# How are electrons considered waves?

1. Sep 17, 2009

### mahela007

Almost every textbook and website just says "This is wave particle duality" but none of them actually explain how or why an electron can be considered to be both a wave and a particle. The double slit experiment proves that wave particle duality is in fact true .. but <again> WHAT does it mean to consider an electron as a wave?

2. Sep 17, 2009

### ytuab

What I know now is as follows,

In page 96 (the Story of Spin)
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He (Shrodinger) tended to think that his wavefunction(phi) was a wave in three-dimentional space.
For example, he considered e phi x phi as the charge density which actually exists in space and tried to treat the bulk of the density as an electron. The idea, however, did not work because phi x phi will spread with time and the density decomes diffuse.
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So, In the Shrodinger equation, the electron is not a wave, the wavefunction means the probability density of the electron.

But In page 110
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The Dirac equation is also the relativistic field equation for the electron and it cannot be considered to be an equation of probability amplitude in x,y,z space. They insisted that a concept like "the probability of a particle to be at x in space" is meaningless for relativistic particles- be they electrons, photons .....
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So they seemed to treat relativitic particles as the matterwave existing in space. (In this case, the wave doesn't mean the probability density...)
It's difficult to imagine, so I don't really understand this meaning.

3. Sep 17, 2009

### mgb_phys

Considering an electron as a wave simply means you can't nail down a position for the electron to less than a certain distance.
It's not just electrons, everything is a wave, it's just that the wavelength gets smaller as the object gets bigger - so you only notice the effect for very small things

4. Sep 17, 2009

### zenith8

The obvious way to 'understand' it is to say that both waves and particles exist. The wave goes through both slits and produces an interference pattern. Particles goes through one slit or the other, and because they are pushed around/guided by the wave they generally end up heaped into clumps around the position of the interference maxima. This is the de Broglie-Bohm interpretation of QM.

This is a perfectly consistent point of view to take, and makes complete sense. Unfortunately for historical reasons (essentially, it was the direct opposite of what the power-mad Heisenberg had repeatedly insisted, and he didn't like being contradicted and made to look a fool) standard textbooks seem to be effectively banned from mentioning it, and and like a flock of sheep go into great detail about how 'weird' everything is. ('No-one understands quantum mechanics!!').

As far as 'understanding' is concerned, the officially-sanctioned viewpoint gives you two options:

(1) 'QM is an algorithm for computing probabilities and the wave function doesn't correspond to anything physical' (which gives up on understanding on principle)

(2) 'The QM wave function represents a physical wave field and this is all that exists' (a viewpoint which leads to everything being 'weird' and does not lead to understanding, suggesting it is wrong).

Many people over the last decade (though not enough to penetrate the mainstream) have begun to realize that the banned third option of saying that particles exist as well as the wave field is the only view that actually allows you to make sense of the quantum world. What else would 'wave-particle duality' mean. Why not adopt it? I don't know.

In this view, QM is just classical statistical mechanics with a different dynamical law. Fun, huh?

Last edited: Sep 17, 2009
5. Sep 17, 2009

### alxm

Look, the answer is that they're neither particles or waves in the classical sense of those things. Neither. Quantum mechanical objects display some of the properties of waves in some ways, and some of the properties of particles in other ways.

That's all.

6. Sep 17, 2009

### zenith8

Which quite clearly could be because sometimes you see the particle and sometimes you see the wave, depending on what experiment you do. As you're not going to admit.

7. Sep 17, 2009

### HallsofIvy

What is true is that the very concepts of "particle" and "wave" are not valid in the very micro, quantum, domain.

8. Sep 17, 2009

### zenith8

Go on, why not?

9. Sep 17, 2009

### Bob_for_short

It is easy. An electron is not unique. We deal with beams of electrons (similarly to photon beams), don't we? For example, to observe something tiny. It happens that the result of observing shows wavy behaviour despite it may contain many separate points. What is important to us - one point or the whole, say, interference picture? Of course the latter. The latter is desctibed with the wave function.

It happens that the electron position cannot be certain in certain cases but one can calculate the average, the dispersion, etc. QM does this just like Maxwell theory for EMF.

Any separate point is useless - it says nothing about a particular situation - no average, no other things. It is highly insufficient to describe a beam. We are interested in beams, not in one event. So QM is a science to describe beams or results of many separate measurements.

10. Sep 17, 2009

### zenith8

Which is exactly what the 'waves and particles' viewpoint explains, no?

One, or a few, particle detections appear to be randomly distributed. It is only after a great many detections that the distribution of spots on the screen begins to look like an interference pattern, because the particles are being guided by the accompanying wave. See the many videos of this process on the internet.

11. Sep 17, 2009

### dx

zenith8,

I have a little question about Bohmian mechanics. Is there any experiment you can perform to determine the trajectories of the particles, either directly or indirectly? I.e., is there any situation in nature where the 'wave' alone is not enough to describe it, and one must also consider in detail the 'particles' and their classical trajectories?

12. Sep 17, 2009

### f95toli

That is simply not correct. There are plenty of examples of individual systems undergoing individual event that are still described by wave functions. One obvious example would be a quantum jump processes a $$\Lambda$$ systems (e.g. a single ion in a trap).

You are basically using the same argument as Schroedinger, but that has turned out to be view that is in conflict with results of experiments: i.e. it is not a valid "interpretation" of QM.

13. Sep 17, 2009

### Bob_for_short

It is mostly our desire to have a deterministic picture. It is not supported or imposed experimentally. For example, when one analyses the particle traces (trajectories) in a detector, one uses them to calculate (measure) energy-momenta of particles in reaction. Nobody compares a specific trajectories with "predictions" of a deterministic theory.

14. Sep 17, 2009

### zenith8

Seriously, there is a great deal of experimental evidence that both waves and particles exist.

Take that as a given, and say that the Schroedinger wave function represents a real wave.

Then, as de Broglie said in 1927, 'it seems a little paradoxical to construct a configuration space with the coordinates of points that do not exist'. So assume that the configuration on which the wave function is defined represents a configuration of particles, then lo.. all the usual predictions of quantum mechanics are reproduced, and we have a complete understanding of what appears to be happening.

It doesn't matter what actually exists in actual fact. What matters is when people say 'waves and particles have no meaning in the quantum domain' or state categorically that 'neither waves and particles exist' they are simply wrong. The could perfectly well exist, and if they do, then that is perfectly consistent with all the results of QM.

See, mahela007, what did I tell you? Everybody really really doesn't want to accept this, including the 2008 PF Award Physics Guru, and Mr. "23960 posts!" PF Mentor... :uhh:

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15. Sep 17, 2009

### Bob_for_short

16. Sep 17, 2009

### zenith8

Well, that's the difference between classical measurement and quantum measurement. The only difference is that in the quantum case the probe is as significant as the probed. Essentially any means of measuring the trajectory (I mean, what do you want to do? Bounce something off the electron every trillionth of a second?) will change the trajectory from what it would have been in the absence of the measurement. That's not metaphysical or weird - it's just an obvious truth.

This is a point as old as QM itself - see Leon Brillouin in a discussion taken from the 1927 Solvay conference proceedings:

"Mr. Born can doubt the real existence of the trajectories calculated by Mr. de Broglie, and assert that one will never be able to observe them, but he cannot prove to us that these trajectories do not exist. There is no contradiction between the point of view of Mr. de Broglie and that of the other authors."

If you want, you can retrodict trajectories e.g. observing where the particle hits the screen in the double-slit experiment tells you which slit it went through, but I don't think that's what you mean.

17. Sep 17, 2009

### alxm

Well, that's essentially what I was saying - that saying a quantum-mechanical thing acted like a particle or wave, is making an analogy to a classical object.

18. Sep 17, 2009

### Bob_for_short

Wrong assertion. Both slots are important for the interference picture which is different from two-separate-slot superimposing pictures.

19. Sep 17, 2009

### zenith8

Oh God, Bob. Keep up. The particle goes through one slit. The wave goes through both.

It's difficult for me to speak slowly when writing - perhaps I should put larger spaces between the words?

20. Sep 17, 2009

### dx

I'm not interested in what you may or may not imagine to 'exist'. You're free to imagine that the particles have classical trajectories if it helps you 'understand' it.

My question is unambigiuous: does the 'classical particle' part of bohmian mechanics have any observable consequences at all? I'm not asking about directly measuring the trajectories of the particles. I understand that bouncing things off small particles affects their state significantly, and there is a consequent uncertainty involved. But does it have any consequences that differ from quantum mechanics? For what reason do its supporters consider it superior to quantum mechanics? Is it purely a matter of taste?

I ask because ordinary quantum mechanics seems to be far superior in both the uniformity of its application and the comprehensiveness of its description of experiments, so I'm trying to undertand the point of view of Bohm supporters.

21. Sep 17, 2009

### Bob_for_short

Larger spaces between your words will worsen readability we all got used to. On the other hand, longer thinking around would work for sure.

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22. Sep 17, 2009

### zenith8

They're not classical trajectories. They're quantum trajectories.

And it does help me understand it, a lot.
Simple. Look at the original post. Like nearly every question about quantum mechanics posted here by a student, it is "Oh wah, I don't understand what [insert result of some quantum experiment] means.". Then if I or another Bohmian doesn't post, they are told to go away and often that they are 'not allowed to ask' for explanations. Once they've been told this 50 times (and 300 other people have weighed in with confusing meta-explanations based on their own misunderstandings) then the original poster will finally get that they must not ask these things, and then they spend the rest of their lives (a) confused and (b) impressing their girlfriends with how profound they are to be studying something so 'weird'. This is despite the fact that a simple explanation in terms of obvious concepts exist. You tell me, why are we 'not allowed to ask' about what actually happens during a quantum process? So even if BM made no predictions different from ordinary QM it is still useful because it allows you to visualize stuff, and things are no longer confusing. And that would save everyone's time - both on this board, and for teachers everywhere.

There are also some observable consequences, yeah. Mainly to do with the fact that particles and waves are now logically distinct entities. For example, the particles do not in principle have to be distributed according to the square of the wave function (but one can show that they do tend to become so distributed under ordinary Schroedinger evolution, and quite quickly too, even if they don't start that way). The experiments that might show up 'non-equilibrium' distributions of particles are tricky but some people have begun to think they can do them. Watch this space.

Bohmian mechanics just is ordinary quantum mechanics. The standard viewpoint has no monopolistic right to think the equations of QM belong to it alone.

Last edited: Sep 17, 2009
23. Sep 17, 2009

### sokrates

How on earth did you make such an incredible observation?
What you write here is most probably wrong, based on your (and only your) way of understanding quantum mechanics.

And you are attacking people because they don't follow this??

24. Sep 17, 2009

### zenith8

Bob, if you're going to take the p*** out of me you need to read your sentences back to yourself before you post.
Look. In Bohmian mechanics the possible electron trajectories cannot cross and there is an axis of symmetry in the middle of the apparatus. Therefore ... if ... the ... particle ... hits ... the ... left ... part ... of ... the ... screen, ... it ... went ... through ... the ... left-hand ... slit. Trust me. Brain the size of a planet.

25. Sep 17, 2009

### zenith8

It's not a real life observation, sokrates. I'm just quoting the results of Bohmian mechanics, as you know. And Bohmian mechanics is just ordinary quantum mechanics, since all consequences result from simply redefining the meaning of a couple of words.

It's not just me either. I mean, there's at least one other person on this forum who's bothered to read about it. Out of 20 million or so.