prepend zeros to the shorter vector to make it match''?
You need to specify the rule for addition because no textbook on linear algebra or matrix calculus would allow you to write this.

And what is the obvious result of my second example?

 

[bhobba]

Why is it not (1,3,5), based on the rule ''prepend zeros to the shorter vector to make it match''?

That's not the obvious definition. I shouldn't have to spell out such trivialities.

Thanks
Bill

 

[bhobba]

Or what is $|up\rangle + |up\rangle\otimes|down\rangle$? Unless you define it explicitly, neither of these expressions has a meaning.

That is not an element of my space.

Thanks
Bill

 

[Lord Crc]

Ever since I learned about Gabriel's Horn in calculus class I thought it was weird. I get the math and it makes sense, but I can't shake the feeling that it's weird.

As for QM, I feel it's as if Gabriel's Horn really existed in nature. That is, nature is weird, so QM must describe this weirdness. I find spin weird. I find entanglement weird. I find the single particle double-slit interference weird.

The math makes sense as far as I can follow (never did take QM), but the concepts still feel weird to me.

 

[A. Neumaier]

Gabriel's Horn in calculus class I thought it was weird

But this has nothing to do with quantum mechanics. If you find classical geometry weird although it has no interpretation problems, you need to practice your intuition.

the concepts still feel weird to me.

Try my book; see post #2. Maybe it changes your feelings.

 

[Makaresz]

Does quantum mechanics have to be weird?

It sells much better to the general public if it is presented that way, and there is a long history of proceeding that way.

But in fact it is an obstacle for everyone who wants to truly understand quantum mechanics, and to physics students who have to unlean what they were told as laypersons.

Hi everybody,

I am not a physicist (I am actually a vet surgeon), but I am interested in the topic and read a few things about it, getting the info mainly from Penrose's The Emperors New Mind. I am not sure if this is correct but I have some layman interpretation of quantum phenomena that I would like to throw in for discussion or rejection.

Entanglement: We have box with two balls in it (a system with 2 particles, electrons, etc). We know that they have the same qualities in many respects eg their mass, size, etc, but they cannot be the same colour,all we know that their colours exactly cancel each other out (we cannot describe one without the other, also this way we cannot statistically exactly describe the system) but we don't know what colours (relates to spin 1/2 and -1/2 , angular momentum, etc with electrons). We take one out without looking and take it to a different room. At this stage the system is in a quantum state of either ball can be of any colour. In the other room we look at our ball and it is green and the 'wavefunction collapses'. Then we immediately know without looking, that the other one is red (to exact hue or wavelength). The colour property can be replaced or accompanied by any property that can be measured but is on a continuous scale and related in some way, eg total electric charge of the system, resonates at cancelling frequencies, etc.

Quantum computing: have a mould with a number of indentations, which are irregular sized, that are not measurable with a ruler. We want to know which is the largest volume. We submerge the whole thing in a basket of sand and shake the excess off. The hole with the most sand in it is the largest.

If my thinking is right, then quantum mechanics is the statistics of continuous states (which is most things in the universe) to put it simply.

 

[A. Neumaier]

quantum mechanics is the statistics of continuous states

Surely not. There is a lot of classical statistics where states form a continuum.

Your specific experiment is off topic in this thread (which is about the general principles); if you want a discussion, open a new thread.

 

[Lord Crc]

Try my book; see post #2. Maybe it changes your feelings.

I'll try to read it, I haven't had Lie algebra so not sure how much I'll get out of it.

 

[A. Neumaier]

I haven't had Lie algebra so not sure how much I'll get out of it.

Lie algebras are the key for a meaningful understanding of quantum mechanics. Indeed, one can say without much exaggeration that quantum mechanics is applied representation theory of Lie algebras. This point of view is extremely fruitful and illuminating.

But to start reading the book you don't need to know anything about Lie algebras, what is needed is introduced in the book.

 

[Makaresz]

Surely not. There is a lot of classical statistics where states form a continuum.

Your specific experiment is off topic in this thread (which is about the general principles); if you want a discussion, open a new thread.

Thank you for the feedback. As I said these are layman terms. As I think the topic is 'quantum mechanics is not weird unless presented as such' trying to suggest that QM can be explained in a simpler form, then my example is actually relevant here, describing a simple approach to the problem that anyone could understand. The question is, is it correct?

 

[A. Neumaier]

The question is, is it correct?

It is far too simplistic to convey anything about the essence of quantum mechanics.

 

[gjonesy]

Just my 2 cent, I believe the core concepts and easily explainable experiments can be comprehended by most people. However other concepts and experiments that contradict commonsense logic and differ from Newtonian type explanation is where this communication of explanations and ideas break down. We lack the simple English words to convey that information. Double slit quantum eraser is a perfect example. I've read everything I can about it. And its still weird to me.

 

[Makaresz]

Double slit quantum eraser

It does sound like faster than light information relaying though, does it not? I mean you can move the second polariser at your leisure and the other photon of the pair will change its behaviour accordingly instantaneously.

 

[gjonesy]

It does sound like faster than light information relaying though, does it not? I mean you can move the second polariser at your leisure and the other photon of the pair will change its behaviour accordingly instantaneously.

Yes, there are so many versions of this experiment out there and just as many interpretations of the result. From complicated to simplified from sound scientific to metaphysical. And everything in between. I had read so many that the only conclusion I'm left with is...that's weird

If quantum mechanics hasn't profoundly shocked you, you haven't understood it yet.

Niels Bohr

 

[A. Neumaier]

If quantum mechanics hasn't profoundly shocked you, you haven't understood it yet.

And if you haven't recovered from the shock and seen what is behind, you also haven't understood it yet.

 

[stevendaryl]

I think that the worry about confusing the layman is overblown. They will be confused, but I don't think that there is any way to talk about quantum mechanics that isn't going to be confusing to the layman. Well, unless you just keep it really short and to the point: Quantum mechanics is a way to calculate probabilities for the outcomes of measurements.

But the stuff about "unlearning"...I don't think that ever really is an issue. You might go into your first quantum mechanics course with fuzzy-minded ideas about observation creating reality, or the moon not being there until you look at, or whatever other fuzzy ideas are around. But then you start learning about solving Schrodinger's equation, and computing amplitudes, and computing probabilities for measurement results, and computing the energy levels of the harmonic oscillator and the hydrogen atom, etc. The stuff layman believe about QM doesn't so much need to be unlearned as it is completely irrelevant to the practice of quantum mechanics. You simply don't need to know "what it all means" in order to do the problems. The fuzzy-minded stuff about QM is almost completely orthogonal to the practice of QM, so I don't think it's actually an impediment in any way.

The problem is not that the fuzzy stuff gets in the way. Instead, it's that some people never actually take a course in QM, and never actually learn how to solve problems in it, and the fuzzy stuff gives them the false impression that they know something about QM, when they actually don't. Is that a problem? I don't know...people are mistaken about an awful lot of stuff, and I don't think it's particularly incumbent on a physicist to fix their misconceptions. It's more useful, if you're going to worry about misconceptions, to try to fix misconceptions about relative likelihood: the odds of winning the lottery, the chances of your child getting autism from a vaccine versus the chance that your child will get seriously ill from not getting a vaccine, the odds of dying in a plane crash versus a car crash. Those are misconceptions that actually impact their lives, unlike the philosophy of QM.

 

[A. Neumaier]

But the stuff about "unlearning"...I don't think that ever really is an issue.

I am a counterexample, and surely not the only one.

I needed many years and a lot of effort to unlearn the weird stuff and to replace it by comprehensible and scientifically justifiable statements.
Getting an introduction similar to the book I wrote would have saved me a lot of searching. Indeed, ultimately, this is why I wrote the book!

 

[stevendaryl]

I am a counterexample, and surely not the only one.

I needed many years and a lot of effort to unlearn the weird stuff and to replace it by comprehensible and scientifically justifiable statements.
Getting an introduction similar to the book I wrote would have saved me a lot of searching. Indeed, ultimately, this is why I wrote the book!

Okay, thanks for that personal bit of evidence.

 

[ohwilleke]

QM is totally weird. Even if one can think about it in a manner that doesn't raise the "collapse of the wave function" in the presence of an observer issue.

There are a couple of ways to think about what it is to be weird.
One very sensible way is to say that it is at odd with an intelligent layman's intuition.
Another very sensible way is to say that it doesn't agree with your emotional perception of who reality should be, even if it is logical.
By either definition, QM is weird.

Let me count some of the ways:
1. The behavior of inorganic objects is probabilistic rather than deterministic. So doing the same thing twice to totally inanimate objects doesn't always produce the same result. TOTALLY WEIRD.
2. Quantum tunneling and virtual particles allow outcomes when the end point doesn't violate conservation of matter-energy, even though naively it would seem that there is an intermediate violation of conservation of matter-energy involved in reaching that outcome. Relatedly, the creation and annihilation of particle pairs out of vacuum energy. TOTALLY WEIRD.
3. The Heisenberg's Uncertainty principle. TOTALLY WEIRD.
4. Quantum entanglement. TOTALLY WEIRD.
5. The path Integral for the particle propagator considers paths for photons at speeds other than the speed of light. TOTALLY WEIRD.
6. Special relativity is part of QM and the notion that time doesn't pass at the same rate for everyone and it is asymptotically more difficult to increase speed as one approaches the speed of light. WEIRD.
7. The behavior of particles can be influenced by paths one wouldn't have thought that they took. TOTALLY WEIRD.
8. The emergence of the Second Law of Thermodynamics in the absence of relevant arrows of time in the equations. WEIRD.
9. The fact that PDFs are necessary to correctly model hadrons. TOTALLY WEIRD.
10. The fact that the vast majority of fundamental particles and hadrons are so ephemeral we can't observe them but exist. TOTALLY WEIRD.
11. Neutrino oscillation. WEIRD.

the following gives the modern view based on reasonable assumptions showing QM is not quite as weird as some make out: http://arxiv.org/pdf/quant-ph/0101012.pdf

This makes a good case for QM being logical and relatively simple. Neither of these has anything to do with weirdness. Indeed, the whole process of deducing a complex system from a few axioms which are not themselves obvious from personal experience is itself WEIRD.