# Matter Waves and Electromagnetic Waves

I don't know if this question should be in the quantum physics section, so i'm just posting it here.
So I have doubts regarding matter wave and electromagnetic waves associated with electron or just any particle.

1. So I understand when an electron is accelerated, it produces electromagnetic waves because it is a charged particle. It also has matter waves associated with it by virtue of its mass. My question is, are these matter waves 'emitted' just like electromagnetic waves ? Can they be visualized as being emitted from an electron just like electromagnetic waves ? And also, since a wave is basically a disturbance created by a certain entity, what is the entity causing the 'disturbance' for matter waves.

2. Is the wavelength associated with a matter wave and electromagnetic wave the same ? My textbook has an expression for the de Broglie wavelength associated with an electron given by, wavelength = 1.227/sqrt(V), where V is the potential difference by which it is accelerated. They have used de Broglie's relation to prove this relation, however the derivation starts with the consideration that an electron is being accelerated through a potential of V. So for an electron that is not being accelerated, what is the associated de Broglie wavelength ? And why does the electron have to be accelerated to calculate its de Broglie wavelength.

3. Finally, does an electron or any particle have to be accelerated to 'emit' matter waves? Or are matter waves even emitted for stationary objects ?

As far as I understand earlier it was assumed by even Schrödinger that electron is getting smeared out but later Max born pointed out matter wave as the wave of probability density and electron remains a particle only(I am curious but not an expert.Please correct me if needed)

bhobba
Mentor
Finally, does an electron or any particle have to be accelerated to 'emit' matter waves? Or are matter waves even emitted for stationary objects ?

You are getting confused with this wave-particle thing.

De-Broglies theory led to Schroedinger's equation but that was subsumed into a more general theory when Dirac came up with his transformation theory in late 1926:

Once that was accomplished it became clear there was no waves, the wavelike solutions that sometimes occurs are not waves in any usual sense.

Unfortunately textbooks do not then go back and show how this new more general theory explains the double slit that spawned it. Here is a paper that corrects that:
http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

As you can see its not really explained by wave-particle duality. What's going on is the slits act as a position measurement which means its scattered in an unpredictable angle due to the uncertainly principle. The interference pattern is caused by the superposition of those different 'scatterings'. Its got to do with the uncertainly principle and superposition principle rather than the wave-particle duality.

Thanks
Bill

WannabeNewton
My question is, are these matter waves 'emitted' just like electromagnetic waves ?

No the electron is the matter wave.

2. Is the wavelength associated with a matter wave and electromagnetic wave the same ?

This is an ambiguous question: what do you mean by "same"? The wavelength of a matter wave is inversely related to the particle momentum: the larger the momentum the smaller the wavelength. Indeed it is simply given by ##\lambda = \frac{h}{p}##. All this really means is the larger the momentum of the particle the more spatially delocalized it will be.

(I've omitted your final question simply because it is based on the false premise that matter waves are "emitted").

dextercioby
Homework Helper
There are no matters waves and such. There are only quantum fields and their typical particle interpretation.

bhobba and vanhees71
vanhees71
Gold Member
2021 Award
You are getting confused with this wave-particle thing.

Unfortunately textbooks do not then go back and show how this new more general theory explains the double slit that spawned it. Here is a paper that corrects that:
http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

Bill

I don't want to be too nasty here, but I don't understand why you quote this paper so often. It's very misleading as unfortunately also many textbooks. Many of the there presented solutions of the Schrödinger equation for the various slit experiments are no states at all but distributions ("generalized eigenfunctions"). When I learned quantum theory I was pretty confused by this in the beginning, because the plane wave which is the generalized (!) eigenfunction of the momentum operator ##-\mathrm{i} \vec{\nabla}## (using units with ##\hbar=1##) is taken as representing a state of the particle. But it's not a state, because it's not a square-integrable function and thus no member of the Hilbert space used in wave mechanics, which is the Hilbert space of square Lebesgue-integrable (complex or spinor valued) functions on ##\mathbb{R}^3##.

Of course, one can use these solutions to create true states from them. You simply have to start correctly with true square-integrable functions in the very beginning, i.e., a wave packet being scattered by the obstacle making up the slits!

Also the use of the ##\delta## distributions for the slits is part of the problem. Using slits of a finite width you can even use the steps in this paper to obtain correct results, and it's not difficult to do the integrals. "One should explain something as simple as possible but not simpler." (Einstein).

So again: I don't understand, why you cite this paper! My general warning is to be utmost careful, when you find a physics text written with word (SCNR)!

bhobba
Mentor
So again: I don't understand, why you cite this paper! My general warning is to be utmost careful, when you find a physics text written with word (SCNR)!

It breaks down the idea that the double slit requires the wave particle duality to explain it.

I know it has issues:
http://arxiv.org/pdf/1009.2408.pdf

But I think the wave-particle duality as the explanation is worse.

The Dirac Delta function is of course an equal crock, but it is used a lot in applied math eg as a short impulse in an electrical circuit.

When I first came across it in my class of differential equations it confused the bejesus out of me and that only got worse when I read Dirac. That lead me on a long sojourn to get to the bottom of it - which I did. After that experience I realised what my teachers told me was correct - just accept it as a funny function for the moment and look into its details later.

Thanks
Bill

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I've got it. For the benefit of those who also have this confusion,
1) Just like what @WannabeNewton said, The particle is the wave. Wave-particle duality basically says that waves behave like particles and particles behave like waves. Particles behaving like waves is illustrated through Davisson-Germer experiment ( for electrons ). It has subsequently been proved for other particles as well. So the matter waves is basically the waveform that the particle behaves like i.e. since particles show wave behavior, the wave associated to that wave behavior is the matter wave.

2) When I said same, I meant numerically equal in wavelength. It is a very badly framed question and confuses many concepts. Basically, wavelength for a matter wave is calculated by the de Broglie relation and is entirely separate from an electromagnetic wave. When an electron is accelerated through a potential difference of V, the wavelength of the matter wave is given by 1.227/sqrt(V). Also, I was confused about whether matter waves existed for stationary particles, my understanding now is that the matter wave associated with a stationary particle will have a wavelength of infinity, since its momentum ( wrt ground ) is 0.

@bhobba That was an interesting paper to read but I don't think I am at the level to completely understand it. Thanks for linking it anyway.

and thanks to everyone who answered, please correct me if I have still made any mistakes in understanding these concepts.

bhobba
Mentor
IThe particle is the wave.

The particle is not a wave - its quantum stuff.

Wave-particle duality basically says that waves behave like particles and particles behave like waves

Sometimes - and note the key word LIKE - they really aren't waves in any usual sense. They are in fact neither.

Thanks
Bill

As far as I understand earlier it was assumed by even Schrödinger that electron is getting smeared out but later Max born pointed out matter wave as the wave of probability density and electron remains a particle only(I am curious but not an expert.Please correct me if needed)
What I find bizarre then is this: if it is a probability wave of finding the entire electron in a certain 3D space around the nucleus, that would seem to indicate that the electron is really orbiting... Doesn't it? But since electron has a charge, orbiting would make it lose its energy in the form of electromagnetic radiation...

So somebody, please, if possible, in a understandable, logical manner, explain this: do electrons really orbit or not. Or we do not know what it does? It is rather impossible to understand clearly, what is a "matter wave".
There are so many misconceptions and interpretations about it. The point is: I can appreciate that this is non-intuitive, what I don't like however, is when the concept is getting muddy, confusing. Complicated- yes, but it should not be confusing.

So what EXACTLY are those matter waves and what exactly are the so-called orbiting electrons doing?
If it is just a probability to find an electron, than one could think they are really orbiting. If they do, what about the supposed loss of energy by radiation?

I apologize if somebody has answered this here (probably has).. But I really feel I need an answer to this specific question, not just round and nonspecific ideas or math without any conceptional explanation.

bhobba
Mentor
What I find bizarre then is this: if it is a probability wave of finding the entire electron in a certain 3D space around the nucleus, that would seem to indicate that the electron is really orbiting... Doesn't it?

No - what its doing when not observed is anyone's guess - the theory is silent about it.

Quantum theory is a theory about this thing called a quantum state that encodes the probability of the outcomes of observations:
http://www.scottaaronson.com/democritus/lec9.html

When not observed - the theory says nothing.

So what EXACTLY are those matter waves

There is no such thing as matter waves. It was an interim idea proposed by De-Broglie that was overthrown when Dirac came up with the transformation theory end of 1926. Schroedinger and Heisenbergs ideas were all subsumed in this more general theory.

Thanks
Bill

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dextercioby and vanhees71
No - what its doing when not observed is anyone's guess - the theory is silent about it.

Quantum theory is a theory about this thing called a quantum state that encodes the probability of the outcomes of observations:
http://www.scottaaronson.com/democritus/lec9.html

When not observed - the theory says nothing.

There is no such thing as matter waves. It was an interim idea proposed by De-Broglie that was overthrown when Dirac came up with the transformation theory end of 1926. Schroedinger and Heisenbergs ideas were all subsumed in this more general theory.

Thanks
Bill

The amount of misconceptions and confusion and messiness in quantum mechanics is mind boggling and honestly, a bit depressing..
The utter inability of so many people to explain things with being logical, critical, while not being condescending is again, depressing.

There are people, who cannot admit they do not understand and then pretend to understand and lie to themselves, hide behind mathematics and laws without explaining them, where and why those laws come from. They start treating quantum mechanics (or whatever science for that matter) as a religion.

So it leads to arguments, such as: are there matter waves or not...
Both sides argue, because they want to be right, rather than to understand, what really happens.

Let me ask this then: if there are no matter waves, then why are they still talking about for example electron's interference pattern?

bhobba
Mentor
[
The amount of misconceptions and confusion and messiness in quantum mechanics is mind boggling and honestly, a bit depressing.

Ok. Here is my bible on QM:
https://www.amazon.com/dp/9814578584/?tag=pfamazon01-20

Although it requires a fair degree of mathematical sophistication QM is developed logically from 2 axioms that I will state:

1. Every observation is described by a Hermitian operator in a complex vector space such that its eigenvalues are the possible outcomes.

2. There exists a positive operator of unit trace P such that the expected outcome of an observation with operator O is trace (PO). P by definition is called the state of the system.

If your math isn't advanced enough to disentangle that then you have to take my word for it - QM indeed follows fully logically from those axioms.

There are people, who cannot admit they do not understand and then pretend to understand and lie to themselves, hide behind mathematics and laws without explaining them, where and why those laws come from. They start treating quantum mechanics (or whatever science for that matter) as a religion.

In my experience people that say that sort of thing do not want to knuckle down and learn the background to understand a book like the one I mentioned above. Regarding math - physics is written in the language of math so sometimes math is required to explain physical concepts. The hallmark of science is correspondence with experiment - all science is provisional and can be overthrown by observation - that's the exact opposite of religion which is more along the lines of 2+2 = 5 and make no mistake about it rather than 2+2 is almost certainly 4 but we need to be careful to ensure its actually the case.

So it leads to arguments, such as: are there matter waves or not...Both sides argue, because they want to be right, rather than to understand, what really happens.

The text I gave as my bible is a standard well respected text and it doesn't even mention matter waves except in its correct historical context. There is a reason for that as people in this thread have tried to explain. However it is an advanced graduate text, and texts at the intermediate level undergraduate sometimes are not as careful as they should be and misconceptions can arise.

Let me ask this then: if there are no matter waves, then why are they still talking about for example electron's interference pattern?

Why do you believe that matter waves is the only explanation? I linked to a paper that explained it without that.

Thanks
Bill

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[

Ok. Here is my bible on QM:
https://www.amazon.com/dp/9814578584/?tag=pfamazon01-20

Can you point to the confusion and messiness in that book?

Bill

Well you are going to have give me time then. I was referring more to people who interpret thoeries and books.
For example, after reading Newton's "Principia", it really opened up, what really Newton meant by various ideas.

For example, those who cannot explain, what mass is, probably haven't even opened up the "Principia", because in his first chapter, he explains it, and very elegantly so.
Many textbooks, who interpret Newtons mechanics, bring many misconceptions into that.

This is just an example.

[
In my experience people that say that sort of thing do not want to knuckle down and learn the background to understand a book like the one I mentioned above.
Bill

This may and may not be so. Many people do indeed that because of the reason you mention. I have read many books and have been thinking about them countless of times. I have read from some of the worst to the best; the assessment is of course my subjective one. But objectivity is something I really rooting for.

[
Regarding math - physics is written in the language of math so sometimes math is required to explain physical concepts. The hallmark of science is correspondence with experiment - all science is provisional and can be overthrown by observation - that's the exact opposite of religion which is more along the lines of 2+2 = 5 and make no mistake about it rather than 2+2 is almost certainly 4 but we need to be careful to ensure its actually the case.

Bill

Physics IS written in the language of math, but note that even equations, that look the same, may have DEEP conceptional differences. The conception behind it, what some equations say, are ESSENTIAL. Nothing comes from nothing. This tendency, to explain things, because "this satisfies this and this equation", is a dangerous one; sometimes necessary, but a dangerous tendency. I realize fully that nature is non-intuitive and not graspable with so called "common sense" (I do not really like the expression "common sense"), but a conception must not be messy. Messy does not equal with non-intuitive or difficult.

Wasn't it Einstein, who said that if you cannot explain it to a 6 year old, you probably cannot understand it yourself. I think he was exaggerating, but he did have a point. Many people teach others while not fully understanding it themselves and then rationalizing the weak points.

About the experiments....I think it is safe to say that experiments are INTERPRETED by human brains. One thing is the experiment, the other thing is the different ideas people read out of and into experiments. This has to be kept in mind, in my humble point of view. Doesn't it make sense?

[
The text I gave as my bible is a standard well respected text and it doesn't even mention matter waves except in its correct historical context. There is a reason for that as people in this thread have tried to explain. However it is an advanced graduate text, and texts at the intermediate level undergraduate sometimes are not as careful as they should be and misconceptions can arise.
Bill

I will look into this texts. I am not very fond of this "intermediate level" and "higher lever" classification though; in my mind, it is not very clear, what makes one thing intermediate or higher. Not really understandable. In my view: things are either messy or explained critically and well. It is like with journalism: there are no different types of journalism, something either is an example of journalism or not. If one takes sides but does not want to provide the full picture objectively, then one becomes a propagandist not a journalist.

If the difference between the "lower" and "higher" is math.. then... pff....The higher math arises from rather "down to earth ideas and problems" ...

I will check the bible. Although, let me say this: calling something a bible is ....well... can a bible make mistakes?

[
Why do you believe that matter waves is the only explanation? I linked to a paper that explained it without that.
Bill

I don't believe it. I can live with doubt or not knowing terminally, what it is. My question is this: many sources bring this example of electrons behaving like waves and are perfectly happy with that explanation. If one says that there are no matter waves, one makes this sound so definite. If we do not know, what the hell they are, then how can we say that it is not matter waves?

If one says that electrons do not orbit around the nucleus, and also they are not standing waves of matter (with their energy spread out in a wave pattern), but they simply are somewhere (in different places) with a certain probability, not moving, but being probably in certain points in space...

This does seem a rather non-explicable explanation: doesn't explain exactly anything.

Can I ask you this: this bible you refer to, what in your mind, to the best of your ability, does this bible say about matter? Can you explain it in for example 5 sentences?

Thank you.

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bhobba
Mentor
For example, those who cannot explain, what mass is, probably haven't even opened up the "Principia", because in his first chapter, he explains it, and very elegantly so. Many textbooks, who interpret Newtons mechanics, bring many misconceptions into that.

Actually that's a very good example of what's going on here.

Newton wrote that centuries ago and it has been superseded well and truly.

Beginner texts explain mechanics along the lines of Newton, but they have many issues glossed over in those texts. For example the first law follows from the second which is a definition of force. Its real physical content is in the third law. What's going on here? Basically Newtons laws are a prescription that says - get thee to the forces. Its the same with texts that speak about matter waves - it was an important stepping stone to modern QM - but is now well and truly superseded.

More advanced texts avoid it entirely and base it on the Principle Of Least Action (PLA). The PLA follows from Feynman's sum over history formulation of QM. The rest, believe it or not, basically follows from symmetry (this is the import of Noether's beautiful theorem) - in fact so does much of QM as explained in my 'bible' text - Ballentine.

It even explains what mass is and why it must be positive.

If this has intrigued you, (and hopefully it does) get a hold of the following beautiful book:
https://www.amazon.com/dp/0750628960/?tag=pfamazon01-20
'If physicists could weep, they would weep over this book. The book is devastatingly brief whilst deriving, in its few pages, all the great results of classical mechanics. Results that in other books take up many more pages. I first came across Landau's mechanics many years ago as a brash undergrad. My prof at the time had given me this book but warned me that it's the kind of book that ages like wine. I've read this book several times since and I have found that indeed, each time is more rewarding than the last. The reason for the brevity is that, as pointed out by previous reviewers, Landau derives mechanics from symmetry. Historically, it was long after the main bulk of mechanics was developed that Emmy Noether proved that symmetries underlay every important quantity in physics. So instead of starting from concrete mechanical case-studies and generalising to the formal machinery of the Hamilton equations, Landau starts out from the most generic symmetry and derives the mechanics. The 2nd laws of mechanics, for example, is derived as a consequence of the uniqueness of trajectories in the Lagragian. For some, this may seem too "mathematical" but in reality, it is a sign of sophistication in physics if one can identify the underlying symmetries in a mechanical system. Thus this book represents the height of theoretical sophistication in that symmetries are used to derive so many physical results.'

It will be an excellent warm up for understanding Ballentine. Both Landau and Ballentine had a deep effect on me.

Thanks
Bill

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bhobba
Mentor
Wasn't it Einstein, who said that if you cannot explain it to a 6 year old, you probably cannot understand it yourself.

On that and a number of things I believe Einstein was mistaken. That is not to denigrate the man - he probably had the most penetrating mind of all time.

Can I ask you this: this bible you refer to, what in your mind, to the best of your ability, does this bible say about matter? Can you explain it in for example 5 sentences?

Interesting question. The best I can come up with is nature is weird - but even weirdness can be reasonable if viewed correctly. What science is about is formulating that weirdness rigorously so it actually becomes beautiful and elegant - and symmetry plays a vital role in that formulation. But for me standard QM is ultimately barren at a fundamental level because it ignores relativity. If you include that you are inevitably led to quantum field theory which actually says something quite deep for me. Everything is a quantum field and particles are excitation in those fields - with the exact meaning of those unfortunately rather trite comments detailed by the theory.

I think that was 5 sentences :D:D:D:D:D:D:D:D

Thanks
Bill

gianeshwar
On that and a number of things I believe Einstein was mistaken. That is not to denigrate the man - he probably had the most penetrating mind of all time.

Interesting question. The best I can come up with is nature is weird - but even weirdness can be reasonable if viewed correctly. What science is about is formulating that weirdness rigorously so it actually becomes beautiful and elegant - and symmetry plays a vital role in that formulation. But for me standard QM is ultimately barren at a fundamental level because it ignores relativity. If you include that you are inevitably led to quantum field theory which actually says something quite deep for me. Everything is a quantum field and particles are excitation in those fields - with the exact meaning of those unfortunately rather trite comments detailed by the theory.

I think that was 5 sentences :D:D:D:D:D:D:D:D

Thanks
Bill
A nice way to put it about a book. Thank you. Interesting.

About Einstein: can we make a compromise and say that he was exaggerating rather than wrong.
I say this, because I have noted it myself: while trying to explain something to students, I uncover so many aspects I haven't considered before or even "misconsidered". I somehow feel, that personally, I hadn't TRULY understood many of the things before I really tried to explain them to the others.
Of course there are things that truly cannot be explained to a 6 year old, I think he meant it as a metaphor, he didn't probably mean literary a 6 year old.

gianeshwar
Ott Rovgeisha and Bhobba!
Your arguments are very interesting,but I need to study much more to enjoy these more. Thank you!

I think in whole above discussion we are agreeing to objective physical interpretation of nature only.In the common background is mutually agreed mathematics(There is no scope to disagree I believe due to universality of rigorous mathematics because 2plus 2 is four for everyone)
Now I wonder how Eugene Wigner might comment here.I think he thought something beyond as well.

vanhees71
Gold Member
2021 Award
There are people, who cannot admit they do not understand and then pretend to understand and lie to themselves, hide behind mathematics and laws without explaining them, where and why those laws come from. They start treating quantum mechanics (or whatever science for that matter) as a religion.
The worst kind of people of all are those pretending you could understand physics (particularly quantum theory) without mathematics. Mathematics is the only language precise enough to describe nature adequately. There's no way without math! Without math you must believe, with math you can understand. Thus it's religion without math.

bhobba
The worst kind of people of all are those pretending you could understand physics (particularly quantum theory) without mathematics. Mathematics is the only language precise enough to describe nature adequately. There's no way without math! Without math you must believe, with math you can understand. Thus it's religion without math.

I do not understand the point of this point. Of course mathematics is part of physics, but only as a tool to describe something.. But the statement that "without math you must believe", forgive me, but does not make sense to me. You can take an equation F =ma, you may interpret this in different ways and ultimately, you also have a choice: believe that F=ma or not. If you want to put in to understanding, then understanding in physics is based on beliefs. Maxwell derived his equations according the observations and he massaged those equations to fit those observations and other important aspects of the electromagnetism. Einstein massaged his equations so as to fit his deductions and AFTERWARDS started the long running period of trying to prove those equations describe what we observe.

So, to be honest, I do not understand at all this assertion that with math one can understand. Math is also based on beliefs; or let me put it differently: on assumptions.

Of course, there are different beliefs... Was it Don Juan from "Don Juan" who was an atheist and was asked, what DID he believe in then? And he answered: "I believe that 2+2=4"
(I am sorry, I first confused Don Juan with Don Quixote, this is an edited post)

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vanhees71
Gold Member
2021 Award
My point is just that you have no chance to understand physics without math. Claiming that physicists are "hiding behind the mathematics" without understanding is thus absurd.

My point is just that you have no chance to understand physics without math. Claiming that physicists are "hiding behind the mathematics" without understanding is thus absurd.
I never claimed that "physicists are hiding behind the mathematics". I prefer to be quoted exactly: "There are people, who cannot admit they do not understand and then pretend to understand and lie to themselves, hide behind mathematics and laws without explaining them"

That is not the same as saying that physicists hide behind the math. Surely you do see that?

and btw:

kith
I don't want to be too nasty here, but I don't understand why you quote this paper so often. It's very misleading as unfortunately also many textbooks. [...] Using slits of a finite width you can even use the steps in this paper to obtain correct results, and it's not difficult to do the integrals.
I find it astonishing that a good treatment of the double slit using the full machinery of QM can't be found in any textbook or paper I know of. It is such a popular example in pop science and introductory chapters of textbooks. Why hasn't anyone bothered to do the maths?

kith
These are nice illustrations but I am looking for a rigorous analysis of the problem. Marcella tried to do this but he wasn't very successful. Or maybe he was successful if we allow his simple state preparation / measurement model. In any case, the critique of Rothman and Boughn shows how classical optics gives a more sophisticated picture.

I just found a paper from 2011 by Beau (http://arxiv.org/abs/1110.2346) which uses the path integral approach and seems promising.

atyy
These are nice illustrations but I am looking for a rigorous analysis of the problem. Marcella tried to do this but he wasn't very successful. Or maybe he was successful if we allow his simple state preparation / measurement model. In any case, the critique of Rothman and Boughn shows how classical optics gives a more sophisticated picture.

I just found a paper from 2011 by Beau (http://arxiv.org/abs/1110.2346) which uses the path integral approach and seems promising.

Actually I think Marcella is ok, since the delta function initial state is fixable (I mean, do we really need rigour here?) I think the main steps that Marcella skipped were that what's actually happening is a position measurement, whereas Marcella calculates a momentum measurement, which is only correct for the very large distance limit (Fraunhofer).

There's also some interesting stuff, necessarily increasingly unrigourous because they include more and more complicated real phenomena like http://arxiv.org/abs/quant-ph/0407245 and http://arxiv.org/abs/1405.4649.

kith
Actually I think Marcella is ok, since the delta function initial state is fixable (I mean, do we really need rigour here?)

I think the main steps that Marcella skipped were that what's actually happening is a position measurement, whereas Marcella calculates a momentum measurement, which is only correct for the very large distance limit.
In classical wave optics, the theoretical description of diffraction at the double slit is well-understood. In order to derive results similar to Marcella's, one solves the wave equation while taking the geometry of the slits into account and by using a number of approximations. I'd like to see a quantum description with the same level of detail. The large distance limit is only a part of this.

Also, there are questions specific to quantum mechanics. For example in the nice visualization you linked to above, a part of the wave is reflected backwards. Doesn't this tell us something about the nature of Marcella's state preparation? And what about dynamics? What can we say about state evolution and what about the time of the measurement? These questions are directly motivated by the postulates of QM, so discussing them is important if the double slit is taken as an example case of quantum behavior.

So no, I'm not satisfied with Marcella's paper. He gives a rough idea of how the formalism could be applied but he doesn't discuss all aspects. And his description is a significant step backwards from the sophisticated classical description.

bhobba
Mentor
The worst kind of people of all are those pretending you could understand physics (particularly quantum theory) without mathematics. Mathematics is the only language precise enough to describe nature adequately. There's no way without math! Without math you must believe, with math you can understand. Thus it's religion without math.

Very true.

In relation to the 6 yo comment I am taken back to a comment Feynman made about books that explain physics to lay persons. It doesn't matter how good the author is they will never be able to do that correctly without math - they will always run in problems and end up saying things that are not quite true. Even he fell into the inevitable trap in his excellent book - QED - The Strange Theory Of Light And Matter. He explained light passing through a medium by absorption and remission - which is wrong:

That's why I love Susskind's Theoretical Minimum books. They require a smattering a calculus but are correct.

Thanks
Bill

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vanhees71
atyy
And what about dynamics? What can we say about state evolution and what about the time of the measurement? These questions are directly motivated by the postulates of QM, so discussing them is important if the double slit is taken as an example case of quantum behavior.

For the dynamics, I was thinking that once the initial state, potential and boundary conditions are specified, it's just unitary evolution. Do you want an analytical solution? I was thinking a numerical solution would be good enough.

As for the observable, perhaps it should be something like ##x \otimes y \otimes 1## (at least conceptually, maybe not technically), where the screen is in the ##x##-##y## plane at a fixed ##z## distance from the slit? There should be a different distribution for each time of observation. The time of observation is not controlled by the experimenter, but it is possible to assign a time stamp to each appearance of a dot on the screen. So one can figure out when god or whoever decided to make something happen, and sort the data according to time stamps, and get different diffraction patterns corresponding to different times of observation, something like what is done in http://www.atomwave.org/rmparticle/ao%20refs/aifm%20refs%20sorted%20by%20topic/ungrouped%20papers/wigner%20function/KPM97.pdf [Broken] (Fig. 3).

But what is hard to get by that method is the density of dots on the plate after a long time. jostpuur and vanhees71 gave the solution for that in posts #57 and #71 of https://www.physicsforums.com/threads/position-eigenstates.764912/.

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kith
For the dynamics, I was thinking that once the initial state, potential and boundary conditions are specified, it's just unitary evolution. Do you want an analytical solution? I was thinking a numerical solution would be good enough.
My astonishment is mainly about pedagogics: the popularity of the double slit makes it seem that it is a standard case of quantum behavior. Yet almost no sources bother to connect it with the full machinery of QM, nor with the well-understood situation in classical optics. I don't think that giving the answers is especially hard although it can be if we make the problem more complex like in the two papers you cited.

vanhees71
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2021 Award
It's true! There's a lack of a correct derivation. It's analogous to the optics derivation for classical em. waves, as e.g. given in Sommerfeld, Lectures on theoretical physics, vol. 4.

atyy
My astonishment is mainly about pedagogics: the popularity of the double slit makes it seem that it is a standard case of quantum behavior. Yet almost no sources bother to connect it with the full machinery of QM, nor with the well-understood situation in classical optics. I don't think that giving the answers is especially hard although it can be if we make the problem more complex like in the two papers you cited.

I think the pattern in the long time limit is not elementary. If you look at jostpuur's and vanhees71's solution the boundary condition is pretty slick.

An elementary solution is not obvious because it isn't obvious how observations happening at different times should be weighted. I wonder whether an elementary (ie. grungy brute force and not sophisticated) solution needs an ancilla, so that after a finite duration measurement interaction, the measurements on the ancilla at any sufficiently late time all yield nearly identical results. I think jostpuur's and vanhees71's boundary condition is a very slick way of modelling a strong interaction with the screen.

vanhees71
No - what its doing when not observed is anyone's guess - the theory is silent about it.

Quantum theory is a theory about this thing called a quantum state that encodes the probability of the outcomes of observations:
http://www.scottaaronson.com/democritus/lec9.html

When not observed - the theory says nothing.

There is no such thing as matter waves. It was an interim idea proposed by De-Broglie that was overthrown when Dirac came up with the transformation theory end of 1926. Schroedinger and Heisenbergs ideas were all subsumed in this more general theory.

Thanks
Bill

You stated above the theory is silent what is the electron in the atom doing when not observed. No problem with that.. but can we categorically say that the electron is not moving when not observed that is why it is not emitting electromagnetic wave (as we know moving charge radiate em wave)?

kith