# Wave-particle duality confusion

1. Jul 4, 2014

### haisydinh

Hi,

I am a high-school student who recently finished the chapter on QM. I thought I completely understood it, but when I started to look back at what I’ve learnt, then suddenly, nothing really makes sense. And one of the things I find really really hard is the nature of electrons. My textbook mentions the Schrödinger’s theory and the Louise de Broglie’s hypothesis about matter’s waves; and the followings are what I currently understand about these two theories:

- De Broglie hypothesized that electron has a wave associated with it; that is, electrons are wave-like particles. We can describe an electron as a wave with the wavelength of λ=$\frac{h}{p}$. And this has actually been tested by the electron diffraction experiment (that of Davisson & Germer)
- However, in Schrödinger’s theory, electrons in hydrogen atoms are described as particles; this is because the wave functions give us the probability of finding the electrons at a particle space in a particular time.

So my first question is that: Is an electron an actual wave (as de Broglie suggested)? or do we describe an electron as a particle in which only its probability is a wave (as Schrödinger suggested)? In other words, when we say electron is a wave, then what is actually waving? The probability or the electron itself?

My second question is that: is there any intuitive ways of explaining the probabilistic nature of the universe and of the electrons in particular? I have not read Schrödinger’s derivations of his equations yet, so I really don’t know what’s out there.

Finally, as far as I know, the wave-particle duality hasn’t really been solved to a fully-satisfying extent. So my last question is that: Have there been any suggestions/hypotheses to how this wave-particle paradox can actually be solved? Or have we accepted that this wave-particle duality is actually the nature of the universe?

I know that a photon must be described as a particle with discrete energy $E=hf$ in order for us to explain the photoelectric effect. But when I asked my teacher: “where do we get the frequency ($f$) from if we think of a photon as particle?”; then he replied: “you should think of photons as packets of waves instead”. So now I often think of photons as actual waves; however, for some reasons, these waves are being chopped up (i.e. divided) into packets with discrete energy. In this way, the wave-particle duality can be solved. Is it the correct way to intuitively think about the nature of the photons?

I am sorry if a similar thread has been posted here before; and if it is the case, can you please post the links to previous threads as well? Thank you so much in advance!

2. Jul 4, 2014

### PhilDSP

Hi haisydinh,

Louis de Broglie clearly stated that in his theory there is a wave associated with a particle. He didn't ever claim that the object is a wave in itself. I think you answered your own question about what is waving when you mentioned packets of energy. But since the trajectory of a possibly associated particle is unknown, the practical interpretation of the sum of the discrete packets has come to be regarded as a probability value.

3. Jul 4, 2014

### WannabeNewton

Yes the electron has a wave associated with it but the electron itself is not a wave. While in some calculations it is certainly useful conceptually to think of it as such, at a formal level this is certainly not true.

They are treated as neither particles nor waves. QM has no such dichotomy. The distinction of particles and waves is a classical or semi-classical one.

Not that I know of. You can read up on the plethora of interpretations of QM in order to learn about what people have researched as far as the conceptual basis of the intrinsic probabilistic nature of "the universe" goes but I think you'd be wasting your time at this point.

It's certainly a good intuition to have about photons but bear in mind that while your professor's suggestion amounts to a great conceptual aid, such intuitions can only be taken so far. QFT doesn't offer much of a conceptual guide as to what photons could be pictured as. They are a rather abstract concept at the formal level. In practice the semi-classical pictures of the photon certainly do come in handy but they aren't formally correct. The same goes for electrons and such of course.

4. Jul 4, 2014

### bhobba

Its neither particle nor wave - its quantum stuff. What's quantum stuff - check out:
http://www.scottaaronson.com/democritus/lec9.html

There is no intuitive way - but we do have this deep theorem called Gleason's Theorem:
http://en.wikipedia.org/wiki/Gleason's_theorem

I have posted a proof of the simpler version of the theorem here:

What was Schroedinger's argument - check out:
http://arxiv.org/pdf/1204.0653.pdf

Well actually it has been solved because since 1927 when Dirac came up with the transformation theory (its basically what we call QM today) its known the so called wave-particle duality is a crock of the proverbial:

'So there is no duality – at least not within quantum mechanics. We still use the “duality” description of light when we try to describe light to laymen because wave and particle are behavior most people are familiar with. However, it doesn't mean that in physics, or in the working of physicists, such a duality has any significance.'

Well since really there is no wave particle duality its the wrong way to think of it. IMHO if you are starting out the best way to think of QM is as an approximation to an even deeper theory called quantum field theory. In that more advanced subject there is no waves, no particles, there are only fields. The following explains that view:
https://www.amazon.com/Fields-Color.../ref=tmm_kin_swatch_0?_encoding=UTF8&sr=&qid=

Thanks
Bill

Last edited by a moderator: May 6, 2017
5. Jul 4, 2014

### bhobba

True.

But I think the idea that everything is a field - not particles or waves - but a field is helpful starting out. You can think of QM as an approximation to QFT.

Of course you are left with fields of what - which in QFT is a very abstract thing.

Thanks
Bill

6. Jul 4, 2014

### PhilDSP

That's a good paper, though maybe a bit more than a high school graduate would want to take on... I believe that author overlooked some technical details that put some statements on very shaky ground, but this is not the thread to go into those.

Very interesting as it is that the Feynman path integral approach is an alternative to de Broglie's and Schrödinger's derivations, that doesn't mean it's necessarily superior over all. Dirac and Feynman's methodologies focus on states rather than dynamics. Each approach has it's uses and possibilities for further development.

Here's a paper that discusses advantages and disadvantages of QED and QFT:
http://arxiv.org/pdf/hep-th/9704139.pdf

Last edited: Jul 4, 2014
7. Jul 4, 2014

### bhobba

Nice paper.

I particularly like:

'The most important lesson that we have learned in this century it is that the secret of nature is symmetry. Starting with relativity, proceeding through the development of quantum mechanics and culminating, in the standard models symmetry principles have assumed a central position in the fundamental theories of nature. Local gauge symmetries provide the basis of the standard model and of Einstein’s theory of gravitation.'

VERY TRUE.

Thanks
Bill