# Particle and wave interaction

In summary, the electron microscope produces smaller waves than the matter they describe. This raises the question of the energy, the wave is a scalar field but the particle is not. Why is the particle energy the whole of the probability field and not a percentage or fraction?

How does the 'particle' view of the electron for example interact with the lattice of matter when matter is also a wave function?

coming from the view that the wave function is a probability field for the particle, so if that is used wouldn't the same need to be done for all possible interactions? Now what about in the case where the wave function is smaller than the wave of matter, like in the case of the electron microscope? The diffraction and Compton scattering is based on what seems to be a mix of particle and wave interactions.

this also raises the question of the energy, the wave is a scalar field but the particle is not. why is the particle energy the whole of the probability field and not a percentage or fraction?

this is coming from after yrs of just accepting the duality of wave/particle and not really looking at it, then deciding to. I also went back and dug up the early work in quantum physics by DeBroglie, Schrodinger, Plank. etc... and found it to be good for getting an understanding on where it started and how it developed but alas it also tends to raise further questions. So much is tied to wave mechanics and thermodynamics in a classical manner and then it seems to come down to the interpretation of Schrodinger's equation.

"what about in the case where the wave function is smaller than the wave of matter, like in the case of the electron microscope?"

I'm not sure I get what you mean there?

That a electron microscope produce smaller waves than the matter they describe? "In electron microscopes, wavelengths as much as 100000 times smaller than those of visible light can be achieved. With such small wavelengths, electron microscopes can reveal features that are as small as 0.000000001 meters (1 nm)"

"In quantum mechanics, all particles also have wave characteristics, where the wavelength of a particle is inversely proportional to its momentum and the constant of proportionality is the Planck constant."

And a electron is described as a particle, but in a atom it only has a orbital, with HUP governing what you can find out about it. Diffraction is about waves, and how they behave meeting obstacles, as far as I know? The higher the energy of that electron the smaller its wavelength and sending it through a single slit will produce a wave interference if the slit is larger than the electrons wavelength. If the slit is smaller you will get a diffraction pattern too, but a spherical one without interference.

"the wave is a scalar field but the particle is not. why is the particle energy the whole of the probability field and not a percentage or fraction?"

That one should be about the energy put in and the energy you get out in a interaction (momentum), and that one connects to the conservation laws as I understands it, that nothing gets lost, it only transforms.

But it's a really good question when it comes to the idea of a wave being 'everywhere'.

Hello, might it help if I stress the point that in classical quantum mechanics (phew what a misnomer) there are no particles? I know it seems like there are, because in vague textbooks or dodgy general explanations one uses things like wave-particle duality and such, or mentions that "|psi|² is the probability of finding a PARTICLE...", but actually the quantum formalism just needs the concept of a wave, not of a particle. When one uses the word "particle" in orthodox quantum mechanics (like in the |psi|²-sentence) it's just shorthand for "a wave function with a really really thin width".

yoron said:
"what about in the case where the wave function is smaller than the wave of matter, like in the case of the electron microscope?"

I'm not sure I get what you mean there?

That a electron microscope produce smaller waves than the matter they describe? "In electron microscopes, wavelengths as much as 100000 times smaller than those of visible light can be achieved. With such small wavelengths, electron microscopes can reveal features that are as small as 0.000000001 meters (1 nm)"

"In quantum mechanics, all particles also have wave characteristics, where the wavelength of a particle is inversely proportional to its momentum and the constant of proportionality is the Planck constant."

OK I'll try and give a better explanation to my ambiguous question. In the case of a SEM the electron beam is scanned across a few angstroms in width, the electron beam w itself is fractions of an angstrom or in most all cases smaller than the lattice. This beam of electrons will impart energy and cause a secondary electrons to emit and these are detected and 'read' as the 'picture' of the scanned material.

Here's my question, as per the 'particle' view that the electron is a particle and this entire process is determined by particle interaction and the wave is considered the probability field then wouldn't the end result only still be a probability of the actual physical structure? It's going to take a certain amount of time between the number of electron interactions and the probability of them knocking out a secondary electron. what about the high energy state of the electron causing a change in the material itself, by the view of a particle that particle will have the energy of the whole field right?

It still seems that even though the use of a particle for calculation works by experiment that there really is no particle, would it be closer to reality to view it as a purely wave interactions? I know this isn't a classical sound wave but it doesn't seem like it fits a classical particle either.

yoron said:
And a electron is described as a particle, but in a atom it only has a orbital, with HUP governing what you can find out about it. Diffraction is about waves, and how they behave meeting obstacles, as far as I know? The higher the energy of that electron the smaller its wavelength and sending it through a single slit will produce a wave interference if the slit is larger than the electrons wavelength. If the slit is smaller you will get a diffraction pattern too, but a spherical one without interference.

"the wave is a scalar field but the particle is not. why is the particle energy the whole of the probability field and not a percentage or fraction?"

That one should be about the energy put in and the energy you get out in a interaction (momentum), and that one connects to the conservation laws as I understands it, that nothing gets lost, it only transforms.

conservation of information is a good point, how does and where is the transformation from a scalar field to a point to insure that this is met? using the scalar as a probability seems to be an assumption as that scalar field carries with it the previous information of a classical wave in purely a mathematical form but then it seems that we say oh wait that field is only the area where we may find it when we look and then all that information is then supposed to be in that one point? how, where is the transformation? and when all that information is now in one point what happens to the rest of the area where the probability was? it previously had information per the equation and now we say it doesn't? it looks like it would be violating a few rules, the field of a probability is simple enough, but there is also information now tied to this field that if it was only a probability would not have, but it does. So now a probability carries with it information beyond just a probability right?

For example I take an electron and assume that it's going to interact at a specific point with another electron, OK simple enough, but in reducing that field to one point I removed the probability of interacting with another electron at another point. what about that other proability electron that is at that other point? the calculated interaction on my part prohibits that probability from occurring. In the end it would seem that no matter how I try and calculate the system I will always be causing the result not finding it.

Due to the sheer number of interactions then and by using the highest probabilities experimental results should be close right? but doesn't that also mean that there is a probability that its also wrong?

yoron said:
But it's a really good question when it comes to the idea of a wave being 'everywhere'.

In the end I think that about best sums it up, is the wave is everywhere and does it fall off or diffuse? if not then that opens up a another question of how many bodies need to be taken into account.

Did you just completely ignore my post?

mr. vodka said:
Did you just completely ignore my post?

Not at all. It's my understanding and if I'm wrong let me know, that it's treated as a particle.

I honestly don't see where the particle comes from. The whole concept and math structure starts as a field and then becomes a probability and then vanishes into a 'point' or to me the location of where the information is at it's highest value due to wave function interaction. and from there it can start another wave function and so on. So where is the particle.

If there is no particle why the use of particle in terms and descriptors. why the multi dimension reduction for interaction?

I honestly don't see where the particle comes from. [...] So where is the particle.
That's my point: there is none! Not in the orthodox quantum mechanics anyway.

If there is no particle why the use of particle in terms and descriptors. why the multi dimension reduction for interaction?
I'm sorry, I don't understand, maybe because English is not my mother tongue. Are you asking why the word particle is still used while I claim that it doesn't talk about it? In that case: in those cases "particle" doesn't mean "particle" in the classical sense of the word, all it means is shorthand for "a wave function with a really small distribution, which looks really localized and hence we call it a particle".
Actually even this (or at least the way I just stated it) is somewhat of an interpretation, because it implies that the wave function is actually 'there'. This, however, is not claimed by orthodox quantum mechanics. As you see, orthodox quantum mechanics claims really little: all it actually claims are the probability of finding numbers on your measuring apparatus, and for this it only needs the concept of a wave, not of a particle. The boundary "what does it really say" and "what is interpretation" is really murky in quantum mechanics, even in the most minimal approaches, since even the separation of "measuring apparatus" and "system" and the assigning of an "operator" to an "actual, physical meassuring apparatus" all require some interpretation.

As an operational theory, quantum mechanics is brilliant; but you see as a theory underpinning reality it is somewhat unsatisfactory, in the sense that it leaves some things unmentioned/arbitrary/vague. Even this is debated: apparently some are satisfied with QM even as a fundamental description of reality, guided by some extremely positivistic view, but the number of people discontent with it is surely not negligble and research on the foundations of QM is alive, so if you feel uneasy about it all, don't fear, you're not alone.

Does this help?