Trying to understand electromagnetic waves in quantum theory

[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]

 

[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

 

[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?

 

[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.

 

[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?

 

[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.

 

[Drakkith]

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?

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.

 

[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?

 

[Drakkith]

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

 

[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? what's 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?

 

[Drakkith]

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.

 

[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?

 

[Drakkith]

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.

 

[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 fundamental question: why waves? hopefully, more will come.

 

[zonde]

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.

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.

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?

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.

 

[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.

 

[bhobba]

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

 

[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!

 

[bhobba]

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?

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

 

[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?

 

[bhobba]

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?

Ok. Einstein's views were actually quite subtle. I wouldn't describe it as determinism - I would describe it more along the lines of objective realism. What Bell showed is you can't have objective realism and locality. So it didn't really prove Einstein wrong. You simply have to get rid of locality - Einstein wouldn't have liked that but if he was still around would simply accept it as fact.

The interesting thing however is, although its not usually emphasised, ordinary QM is based on the Galilean transformations which are non local anyway. For locality to be an issue you have to go to Quantum Field Theory. But in that theory locality is replaced by the so called Cluster Decomposition property:
http://en.wikipedia.org/wiki/Cluster_decomposition_theorem

It will likely be gobbley gook, but the important thing to take away from it is it only applies to non correlated systems. EPR concerns correlated systems. This clouds the whole issue of locality in QM - it boils down to what do we mean by locality in correlated systems? To some extent the whole thing is definitional.

Thanks
Bill

 

[monesh]

another slight problem...just started reading your first reference which contends, in part, that qm does not assert that nature is fundementally random. but I've read so many secondary sources that claim the opposite. similar to your characterization of einstein not really disagreeing with qm; seems like a minority view. it's difficult for an outside student, so to speak, to find a teacher that is teaching a majority view on a topic that the student isn't fully able to evaluate, so I'm uncertain. but it goes to part of my question: is there something known to be determining the wave pattern, and if so, what?

 

[atyy]

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 fundamental question: why waves? hopefully, more will come.

Who knows, and who cares? Science is not about why, but about a compact way of describing what we have seen and predicting what we will see.

 

[atyy]

another slight problem...just started reading your first reference which contends, in part, that qm does not assert that nature is fundementally random. but I've read so many secondary sources that claim the opposite. similar to your characterization of einstein not really disagreeing with qm; seems like a minority view. it's difficult for an outside student, so to speak, to find a teacher that is teaching a majority view on a topic that the student isn't fully able to evaluate, so I'm uncertain. but it goes to part of my question: is there something known to be determining the wave pattern, and if so, what?

QM says nothing about whether nature is random or deterministic at a more fundamental level. What it does say is that if there is a more fundamental level that is like a classical reality, that reality is nonlocal. Secondly, it does not rule out that particles in non-relativistic quantum mechanics have trajectories at a more fundamental level. It does rule out that particles traveling those trajectories have simultaneously well-defined position and canonically conjugate momentum.

 

[monesh]

atyy: hmmm...is science really like that? scientists know a lot, and scientists care about a lot, especially compared to non-scientists, who might say of all of science, who knows and who cares (about any science). and science is about why to some degree: why did that catch on fire? why does the moon have a shadow? on and on and on; perhaps the longest narrative chain of whys anywhere, right up to the fundamental whys - maybe those are unanswerable - but even there: the big bang, the first few minutes after, the first few seconds, science trying to get closer and closer to the ultimate why. finally is it just predicting what we will see? since involves say, dinosaurs, but are we expecting to see dinasours - or the big bang? and compact? I'm reminded of Kuhn's characterization of the differences between the ideals of science and the actual fixedness of some scientists. finally, if nothing else, i care, i want to know, so I'm trying to see if someone like me is out there with more experience and answers in this area.

 

[monesh]

in any case, can i ask you, atyy (as I'm still checking bhopp's references) what is causing the wave pattern in em radiation - is it possible to put it in simple terms at first, perhaps in some kind of crude analogy?

 

[atyy]

in any case, can i ask you, atyy (as I'm still checking bhopp's references) what is causing the wave pattern in em radiation - is it possible to put it in simple terms at first, perhaps in some kind of crude analogy?

In fact it is possible to conceive of things waving in an EM wave. But that is advanced. The way to teach basic science is not to dumb it down. The EM wave is a wave. Period. It is described by Maxwell's equations.

 

[monesh]

and bhopp, it seems you've given me very thick and lengthy references to study, which amounts to saying, if i just study a lot of qm for a while, i will eventually find the answer to my qm question. er, yes, but the reason i came here is to first see if there isn't a more direct route to answering my original question. i mean, isn't there some kind of more straight forward way to explain how the waves in em radiation are being produced by blinking (non-waving?) electrons?

 

[monesh]

the way to teach is now part of the question, and i feel i have as much expertise here as anyone. i think the way to teach is to find progressive approximations to the truth. this is what humans use in languge that express (but simplify) feelings, myths that characterize (but simplify) culture, and even in science that describes (but simplifies) nature. if we took the answer "that's just how it is. period." would we even have started science in the first place? all this means that i believe there is some way to approximate a reasonably good answer to my question that is better than just saying don't ask. and by the way, if you're bothered by me asking, you really don't have to try to be the one to answer.

 

[monesh]

i guess at this point i at least wonder if i could just accurately say "most scientists have no explanation for exactly how em waves are produced, in the form of waves, from electrons" - or is even this true? is this just the view of the few i have run into here, or is this really the majority view? maybe you guys could at least help me refine this statement, in case a student asks the quite natural question: why waves?

 

[Drakkith]

i mean, isn't there some kind of more straight forward way to explain how the waves in em radiation are being produced by blinking (non-waving?) electrons?

You don't need quantum physics for this. Classical physics already does exactly what you're asking.

 

[bhobba]

another slight problem...just started reading your first reference which contends, in part, that qm does not assert that nature is fundementally random.

The key word here is FUNDAMENTALLY. We have interpretations where its deterministic in the usual sense - the probabilities appear due to lack of knowledge about initial conditions (one is called Bohmian Mechanics).

Thanks
Bill

 

[bhobba]

atyy: hmmm...is science really like that? scientists know a lot, and scientists care about a lot, especially compared to non-scientists, who might say of all of science, who knows and who cares (about any science). and science is about why to some degree: why did that catch on fire? why does the moon have a shadow?

These days we know why QM (I posted it before - but will repeat it again):
http://arxiv.org/pdf/quant-ph/0101012.pdf

Its basically the most reasonable generalised probability model that allows continuous transformations between pure states. This is what you want to model physical systems because if a system transforms to a state in one second then it should go through another state in half a second.

The issue is these are not explanations in everyday terms - its highly mathematical which people often have trouble believing is an explanation. They say its just math, it can't be reality - you hear all sorts of things if you answer questions on science forums. They haven't quite grasped that math is itself a language and its explanations are just as good as what they are used to.

As I said previously the hardest part in all of this will be breaking down misconceptions from the populist press. Rest assured whatever you are told here is correct. What I have been saying for the most part is from the following standard textbook:
https://www.amazon.com/dp/9814578584/?tag=pfamazon01-20

Its graduate level ie what students are taught at graduate school or upper undergraduate courses. It's deeper, more mathematically sophisticated - but to compensate is correct.

Thanks
Bill

 

[nikkkom]

in any case, can i ask you, atyy (as I'm still checking bhopp's references) what is causing the wave pattern in em radiation

Gosh.
Waves are the consequence of the fact that Standard Model is built on quantum field theory equations. Anything else than reasonably smooth differentiable functions will not be able to satisfy QFT equations; and they can't be exponents or other unlimited functions since integral of square of absolute value over all space must be finite (equal to one, if you are looking at just one particle - IOW, "probability of this particle to be somewhere in the Universe is one"). This leaves you with one class of functions, the "wavy" ones.

(There are exceptions. Higgs field almost everywhere is not a wave, but a nonzero constant (i.e. its integral over all space is not finite). The Higgs particle is a wave _on top_ of this constant level).

 

[andrevdh]

We like to explain unknown things in terms of things we "do know", otherwise we have to start from scratch!