On the probability interpretation of quantum mechanics
Contents
The irreducible see saw between size and speed
Electrons density clouds in atoms (atomic orbitals – electrons in stable states belonging to the atom) can not be smaller than the innermost electron shell. If electrons in atoms would be smaller than the innermost electron shell (in a non virtual sense - more on that later) then they would need to have so much impulse (and kinetic energy) that they would leave the atom promptly. Why? Because electrons clouds in atoms have the smallest possible product of blurriness in space and blurriness in mass-motion (proper term: impulse). Squeezing the cloud any further down in space blows up the electron cloud in an abstract but very useful mass-motion space (proper term: impulse space). A "space" which describes a distribution over motion directions and speeds. This smallest possible product of blurriness in space and blurriness in impulse is called the "plank constant". The seesaw effect that:
- makes tightly constrained electrons move more vigorously and that
- makes electrons with a very precise temperature (very cold is easiest) very big
is called the "Heisenberg uncertainty relationship".
Electrons as density clouds
A decent intuitive picture for atoms are soft/blurry clouds that are (in a certain mathematical sense) as smooth as possible and can exert soft forces on other of these clouds in case they come close. There are no hard surfaces and certainly no sharp planet like orbits. These clouds are made of so called "electron density". Atoms basically are electrons (determining all volume an chemistry). The electrons in atoms (especially the outermost ones) not just have the size of atoms they literally are the atoms.
There are the earlier mentioned "virtual energy fluctuations" of electrons (not to confuse with the related virtual matter antimatter particle pairs arising from vacuum) which "exist" in the sense that they lead to measurable effects (forces). They do not "exist" though in the sense that they can be directly measured / observed. The electron cloud size that would correspond to these fluctuations can be much smaller than atoms (how small open is an question - but infinitely small points are a sure sign of a model breakdown).
Probability interpretation likely motivated by results of scattering experiments
Collision experiments can strongly mislead one to believe that one can catch a snapshot of the electron when it was orbiting the nucleus in a classical way, since with a collision one can force an atomic orbital electron cloud to "collapse" to a much smaller size than the atom. There are two reasons why this is problematic: "hidden variables" and "delayed choice". An elaboration follows.
Such a collision experiment could look roughly like so (largely simplified to be suitable as thought experiment): One shoots e.g. a second electron (a free electron) at a stable atomic orbital electron cloud in a hydrogen atom. This other "projectile" electron is best pictures as a wave package in the shape of cloudy disk much thinner than the atom. The diameter of the disk is of no particular importance it can be much bigger than the diameter of the atom. (Side-note: An actual experiment would have more of a fat disk / stream / dispersed wave front, with many electrons hitting many atoms.)
In the probabilistic view (Copenhagen interpretation of QM) one gets some collision probabilities from the overlap of the two electron clouds that occurs when the disk shaped projectile electron cloud passes through the electron that constitutes the majority of hydrogen atoms volume. In case a collision is detected the location of this collision and thus the location of the electron of the atom can (theoretically) be resolved much finer than the size of the atom.
"Virtual" just means "not outside of a quantum entanglement" and thus us not knowing where it is dies not imply a lack of knowledge. From this perspective the electron really isn't in virtual Heisenberg relation violating spot.
I guess one can discuss that to death. As long as the math works out the same it really makes no difference. From a non particle physics perspective nanotechnology perspective the electron density cloud interpretation just seems nicer.
A problem with the probability interpretation
When measuring a high energy electron-electron collision the result will tell us that the electron in the atom was in a smaller space than the whole atom. But the electron was actually definitely not (in a non virtual sense) in a smaller space than the whole atom just before the collision. Well one still can define virtual electron states that violate Heisenbergs principle as "real". In a sense they are real since they cause real forces.
But there's a second problem even when accepting virtual particles as real.
Assuming the electron was (in a virtual sense) already in this overly localized spot before the collision occurred would be equilalent to assuming hidden local variables, which we now are not real from the bell experiments that proved that quantum entanglement is more than just a lack of knowledge in form of a real statistical difference.
Well one still can maybe ponder about global hidden variables maybe (pilot wave interpretation of QM).
Wave collapse at the latest possible time
Assuming the electron was in the measured freshly kicked out strongly localized state right after the collision is also inconsistent with quantum mechanics. Actually it is more like all possible collisions occur in a quantum parallel fashion (superposition of many freshly kicked out states) and the wave collapse only happens when the scattered electrons hit the detector (multi world interpretation of QM) or even later when you feed the measurement results without detour into a quantum computer. (One could say that parallel worlds "exist" in the sense that they can do useful work in form of quantum-parallel-computation and have measurable effects. Parallel worlds don't "exist" in the sense that they can't provide as much power as actual parallel computation - not that it could be implemented, and they don't "exist" in the sense that they can't be checked one after another exhaustively.)
