# How can objects have wavelengths?

1. Nov 18, 2009

### engi2013

I'm really confused about the de Broglie wavelength thing. Like I understand that according to the formula large objects have wavelengths that could not be observable in the real world but i still don't understand what type of wave de Broglie is referring to.

Is he referring to longitudinal waves or something? Would that mean that a baseball bobs up and down or side to side or back and forth when it moves? If so what causes that motion in objects? If it's not longitudinal, what type of wave is he talking about?

2. Nov 18, 2009

### mgb_phys

Think of the wavelength as the uncertainty in the size, or the position of the edges, of the object.
In quantum mechanics all objects are a little fuzzy around the edges.

For a photon (with no mass) there is no solid lump of photon in the middle so the uncertainty - the fuzzyness - is the size of the photon = wavelength.
For an electron there is a bit of fuzzyness, enough to be useful in a few pieces of equipement.

For a large object like a golfball, the wavelength and uncertainty is small enough not to be observable

3. Nov 18, 2009

### lightarrow

It's not what you think, but something totally different. It's a *probability* wave. It means that you cannot know where the object is, since you can detect it in a position or in another, according to different values of the probability wave. Actually, an object as something we know from sensorial experience, that is a classical object, doesn't exist anylonger in the QM reign. We are used to think of the world in terms of these classical objects, but, if we were educated differently (quantum mechanically) then we would find *strange* the existence of classical objects; we would say: "wow, that ball has a precise spatial localization! What a wonderful thing"

4. Nov 18, 2009

### zenith8

What de Broglie actually meant by it was as follows. His theory was that there is an objectively existing wave (mathematically represented by the quantum-mechanical wave function) and that there were objectively existing particles, which are pushed around (or 'guided' by) the wave. This might sound crazy to modern ears, but it remains to this day fully in accord with experiment and all the predictions of QM.

'Things' are made of particles, and the de Broglie wavelength is the wavelength of the accompanying wave. Using this theory he won the Nobel prize for predicting that particles accompanied by the guiding wave would show 'diffraction' effects when their trajectories passed through narrow slits. Amazingly, for most of the rest of the 20th century, the experiment was often cited as evidence that particles couldn't have trajectories!

Strictly speaking of course, the accompanying wave need not be periodic in which case it can't have a strictly defined wavelength i.e. the usual formula $$\lambda=h/p$$ (which connects particle and wave properties) is only applicable to plane-waves. What it can have is a sort of 'local wavelength'. For a general wave, the obvious generalization of the wave vector $${\bf k} = 2\pi/\lambda$$ is the local wave vector $$\nabla S({\bf x} )/\hbar$$ where $$S$$ is the position-dependent phase of the wave and $$\hbar$$ is a constant with appropriate units. From this you can see $${\bf v}=\nabla S/m$$, or equivalently $${\bf p} = \nabla S$$ which is just the usual guidance equation from the http://en.wikipedia.org/wiki/De_Broglie-Bohm_theory" [Broken] of QM giving the momentum of the particles (though this is emphatically not the usual way of deriving it).

The full historical story is given in http://books.google.co.uk/books?id=0oumHAAACAAJ&dq=crossroads+valentini" [Broken] (also available for free on arxiv.org somewhere).

Last edited by a moderator: May 4, 2017
5. Nov 18, 2009

### Staff: Mentor

http://arxiv.org/abs/quant-ph/0609184

Last edited by a moderator: May 4, 2017
6. Nov 18, 2009

### ytuab

Can you explain the spectrum results of the Anomalous Zeeman effect and fine structure (the energy difference between 2P1/2 and 2P3/2) In BM?

The BM's experimental results of them is the same as the results in standard QM?

(Sorry. I have wanted to ask this question once.)

7. Nov 18, 2009

### zenith8

Hi ytuab,

No offence, but my lethargy with writing invited de Broglie-Bohm essays has become such that I'm going to have to impose some rules. I might answer you if (a) you start a new thread (the question is not relevant to this one), and (b) you first make some attempt to tell me why you think it wouldn't be explainable in de Broglie-Bohm theory.

Actually, now I think about it - you've got as far as the anomalous Zeeman effect, which means you must understand de Broglie-Bohm theory to a pretty advanced level. Why don't you suggest to me in a few lines how it might work, then I'll tell you if you're right..

8. Nov 18, 2009

### DrChinese

That is really cool, and very much worth looking at for anyone. Plenty of interesting theoretical discussion, in addition to the historical perspective.

But boy, they do betray their interpretational preferences.

9. Nov 19, 2009

### zenith8

Do you think so? I thought their point was that three interpretations were presented at the 1927 Solvay conference (de Broglie pilot-wave theory, Schrodinger wave mechanics, Heisenberg et al matrix mechanics). More or less equal time was given to them at the conference. Valentini and Bacciagaluppi give them equal time in the book.

I don't think that because they don't dismiss de Broglie in a footnote that means they're 'betraying their interpretational preferences'. Bacciagaluppi at least is not even a de Broglie-Bohmian!

10. Nov 19, 2009

### DrChinese

The number of pages devoted to dBB was equal to the other 2 combined. There are actually good reasons for that, as dBB usually gets shorted as you say. But the tone of the text is telling too. I see a lot of support for dBB ideas and a number of criticisms of more traditional forms. But in all honesty, I thought they covered a lot of good ground and the tone was not so severe that it because unreadable.

The thing is, most dBB supporters look right past the criticisms of dBB and generally dismiss them with the wave of a hand. On the other hand, I think supporters of orthodox QM are well aware of their interpretational issues: what is collapse? where is the line between observer and system? So I wish dBB advocates were a bit more sensitive to the nuances of interpretational issues.

De Broglie's ideas about matter waves are nicely reported, and it is flabbergasting to me that his Nobel was awarded for groundbreaking work done in a PhD thesis! Whew!

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