[ron123456 (OP)]

Electrons through a double slit produces an actual physical interference pattern..... How does this mathematical wave function produce a physical reality?.... What is the physical wave conversion process?.... Please, no space time, if actually possible?..….How does this mathematical probability expression actually convert itself to true physical reality?

[evan_au]

Electrons through a double slit produces an actual physical interference pattern..... How does this mathematical wave function produce a physical reality?

A wave function takes on complex values.
- The physicist Born proposed that the mathematical operation of "squaring the modulus" of the wave function produces the probability of finding a particle at a particular place.
- Probability ranges from 0 to 1.
- For the double slit experiment, you detect a series of bright and dark bands, where the probability of finding an electron ranges from small to practically 0.
- You can get pretty much the same answer by assuming that the electron is a classical wave, and applying some geometrical considerations. This ignores all quantum effects.

See: https://en.wikipedia.org/wiki/Wave_function

Please, no space time, if actually possible?

- "Spacetime" is defined by Einstein's General Theory of Relativity, describing how space is distorted by the presence of mass.
- "Wave Functions" are defined by quantum theory.
- The good news here (if there is some good news) is that Physicists have not yet produced a quantized version of General Relativity, so nobody today can give you a complete answer for wave functions involving spacetime. It falls down in the "Strong field" case (eg near a black hole).

The other good news is that in the "Weak Field" case (eg in our Solar System), quantum theory works fine if you just ignore spacetime (or add it as a small correction later). 

However, in the case of electrons, you can't ignore Einstein's Special Relativity, as electrons reach a significant fraction of the speed of light, and that affects the mass of the electron, and that affects the wavefunction, and that changes the spacing of the interference bands.
- That's why a high-voltage electron microscope can see more details than a low-voltage electron microscope (all other things being equal...)

[puppypower]

An electron has wave-particle duality. The particle aspect of the duality is like a moving point in space-time, while the wave is like the wake of a ship, which is induced by and propagates away from the ship, as the ship  moves. The wave function is dealing with the wake induced by the particle. The diagram below deal with an aircraft that is traveling faster than the speed of sound, so the wake is always behind.

In the case of the electron, the particle travels slower than the induced wave, since the particle has inertia and does not travel at the speed of light, while the wave is connected to EM force which moves at the speed of light. The wave is what we measure, which is not quite the same as the particle in real time. The result of the wave, are the probability functions.

Say we have a ship traveling in a spherical path like a 1S orbital. The wake is propagating from the particle at all angles, depending on the instantaneous vector of the particle. These various waves are adding and subtracting as they propagate. We get a probability function for the particle, but this is still uncertain, since the wave and particles are in different frames; speed of light versus inertial.

[alancalverd]

How does this mathematical wave function produce a physical reality?.

It doesn't. Physics models reality, not the other way around.

The problem is that photons and subatomic particles exhibit more complicated behavior that either billiard balls or ocean waves, so we often need two mathematical models to describe them.

[Bored chemist]

An electron has wave-particle duality.

So does a bus.

The wave is what we measure, which is not quite the same as the particle in real time. The result of the wave, are the probability functions.

Does not parse.