# Can quantum theory be explained?

1. Dec 6, 2004

### 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"!

Thanks.

2. Dec 6, 2004

### ^_^

Because the empirical evidence says so.

3. Dec 7, 2004

### 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

Last edited: Dec 7, 2004
4. Dec 7, 2004

Staff Emeritus
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.

5. Dec 7, 2004

### dextercioby

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!!

6. Dec 7, 2004

### Coelum

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

7. Dec 7, 2004

### imabug

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.

8. Dec 8, 2004

### Kane O'Donnell

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!

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

Cheerio!

Kane O'Donnell

9. Dec 8, 2004

### QuantumTheory

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

10. Dec 8, 2004

### Tom Mattson

Staff Emeritus
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.

11. Dec 8, 2004

### 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

12. Dec 14, 2004

### 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.

13. Dec 14, 2004

### 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.

14. Dec 14, 2004

### Kane O'Donnell

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. )

15. Dec 14, 2004

### Mike2

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?

16. Dec 14, 2004

### ZapperZ

Staff Emeritus
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.

17. Dec 14, 2004

### 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

18. Dec 14, 2004

### cartuz

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

Last edited: Dec 14, 2004
19. Dec 14, 2004

### Tom Mattson

Staff Emeritus

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 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.

20. Dec 15, 2004

### Kane O'Donnell

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