Are we saying that because there is in fact no "particle" as such that it is not just an inability to measure the two quantities (position and momentum) without affecting one or the other as is often implied. Instead it is because there is in fact no definite values of these quantities to even measure? Because QM is inherently probabilistic. Therefore it is just a "probabalistic smudge" rather than an actual particle that we are in fact considering?
Hey, I just thought I'd give explaining this a go. If you start out with the hypothesis that position and momentum have definite values that you just happen not to know, you can create a probability theory to describe this. However any theory where probability arises in this way (that is through ignorance) makes fundamentally different predictions than QM. Experimental tests support QM and refute such theories. QM uses a different type of probability, a type of probability that is not the result of ignorance of the truth. What does it result from? That's basically part of the difficulties of interpreting QM.
Now the bit about position and momentum affecting each other is also true and relates to this point I've just made. In the type of probability that QM uses measurement of one quantity can destroy information you used to have about a previous quantity. So measuring momentum nullifies anything you knew about position. It isn't like usual probability where you can keep learning and hence reduce your ignorance of both quantities.
If you want a way to think about I can offer you the opinion of Niels Bohr. In his mind, quantum particles do not have positions and momentums, they are simply something else we cannot imagine or perhaps not even discuss sensibly. However we must use these classical concepts to analyse them experimentally. When we measure position we are not learning about some objective quality of the particle, but rather using one way of projecting its existence into our classical world. To it put another way making a choice of a classical screen through which we view the quantum world. Then there seems to be a fundamental incompatibility between the position screen and the momentum screen. I cannot use both at the same time to capture an image of the quantum particle.
However that was just Bohr's way of viewing it, there are other ways. However the first two paragraphs are the facts. QM uses a probability not due to ignorance, so there isn't a real position or momentum of the particle that we happen not to know. This new probability also implies that measuring the momentum of a quantum particle and hence making it give a value of this quantity to classical instruments, will mean it no longer will give the value of position you measured earlier.
Some other views besides Bohrs are similar to what you stated in that the quantum particle is just a probabilistic smudge. Or put another way a quantum particle is nothing but a collection of probabilities for different values of different quantities to be observed. Reducing the probabilities of one quantity (by measuring momentum and seeing it have specific value) will increase them in another (position will now have probabilities for any location).
A final view (Rudolf Haag and others) is that position and momentum are properties of the interaction of the experimental apparatus and the quantum particle, not the quantum particle itself. So measuring a momentum with value "p", doesn't mean the particle has momentum "p", but rather that is delivered momentum "p" to the apparatus. Similarly measuring position "x" means that particle and the apparatus interacted with each other at "x", not that the particle is at "x".
This view connects with the idea that QM is not a theory of subatomic particles, but rather a theory of subatomic measurment.
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