I just found this little gem:
The measurement problem in quantum mechanics is the problem of how (or whether) wavefunction collapse occurs. The inability to observe this process directly has given rise to different interpretations of quantum mechanics, and poses a key set of questions that each interpretation must answer. The wavefunction in quantum mechanics evolves deterministically according to the Schrödinger equation as a linear superposition of different states, but actual measurements always find the physical system in a definite state. Any future evolution is based on the state the system was discovered to be in when the measurement was made, meaning that the measurement “did something” to the system that is not obviously a consequence of Schrödinger evolution.
Pretty cool eh?
This certainly is a difficult problem isn’t it? But, actually, it’s not if you can think properly. Let’s see how the Measurement Limit transcends the Measurement Problem.
Let’s consider a single electron. Since it is the smallest non-zero nonstatic charge (in that it is what is displaced under voltage potential differences), it does not have a “volume” in the same sense that we deduce the volume of something with our measurement devices. We can imagine its volume as existing within an energetic potential space which is nonphysical, yet manifests physical effects. Since Entropy applies on every scale of magnification, we expect that if the electron is not under the action of some external force, it ought to occupy the configuration of greatest Entropy, which ought to be isomorphic to a sphere.
Proof ~ A Single Electron Behaves as an Entangled Spherical Potential Form
How can we prove that a sphere is the configuration of greatest Entropy of a single charge? Let’s suppose that it is not a sphere. For wherever this shape deviates from a sphere, there must exist some difference in the electric potential. This is contradicted by the definition: that it is a maximal Entropy state and since no external force acts on the electron, no potential difference can exist. Therefore we have proven by contradiction that the electron potential function is energetically isomorphic to a sphere even though it occupies no observable volume.
The potential function of a quantum mechanical waveform is one of the more difficult things to visualize, but it is possible with practice. To begin, we must accept that for any measurable system, there exist 3 space-like and 1 time-like dimensions. These dimensions are maximally independent but connected (i.e.: Special Relativity connects the space and time-like coordinates on the macro-scale).
Additionally, we must realize that space and time are not exactly how we experience them, but intrinsic aspects of the Universe that manifest differently on different scales. We are certain that they are the same everywhere because this is what is observed everywhere: a distribution of spacetime events over all orders of magnitude. (But Jen, aren’t the orders of magnitude spatial and thus included into the spacetime event? There is an answer to this question but it’s another level of abstraction, so let’s stick with manifest (massive & electric) matter for now!).
What this formalism implies (and is indeed observed) is that when the electron (spherical) waveform reaches the slit, its spatial complexity is reduced and therefore a diffraction pattern is observed on the screen. This may seem hard to imagine, but it is indeed how the waveform behaves. Is the slit diffraction pattern still a maximal Entropy state? Yes, but it is a reduced waveform and no longer occupies the spherical configuration. Why? If it did, the pattern generated at the screen would be indistinguishable from the original state of greatest Entropy and this is contradicted by the diffraction pattern observed at the screen. Thus the reduced waveform must occupy a distribution which is non spherical yet also the configuration of maximal Entropy (for the reduced waveform). Upon diffraction through the slit, the electron potential waveform goes from spatial complexity 3 to 2.
We can visualize the interactions as a type of polarization, but it is massive (not the more familiar electric) since the slit is uncharged. This is because the mass of the electron does not change, rather the screen forces it into one of its eigenstates.
This also explains why, when a magnetic field is introduced between the slit and the screen, a line pattern appears on the screen (not the usual diffraction pattern). This is because the magnetic field reduced the spatial complexity of the electron waveform (again), this time from 2 to 1. These two actions (slit & magnetic interference) each represented a measurement performed on the electron potential function.
Waveform behaviour is much easier to discern when we understand that the 3 + 1 measurement limit is indeed the basis of reality. We exist as solid because sufficiently many waveforms have been reduced so as to be confined to a fixed physical space. A solid can be visualized as “fully self-observed” while a liquid is “partly self-observed”. Gases would then be “slightly self-observed”. We can then interpret physical systems on a continuum from fully realized to fully unrealized (though neither state can technically be observed).
The mechanics displayed by any system are therefore determined by the measurement limit: both by the state variables of the system and by the particular configuration of the measurement device. In the case of the former, we have familiar Classical Mechanics and in the case of the latter, and only when the limits of the Uncertainty Principle are approached, we obtain the more esoteric Quantum Mechanics.