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today I had a thought coming across my mind when I woke up, and I think it might be an explanation for the particle-wave duality.

Now, when we are talking about a particle, one thing that has to be mentioned is the uncertainty principle. If you divide space into equal volumes for ex. imagine a 3D grid of cubes, and you put a particle in it, you can assign a number to each cube, which represents the probability of that particle being in that cube. If we consider a moving particle this probability will represent a change rather than a constant value. If the particle is moving towards a cube, this number is positive because the chance that it can be found in that cube is increasing, and when its moving away from a cube then the number is negative. Take every cube, and assign a probability for each cube, and lets call the sum of these a probability field.

I think that the phenomenon what we experience as a wave is caused by this. Its not the particle that is interfering but the probability field of the particles possible paths.

For example where you see dark areas in the double slit experiment, this can be caused by the possible paths of the same particle interfering with each other.

When you fire a photon, in the moment of the launch it has a chance to pass each slit, say it goes through each slit 50 times from a 100 experiments. This means 50% of the possible paths are divided between the two slits. The paths are different in length, and because of this after the particle passes the slit there will be a shift in the phase of probability changes. On dark areas there are several paths of the particles interfering with each other so, that they sum up to 0. For ex a path that represents particle 'X' coming from slit 'A' towards a dark point adds 0.5 chance to the volume (the cube), while on the other possible paths from slit 'B' particle 'X' has already left the same volume with 0.5 chance. The end result the incoming(+0.5) and leaving (-0.5) particle paths is a chance of 0, meaning that there cannot be a change in that volume.

You can also view this from a geometric perspective. Before you launch a particle count all the possible paths were it can go through. Separate them and assign each one to a separate 3 dimensional space. Each particle (or better to say each possibility of the particle) in every one of these 3 dimensional spaces interfere with all other particles in a 4 dimensional space (consisting of the sum of the 3 dimensional ones ) and the interference pattern is we see is caused by this.

In our 3 dimensional space what really happens is not that the particle goes through two slit at the same time and it interferes with itself, it passes only one slit and doesn't interfere with anything, its just the possible paths that are limited for it, and it simply does not cover those places that are impossible for it to go through.

The interference does not happen between particles, it happens between probabilities, and the particle is not a wave, rather

__because the imperfect way how we examine__it makes it for us to seem as a wave of probability.

Now I can't prove this with equations, and the idea just came across my mind somehow, and I wonder if it could be true ? What do you think ?