# Wave-particle duality in the Standard Model

1. Jul 16, 2013

### sulemanma2

I posted this question in an another forum but I didn't receive any answers, so I'll post it here again:

Do all the fundamental particles in the Standard Model (61 fundamental particles) exhibit wave-particle duality?
From my understanding, a photon acts more like a wave than it does a particle because it has a lower frequency, whereas an electron acts more like a particle than it does a wave because it has a much higher frequency. But both an electron and a photon show wave-particle duality.

Another example for you to test my understanding is this:
A photon that is a gamma ray behaves more like a particle than a wave because of its higher frequency, whereas a photon that is a radio wave behaves more like wave than a particle because of its lower frequency.

Does this mean there is no such thing as "mass" per se, but that everything is a wave with a frequency with it? Would this apply to all the particles in the Standard Model?

2. Jul 16, 2013

### Dreak

As far as I know, everything has wave/particle duality. Which means even you and me have WP duality.

I don't really see why a photon is more wave than particle and opposite for electrons. It all kind of depends of the situation.

3. Jul 16, 2013

### The_Duck

Yes. This is just a property of quantum mechanics, which is more fundamental than the Standard Model.

This is pretty accurate.

Everything is a wave, but we don't need to throw out the idea of mass. The particle formula

kinetic energy = (momentum)^2 / (2 * mass)

translates into the wave formula

angular frequency = (2 pi / wavelength)^2 / (2 * mass).

The mass appears in both cases.

4. Jul 16, 2013

### wotanub

I always just say that there's no such thing as a wave or a particle, the standard model just has these things that behave like what we call "waves" or "particles" depending on the situation.

5. Jul 16, 2013

### sulemanma2

Thank You guys for your answers. So this means that photons do indeed have mass but that mass is behaving more like pure energy. So for photons we have the Electromagnetic SPECTRUM, where the higher the frequency the more energy it has. Therefore we can say that the electron has a frequency that is so high that it behaves more like mass, and we can measure that mass with our instruments (whereas we can't measure the mass of a photon with our instruments).

Therefore I guess we can say that all the particles in the Standard Model lie on a Mass-Energy SPECTRUM, just like the photons lie on an Electromagnetic Spectrum. The only differences that arises in the particles is due to which of the four forces is involved (Electromagnetic, Gravity, Strong Nuclear, Weak Nuclear). I am basing this argument on Eienstien's Equations:
E=hc and E=mc^2 , where h is the planck constant, c is speed of light, m is the mass.

So are my assumptions correct? Especially about the Mass-Energy Spectrum part? Also if the spectrum part is correct, what happens at the ends of the spectrum? Is a black hole at the mass end of the Mass-Energy spectrum? And what could be at the energy end of the Mass-Energy Spectrum?

6. Jul 16, 2013

### wotanub

Make no mistake, photons don't have any mass.

It's more appropriate to say that mass is energy rather than energy is mass.

7. Jul 16, 2013

### The_Duck

No. At least, this is not how physicists use the term mass. In standard parlance, photons have zero mass. If you want to talk about photons, you need to use the special relativistic version of the formula I wrote earlier, which is:

(hbar * angular frequency)^2 = (2 pi * hbar * c / wavelength)^2 + (mass * c^2)^2

This one makes sense for mass = 0, while the earlier one I wrote doesn't.

This is not how any physicist would use the term "mass." If you want to think about it in terms of waves, mass is just a term in the above equation that relates angular frequency to wavelength. I'm not sure what it would mean for an electron to "behave like mass."

I suppose you could say that each type of particle has its own "spectrum." The electromagnetic spectrum is the energy spectrum of the photon. Electrons have an analogous energy spectrum, but this is just the statement that electrons can come in all energies.

In no sense do different types of particles lie on the same "spectrum."

Particles are distinguished by:

* their mass
* their spin
* which forces they interact with, and how strongly

You seem to have the wrong idea about "mass-energy." Mass is a form of energy, in the sense that massive particles have energy due to their mass even when they are at rest. There is no spectrum "between" mass and energy.

8. Jul 16, 2013

### sulemanma2

So wotanub, are you implying that E=mc^2 is an extremely extremely accurate equation for most uses but not 100% accurate (Since mass is actually just Energy, and mass doesn't really exist). IS Einstein's other equation E=hc the most accurate depiction of reality? Is this equation 100% accurate? Or is this equation's accuracy lies on the determined Planck constant?

9. Jul 16, 2013

### sulemanma2

Oh rereading the thread, I think I got confused with the Mass-Energy Spectrum. What I meant was the Particle-Wave Spectrum of all the particles in the Standard Model. So do all the particles lie on a Particle-Wave Spectrum, where high frequency means more like a particle and low frequency more like a wave. (But all them still exhibit the duality). And what happens at the two ends of the spectrum?

Sorry for the confusion.

10. Jul 16, 2013

### wotanub

Wait a minute. $E_{0} = mc^{2}$ just says that a particle has some energy due to it having rest mass.

$E_{\gamma} = h\nu$ is an equation describing the energy of a photon.

They describe two different things. The similarity being a photon has energy because it is, and a massive particle also has energy because it is.

There's really no "spectrum" from particles to waves. A photon could have any frequency, even very high ones. Similarly, something with mass could have a low de Broglie frequency. There isn't a sliding scale where at some point a particle becomes a wave.

Particles and waves are just representations of physical objects we constructed based on our classical intuition. It turns out that quantum mechanically, anything can be described with either of these interpretations.

The question is when do these object behave like particles, and when do they behave like waves? If you do an experiment to measure som wave-live property, you'll see it behaving as a wave, if you're testing some particle behavior, it's like a particle.

For example, de Broglie had the crazy idea like "What if electrons diffract when put on a grating? That would mean they're a wave." then if worked. But you could easily shoot electrons out of a "gun" as if they were particles as well.

As for the question about what happens at the ends, you could apply sanity checks to intuit why we would never see these limiting cases.

$λ = \frac{h}{p}$
If the wavelength were zero, that would imply momentum is infinite, there can't be a particle with infinite momentum as this means the kinetic energy would be infinite.

If wavelength approaches infinity, the momentum approaches zero. But anything divided by zero is physical nonsense.

$E_{\gamma} = h\nu$
If energy is zero, the frequency is zero: this corresponds to no photon.
If energy is infinite (not happening in real life) then frequency is infinite.

11. Jul 16, 2013

### sulemanma2

So wotanub, my original question/interpretation in the first post is not correct? Especially the part about a gamma ray photon behaving more like a particle than a wave (but still both) and a radio photon behaving more like a wave than a particle (but still both)?

12. Jul 16, 2013

### wotanub

Yeah no. The interpretation of the light depends on the experiment.

Not that it really matters what you call it though... Why try to label anything as more like a particle or more like a wave anyway? It is what it is. I think the point of wave-particle duality is that there are no pure particles or waves, they're just mnemonic devices that carried over from classical mechanics that help us understand the physics of what's going on.

13. Jul 16, 2013

### sulemanma2

So this means a gamma photon, when we observe it crudely, will look more like a particle and when we look at a radio photon it looks more like a wave.

But both particles exhibit wave-particle duality, "equally" per se, regardless of their energy, frequency or any other parameters in the Standard Model for the photon, or any other particle (like the electron) in the Standard Model.

This means the term wave-particle "duality" is leading to my confusion. There is no "duality", it should instead be called wave-particle "oneness". And there is no spectrum associated with it.

Is my interpretation finally correct?

14. Jul 16, 2013

### wotanub

Yes, wave-particle duality is an idea from old quantum theory.

I agree a better term would be "oneness."

For example the Photoelectric effect experiment only makes sense if light is particles, but diffraction only makes sense if they're waves. How we should interpret the phenomenon depends on the experiment.

15. Jul 16, 2013

### sulemanma2

Another question, based on what a poster above brought up:

A photon has no rest mass and it exhibits a "frequency" based on its wavelength. Does this frequency have a specific name? I'll just assume for this post that it doesn't (if there is let me know):

An electron has rest mass and it exhibits a "de Broglie frequency" that is only exhibited by something that has rest mass. This frequency has a name "de Broglie" while the other doesn't. So does an electron exhibit the no name "frequency"?
IS it that when an electron is moving it exhibits both the no name "frequency" and the "de Broglie frequency" and when it is completely still it only exhibits the "de Broglie frequency?

16. Jul 16, 2013

### wotanub

Frequency and wavelength are just regular properties of waves. They're related by the constant of proportionality, wave speed (c for E&M waves), so they're basically the same thing.

Louis de Broglie hypothesized that matter (particles) could also be thought of as a wave, and he was right so they named the concept (de Broglie wavelength) after him. I've never seen the tern "de Broglie frequency" used, but I just coined the term to speak about the frequency associated with the de Broglie wavelength.

http://en.m.wikipedia.org/wiki/Matter_wave

17. Jul 17, 2013

### sulemanma2

So according to de Broglie, or my interpretation of it, every particle in the Standard Model is a wave. And this waves frequency is determined by adding its kinetic and rest energy.

A photon has only kinetic energy and no rest energy(because no rest mass), but can it still be described by the de Broglie equations?

Or do de Broglie equations only apply to things that have rest energy and kinetic energy at the same time?

An electron has both kinetic energy and rest energy, and can be described by the de Broglie equations.

Can an electron that has rest energy but no kinetic energy be described by the de Broglie equations?