# Trying to understand electromagnetic waves in quantum theory

1. Apr 28, 2015

### monesh

I am an 8th grade science teacher who has regularly used the pre-Bohr planetary-like model of the atom (like most 8th grade science teachers and textbooks) to help students start to understand atomic physics. But in my free time, I have repeatedly tried, and failed, to really understand the quantum theory model of the atom. I guess I have made some progress, but some of it has made me go back and question even what I thought I wasn't a problem, which leads me to my seemingly simple, but really loaded, question here: What is a wavelength? I mean, if electrons and photons can be described as moving in waves, and if the frequency of photon waves determine whether radio/visible light/x-rays/etc. are emitted, but if quantum theory says that these waves are actually just waves of probability, why are some somes parts of the wave more probable and others less probable for the appearance of a photon or an electron, and why do different probabilities turn into x-rays while others into color, etc? I suspect all my ideas are muddled together and I'm not even asking the question in the right way - can anyone help me sort this out about waves? Many thanks!

[Mentor's note: Thread edited to remove homework template]

Last edited by a moderator: Apr 28, 2015
2. Apr 28, 2015

### Paul Eccles

Wavelength is still wavelength. Different waves have different wavelengths just as you imagine. As for the probability density, that means that the wave is localized (confined to a certain area, sort of like a particle), but it's still a wave. The picture you're looking for is a wave packet. http://en.m.wikipedia.org/wiki/Wave_packet

3. Apr 28, 2015

### monesh

oh great - i got a response - thank you so much! and ok, i can picture a wave packet. but i guess my question is why is anything' waving'? before i read quantum theory, i thought there was something physically oscillating, like an electron, that emitted a line , like a line of photons, in a wave - like water from a garden hose being moved up and down. but in quantum theory, the wave is said to be a probability wave of where the electron or photon is most likely to be. ok, but why are probability paths still shaped like a wave? what is 'oscillating' the probability?

4. Apr 28, 2015

### Paul Eccles

Well, unfortunately nobody really knows beyond that, quantum physics doesn't say anything about the underlying nature of reality, or structure of reality. All of that is philosophically left open. All that it does describe, is what we can measure. There are different philosophical interpretations of the results, and this is discussed under philosophy of quantum physics.

5. Apr 28, 2015

### monesh

oh. so maybe, at least, my level of confusion is up to the common standard (on only this one point, anyway. but are you saying that at the atomic level, we have no idea what is making the difference between an x-ray or a radio wave being produced, other than different levels of excitement on an electron - but no idea exactly how the electron makes the radio wave or the x-ray wave in the shape of waves?

6. Apr 28, 2015

### Paul Eccles

Well, we know a lot, and then we don't know a lot. Some questions can be answered, some cannot. We can make a lot of very accurate predictions and all. Classically the radio wave and x-ray are oscillations in the magnetic field, and the electric field, which is usually a good enough answer.

But one could ask "what are these electric fields, and magnetic fields?", is and that is not a question that can really be answered. we can describe them, but where they come from or what they exactly are, or why they are there remains fundamentally mysterious, will probably always remain shrouded in mystery.

Science has given up on trying to understand everything in the universe, we are now just attempting to discover theories which describe its properties.

For example, take gravity, which we understand very well, we have a very good and precise understanding of, but we don't know why it exists.

7. Apr 28, 2015

### Drakkith

Staff Emeritus
I think we know exactly what the difference is between those two frequency ranges. We certainly know the difference in classical physics, and I'm nearly certain Quantum Electrodynamics accurately describes the creation of both with extremely high precision.

8. Apr 28, 2015

### monesh

hmmm...well, thank you again for your time. but let me ask this: is my garden hose and water stream wave a good analogy of how we thought em waves were being emitted from oscillating electrons BEFORE quantum theory came along? or would it have been a bad analogy even back then?

9. Apr 28, 2015

### Drakkith

Staff Emeritus
Considering that EM waves are oscillating field vectors, no, I don't think it's a good analogy.

10. Apr 28, 2015

### monesh

oh, thanks to you too, drakith, for answering. and yes, i understand we know the precise difference in effect, but i guess i'm trying to pin down the immediate cause. why are they waves? whats waving? photons from a waving electron? or probabilities, rising and falling in a physical path - but why rising and falling probabilities? why not just a cone of possible possitions, or a tube - why a wave inot from a physically oscillating source?

11. Apr 28, 2015

### Drakkith

Staff Emeritus
First and foremost, photons aren't little particles like you're probably imagining. They are packets of energy. As far as I know, based on my very limited knowledge of quantum physics, an EM wave doesn't even have a set number of photons, but is composed of a superposition of many photons that cover a range of energies.

As for why particles behave in a wave-like manner to begin with, I don't know.

12. Apr 28, 2015

### monesh

responding to drakith: yes, i may be totally wrong. but let me put it like this: isn't the electron the source of em radiation? and isn't em radiation, like in the double-slit experiment with visible light -em radiation, moving in waves of probable locations? so what is the electron doing - how is it fluctuation - to make some parts of the wave more or less probable to have a photon appear?

13. Apr 28, 2015

### Drakkith

Staff Emeritus
I'm sorry monesh, I don't feel comfortable answering these questions. I simply don't know enough to give you an accurate answer. I'm surprised none of our more knowledgeable members have posted yet. Just give it a little while and see if any show up.

14. Apr 28, 2015

### monesh

no problem, and thanks for trying - maybe some of what u said will work into the final answer. can't wait for more responses. it seems to be a pretty fundemental question: why waves? hopefully, more will come.

15. Apr 28, 2015

### zonde

You are taking quantum theory as description of microscopic reality where different mathematical objects in theory correspond to physical elements in reality (not described by any other physics theory), right? If that's the case you might have a hard time.
But you can view quantum theory as phenomenological theory. Say, find out what experiments contributed to mathematical models of quantum theory and in what way.

There are two things that are different for radio/visible light/x-rays/etc., it's energy of quanta (photon) and wavelength and you can't have in experiment photons with the same energy but different wavelength (or vice versa). So you can't test experimentally your statement "frequency of photon waves determine whether radio/visible light/x-rays/etc. are emitted" it could be energy or there could be no meaningful way to speak about the two properties separately at microscopic level.

16. Apr 28, 2015

### monesh

thank you for responding, zonde. yes, i see what you mean about quantum theory trying to just be a phenomenological description, leaving unanswered the underlying "reality". but, on the other hand, wasn't this einstein's position - that quantum theory was just talking about knowledge, not underlying reality, so the reality could still be deterministic, according to einstein, in some yet unseen way. but wasn't einstein's position refuted (in a way that i don't entirely understand) by the Bell inequalities experiemnet, which was exactly meant to show that it wasn't just a question of undecided knowledge, but that reality itself was 'undecided' (until measured), which is a description of underlying reality, isn't it, not just phenomena? relating this to my original question, isn't the electron shell around the atom now seen not to be like an orbiting planet, but like a rapidly appearing and disappearing blip of an electron in random multiple spots? that is, not just that we don't know where it is (while thinking that it is somewhere certain), but that we know that it is jumping around in a way that makes it's exact position uncertain and maybe even in multiple simultaneous positions? and, most importantly for now, how does this blipping electron produce a wave shape of em radiation? why shouldn't the projection be in a totally random stream-shape, or like a tube, or an expanding balloon? how is there anything to do with a wave from a 'whak-o-mo'-like electron? sorry this is so long but you guys are helping me already to formulate my exact question a little more precisely.

17. Apr 28, 2015

### Staff: Mentor

Ok I will try and answer for electrons - not for photons because that involves Quantum Field Theory which is a whole new ball game - but sticking to electrons involves ordinary QM.

First you have probably been exposed to myths like the so called wave particle duality - its one the many myths perpetrated in popularisations and beginner texts. Best to get those out of the way:
http://arxiv.org/pdf/quant-ph/0609163.pdf

Another is the usual treatment of the double slit experiment. Here is a correct analysis (note even it has issues - but everyone has to start somewhere and its way better than the usual treatment):
http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

With that we can see the modern view of what QM is:
http://www.scottaaronson.com/democritus/lec9.html
http://arxiv.org/pdf/quant-ph/0101012.pdf

Now using that background we can look at one of your issues:
'but if quantum theory says that these waves are actually just waves of probability, why are some somes parts of the wave more probable and others less probable for the appearance of a photon or an electron'

This wave stuff comes from solving Schroedingers equation for a free particle:
http://www.physics.ox.ac.uk/Users/smithb/website/coursenotes/qi/QILectureNotes3.pdf

Interestingly in that case, even though its a wave-like solution, the particle can be anywhere - strange hey - but it's what QM says. That however is the simplest case. In other cases like a particle in a box its a different matter and if you were to observe it you would find it only in certain locations - as the above explains.

So the question is why Schroedinger's equation? Good question (Schroedinger's original derivation is basically a crock - but that is another story - do another post if you are interested) - with an equally interesting answer. Believe it or not its because of symmetry - specifically the probabilities do not depend on your co-ordinate system (it would be very strange if it did - its so intuitive many would consider it not even an assumption its so obvious). The details are advanced - but just for reference they can be found in Chapter 3 of Ballentine - Quantum Mechanics A Modern Development.

I will leave it there for now - you likely have further queries - but best to digest the above first.

Thanks
Bill

Last edited: Apr 28, 2015
18. Apr 28, 2015

### monesh

wow, bhoppa, thanks so much. you did a lot of work just to give me a good answer so i will really look into every part. Thanks!

19. Apr 28, 2015

### Staff: Mentor

Our own Dr Chinese explains Bell brilliantly:
http://www.drchinese.com/Bells_Theorem.htm

What Bell proved is that local realism is dethroned:
http://en.wikipedia.org/wiki/Principle_of_locality

It wasn't that Einstein was wrong - Einstein's views were more subtle than that - but it resolved one of his objections. Actually its a misnomer that Einstein didn't agree with QM - in the end he fully accepted it as correct - and was one of the initial advocates of the ensemble interpretation which I hold to:
http://en.wikipedia.org/wiki/Ensemble_interpretation

He understood QM quite deeply. He simply believed it incomplete ie it was an approximation to a deeper theory like classical physics is an approximation of QM.

Thanks
Bill

20. Apr 28, 2015

### monesh

hmmm... i still have to research your excellent references in your second to last post, but on your very last post, there may be some unimportant nuances being overemphasized. dethroning local realism is equivalent enough to what i said, that [local] reality was uncertain, dethroned, not deterministic. likewise, "resolving an objection" is equivalent enough to finding something wrong, in this context, as einstein famously said it wasn't a dice-roll, and now, we clearly say it is a dice roll. Further, saying Einstein disagreed initially doesn't discount that he may or may not have finally agreed. i just said he did disagree at one point in order to establish the argument he made at that point, (which is that it was just about hidden determinism). And of course, i'm sure einstein understood qm extremely well - not implying he didn't. but i think you may be downplaying the implication of him saying it was incomplete - i believe he meant that determinism could still be discovered when qm was completed. this is a huge difference from asserting outright non-determinsim and randomness, as is now done. these are off the original point, but i guess important to clarify, don't you think?