That's a lot better. However, the most modern view is not a particle or a classical wave, and the simpler way of stating that is it is neither a particle nor a wave. The only catch is we have to specify what kind of wave it is, and that's where the probability wave comes into the picture. It's not a classical wave.
I'm not sure I can explain this in an instant, but it might be said that the water wave could be viewed as a probability wave if we just think of the amplitude as being a matter of probability not a direct measurement that we are usually used to doing. To take it further, nothing we see has a non-probabilistic nature, it just looks that way because the probability is so low it's almost nonexistent. "Almost" is the key word though because it is still probabilistic but some of the probability factors are so low that they may not occur for the entire life of the universe. Pretty nutty, and the really nutty part is that it actually could happen before that, it's just not very likely.
I guess the simpler explanation is that we are constantly projecting our previous knowledge onto the new discoveries. It takes a contradiction to show us how wrong we might be.
There are no special "probability waves" that require a different kind of wave physics. The same mathematical tools of wave analysis can be applied to all kinds of waves, what changes is what the wave represents and what its amplitude means.
In particular, I would be careful about treating a probability wave as a physical wave that actually exists in space. Probability is a mathematical way of describing a system when we do not have direct access to all of its underlying details.
For example, suppose you secretly choose a number from 0 to 9 and don't tell me which one. You can give me various pieces of indirect information about your choice. From that information, I can construct a probability distribution describing how likely each number is. The more information you give me, the more accurately I can determine that distribution.
However, no matter how much information you give me, I can never know with absolute certainty which number you actually chose. Even if you tell me the number directly, I still cannot be absolutely certain that you are telling me the truth. I have no independent way of checking what number you actually chose.
But that does not mean that you did not choose a definite number and that there is actually a probability distribution inside your head instead of a specific number. The number you chose is perfectly definite, the probability distribution exists in my description of the situation because I do not have direct access to your mind to check it.
I think something similar is worth keeping in mind when talking about probability waves. A probability distribution is not necessarily a physical substance or a new kind of wave. It is simply part of our mathematical description of what we can and cannot know about the system.
I thought I explained all that, but I'll add this............
A probability wave is simply this:
A spread-out pattern that tells you how likely a particle is to be found in different places.
That’s it in one line.
What it actually means, physically...
It’s not a wave of stuff.
It’s not a wave the particle rides on.
It’s a wave whose height at each point corresponds to the probability amplitude.
Squaring that height gives the actual probability of detecting the particle there.
So the wave is the rulebook for where the particle could show up.
[note the particle here is what we refer to which is really the result of the measurement process it does not have to be an actual particle like a speck of dust]
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That's probably the best way to talk about it, but another way to say it could be the engineer-to-engineer version...
A probability wave is the complex-valued state vector whose squared magnitude gives the spatial probability density for a particle’s detection. Its evolution follows a linear differential equation (Schrodinger), and collapse is a stochastic sampling of that density.
In pure signal-processing language:
It’s a distributed complex signal whose power envelope determines where the 'particle' can be absorbed.
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One more angle about the measurement process itself which is what I had also been talking about...
Measurement collapse is not something the photon does.
It is what the detector’s degrees of freedom allow when it absorbs energy.
Collapse is the detector transitioning to a definite state after interacting with the field.
In other words, collapse is the system update that happens when the EM field dumps one quantum of energy into a 'charged' degree of freedom.
Nothing “shrinks,” nothing “localizes,” nothing “jumps.”
The interaction is what becomes localized.
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What happens here and in other areas of physics is we are looking for simple answers that match what we ALREADY know about reality. In the case of the waves and particles and stuff like that, we haven't yet completely figured out what reality really is so we are in the middle ground somewhere trying to get from not completely understanding to completely understanding. The above is about the best we can get right now I think.