Can quantum theory be explained?

[Cheman]

Can quantum theory be explained? Is it possible to look at quantum theory and say "this calculation works because in terms of physics...."? (even if the physics does not entirely correlate with classical ideas)

Eg - is it possible to explain in physics terms why electrons can only exist certain distances from nulcei in quantized energy level? Not just "cause the equations say so"! :biggrin:

Thanks. :smile:

[^_^]

Because the empirical evidence says so.

[Kane O'Donnell]

Because the whole universe hasn't collapsed in a massive radiation burst? Is it just me or does someone ask this question every second day on this forum?? I'm not sure people who ask that question actually know what a 'physical' explanation is - hell, I would have a hard time trying to come up with a good definition, if one existed.

There are such things as questions that only exist because English is able to put abstract words into a grammatically correct sentence, like "what is the square root of poetic yoghurt?". I respectfully submit that asking for a 'physical' explanation, which really means a NON-physical explanation (since physicists, the professionals charged with actually DOING physics, give an explanation that IS physical (it is physics after all) but apparently not acceptable), is a question in the latter category.

People asking questions like this should perhaps try instead challenging themselves by asking themselves what a physical explanation IS.

Ok ok, I'll throw a bone here - discrete orbits are a consequence of discrete energy levels which are in fact discrete eigenvalues that arise as a property of certain operators on certain dense subsets of a Hilbert space that defines the state of the dynamical system. The operator describing the Hydrogen atom has countably many discrete energy eigenvalues (as well as a continuous positive energy spectrum), and hence the bound states of an electron are discrete.

Kane O'Donnell

[selfAdjoint]

Newton began the fashion of going by prediction rather than explanation (hypothesi non fingo), and physicists have run with that ball ever since. But it's something that doesn't come naturally to most people and those who encounter advanced physics (whether QM or SR) for the first time are understandably confused. They don't deserve to be brushed off. What we need is a sticky on the subject of explanation versus prediction, with a good presentation given and then the thread closed so cranks can't add their two cents.

[dextercioby]

Discrete orbits are a consequence of discrete energy levels which are in fact discrete eigenvalues that arise as a property of certain operators on certain dense subsets of a Hilbert space that defines the state of the dynamical system. The operator describing the Hydrogen atom has countably many discrete energy eigenvalues (as well as a continuous positive energy spectrum), and hence the bound states of an electron are discrete.

Kane O'Donnell

You're mixing things and it's not good...Bohr theory (semiclassical) and QM.Yes,discrete orbits are a consequence of the discrete values for the angular momentum of theelectron rounding a nucleus on a circular path/orbit.Yes,discrete energy levels are a consequence of the discrete values for the total angular momentum of the electron rounding the nucleus.
At least that's how i was presented with Bohr's theory in highschool and i reasons to believe it's hystorically and logically correct.
Yet i subscribe for the QM part u posted.Possible quantum states of a system are the eigenstates of the Hamiltonian.

Good idea,SelfAdjoint...Put in practice!!

[Coelum]

Can quantum theory be explained? Is it possible to look at quantum theory and say "this calculation works because in terms of physics...."? (even if the physics does not entirely correlate with classical ideas)


Have you read R. Feynman's QED? It answers your question - at least IMHO - and is a highly recommended reading.

[imabug]

Can quantum theory be explained? Is it possible to look at quantum theory and say "this calculation works because in terms of physics...."? (even if the physics does not entirely correlate with classical ideas)

Eg - is it possible to explain in physics terms why electrons can only exist certain distances from nulcei in quantized energy level? Not just "cause the equations say so"! :biggrin:

Thanks. :smile:

I would argue that QM is an explanation/model of the world we see (at the small scale) and therefore trying to explain it would be rather redundant. You'd be trying to explain an explanation. You look at the physical phenomena (quantized energy level) and come up with a model to explain it (quantum mechanics). If it fits, then you use the model to predict other physical phenomena and try to find evidence of it. You seem to be trying to go the other way which is only going to make life difficult for you.

[Kane O'Donnell]

You're mixing things and it's not good...Bohr theory (semiclassical) and QM

Um. I don't understand what you mean by this. I wasn't referring to Bohr theory at all.

I've been trying over the last half hour or so to write a short post on how quantised 'orbits' arise from QM, but it has been difficult to make it concise without sacrificing accuracy and I find that unsatisfactory in the context of this thread. However, the main problem is of course deciding what an 'orbit' is going to be characterised by - for example, you have suggested angular momentum, and it is indeed possible to show that the bound states (E < 0) in a Coulomb potential have a discrete angular momentum spectrum. This is by no means referring to the Bohr model - obviously in the Bohr model there is no question of what an orbit means.

What I said in the previous post was that discrete energy spectrum => discrete orbits. It's probably a bit loose. What I mean, technically, is that the operator \hat{L}^2 shares a non-trivial set of eigenvectors with the Hamiltonian \hat{H} . All of the eigenfunctions corresponding to the eigenvalues in the bound spectrum of \hat{H} (E < 0) have periodic angular boundary conditions imposed, and this gives rise to a discrete angular momentum spectrum.

Cheman - I must apologise for being rather rude. Obviously I want everyone to want to learn about QM, but I find it very frustrating when someone asks for a 'physical' explanation, when by definition 'physical' means 'according to physics' which in this case really does mean according to quantum mechanics, and even Feynman, Lord of the Physical Explanation, didn't try to give a better explanation for such a thing. The de Broglie model of course does explain quantised orbits, but QM says that such orbits aren't really physical anyway, so basically using the Bohr model/de Broglie model to explain such a thing would be giving a 'physical' explanation to an essentially unphysical phenomena! :smile:

I strongly agree with selfAdjoint on the explanation vs prediction matter, although I have a feeling it is such a subtle point that the crackpots would have plenty of time to rush in before the presenter could finish. I recommend reading this:

http://www.fotuva.org/online/science.htm

although Feynman is well known for his strong views on the scientific method :smile:

Cheerio!

Kane O'Donnell

[QuantumTheory]

Um. I don't understand what you mean by this. I wasn't referring to Bohr theory at all.

I've been trying over the last half hour or so to write a short post on how quantised 'orbits' arise from QM, but it has been difficult to make it concise without sacrificing accuracy and I find that unsatisfactory in the context of this thread. However, the main problem is of course deciding what an 'orbit' is going to be characterised by - for example, you have suggested angular momentum, and it is indeed possible to show that the bound states (E < 0) in a Coulomb potential have a discrete angular momentum spectrum. This is by no means referring to the Bohr model - obviously in the Bohr model there is no question of what an orbit means.

What I said in the previous post was that discrete energy spectrum => discrete orbits. It's probably a bit loose. What I mean, technically, is that the operator \hat{L}^2 shares a non-trivial set of eigenvectors with the Hamiltonian \hat{H} . All of the eigenfunctions corresponding to the eigenvalues in the bound spectrum of \hat{H} (E < 0) have periodic angular boundary conditions imposed, and this gives rise to a discrete angular momentum spectrum.

Cheman - I must apologise for being rather rude. Obviously I want everyone to want to learn about QM, but I find it very frustrating when someone asks for a 'physical' explanation, when by definition 'physical' means 'according to physics' which in this case really does mean according to quantum mechanics, and even Feynman, Lord of the Physical Explanation, didn't try to give a better explanation for such a thing. The de Broglie model of course does explain quantised orbits, but QM says that such orbits aren't really physical anyway, so basically using the Bohr model/de Broglie model to explain such a thing would be giving a 'physical' explanation to an essentially unphysical phenomena! :smile:

I strongly agree with selfAdjoint on the explanation vs prediction matter, although I have a feeling it is such a subtle point that the crackpots would have plenty of time to rush in before the presenter could finish. I recommend reading this:

http://www.fotuva.org/online/science.htm

although Feynman is well known for his strong views on the scientific method :smile:

Cheerio!

Kane O'Donnell

Ok, I'm 16, and am learning calculus. I am deeply interested in space and quantum mechanics. I know alot about derivitives, integrals, and some of vector calculus.

I really don't appreciate you trying to show off on how 'skilled' you are in physics. I don't care if your some genius, you don't have to show off, and it really upsets me.

This person asked a honest question, I come here with only a medium amount of knowledge about calculus, yet you try and show off so not alot of people can understand it.

I like this forum alot, especially this section, I like it when I can understand what I read, or when people actually try and post something constructive rather than explain the world with equations.

Now, I wanted to ask you a question. What does the ^ mean above some of the (constants?) varibles, you wrote?

I'm familiar with that as the square sign, ive seen it in advanced vector calculus books, but never understood it.

Thanks

[Tom Mattson]

Now, I wanted to ask you a question. What does the ^ mean above some of the (constants?) varibles, you wrote?


The hat denotes an operator (as opposed to an eigenvalue or a function).

For instance, in the equation \hat{p}|p'>=p'|p'> , \hat{p} is the momentum operator, while p' is the eigenvalue of the momentum operator that corresponds to the eigenket |p'>.

In short, the 'hatted' p acts on vectors in momentum space, and the 'unhatted' p' is just a number.

[Kane O'Donnell]

*sigh*

Look, what I wrote wasn't showing off. It's the answer to the question. The point is, it's not in *any way* a trivial thing to answer "why" using Quantum Mechanics, it takes work.

I'm glad that at 16 you know a lot about calculus. When I was 16 I didn't know anything about calculus. However, there is a *lot* of maths, and I really mean that, between the mathematical framework of quantum mechanics and calculus, and I can't just reduce an answer to "you integrate this, then substitute this and differentiate there". That doesn't give a *reason*. It's just the legwork - the reasons come from the properties of the underlying framework, and it takes a bit to get them out. I'm not the one who should be apologising to you for that.

Physicists *do* explain the world using equations - you have to come to grips with this. Explaining a phenomenon means having a set of rules that describe as many aspects of the phenomenon as possible, and it has to be that way - how else can you explain things? Metaphor? Misleading. Pictures? Not in 4D, buddy, and they don't usually contain enough information. Words? Well, words represent a way of getting a thought in our head out into the 'world beyond' and vice versa, so that isn't going to help if we have to define the words themselves.

At the end of the day, we have the scientific method, and to effect it, we need a consistent, precise and concise way of representing all our models and explanations. These requirements are fulfilled by mathematics. I would not dare to say that that is all there is to maths - maths is something in itself, but as a tool, it's what us Aussies put in the category of "bloody useful".

I am still learning! Everyone who seriously studies physics is always learning, but at a certain point, the only way to go forward is to throw yourself into a very mathematical world. I really hope that one day I can burst out the other side and have as much clarity and confidence in my viewpoint as Feynman or Einstein or Dirac, but I'm nowhere near there and until then, mathematics has to be my guide.

Regards,


Kane O'Donnell

[Louis Cypher]

If what we are looking at has no tangible evidence than could we not be mistaken at least in some of the finer points of quantum mechanics, we have set up experiments for quantum mechanics for years, which have both bemused and amazed us but, sometime I do rather feel like we're looking for an answer without asking the right questions. indetreminacy throws a rather grey palour over QM, but it's also what makes it so interesting.

I think we need to take a more scientific approach, I know we have no direct proof, but a little more subjectiveness, would help, after all it's all very well saying there is an infinite number of 'ghost' quark pairs formed between the quarks, but what does that really mean, there could easily be nothing but the quarks themselves, I just feel that perhaps we need to start looking a bit more criticaly at some of the things we hold to be true, or somewhat factual, and start questioning the foundations of something that Einstein and Schrodinger both understood was not the whole answer; Qm is our best guess for now, however it's far from the truth, Schrodinger and Einstein realised they probably would not see proof of it's downfall in their lifetime and by downfall I mean progress to somehting closer to the truth, but will we ever see direct proof in the future and if we dont what does QM scientific value? if we don't start looking for ways to question our firmly established belief, we may well find that one day we are perched upon a stack of cards; are we still just stumbling around in the dark looking for answers which aren't there, I don't know but I'm more willing to ask questions, than speculate on speculation to find answers.

[Chronos]

QM is conceptually difficult [As is GR] because it does not obey the 'common sense' rules we are accustomed to dealing with in our slow moving, low energy, macroscopic reference frame. It only makes sense mathematically and that is the only way [AFAIK] it can be expressed intelligibly.

[Kane O'Donnell]

Qm is our best guess for now, however it's far from the truth



How far do you claim it is? Quantum Electrodynamics is the most accurate theory physics has ever had, they're up to 12 significant figures now aren't they? How can you say that a theory that agrees so well with experiment is 'far from the truth'?

It is more accurate to say that whilse QM has excellent predictive powers, we would like an underlying theory that perhaps shows why the postulates of QM arise.

Of course, there may not *be* such a theory - maybe the commutator postulate is simply a property of the universe. I wouldn't want that to be true of course because that leaves the value of hbar unexplained, but if it's the case, tough. Most high-energy physicists are looking for a theory that has the least possible number or arbitrary numbers in it, or even better, none. The whole "Einstein was against QM" argument has been heard over and over, and the fact remains that QM's predictive power is a testimony to the fact that *it* at least is very likely a partial truth*. This is more than can be said for string theory or loop quantum gravity.

Besides, I hardly think it's correct to say that up until now we haven't had a 'scientific' approach to QM - it's one of the most thoroughly investigated fields in Physics and indeed all of Science, and the modern theories have passed every experiment, which is one of the problems facing people who are looking for deeper theories.

Regards,


Kane O'Donnell

(*The usual disclaimer applies to any association of a theory with truth. I strongly suspect QM won't be destroyed utterly, but there are of course no guarantees. :wink: )

[Mike2]

How far do you claim it is? Quantum Electrodynamics is the most accurate theory physics has ever had, they're up to 12 significant figures now aren't they? How can you say that a theory that agrees so well with experiment is 'far from the truth'?

It is more accurate to say that whilse QM has excellent predictive powers, we would like an underlying theory that perhaps shows why the postulates of QM arise.

Of course, there may not *be* such a theory - maybe the commutator postulate is simply a property of the universe. I wouldn't want that to be true of course because that leaves the value of hbar unexplained, but if it's the case, tough.
Oh come on... the square root of a negative number??? How could a theory incorporating imaginary numbers be anything except an effective theory of something deeper?

[ZapperZ]

Oh come on... the square root of a negative number??? How could a theory incorporating imaginary numbers be anything except an effective theory of something deeper?

Hey, if there are people who make claims based on their own imaginary understanding of QM, then QM can certainly incorporate imaginary numbers into its theory.

Zz.

[Modey3]

"Oh come on... the square root of a negative number??? How could a theory incorporating imaginary numbers be anything except an effective theory of something deeper?"

Hah, that is funny. The incorporation of " i " into exponential functions represents a wave through the Euler realtionship with orthagonal real and imaginary parts. The answer comes from Diff EQ. I know its a difficult concept to grasp, but it works mathematically- which is the basis of all logic.

I think the real question of QM is why can't an electron exist in one place, why are electrons "spread out" over real-space in discrete wave like patterns? The result of the Double-Slit Experiment still fascinates me to this day. The answer lies there. How can an electron pass through both slits at the SAME time? The only answer that works is that electrons are not the billiard balls that we want them to be.

Anyways, I'm new to this forum. So I would like to introduce myself. I am a Materials Science & Engineering grad student, but I'm a physicist at heart. I have an interest in Condensed Matter Physics and its parent QM. I honestly don't think we as human beings will know why QM works.

Modey3

[cartuz]

"Oh come on... the square root of a negative number??? How could a theory incorporating imaginary numbers be anything except an effective theory of something deeper?"

Hah, that is funny. The incorporation of " i " into exponential functions represents a wave through the Euler realtionship with orthagonal real and imaginary parts. The answer comes from Diff EQ. I know its a difficult concept to grasp, but it works mathematically- which is the basis of all logic.

I think the real question of QM is why can't an electron exist in one place, why are electrons "spread out" over real-space in discrete wave like patterns? The result of the Double-Slit Experiment still fascinates me to this day. The answer lies there. How can an electron pass through both slits at the SAME time? The only answer that works is that electrons are not the billiard balls that we want them to be.

Anyways, I'm new to this forum. So I would like to introduce myself. I am a Materials Science & Engineering grad student, but I'm a physicist at heart. I have an interest in Condensed Matter Physics and its parent QM. I honestly don't think we as human beings will know why QM works.

Modey3

Can I write my opinion? I understand double-slit experiment as the pattern of classical test particles is in the gravitational background of random gravitational fields and waves. It is the total classical interpretation with classical random fields and waves. That interpretation I named Stochastic Gravitational Interpretation. We do not surprised why we can see the interference at the surface of the water, for example. Double-slit experiment is analog to this pattern. Quantum property is not the property of the particles. It is the property of environment (background) with resonant property of particles.
Quantum Property=Background Property+Resonant Property of Particles
You can read about this interpretation in T.F.Kamalov, How to Complete the Quantum-Mechanical Description?// In the book “Quantum Theory: Reconsideration of Foundation-2”, Vaxjo, Sweden, June 1-7, 2003, p. 315-322, E-print arXiv: quant-ph/0212139.
http://xxx.lanl.gov/abs/quant-ph/0212139

[Tom Mattson]

Oh come on... the square root of a negative number??? How could a theory incorporating imaginary numbers be anything except an effective theory of something deeper?

:rolleyes:

1. Arguments from incredulity are never valid.

2. Anything that can be done with imaginary numbers can also be done without them.

3. Imaginary numbers enjoy the same ontological status as real numbers. You are just getting confused by the unfortunate naming scheme that we are stuck with.

Please see the following thread: Imaginary numbers (http://www.physicsforums.com/showthread.php?t=56771) that was just posted today. It has some information that will help you understand that complex numbers are a natural, well-defined extension of the real numbers.

[Kane O'Donnell]

Oh come on... the square root of a negative number??? How could a theory incorporating imaginary numbers be anything except an effective theory of something deeper?

What's wrong with a theory incorporating imaginary numbers? They're *extremely* well understood mathematically. Your argument is just like saying the number \pi doesn't exist because you can't write it down. Well, saying that you can't write it down means that it isn't a *rational* number, but it is a well-defined *concept* as well as being an element of the irrationals and hence the real numbers.

So are we allowed to use pi? No? Oh well, can't find the area of a circle anymore.

Seriously, the issue that needs fixing with QM is where all the constants come from.

Besides, the fact that the numbers can be imaginary is a very important feature of the mathematical framework. For example, since an arbitrary phase factor multiplied by the wavefunction doesn't change the probability distribution, an action by symmetries on the underlying Hilbert space can be 'symmetic' modulo the set of complex numbers with modulus one. This allows us to represent a symmetry as a unitary transformation (the existence of such a unitary transformation is a theorem of Wigner).

Imaginary numbers are not a problem with QM. I will accept that they give QM a distinctly different flavour to say, classical mechanics, but I don't see how that affects it's viability.

Besides, I don't claim that QM is the ultimate truth, I just claim that it isn't *so* wrong that some new theory is going to totally blow it out of the water. It's a possibility, but QM's experimental success suggests it is at least *mostly* right.

Regards,

Kane

[Kane O'Donnell]

Modey3:

Hi :) Just wanted to point out that mathematics isn't the basis of all logic, it's sort of the other way around :D

Cheerio!

Kane

[cartuz]

About imaginary numbers in Quantum Mechanic. Sorry, but I can not see the problem here. In Special Relativity Theory you can see the systems of coordinates with axis ict. Here c is light velocity. It is forth direction which orthogonal to 3-dimentinal space. Imaginary axis (time axis) is mean that time axis is orthogonal to 3-dimentinal spaces only, I think.

[ZapperZ]

Can I write my opinion? I understand double-slit experiment as the pattern of classical test particles is in the gravitational background of random gravitational fields and waves. It is the total classical interpretation with classical random fields and waves. That interpretation I named Stochastic Gravitational Interpretation. We do not surprised why we can see the interference at the surface of the water, for example. Double-slit experiment is analog to this pattern. Quantum property is not the property of the particles. It is the property of environment (background) with resonant property of particles.
Quantum Property=Background Property+Resonant Property of Particles
You can read about this interpretation in T.F.Kamalov, How to Complete the Quantum-Mechanical Description?// In the book “Quantum Theory: Reconsideration of Foundation-2”, Vaxjo, Sweden, June 1-7, 2003, p. 315-322, E-print arXiv: quant-ph/0212139.
http://xxx.lanl.gov/abs/quant-ph/0212139

If you are going to use a "fringe" science as an explanation, you need to show peer-reviewed citation rather than someone's book or e-print arxiv article. Otherwise, this "opinion" of yours has not been verified by your peers to even be considered to have any validity, and it will go into the TD wasteland.

Zz.

[jtbell]

In Special Relativity Theory you can see the systems of coordinates with axis ict.

Which nobody uses nowadays, as far as I know. The ict fourth dimension was an early attempt to make Einstein's space-time look more like a four-dimensional Euclidian space by letting us write the invariant space-time interval as s^2 = x_1^2 + x_2^2 + x_3^2 + x_4^2 = x^2 + y^2 + z^2 + (ict)^2 = x^2 + y^2 + z^2 - c^2 t^2.

Nowadays we prefer to acknowledge that space-time isn't really Euclidian by showing that "-" sign in the last version explicitly and defining the space-time interval as

s^2 = x_0^2 - x_1^2 - x_2^2 - x_3^2 = c^2 t^2 - x^2 - y^2 - z^2

(which is of course the negative of the previous definition, but we do it consistently so it doesn't matter)

Similarly the invariant mass (squared) is

(mc^2)^2 = E^2 - p_x^2 - p_y^2 - p_z^2

and in general the invariant product of two four-vectors is

a_0 b_0 - a_1 b_1 - a_2 b_2 - a_3 b_3

We could in principle reformulate quantum mechanics without i by postulating that a particle's probability density is determined by two real wave functions that correspond to the real and imaginary parts of the \psi that we all know and love. We might call them \psi, the wave function, and \phi, the "wave co-function". Then we would define the probability density as

P(x) = \psi^2 (x) + \phi^2 (x)

and instead of a single Schrödinger equation we would have two coupled differential equations which in one dimension would look like

-\frac{\hbar^2}{2m}\frac{\partial^2\Psi}{\partial x^2} + V\Psi = -\hbar\frac{\partial\phi}{\partial t}

-\frac{\hbar^2}{2m}\frac{\partial^2\phi}{\partial x^2} + V\phi = \hbar\frac{\partial\psi}{\partial t}

I suspect that we don't do this because the complex-number formalism makes things so much more convenient here than in relativity, and physicists were already familiar with using complex numbers in describing waves, simple harmonic motion, etc.

[ZapperZ]

The problem here isn't the "imaginary number". The problem here is that the person making the point has a history of having only a superficial knowledge of physics and, as is obvious here, mathematics. As Tom has pointed out, there is NO difference in terms of mathematical "status" of real and imaginary number. Anyone who has done any amount of complex algebra can already see this. The name "imaginary" number doesn't mean "I-made-it-up-all-in-my-head" number. It is silly to think that if I use sin (\omega t), then I'm OK, but once I use e^{i\omega t}, then my theory no longer has any meaning just because I have a complex number there!

Again, imagination without knowledge is ignorance waiting to happen. Except in this case, it has already happened.

Zz.

[Mike2]

:rolleyes:

1. Arguments from incredulity are never valid.

2. Anything that can be done with imaginary numbers can also be done without them.

3. Imaginary numbers enjoy the same ontological status as real numbers. You are just getting confused by the unfortunate naming scheme that we are stuck with.

Please see the following thread: Imaginary numbers (http://www.physicsforums.com/showthread.php?t=56771) that was just posted today. It has some information that will help you understand that complex numbers are a natural, well-defined extension of the real numbers.

I read your post on how counting numbers lead to whole number which leads to integers which leads to rational numbers which leads to irrational number which leads to complex numbers. The last step is non-sequitur.

I'm not arguing from incredulity. I'm arguing from inconsistency. For there simply is no number the square of which equals a negative number. The square of a positive number gives a positive number, and the square of a negative number gives a positive number. So the square root of a negative number existing is not consistent with the definition of multiplying a positive by a positive, or multiplying a negative by a negative. Both multiplications are positive, so the square root of a negative does not exist.

Yet we have the most accurately confirmed theory of physics based on it. If you can get rid of the imaginary number in the equations of QM or QFT, then by all means do so.

Thank you.

[selfAdjoint]

I'm not arguing from incredulity. I'm arguing from inconsistency. For there simply is no number the square of which equals a negative number.

Dead wrong. Numbers on the real line all have positive squares, but i is on the line at right angles to the real line. Complex numbers are vectors in the plane with one real and one "transverse" (Gauss) component. But those are vectors not numbers, you protest. They are numbers because they satisfy all the rules of arithmetic: addition, multiplication, subtraction and division, commutative in both additive and multiplicative operations and with a distributive law, they behave just like rational or real numbers and better. Every root of every polynomial with complex coefficients is a complex number; you can't say the corresponding thing for rationals or reals.

[humanino]

I read [...]

For there simply is no number the square of which equals a negative number.
Did not you notice when you read, that every motivation for the next constructions is always providing solution to problems that previously seemed impossible to solve ? There is not much more, but that is already a great deal.

People used to say "but there is no way that, if you add a (strictly positive) quantity A(>0) to any quantity B, you get a result which is zero". Alas, if B is negative it actually works. Simply those people would not accept negative quantities as element of reality, because you never have a negative number of coins in your pocket. They could argue as long as they want, it does neither make negative numbers less useful, nor less in contact with reality.

When Fourier was writing heretic formulae, he was actually able to find physical quantities (namely he was studying the propagation of heat). It took several centuries, and the construction of what is now called distributions, to rigorously built the framework in which Fourier's calculus were justified.

So you can argue against compex numbers, but you only succeed to display your misunderstanding.

And a beautiful word such as "non-sequitur" is not an argument :wink:

[Tom Mattson]

I read your post on how counting numbers lead to whole number which leads to integers which leads to rational numbers which leads to irrational number which leads to complex numbers. The last step is non-sequitur.


No, it isn't. Mathematical objects are defined by their properties. As long as the properties don't lead to any inconsistencies in the mathematical system, there is not problem. Note, by "inconsistency" I mean "inconsistency within the formal system", not "inconsistency with Mike2's preconceived notion of consistent".


I'm not arguing from incredulity.


You most certainly did argue from incredulity. Look again at the post of yours that I quoted. It is a textbook example of an argument from incredulity.


I'm arguing from inconsistency. For there simply is no number the square of which equals a negative number.


Actually, there is. It's called 'i', and its square is -1.


The square of a positive number gives a positive number, and the square of a negative number gives a positive number. So the square root of a negative number existing is not consistent with the definition of multiplying a positive by a positive, or multiplying a negative by a negative. Both multiplications are positive, so the square root of a negative does not exist.


It is readily seen and acknowledged that the rule that allows us to multiply under a radical does not hold when imaginary numbers are admitted. This is only a problem if one is determined to keep that rule.


Yet we have the most accurately confirmed theory of physics based on it. If you can get rid of the imaginary number in the equations of QM or QFT, then by all means do so.


Why? It is mathematically perfectly well defined, and it is extremely powerful. Of course, we could dump imaginary numbers in favor the group of 2x2 matrices that is isomorphic (under matrix multiplication) to the group of complex numbers under multiplication. But that's a foolish idea, because we would not be able to readily use such things as contour integration or conformal mapping. You are advising that we throw away all of this simply because you do not understand how complex numbers fit into mathematics as a whole. That's bad advice.

[cire]

[QUOTE]
Oh come on... the square root of a negative number??? How could a theory incorporating imaginary numbers be anything except an effective theory of something deeper?
[QUOTE]
without the i in the shcrodinger equation the propability amplitudes tend to 0 as time increases!
what is wrong in having complex numbers? i is a number with beautiful properties and having them there have a lot of sense,

[Mike2]

Why? It is mathematically perfectly well defined, and it is extremely powerful. Of course, we could dump imaginary numbers in favor the group of 2x2 matrices that is isomorphic (under matrix multiplication) to the group of complex numbers under multiplication. But that's a foolish idea, because we would not be able to readily use such things as contour integration or conformal mapping. You are advising that we throw away all of this simply because you do not understand how complex numbers fit into mathematics as a whole. That's bad advice.
Of course not. I'm an electrical engineer. I use imaginary numbers all the time. But I recognize that it is a contrivance designed for convenience to represent more basic physics that does not rely on imaginary numbers. I've also taken graduate level mathematical physics where we did contour integrals, etc. I'm aware that some famous mathematician claimed that any integral that could be done with real numbers could also be done with complex numbers. My complaint is when we start assigning physical reality to things described with imaginary numbers. I cannot conceive of how imaginary numbers can be a direct description of something real. I of course can understand how imaginary number can be USED for convenient calculations. It just seems that the diff eqs of QM seem to be the most fundamental entities from which physics derives its meaning. So it seems as though the actual physical entities are being describe with imaginary numbers. And this boggles my mind. Now, if instead the complex diff eq turns out to be a curve fitting device or just a contrivance for conveniene, then I can live with that. We do that in electronics all the time. So for me the complex numbers point to some more basic reality for which the complex equation is just a convenience, like in electronics.

[Tom Mattson]

My complaint is when we start assigning physical reality to things described with imaginary numbers. I cannot conceive of how imaginary numbers can be a direct description of something real.


Again, the argument from incredulity.

Imaginary numbers are only terms in mathematical statements, just like reals are. A priori, they are no more or less suitable for the task of describing physical phenomena than the reals are. Restricting yourself to the reals in quantitative physical descriptions makes no more sense than restricting yourself to 2-syllable words in qualitative physical descriptions.

[Nereid]

Welcome to Physics Forums, Modey3!I think the real question of QM is why can't an electron exist in one place, why are electrons "spread out" over real-space in discrete wave like patterns? The result of the Double-Slit Experiment still fascinates me to this day. The answer lies there. How can an electron pass through both slits at the SAME time? The only answer that works is that electrons are not the billiard balls that we want them to be.And how cool is it that it's not just electrons, also photons, neutrons, neutrinos (?), H atoms, He atoms, C atoms, water molecules, ... even bacteria, ants, and humans??Anyways, I'm new to this forum. So I would like to introduce myself. I am a Materials Science & Engineering grad student, but I'm a physicist at heart. I have an interest in Condensed Matter Physics and its parent QM. I honestly don't think we as human beings will know why QM works.Well, from my POV, Kane O'Donnell already got the key part ... it's consistent with good observational and experimental results ... to 12 decimal places! What more can you ask of a scientific theory than that it is extraordinarily successful within its domain of applicability?

With QFT, we also have mobile phones, PCs, lots of 'consumer electronics', ATMs, (indirectly) VoIP, SQUIDs, .... three cheers for QM!
:smile: :approve:

[cire]

So it seems as though the actual physical entities are being describe with imaginary numbers. And this boggles my mind.
Mike2
an imaginary number is something as "real" as number 2 is, having i for example in the schrodinger equation make a lot of sense and it is in that way that nature is
go to http://www.physicsforums.com/showthread.php?t=56771 when the "history" of complex number is presented

[Hurkyl]

Mike2: think about why we use real numbers. It's not because real numbers are inherently "right" -- it's because they share properties with the things we're trying to describe, such as being ordered (we can tell if somethings longer than another) or addable (we can concatenate two lengths to add them).

We use complex numbers for precisely the same reason. Complex numbers share with many things the property of having a phase and magnitude. Thus, complex numbers are a natural choice for describing such things.

[Mike2]

Mike2
an imaginary number is something as "real" as number 2 is, having i for example in the schrodinger equation make a lot of sense and it is in that way that nature is
go to http://www.physicsforums.com/showthread.php?t=56771 when the "history" of complex number is presented
OK then... what physical thing is being described by the imaginary portion of Schrodinger's eq?

[cire]

for example that the probability of finding the particle at (x,y,z) doesnot goes to zero (or infinity) when time increase

[Kane O'Donnell]

OK then... what physical thing is being described by the imaginary portion of Schrodinger's eq?

This is actually a very subtle and interesting question!

Well, sort of.

When you separate time and space variables, the space equation is purely real (though it may have complex solutions of course). On the other hand, the time equation is of the form:

i\hbar\frac{\partial T}{\partial t} = E T(t)

where E is the separation of variables constant and as we all know, turns out to be the energy of the solution. Before I go ranting on about the solutions, compare the above to the time equation derived from the electromagnetic wave equation:

\frac{\partial^2 T}{\partial t^2} = -\omega^2 T(t)

It looks like the latter is just the second order form of the first. However, note that sin(wt) and cos(wt) can be solutions to the latter independently. That is, both:

T_{1}(t) = A_{1}\cos{\omega t}, T_{2}(t) = A_{2}\sin{\omega t}

are solutions to the EM time equation. On the other hand, T1 and T2 are *not* solutions of the QM time equation. A particular linear combination is, though - if A2 = A1, then:

T_{3}(t) = T_{1}(t) - iT_{2}(t) = A_{1}(\cos{\omega t}-i\sin{\omega t})

is a solution provided \omega = \frac{E}{\hbar} . But the solution above can be recognised as our old friend:

T_{3}(t) = A_{1} e^{-i\omega t}

the complex exponential. Notice that physically, the electromagnetism solutions can be made to change phase forwards or backwards in time (for a given "forwards" direction) - they are symmetric in that respect, whereas the first-order QM equation only allows one direction of time evolution - to obtain time-reversed solutions one must change the sign of the i in the TDSE.

Now, why does this matter?

Well, let's examine the *observable* probability distribution. If a solution to the TISE is described by a space-solution multiplied by a time-varying sine (say), our probability distribution would look like: (* denotes complex conjugation)

\Psi^{*}\Psi = \psi(\vec{r})^{*}\psi(\vec{r})\sin^{2}{\omega t}

That is, the probability distribution would *change* periodically in time. This would be fine, say, for linear combinations of stationary states, but certainly not for single stationary states. On the other hand, when the complex exponential is used, the time variance with the probability distribution is not present. This is one way of explaining what the 'stationary' in 'stationary state' means. Indeed, if we push degeneracy to one side, every stationary state is forced by the Schrodinger equation to have a time-independent probability distribution.

So both the EM and QM time equations allow us to assign a number called 'frequency' to the periodic phase changes that the wave functions go through. However, the fact that the TISE is first order in time forces us to use a particular kind of function to represent this periodic aspect of a quantum mechanical object.

Of course, the EM equation admits the complex exponentials (in both time directions) as solutions too, but I'm not sure whether that is interesting here.

As a side note, I should point out that the complex exponential here is one of a more general class of unitary operators that *implement* symmetries on the underlying state space. Every unitary operator has the form:

U = e^{iS}

where S is the infinitessimal generator of the operator. What this exponential actually *means* is basically the subject of the functional calculus. Unitary operators have the property that they don't change the probability distribution. The simplest subclass of such operators are the constant phase factors e^{i\lambda} , where lambda is a real number.

This is sort of what I meant when I said the framework of Quantum Mechanics is strongly effected by the fact that the operators are complex. As has been mentioned, we could switch to a two-component formalism such as is used in electromagnetism, and we would then get real operators, but there isn't really much point.

Regards,

Kane O'Donnell

[Mike2]

Again, the argument from incredulity.

Imaginary numbers are only terms in mathematical statements, just like reals are. A priori, they are no more or less suitable for the task of describing physical phenomena than the reals are. Restricting yourself to the reals in quantitative physical descriptions makes no more sense than restricting yourself to 2-syllable words in qualitative physical descriptions.
Excuse me??? You are introducing an entirely new dimension to solve an equation of one variable, and you find this perfectly understandable?

Thanks for the effort Kane O'Donnell.

[Tom Mattson]

Excuse me???


Excused. :rofl:


You are introducing an entirely new dimension to solve an equation of one variable, and you find this perfectly understandable?


What on Earth are you talking about?

Take a vector space of dimension n and basis {xi}n, such that an arbitrary vector v in the space is formed by taking linear combinations of the xi with real coefficients ai. Now extend the definition of the vector space to admit complex coefficients ci.

Guess what? The dimension of the space is still n. Admitting complex numbers has nothing to do with dimension.

Now, if you have an argument that is based on something other than incredulity, I'll be happy to consider it.

edit to add:


You are introducing an entirely new dimension to solve an equation of one variable,


This reflects a deep misunderstanding of QM. Imaginary numbers aren't used to solve the Schrodinger equation. They are part and parcel of it. Note the difference.


and you find this perfectly understandable?


Yes. As any advanced undergraduate in physics knows, it is not possible to account for the quantum world without complex numbers, or something isomorphic to them. And when it comes to spin, it turns out that it is not possible to account for that without complex vector spaces.

[somy]

The theory says so!!! Go and ask from him or her!!!

[ohwilleke]

Can quantum theory be explained? Is it possible to look at quantum theory and say "this calculation works because in terms of physics...."? (even if the physics does not entirely correlate with classical ideas)

Eg - is it possible to explain in physics terms why electrons can only exist certain distances from nulcei in quantized energy level? Not just "cause the equations say so"! :biggrin:

Thanks. :smile:

The short and sincere answer is that no mechanism more fundamental than quantum theory is known to exist. (The question you have asked is basically one of mechanism), and physicists are business looking for mechanisms that would explain the version of quantum mechanics known as the standard model, because the see apparent inter-relationships between the elements of the standard model that seem to have some sort of deep connections, but can't quite figure it out.

People like string theorists, brane theorists, and the like make their livings trying to find mechanisms more fundamental than the standard model.

Most of the "mysterious" parts of QM, however, are likely to be equally mysterious in any more fundmental theory from which the standard model would emerge. They would simply have fewer moving parts (e.g. fundamental particles and constants).

[donjennix]

Golly - we need another 2 cents worth here for sure --- but I did not see anyone mention that without the complex solutions to Schroedinger you don't get "amplitudes" and you don't get the marvelous predictive power of QED. Adding amplitudes when indistinguishable outcomes are in the stew is the only way to predict the observable probabilities (I'm no expert in this and I am trying to quote Feynman vol 3 from memory). I'd think that would be enough to justify comlex numbers.

[reilly]

The concept of i = sqrt(-1) is as real as the concept of "the". That is to say, both are parts of a language use to describe Nature All mathematical science can be done without i -- often it's enough to replace complex exponentials by a sine cosine pair -- but why bother? (Check out any books on physics, differential equations.)

It's amazing what "i" can do -- the calculus of complex variables is many more times powerful than the calculus of real variables (itself a part of complex variable theory)


If "i" is too crazy, then think of it as a useful notational device.

Regards,
Reilly Atkinson

[jcsd]

Excuse me??? You are introducing an entirely new dimension to solve an equation of one variable, and you find this perfectly understandable?

Thanks for the effort Kane O'Donnell.

I think what has you confused is that the complex numbers are themselves a two dimensional vector space over the reals and there is therefore a fairly obvious one-to-one corresponfdnace between the vectors in any N dimensional complex space and the vectors in any 2N dimensional real space. Though as Tom says this has nothing to do with the actual dimensions and what's more clearly an 2N dimensional vector space over R is not isomorphic to an N dimensional space over C as by definition the maximal set of linearly indepednt vectors in each space is different.

[godzilla7]

o:) I think what confuses the issue is what we percieve if light appears as both a wave and a particle whichever way we look at it we have to take into account that we might not in fact be being objective, we are all just conditioned by DNA to see what isn't there? Or are we? I'm fed up of people asking this very question and being bombarded with so called proof? we must use philosophy to discuss physics; that why it's called a Doctorate of Philosophy, you are all just being sophists, sophistry is fine but dont say its prooven till the results are irrefutable, then question your own frame of reference and proove it wrong :tongue:

Think out of the envelope people. :rolleyes:

QM is wrong? No just missing a few vital pieces, discussing our percetion is the key to understanding what if anything we're missing not discussing string theory as if it were prooven or QM for that matter, as Schrodinger once said his only regret was that he wouldn't be alive to see QM prooved wrong.

build a robot or computer which uses fuzzy logic to learn to think, have it do the same expereiment a million times and see what it comes up with, then trash it and start again:-)

or are we just monkeys with typewriters :biggrin:

Something to think about anyway?

Wake up with a hypothesis, proove it wrong over breakfast, then we are ready to work

me just then, plaguerising another scientist :smile:

Velly good chaps keep it up!

[alexepascual]

I think you guys have fallen into a very unfoccused conversation. Have you noticed that Cheman is not here anymore? He started the thread, but you got so involved in your discussion about the meaning of quantum theory that you didn't notice him leaving.
What we have here is someone who does not have a lot of mathematical knowledge but who is interested in understanding quantum mechanics.
I think that with the disclaimer that quantum mechanics is a highly mathematical theory and can only be properly understood after having mastered a good deal of math, it is possible to have an intuitive understanding of some of the features of this theory before having the required mathematical knowledge.
Probably some of you guys learned all the math and all the equations without trying to ask questions prematurely. You never interrupted your instructor and you did all your homework. Good for you. But not everybody comes form the same direction. Some people find it more fruitlul to have an understanding in terms of pictures before tackling the math. Some may not have the capacity, persevearence, or interest to tackle the math and are just happy to have a rough understanding. I don't think we should brush them off.
Going back to the original question,
Cheman,
(If you are still around)
Have you studied transverse waves on a rope? this would be very "physical". Don't you think so?
Well, it happens that electrons have wave properties and their motion and distribution can be understood in terms of these waves. Consider a circular orbit for an electron. Don't look at it as a planet circling the sun. In reality the electron does not have a definite position. So please replace the picture of a particle located some place in the orbit by some wave that wraps around the nucleus following the line of the orbit.
Now lets go back to the rope. (if you don't remember this stuff go back to your elementary physics book). You know that when you wiggle the rope, waves travel along it with certain speed. But you also know that if the rope has certain finite length, the waves are reflected at the other end and bounce back. When the rope has certain precise lenghts, the waves travelling in both directions form what is known as "standing" waves. This happens when the lenght of the rope is some multiple of half the lenght of the wave (wavelenght). The same would happen if you had a rope forming a circle. You would have standing waves forming when the waves fit a whole number of times in the circumference.
The same thing happens in the case of the electron circling the atom. Now, you know that the energy of the electron will depend on the distance from the nucleous and therefore from on the length of the orbit. But it also happens that the wavelength of the waves also depends on the energy of the orbit (deBroglie relationship). When you consider both relationships together, it will be only for certain distances from the nucleous that you will be able to fit a whole number of waves and form standing waves. I appears that only standing waves are possible. That rougly explains quantization of the orbits (and therefore of the energy levels).
Now, while the waves on a rope represent a sideways motion of its different segments, the waves in QM. are something different. They don't represent a motion of some "stuff" in space. They have a connection with probability distributuions, but if you have an electron moving in straight line in space, the probability of finding the electron at different points in the trajectory is the same (when you know the momentum precisely). This tells you that these are not really "probability waves" where the probability is more "compressed in certain regions". We could say that the "waving" corresponds to something that is going on in another dimmension, but we still don't know enough about that. But we do know very well the properties of these waves to the point of being able to make good predictions. We know that the frequency (how fast they wiggle) of the waves depends on the energy of the particle. And we also know that when we superpose two waves corresponding to the same particle then we do get probabilty waves with regions of space where is more likely to find the particle. Physicists have found that the best way to describe this oscillation is using imaginary numbers. For this and other reasons, it is important to understand a lot of math in order to gain a good understanding of quantum mechanics.
Another phenomenom that you may want to explore and which is simple and very important is the "double slit experiment".
I also recommend that you look for popularizations of quantum mechanics which are non-mathematical books that you can may be able to find in your local bookstore.
Titles that come to mind:
"Thirty years that shook physics" (Gamow)
"In search of schodringer's cat"
"Schodringer's Kitten"
"Quantum Reality"
Authors: Gribbin , Herbert
But remember that after reading these books you won't be able to say that you really "understand" quantum mechanics. In order to understand quantum mechanics you would have to study many years. And even then, there are many aspects of quantum mechanics that remain controversial, to the point that some would say that nobody really "understands" quantum mechanics.
With respect to may explanation of the quantized energy levels, I have to admit that it is very incomplete. But it would take a very long post to make it decently complete. So the best for you is to get that information from books. This forum is great for learning but you are only going to learn bits and pieces. It is best to read the books and come back here with questions about the things you don't understand from the books.
Godd luck.
Alex Pascual

[Cheman]

Yes, I am still hear. :wink: I'm glad somebody noticed what I was trying to get at - surely there must be a reason why all the maths works. It is not really "correct" to have a theory that say "everything happens in the universe because this 2nd order differential equation says so" or "the atoms works like this becase the integral of this derivative is.....", etc. Fair enough, it makes the theory useful and we are able to work things out, but it doesn't really give us an understanding of the nature of things. There must be a reaon WHY things happen. After all, lets reflect on the flawed yet still quite ingenious concept of classical physics - when talking about, say, electricity we dont just say "Voltage = Current * Resistance; the end!" :biggrin: We say "this is because current is the number of electrons passing a point per second and this will double if we double the 'attractiveness' of the battery - this is voltage..........etc".

So when I asked "can quantum theory be explained" I wasn't asking for you to show off how much hardcore maths you;ve learnt or tell me "how can a theory which explains how things work be explained you silly boy" - I just wanted to know exactly what the maths meant. If nobody actually knows then thats fine - you just had to tell me. :smile:

Fair do's?

Thanks Alexepascual. :wink:

Cheman.

[|2eason]

I was of the understanding that theories such as the MWI were proposed as the physically descriptive underlaying mechanisms for QM.

[godzilla7]

Finally someone with some sense :approve: , just bating the maths heads, I am about to take a Degree in physics, but dont have great maths knowledge yet, I have however read extensively on the subject in preperation and have some learning in differentials and integrals pyhtagoras etc, so can discuss the maths; I read a report that the problem with physics is that the maths scares people off and that it would be better to introduce the theory before bombarding peoople with complex math, this way the widespread shortage of physisists would be somewhat assuaged, I'm tallking only about in England here. I dont know about the rest of the world.

Please maths heads, there are plenty of maths forums for you to mentally masturbate in, when someone asks you a question going into long complicated equations is not very apt, especially if there new to the subject! :rolleyes:

Theres plenty of maths forums if you want to go over the symantics of a theory, anyway thanks dood. :smile:

If your not shocked by Quantum Mechanics then you have not really understood it properly

Plank

[Kane O'Donnell]

There must be a reaon WHY things happen

This is a *very* loaded statement, Cheman - can you prove this? Also, this creates an infinite chain - if there's a reason why things happen, then there must be a reason why there's a reason why things happen, etc etc...in which case, doesn't the idea of a 'reason' become a bit fuzzy?


it would be better to introduce the theory before bombarding peoople with complex math

They do, at least at most of the Australian universities. It's very painful for people who take a parallel maths stream, in my experience. On the other hand, this allows people who aren't going to actually *contribute* to quantum mechanical theory but need to have a good grasp of it in their field (photonicists, some electrical engineers, chemists) to keep up with the physics students. I would have preferred, during my 3rd year, to have had an advanced QM course taught at a higher level for students with a strong mathematical background.



Theres plenty of maths forums if you want to go over the symantics of a theory



I want to point out here that a lot of the thread wasn't about the semantics of the mathematical framework but with the idea of 'understanding' and 'explaining' and so on. This forum is an excellent place for such a discussion, since QM is almost (*almost*) unique in the number of headaches it gives to people seeking simple explanations (I'd whack SR/GR in this category too).



If your not shocked by Quantum Mechanics then you have not really understood it properly



This is an often-quoted saying, but a lot of us have grown up with quantum mechanics and are therefore a hell of a lot less shocked than some people think we should be. I believe the statement was made by Bohr around 80 years ago, maybe it's time it should be re-evaluated. QM has become somewhat stranger since Bohr made the remark - it's not immediate that Bohr would be in a position to make such a statement given the advances made over the last 80 years.


Regards,

Kane O'Donnell

[Cheman]

"who aren't going to actually *contribute* to quantum mechanical theory but need to have a good grasp of it in their field (photonicists, some electrical engineers, chemists) to keep up with the physics students."

Hmmm, surely its a different type of contribution?! Afterall, fine the "maths heads" can work stuff out which makes our ability to do things much easier but it gives us understanding of what things are really like - that is the contribution that eg chemists make. We can actually SEE and PICTURE what is going on. Eg - take an atom; what your saying is that it is ok to describe an atom as a load of maths. Fine - but what does that mean its actually like?! It seems that quantum mechnics has all the maths and knows what it does but does'nt know what it is refering to, etc. Correct me if im wrong.

[Kea]

It seems that quantum mechnics has all the maths and knows what it does but does'nt know what it is refering to, etc. Correct me if im wrong

In fact, the mathematics of QM is relatively simple by today's
standards. If one wants to REALLY understand QM one should
at least know the maths in which it was formulated in the early
20th century. Many physicists have a better idea of what QM is
referring to than they have the maths with which to formulate
it....but this just leads to MORE maths.......

Kea

[Eye_in_the_Sky]

If your not shocked by Quantum Mechanics then you have not really understood it properly

This is an often-quoted saying, but a lot of us have grown up with quantum mechanics and are therefore a hell of a lot less shocked than some people think we should be. I believe the statement was made by Bohr around 80 years ago, maybe it's time it should be re-evaluated. QM has become somewhat stranger since Bohr made the remark - it's not immediate that Bohr would be in a position to make such a statement given the advances made over the last 80 years.Yes, it was Bohr who made such a statement.

... For the record, here are three more (more recent) quotations:

Feynman (1964)

I think it is safe to say that no one understands quantum mechanics. Do not keep saying to yourself, if you can possibly avoid it, "But how can it be like that?" because you will go "down the drain" into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.Gell-Mann (1981)

Quantum Mechanics, that mysterious, confusing discipline which none of us really understands but which we know how to use.Feynman

What I am going to tell you about is what we teach our physics students in the third or fourth year of graduate school ... . It is my task to convince you not to turn away because you don't understand it. You see my physics students don't understand it ... . That is because I don't understand it. Nobody does.--------

On another note, here are two more quotations of Feynman regarding the role of Mathematics:

One cannot understand ... the universality of the laws of nature, the relationship of things, without an understanding of mathematics. There is no other way to do it.To those who do not know Mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty of nature. ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.

[Kane O'Donnell]

Yep, I'd agree with the 'no one understands it' approach.

Cheerio,


Kane O'Donnell

[tavi_boada]

I think it's somewhat arrogant to say we understand classical physics. First of all, what worries me less of QM is the discreteness of some magnitudes, e.g. energy of electrons in H atom. There are many examples of discrete energies in Classical Physics such as a rope oscilating with its endpoints fixed (many equations with suitable boundary conditions yield discrete values).

Why, then, do people claim QM is not understandable? Or why do people say its indeterministic? Amplitudes are completely determined by the theory. Can you explain further why you say QM is not understandable?

I'm sorry if I've said things already posted, I haven't had time to read all the posts.

[Kane O'Donnell]

Why, then, do people claim QM is not understandable?



What I'm referring to is that we can't, in QM, say *why* the mathematical framework is the way it is (with probability amplitudes, wavefunctions, operators, etc). We've made a lot of progress, in fact, in explaining the 'why', but unfortunately for those who crave an explanation in simple pictorial form or something like "balls travel in a wind-bent parabola because of gravity", the (partial) explanations of the 'why' in QM are mathematically quite sophisticated.

For a simple (ish) example, why do we want self-adjoint operators? Well, from linear algebra we know that in finite dimensions SA operators have real eigenvalues. We know that this can be generalised to bounded operators on an infinite dimensional space too. Real numbers are the only kind we can measure, so no wonder we want real eigenvalues if we're interpreting eigenvalues as the measurable values of an observable. Problem is, there are *lots* of unbounded operators, including the momentum operator, the kinetic energy operator and hence the Hamiltonian.

We already know that the TISE works magnificently well for some systems. As such, we really, really want to have some reason why this unbounded operator (the Hamiltonian) has a real spectrum for a wide variety of potentials. If we can do this, we will be able to write down a more general QM axiom that tells us the class of operators we are allowed to use as observables in QM. (obviously, since non-relativistic QM has been studied in depth for years, we would guess that the answer is already known, and it is).

It turns out that the notion of self-adjoint generalises in the unbounded case, although in order to generalise we have to restrict the class of wavefunctions upon which the operators can act. This is excellent, because the restriction, usually, is to require that the wavefunctions be continuous and differentiable to some degree, hence explaining the requirement for a continuous/differentiable wavefunction without referring to infinite energy gradients and so on (the latter explanation is sort of a circular argument, I would guess).

Ok that got a little technical at some points, but I hope it's a reasonable example as to what explanation might mean when we try to 'understand' quantum mechanics. In this sense, we don't understand QM, because it's mathematical framework is not fully understood as being a requirement of some underlying conditions.

Regards,

Kane O'Donnell

[tavi_boada]

Are you saying that people say they don't understand QM because of the problematics of unbound operators being self adjoint?

[dextercioby]

Are you saying that people say they don't understand QM because of the problematics of unbound operators being self adjoint?

No,that part of QM is perfectly understood.I'll post again the famous quote from Feynman:
"I think it is safe to say that no one understands quantum mechanics".
My guess is that the key word from phrase is not "understand",but "safe".Feynman must have meant:Okay,let's assume the situation in which some individual claims he masters QM,he understood it.But then,another guy comes to him and says:"Hey,use your QM knowledge to explain this..."(and gives him an example).And so our "QM expert" makes a fools outta himself,as he cannot explain some awkward phenomenon.

So all of us theoretical physicists should "play it safe" and say that we don't really know every aspect of this theory and moreover we cannot give answers to the fundamental question "why?".

Daniel.

[Kane O'Donnell]

Are you saying that people say they don't understand QM because of the problematics of unbound operators being self adjoint?

No, it was just a simple example that hopefully illustrated the kind of things theoretical physicists *do* when they're investigating a theory in order to try to 'understand' it.

Kane O'Donnell

[Louis Cypher]

Yes, it was Bohr who made such a statement.

... For the record, here are three more (more recent) quotations:

--------

On another note, here are two more quotations of Feynman regarding the role of Mathematics:


Thanks for putting me straight on the ins and outs; yes precisely my point although rather cryptically made do not try to understand what we cannot yet understand is perhaps a dangerous way of looking at things, with the current understanding it beehoves us to find ways to understand the mysteries whether we are able to really see what's going on after all that's what science is about; maths is usefull in giving us an appreciation of a theory if we are mathematically inclined and experiment is taking said maths and then seeing if its congruent with reality both are to be applauded; though one should be carefull in making predictions based on predictions; the house of cards thing; because say qm is wrong then surely string theory is wrong by an order of magnitude and m theory well now were possibly in the realms of the absurd; much as I like the simplicity of string theory it's tenuous existence rests solely in the hands of mathemeticains who in my opinion are being driven slowly insane by there incomprehension of the infinite and the infinitesimal. :smile:

I think we should take a long ahard look at that which we hold true and try and proove that b4 flying off into a philosophical debate about strings,I'll leave that to the Doctors of Philosophy. PhD fellows after all there eminently more qualified to explore it than I.

Facinating though theories are at the end of the day there just theories, like the Theory of Gravity, one day someone will find the flaws in QM and it will come crashing to the ground :biggrin: replaced by a new mechanics simillar but closer to the truth; God help us if we ever reach a point where we find the truth, I'd have to give up my degree because there'd be no future in physics :smile:

Nice quotes like it. :wink:

[lawtonfogle]

If we found the truth would we want to know it.

The truth might be better off never being found.

The government keeps secrets from the public for its safety. If the public ever found out about a (lets just say, nuclear threat from terrorist) there would be a panic.

Who says this 'truth' is not the same.

[Louis Cypher]

I think your missing the point here, natures truths are beautiful and we would benefit greatly from knowing them, I dont necessarily need to know if a major terrorist threat has been averted at the time, because the panic caused by said threat would be counter productive to intelligence gathering.

To catch a glimpse at how the universe would be great, nature cannot keep secrets from us forever just like governments cant keep secrets indefinitely, people have a way of hearing the truth all be it an objective truth - or an obfuscated and fudged truth in the case of governments - sooner or later, but is it truth?

Anyway enough philosophy

[kristobal hunta]

Right now QM is more describing than explaining. Actually its authors never put the goal to explain why it happens, instead they just tried to make predictions what would happen in the experiment. And this is normal. Newton first make mathematical model for gravity, but only after Einstein we know that it is explained by curvature of space-time.....well now we have to wait until somebody would explain to us what the space-time is and so forth....:confused:

I mean don't try to make mechanical models of QM or trying to understand it. First you need to feel it mathematical sense and later maybe you would feel like you "underdstand" it.

Maybe in another hundred years there will be an answer to your question. And the rules of QM would be just a simple consequence of space-time properties or whatever.... :smile:

[Louis Cypher]

Personally I think the problem with QM is devide between the mathemticians and the experimentalists.

A good pysisist is both, getting tanlged up in mathematical somantics is fine and worthy work but if that's all you do then your wasting your time; pure maths is pointless for a physisist after all aren't we really asking a simple quiestion abput everything, and if so dont we need to put our elgeant theories to some practical use? Einstein was relatively poor at maths compared to his colleagues so he got them to do the maths for him and then when he learnt to be more fluent in maths he invented mathematics to explain his theories, his outlook as a Scientist was to theorise and then experiment and then invent formulae it bemuses me that people now do the reverse ? both is fine but both need to be done by all surely, It's no longer science mathematics its philosophical sophistry it seems. Fine if your doing a PhD but innapropraite for most :biggrin:

[trosten]

In the beginning the Universe was created. This has made a lot of people very angry and been widely regarded as a bad move.
Douglas Adams

I just want to say its great that someone quotes D. Adams if u really want to know whats going on I think his books can help you.

In the beginning I started studying QM to learn why the world behaves they way it does, is there a god etc. Now I find myself studying it because Im stunned by the way the world behaves, its just simply amazing.

I aslo feel that Bell with the Bell inequality made it clear that there is no answer to the question why things behave the way they do.

[godzilla7]

I meant no offence about the maths heads, just a little more explanation than maths would have been nice or some sort of description of the concepts. Anyway, I used the shocked quote to convey the way I felt when I first had to get to grips with the wierd world of QM, I didn't mean it to be taken in its original context, perhaps I should have made that clear. And unfortunately in England there isn't the choice to avoid some of the more theoretical maths, the first year is always spent going through the complex anture of classical and quantum maths, sa shame I think it would be better to run through the maths after exploring the concepts, so as not to scare people off and to tweak there imagination, show I'm learning and it helps to have a grip of the aplication of maths before you fully understand it I find the reverse way more stimulating and infinitely more interesting than the rather dry pure maths ythat are the precursors to the course.

[misogynisticfeminist]

I meant no offence about the maths heads, just a little more explanation than maths would have been nice or some sort of description of the concepts. Anyway, I used the shocked quote to convey the way I felt when I first had to get to grips with the wierd world of QM, I didn't mean it to be taken in its original context, perhaps I should have made that clear. And unfortunately in England there isn't the choice to avoid some of the more theoretical maths, the first year is always spent going through the complex anture of classical and quantum maths, sa shame I think it would be better to run through the maths after exploring the concepts, so as not to scare people off and to tweak there imagination, show I'm learning and it helps to have a grip of the aplication of maths before you fully understand it I find the reverse way more stimulating and infinitely more interesting than the rather dry pure maths ythat are the precursors to the course.

agreed, i strongly believe that the conceptual foundations of QM should be presented non-mathematically before the math comes in. I believe that this helps students appreciate the theory better and realize that there's much beauty undelying quantum mechanics other than elegant mathematics or excellent predicting power.

[ZapperZ]

agreed, i strongly believe that the conceptual foundations of QM should be presented non-mathematically before the math comes in. I believe that this helps students appreciate the theory better and realize that there's much beauty undelying quantum mechanics other than elegant mathematics or excellent predicting power.

In the Malay/Indonesian language, there is a word to refer to a singular third person without refering to his or her gender. The word is "dia". However, this word does not exist in the English language. I cannot refer to a singular third person easily without knowing that person's gender, or making either tedious, or awkward, or impersonal-sounding statement, such as using "he/she", "that person", etc.

Now, what does THAT have to do with what you just said? I'm trying to illustrate the fact that it is a distinct possibility that QM is describing something in which our currrent "language" or understanding has no ability to accurately convey! Our understanding, concepts, and qualities are inherently tied to the classical world that we already understand, such as the meaning of "position", "momentum", "energy", etc... Yet, such concepts may have vague, or even faulty meanings when we try to apply that in the QM realm. I am convinced that it is why when we measure these things, they give us "weird" answers. You are forcing a square block through a round hole, and you get an outcome that has the appearence of a square block, but with chopped corners. Yet, we complain about the round hole, never the fact that we had square blocks in the first place that wasn't MEANT to be passed through a round hole.

QM isn't supposed to make classical sense. That's the whole point! Therefore, how does one convey the "conceptual foundation" of QM without having the mathematical rigor first? If you have paid any attention to the quackeries on here, you will have noticed that most of them have the impression that they understand the concepts of QM, and yet, lacking severely the mathematical understanding of what it is. This usually results in outright bastardization of what QM is and often leads to hysterical conclusions.

So no. I disagree with the assertion that one must first teach and establish "conceptual understanding" of QM before any mathematical description. For most of us who have gone through the process, our "conceptual understanding" of QM is still evolving and hopefully, progressing. To think that one can simply describe in words the conceptual foundation of QM is to trivialize the complexities of QM, and to "dumb down" the intricate details of its description. I do not see anything good coming out of that for students about to learn the subject.

Zz.

[misogynisticfeminist]

I do understand what you mean Zapperz and i myself have come across "quackeries" where QM is concerned. But actually, establishing the context of what I said, I meant that non-mathematical descriptions of "conceptual foundations" be introduced first to incite curiosity and excitement amongst those who learn them.

In fact, it was the counter-intuitive nature of QM that first attracted me to physics. But of course this does not undermine the importance of mathematical rigour in really understanding QM but I think that before you learn something, you got to get excited about it first.

I do not see non-mathematical descriptions of QM as a suitable substitute for a mathematical course and the education of someone studying QM is FAR from complete without the math. But like i said, the purpose of non-mathematical descriptions is to incite curiosity.

[godzilla7]

Yes I am not arguing that you should forgo the maths simply that as Misogynistic Feminist said, you encourage some excitement and wonder in students before, bombarding them with maths, what I'm suggesting is that for the first 3 months of say a degree, they learn the quantum and classical applications of physics, and the application of this on the astronomical scale, doppler effects simple mathematics like parsec equations and photon energy math, relativity, special relativity, nuclear physics, stuff to show the vast application of physics, to encourage imagination and then delve deeply into the equations to see how we can use our mathematical understanding to solve some of QM's problems this would in my view be a far better way of encouraging more physisists than turning off people who realise that there maths needs work and drop out cause they think they can't keep up, if the student who's maths needs work is excited about the implications behind the concepts he/she will be more likely to stay the distance, this approach may well ease the shortage of physisists and help to encourage people to think about physics as a career.

[ZapperZ]

Yes I am not arguing that you should forgo the maths simply that as Misogynistic Feminist said, you encourage some excitement and wonder in students before, bombarding them with maths, what I'm suggesting is that for the first 3 months of say a degree, they learn the quantum and classical applications of physics, and the application of this on the astronomical scale, doppler effects simple mathematics like parsec equations and photon energy math, relativity, special relativity, nuclear physics, stuff to show the vast application of physics, to encourage imagination and then delve deeply into the equations to see how we can use our mathematical understanding to solve some of QM's problems this would in my view be a far better way of encouraging more physisists than turning off people who realise that there maths needs work and drop out cause they think they can't keep up, if the student who's maths needs work is excited about the implications behind the concepts he/she will be more likely to stay the distance, this approach may well ease the shortage of physisists and help to encourage people to think about physics as a career.

There is a difference between "motivation" to learn a subject and "effective teaching and understanding" of the subject. A good instructor will combine the two. I was addressing the latter mainly because the impetus for motivation can come from a wide variety of external sources. A "conceptual understanding" of QM is a dicey matter in trying to first learn and understand it. More often than not, one resorts to analogy and primitive examples. I've seen way too many of these being misinterpreted or giving off the wrong impression.

Zz.

[slyboy]

Now, what does THAT have to do with what you just said? I'm trying to illustrate the fact that it is a distinct possibility that QM is describing something in which our currrent "language" or understanding has no ability to accurately convey!

There is a "language" that can convey the concepts accurately. It's called quantum logic.

I'm not saying that revising logic is necessarily my preferred approach to the foundations of QM, but logic is supposed to be the study of formalized languages. Therefore, if you believe the conceptual problems are due to our use of language then maybe you should be promoting quantum logic.

[ZapperZ]

There is a "language" that can convey the concepts accurately. It's called quantum logic.

I'm not saying that revising logic is necessarily my preferred approach to the foundations of QM, but logic is supposed to be the study of formalized languages. Therefore, if you believe the conceptual problems are due to our use of language then maybe you should be promoting quantum logic.

Er... mathematics IS a formalized language of logic. Furthermore, one needs to know the rules of "quantum logic" to be able to use it. As physicists, one can't just learn the rules out of nowhere without understanding QM. So it boils down to learning QM first, and we're back to square one.

Zz.

[godzilla7]

i happen to be one of the lucky few to who maths has always come quite easily 'tis a language I'm currently getting to grips with on my course, and Im finding that I can readily accept the strict logical progression of its rules, having said that, I think for some it can be a strugle it isn't my idea to promote physics degrees in a different way the idea has been around for at least 30 years, sjust the huge shortage of physisists has brought the issue to the fore gain; what have they done to change the subject in that time: very little, some of the posts above would suggest that the inherent fear of change in the world of maths is partly the problem, we have to know the maths to truly understand the concepts, ok fine, but whats wrong with reversing the order of learning, learn the concepts then delve into the maths behind them, I really dont see how this would be any different from doing the math then understanding the concepts, same time of study, the only differenece is an increase in students? Of course the maths heads, say no, we must spend 3 years doing nothing but hardcore maths untill our ears bleed, explain to me why bearing in mind 2 years and 9 months of hardcore maths and a few months of introduction is all im asking. The unviersity in which I'm studying already does exactly this in its foundation courses, this should start at A level, and proceed into the degree so that students feel motivated, how many students do you think have left a physics degree because they struggled with the maths at first;it's already difficult in the first year to find your feet at university, without being forced to keep up from the get go. I work in a medical physics dept, so I've spoken to many with a physics degree, and many seem to think it might be an idea, from clinical scientist to administrative mangers, you dont have to be a genius at maths to have a rewarding career in physics, spoken to many who struggled, why is it so hard for people to change there approach to physics, Einstein wasn't the greatest mathemetician of his day, just the greatest thinker. I think it's just the innate fear of trying something new, to alleviate a problem, when the old fashioned just seems so comfortable. I think the word knockheads comes to mind, anyone like to think outside the envelope perhaps, try something to assuage a problem, no perhaps not then :rolleyes:

[godzilla7]

And s'all very well talking about teaching methods to motivate students, but when the course has a set progression, then you'll probably find having just the dry material to work with would make it difficult to motivate anyone.

[ZapperZ]

i happen to be one of the lucky few to who maths has always come quite easily 'tis a language I'm currently getting to grips with on my course, and Im finding that I can readily accept the strict logical progression of its rules, having said that, I think for some it can be a strugle it isn't my idea to promote physics degrees in a different way the idea has been around for at least 30 years, sjust the huge shortage of physisists has brought the issue to the fore gain; what have they done to change the subject in that time: very little, some of the posts above would suggest that the inherent fear of change in the world of maths is partly the problem, we have to know the maths to truly understand the concepts, ok fine, but whats wrong with reversing the order of learning, learn the concepts then delve into the maths behind them, I really dont see how this would be any different from doing the math then understanding the concepts, same time of study, the only differenece is an increase in students? Of course the maths heads, say no, we must spend 3 years doing nothing but hardcore maths untill our ears bleed, explain to me why bearing in mind 2 years and 9 months of hardcore maths and a few months of introduction is all im asking. The unviersity in which I'm studying already does exactly this in its foundation courses, this should start at A level, and proceed into the degree so that students feel motivated, how many students do you think have left a physics degree because they struggled with the maths at first;it's already difficult in the first year to find your feet at university, without being forced to keep up from the get go. I work in a medical physics dept, so I've spoken to many with a physics degree, and many seem to think it might be an idea, from clinical scientist to administrative mangers, you dont have to be a genius at maths to have a rewarding career in physics, spoken to many who struggled, why is it so hard for people to change there approach to physics, Einstein wasn't the greatest mathemetician of his day, just the greatest thinker. I think it's just the innate fear of trying something new, to alleviate a problem, when the old fashioned just seems so comfortable. I think the word knockheads comes to mind, anyone like to think outside the envelope perhaps, try something to assuage a problem, no perhaps not then :rolleyes:

First of all, it was VERY difficult to read this. May I suggest you consider adding paragraphs to your posting to give it some structure?

Secondly, I did NOT advocate "..we must spend 3 years doing nothing but hardcore maths untill our ears bleed.." You are confusing learning the formalism of QM with learning the language of QM. One can have the adequate skills to know the language of QM with a mere 5 or 6 courses in mathematics/mathematical physics at the undergraduate level. This is NOT "3 years of hardcore maths".

Thirdly, how do you "conceptualize" something in which there are no classical equivalent? Look at how many times we have to correct the impression that an electron "orbits" the nucleus in an atom. Now skip ahead and look at the "orbital" solutions to a hydrogenic atom and tell me those LOOK like "orbits". This is one clear example where "conceptualizing" does more harm than good.

Fourth: who said anything about being a "math genius"? I'm very good at mathematics, but I have no patience for mathematics in of itself. It is why I have continuously advocate physics students to get as much necessary mathematics as quickly as possible without having to go through all those mathematics classes. One does this via going through a mathematical physics course, or book, so that one is well-equipped to handle the formalism presented in classical mechanics, E&M, QM, etc. Experimentalists, especially, have very little patience and inclination to spend most of their undergraduate years taking that many mathematics classes.

You learn something via understanding. Only upon understanding, do you have an accurate, and adequate conceptualization of what it is. Till then, all you have is a superficial image of what you THINK it is.

Zz.

[godzilla7]

I think I did it all in one paragraph,cause there was no change of subject, so technicaly I didn't have new paragraphs, but point taken.

Anyway I have and understanding of the electron cloud produced by the hydrogen atoms, because, I have been shown computer representations of these and the photographs of the original experiments, I dont know the derivations of the eigen values behind this yet, but then when I do learn the equations, I'll have a moment of inspiration where I can say it's all clear now, I know little of the maths behind it, I can understand why an electron doesn't literally spin but has an expected range of values, by looking at a model of an electrons range of values. I think your creating problems where none exist, a good computer model well presented and with a good teacher can present the misconceptions of physics without complex maths; I understand that without care, students may be mislead, but I have learnt the reality behind the myth cause I had good literature and good course material that pointed out the reality behind the maths. I'm nothing special but If I know about the concepts without maths, then why believe that other people wont get it to. bear in mind that I have no on site tutor to talk to face to face, just course material and contact numbers and emial.

Anyway the reality is, students in England aren't studying physics or are dropping out early from courses, because of the maths element; what do you suggest we do about this brain drain towards other subjects?

We need some ideas, not saying what I'm saying is necessarily the best way, but then neither is advocating the status quo, its not working what do we do about it?

[ZapperZ]

Anyway the reality is, students in England aren't studying physics or are dropping out early from courses, because of the maths element; what do you suggest we do about this brain drain towards other subjects?

We need some ideas, not saying what I'm saying is necessarily the best way, but then neither is advocating the status quo, its not working what do we do about it?

It is one thing to say that there is a drop in students majoring in physics. It is ANOTHER to BLAME it on the way it is taught. Some of the DRYEST lectures I've been in while in school was in an engineering mechanics class. Yet, you don't see people abandoning that field because of that!

Please don't get me started on the ineffectiveness of society and many in the physics profession of selling their profession. I had just come back from talking to a bunch of high school kids and trying to flush out of their mind that physics and physicists are either "string theory" or "particle physics" or "astronomy", or something esoteric of that nature that simply has no effect on their lives. How about promoting that field of study and its undenyable importance, not only in the advancement of knowledge, but what it has done and can do directly to people's lives? Is this such a novel concept to get more people to be interested in it?

I would also advice you to withold your claim that your current "conceptual" understanding of atomic orbitals based on some computer simulations or pictures is an accurate representation of what it really is as formulated within QM until you have fully seen it in detail. You will find that QM holds a lot more surprises than what you think.

Zz.

[godzilla7]

Sounds like what your doing is a valuable contribution to physics, I am attacking not physics itself but the idea that we can allow the decline of physics to continue, Where I live Portsmouth University has no physics department at all, it was closed five years ago because it wasn't cost effective. I hate to see closures of physics dept.

It's not necessarily the courses fault, after all given the choice of a good job regardless of the degree, would you chose physics or something supposedly less taxing like media studies, a lot of high payed jobs don't require any specific qualification just a degree level education, (interesting side note: back in the 90's many hundreds of physicists were poached by the financial markets) and so people do something that would be considered less difficult than the sciences, and physics is not the only science subject that's suffering chemistry is also I've heard.

It's not surprising that a lot of students consider physics to be of no practical use, for a long time after its inception much of quantum mechanics was just that, it's only now with nano-technology and quantum encoding and a vast array of avant garde technologies that it's really gained the practical momentum it deserves; students need re-educating, it's not a crime to say that teachers need re-educating to re-educate students, I'd be surprised if you yourself hadn't changed your approach over the years.

The media seems obsessed with strings and the quantum, little is mentioned about optics, classical physics, Nanotech and the myriad of other physics applications, so I guess the average person only sees the smallest theoretical parts of physics.

Starting at school it has been suggested - not by me I hasten to add but by academia(or at least part of it) - and then college level(16-18 year olds in England) physics courses need to start enthusing students with the concepts behind things not just the classical mathematics but at A level(these are college courses kind of specifically geared to prepare students for a degree in a subject/ say if you wanted to go into physics, you'd study maths:pure and applied, physics, maybe computer studies and perhaps chemistry and or something else similar, some of the brighter students do 5 A levels) they now study the quark model, why not introduce some of the reasoning behind this, hey even some of the less arduous maths, starting pushing the theoretical concepts I still think would be a good idea. It's not >I< that had highlighted the problems with physics in my country, it is other physicists who are saying the maths element is turning students off,snot solely to blame, never that simple, but it's an element that needs some thought.

Standing on the other side of the fence as a student It worries me that there is such little interest in the subject.

Just advocating that at degree level we spend a short while enthusing students, I guess this is not the way to go, after all the way it's taught now is obviously working :wink:

[selfAdjoint]

I personally am all for an early teaching of the reasoning, as opposed to the stamp collecting aspect that "teaching the quark model" or any other model so easily slides into. In the US bright high schools students take calculus; why shouldn't there be an intro physics theory course for them? First semester, relativity with rapidity and hyperbolic functions, solving sensible problems and classic puzzles, maybe doing the muon lifetime. Second semester one dimensional Schroedinger physics, working up to the square well.

Of course there are always the two constraints: money and teacher talent. Anything "highbrow" like this has to compete with "relevant" courses as politicians and parent groups define them. And sad to say, really talented teachers are few and far between.

[Mike2]

I personally am all for an early teaching of the reasoning, as opposed to the stamp collecting aspect that "teaching the quark model" or any other model so easily slides into. In the US bright high schools students take calculus; why shouldn't there be an intro physics theory course for them? First semester, relativity with rapidity and hyperbolic functions, solving sensible problems and classic puzzles, maybe doing the muon lifetime. Second semester one dimensional Schroedinger physics, working up to the square well.

Of course there are always the two constraints: money and teacher talent. Anything "highbrow" like this has to compete with "relevant" courses as politicians and parent groups define them. And sad to say, really talented teachers are few and far between.

So do a video series on DVD, what? Tests can be done on-line, what?

[selfAdjoint]

Mike, this is a great idea! I am not the man to do it, but some who post here could really make a public contribution! Might take a few videos with accompanying text, but as you say, tests of a kind can be done on line. This IMHO is the weak point of the online courses I have taken (Relativity, Strings 101, QFT 101, Quantum Physics 101); they used offline homework from the textbooks whereas simpler online exercises could have been worked up and provided an active feedback loop. Just excercises on understanding the concepts and manipulating the formalism until you get good enough (in the moderator's and your own opinion) and only then the harder type they put in graduate textbooks.

Somebody posted about the "click" when what you are laboriously trying to learn/do jells and suddenly it's like a different world. Bicycle riding or group theory or whatever. This experience, in the context of basic relativistic and quantum manipulations is what we should be trying to bring to young people. But it involves a LOT of work; those online excercises and tests have to be DESIGNED from scratch, not just copied from a book or pulled off the top of somebody's head.

[reilly]

There's a standard cliche that you don't really understand a subject until you have taught it. After teaching a year of graduate level QM, my "understanding of QM jumped big-time -- true also for mechanics, and E&M --, as did my appreciation for the complexities of teaching QM.

What's to understand? Do we really understand classical physics, or, perhaps, because we are so familiar with the ideas and techniques and successes, that we gloss over the problems -- why does Newton's 2nd Law apply to nature? I suggest that when we claim understanding of classical mechanics, we mean that we understand the implications of the basic equations of mechanics. During the time of the Greeks, the ideas of Newton would not have been understood at all.

As far as I'm concerned I understand QM in the sense that I'm familiar, from lot's of experience,.with many of the implications of QM -- atomic theory, superconductivity, nuclear physics, particle physics. My understanding is empirical and practical in nature, and does not deal with the "why does it work" issue, which is a basic question for classical as well as quantum theories.

Those elusive basics are no farther away in QM than they are in classical physics. Familiarity brings, well, more familiarity. Because of centuries of acclaim and success, Newton's laws are as familiar to us as is driving a car -- they are in our classical comfort zone.

QM is clearly here to stay, perhaps modified somewhat, and the myriad successes of QM just keep on coming. My bet is that in another generation or two, people will be puzzled by the don't/can't understand QM statements. To understand QM, you have to rid yourself of much of classical physics, and thus, with all due respect, those quoted (#54, Eye-in-the-Sky) Feynman, Gell-Mann, et al didn't do that.

Really, if you take QM in its standard every-day working-physicist form, what's to understand? The Schrodinger Eg. is just another partial differential equation. The absolute square of a solution is, according to Born, a probability density. You got your bound states, your states in the continuous spectra, scattering theory all of which have immediate physical interpretations based on mathematically similar classical problems. (There's a lot of highly technical mathematical tools that are essential to the mastery of the subject, like angular momentum theory.) We'll leave relativity for another day, and EPR and all that. Except to note that the controversy over the EPR-type experiments, does not seem to have hampered the progress of physics -- experimental and theoretical.

Why does QM work? Why are we stuck with probability? Why does mass generate gravitation? Why is math so powerful in science -- Wigner wrote about this. In physics, why does math work?

QM's whys are no worse than any other major scientific theories -- they are a bit outside our comfort zone. But that is sure to change -- everybody loves a winner, well arguably.



Regards,
Reilly Atkinson

[godzilla7]

I think this is true, as part of my course it is advised you discuss the subject with someone who doesn't know what it is your talking about, so that you can clarify your own ideas, I found it extremely useful to go through how I understood something to work with someone else.

I think difficult concepts like spin and colour charge and electron superposition can be expressed in simple diagrams and computer models, I have seen such models, as long as it's made clear that to truly understand what's going on to any thing approaching accuracy we need to look at the maths behind it, then students can get some feel for the processes, carefully showing that things are quite weird in the quantum world would not be impossible.

I think the quantum needs to be explained in non mathematical language at first, otherwise when you look at the maths your going in cold with no idea what to expect, going in with some ideas, however inacurrate or erroneous, only helps to strengthen our concepts when we say I have it so the Eigen value of psi or whatever is non deterministic in the range of. so the electron is in a superpositon we can pinpoint it's location but this will alter its speed and thus we can never truly know it's location. now If I use Bohmian Mechanics equations I can show etc. etc. we may not have a non mathematical language for QM but I don't think it does any harm to visualize our complex calculus in a form a non mathematician can grasp, may not be the whole picture, but if we make it clear it isn't there's no harm there.