Quantum Mechanics

Quantum Mechanics
My ideas (listed first so that I can explore them later)
- Idea Part 1
- Idea Part 2
Shortcomings
Various Interpretations of the Model

My ideas (listed first so that I can explore them later)

The problems with this are listed further in this page, here.

Idea Part 1

My usual interpretation was based on the "classical wave optics formulation". But it looks like I need to consider the individual particle double slit experiment more. Well, my idea is still then to consider the complex part of the wavefunction instead of neglecting its value.

Individual particle effect observed with light

But the third paragraph on the Wikipedia page about double slit experiment shows that the individual particle effect was also observable with laser beams of photons. Now that's something I'll need to explore too.

In the basic version of this experiment, a coherent light source, such as a laser beam, illuminates a plate pierced by two parallel slits, and the light passing through the slits is observed on a screen behind the plate ([7][8]). The wave nature of light causes the light waves passing through the two slits to interfere, producing bright and dark bands on the screen – a result that would not be expected if light consisted of classical particles ([7][9]). However, the light is always found to be absorbed at the screen at discrete points, as individual particles (not waves); the interference pattern appears via the varying density of these particle hits on the screen ([10]). Furthermore, versions of the experiment that include detectors at the slits find that each detected photon passes through one slit (as would a classical particle), and not through both slits (as would a wave) ([11][12][13][14][15]). However, such experiments demonstrate that particles do not form the interference pattern if one detects which slit they pass through. These results demonstrate the principle of wave–particle duality ([16][17]).

Idea Part 2

Another interesting thing is how if we scale the solar system (I know it's just an arbitrary, and a mostly planar system, still) to the size of an atom, to assume it being the atom of a world, and see ourselves as being made of these solar system atoms, then if we consider our normal motion in terms of a new unit, say 🅱️eters/sec (I'm not sorry for this) instead of meters/sec, if we compare the speed of normal motion to the speed of these 🅱️etres per second, the ratio would be similar to the ratio of our normal speed to the Planck speed. Well the same could apply to the planets too, as having the equivalent sizes of atoms or the Planck length. I don't remember how much exactly, but it was kind of close to subatomic levels with a few magnitudes of order off here and there.

The point is not about the importance of the solar system model, it's about, if the motion of a system is faster than the Planck time/Planck second, which is simply the speed of light, if we think of Planck frequency as the FPS or refresh rate of the universe, won't we only be able to see the positions of the particle as snapshots at certain points rather than as it having a traceable path? And if that's the case, wouldn't we only interpret it as random motion?

It still gives room for us to find a theory of motion where some of the motion happens faster than light, and hence outside the universe. That would kind of make sense too, unless the maths contradict it in some manner, because space and time are inversely related with respect to c, as \(c=x/t\). Of course, the math would contradict it right away, because we would be trying to look at it from the model of our current theories. But rather, I'm expecting to think of it by not looking at the theories, but at the empirical observations only, and unless it contradicts it, we may be able to see something.

A very wild addition to this, perhaps \(c\) is the constant of our universe, but an event faster than \(c\) could happen outside the universe, with it's manifestations snapshotted at specific intervals, much like a computer rendering a simulation. I'm not even talking about the multiverse theory, but it just felt like it to me XD. Maybe thought works faster than light?

Shortcomings

"God does not play dice" - Einstein
Is the electron a probability wave (\(\psi^*\psi\)), or is it the orbital itself (\(\psi\))?
It could be that the wave is vibrating in 4D space, like a string is vibrating in 2D space. ^my-idea
- These theories are grouped under the "Hidden Variable Theory"
  - e.g. Pilot Wave Theory (or de Broglie-Bohm Theory)
    - Has hydrodynamic analogues
  - The problem with most hidden variable theories is that when you try to write a Lagrangian for such a system, you aren't able to incorporate the Lorentz Invariant to start with.
  - This answer says, it doesn't fit with special relativity, and violating it would be kind of a major sin because of how successful it is: https://physics.stackexchange.com/a/666576
    - He also explains how string theory aims to solve this
    - He says Heisenberg just showed how the first quantization and second quantization are equivalent, which people misunderstood as everything is quantum fields

Various Interpretations of the Model

Ensemble interpretation
Copenhagen Interpretation
- Doesn't tell you what \(\psi\) means, but just tells you that \(\psi\psi^*\) gives the probability of finding a particle at a point (https://www.youtube.com/watch?v=WcNiA06WNvI)
Pilot Wave Theory
- The silicon droplet hydrodynamic analogue
Quantum Logic
Time Symmetric Theory
Many Words Interpretation
Consciousness Causes Collapse
Many Minds Interpretation
Consistent Histories
Transactional Interpretation
Objective Collapse Theories
Relational Interpretation
QBism