On the particle wave duality
Contents
Intro
A problem with infinitely small (non virtual) particles
Particles definitely cannot be points with truly infinite small size and truly infinite density since infinite singularities always point to a breakdown of a mathematical model that is trying to describe reality. Also infinitely small points would need to have infinite impulse and thus infinite energy energy due to the Heisenberg principle (unless they are virtual particles). Before even that they would form a microscopic black hole.
Wave packages in 3D space cannot help explaining (shapeless) particle quantizations
What if the wave-particle duality is not about particles as in "point like particles in space" in the first place?
While an interpretation of particles as almost arbitrarily (down to Planck scales) compact wave packages naively and superficially may seem as a solution at first it does not explain particle quantization which is the actual essence of the wave-particle duality. Particle quantization (like quantization of photon energies and the indivisibility of electrons) can not be explained by interpreting wave packages as point like particles. Wave packets in space are an inapplicable tool even.
One rather needs second quantization to explain these qunatized particle like properties.
A conflation of concepts that complicates discussion
A problem with "wave-particle duality" may be that it conflates:
- particles in the sense of quantizedness
- particles in the sense of straight ray like behavior
And neither of both is about point like particles.
Which makes a massively confusing mess.
Examples
Waves as (quantized shapeless) particles
In case of the photoelectric effect the quantization of light into particles is independent of the shape of the wave function that describes the light. Well, more accurately a photon particle with it's very specific sharply defined energy (E = h * nu) and thus sharply defined impulse would need to be maximally de-localized in space. That means it would need to be a plane wave with infinite size.
Side-note to the photoelectric effect
The photoelectric effect says that when the energy of individual photons is not sufficient then,
no matter how much one cranks up the lights intensity (intensity means the number of photons per time and area),
there still won't be dislodged any electrons form the metals surface.
(Assuming no secondary effects like thermal heat-up reducing the work function)
There is an exception to this rule though.
If intensity gets so high that two photons arrive at the same time (this is really very high typically only reachable by pulsed lasers)
then their energies can add up. These are two photon processes lifting bond electrons to higher energy levels and these are used for
- optical superresolution microscopy and
- optical superresolution nanoscale 3D printing
It should work for lifting electrons out of metals too.
Related: The "UV catastrophe".
The realization that photon quantization is necessary to explain non-divergent black body radiation spectra.
(Quantized shapeless) particles as waves
No regurgitation here
Discussion of the particle-wave duality usually starts with the double slit experiment. There's an endless amount of discussion of that on the web already so let's go in a bit of a different direction here: (If the reader is unfamiliar with the concept they are advised to read up on it elsewhere.)
In the classical double slit experiment electrons need to be shot onto the double slit
- as sufficiently widely de-localized locally planar waves
- at low enough energies
The indivisible quanta of charge and mass being the true "particles" and they have no shape
There are two transitions in the double slit experiment.
- "waveification": Shooting one electron after another to proof they can do self-interference.
- "particelification": Detecting electrons at the sensor (at a quantum random position) makes their wave function collapse into localized whole electrons again. There are no fractional charges distributed over the detector sensor.
Note that cooling and isolating the detector (and the immediate data post processing) sufficiently from the environment hypothetically could retain quantum superposition of detection within the detector. Final evaluation outside the well isolated detection and data preprocessing part of the experiment could then be done in such a way that the detection of an electrons position on the detector is not narrowed down to one single pixel but instead is narrowed down to a just sub area of the detector. This does not mean that we don't know which pixel the electron was detected. The electron really passed through quantum parallelly though the whole subarea of the detector.
(Ray like acting shapeless) particles as waves
Why particle-ray like behavior is following from maximally wave like character
If an electron is shot onto the double slit with one specific very high speed
(that would be a "maser" – a matter laser – not happening by accident) then:
- (1) The electron has a one specific wavelength that is much shorter than the slits wideness and there will be no interference pattern. A very macroscale point particle like behavior.
- (2) The electron necessarily has a big non point like extension in space. It has the shape of a wave front that is spacially wide extended. A very wave like property. This is due to the Heisenbergs uncertainty principle.
Why matter wave packets (in free space) make no good particle-ray like behavior
If an electrons is shot onto the double slit as a strongly localized wave package (not happening by accident), then (due to the Heisenberg principle) it necessarily has a wide distribution of impulses, speeds and corresponding wavelengths. The low frequency parts will act like a wave the high frequency parts like a shot solid macroscale sand grain particle when passing through a slit.
Plus the initially strongly localized wave package will disperse. That is: It will widen due to different contained wavelengts moving at different speeds. A consequence of electrons not being massless.
Misc
Waves as rays
(wiki-TODO: Some repwtition here. Maybe to merge.)
Given the wavelength of photons or electrons is short enough compared to features of a shadowing screen, there will be cast a straight-ray-shadow that matches to what would expect from point like particles. The "particles" here can be highly de-localized waves here though.
Approximating point like particles with highly localized wave packets one necessarily gets widely distributed impulse. For matter waves where different impulses mean different speeds the "particle" will run apart the faster the more localized it started out. While there are high frequency parts in the impulse spectrum that act particle-ray like there are also low frequency parts in the spectrum that act more wave like.
Second quantization rather than spacial localization
Note that in the first two examples above we call quantized chunks of matter or light particles despite this having noting whatsoever to do with a localization in space. Wave packages in space do not help to explain these non-spacial quantizations.
Where else does the quantization come from then?
Quantization is always coming out of waves with imposed boundary conditions.
But these boundary conditions do not necessarily lie in 3D space.
This leads to second quantization.
Second quantization meaning that the boundary conditions do not lie in 3D space but
instead in the dimensions that carry fields (to check).
An alternate better naming?
The association of "wave-particle duality" with "spacial point particles" is probably mostly due to history and choice of naming. What about better alternatives names?
- "wave quantum duality" ... seems bad due to very likely incomprehension due to confusion with first quantization
- "wave chunk duality" ... could work maybe?
Should "wave" even be part of the name?
More thinking needed.
Suggestions welcome.
(TODO: Find a better term for wave particle duality.)
Even if finding a good one, promoting its usage seems like an impossibly tall order.
Differences for quantization into particles
Quantization of photons and electrons as individual particles is very different.
Quantization of energy levels of electrons in the shells of atoms is even more different (first quantization).
- Electrons only come in one size of charge and mass.
- Photons can come with any energy desired.
As frequency is not quantized.
