# Matter Waves and Electromagnetic Waves

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1. Dec 20, 2014

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 ?

2. Dec 20, 2014

### gianeshwar

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)

3. Dec 20, 2014

### Staff: Mentor

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

4. Dec 20, 2014

### WannabeNewton

No the electron is the matter wave.

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").

5. Dec 20, 2014

### dextercioby

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

6. Dec 20, 2014

### vanhees71

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)!

7. Dec 20, 2014

### Staff: Mentor

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

Last edited: Dec 20, 2014
8. Dec 21, 2014

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.

9. Dec 21, 2014

### Staff: Mentor

The particle is not a wave - its quantum stuff.

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

Thanks
Bill

10. Jan 16, 2015

### Ott Rovgeisha

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.

11. Jan 16, 2015

### Staff: Mentor

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

Last edited: Jan 16, 2015
12. Jan 25, 2015

### Ott Rovgeisha

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?

13. Jan 25, 2015

### Staff: Mentor

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Ok. Here is my bible on QM:
https://www.amazon.com/Quantum-Mechanics-Modern-Development-Edition/dp/9814578584

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.

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.

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.

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

Thanks
Bill

Last edited by a moderator: May 7, 2017
14. Jan 25, 2015

### Ott Rovgeisha

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.

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.

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?

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?

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.

Last edited by a moderator: May 7, 2017
15. Jan 25, 2015

### Staff: Mentor

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/Mechanics-Third-Edition-Theoretical-Physics/dp/0750628960
'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

Last edited by a moderator: May 7, 2017
16. Jan 25, 2015

### Staff: Mentor

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

17. Jan 25, 2015

### Ott Rovgeisha

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.

18. Jan 25, 2015

### gianeshwar

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

19. Jan 25, 2015

### gianeshwar

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.

20. Jan 25, 2015

### vanhees71

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.