Two habits of thought run through ordinary physics so deeply that they are hard to see. The first is that particles are separate little objects that travel toward each other and interact when they meet. The second is that, looked at closely enough, a particle is a fuzzy cloud — a smear of probability rather than a definite thing. In Infinite-Dimensional Wave Theory both are wrong, and they are wrong for the same single reason.
There is one wave. It is called \(\Psi_\infty\), and it is the only object there is. Everything we name as a particle — the photon, the electron, a quark, the tau — is a feature of that one wave: a ripple in it, localized at a particular depth. Once that is the starting point, the two habits dissolve together.
Nothing crosses a gap
If there is one wave and every particle is a feature of it, then no two particles are ever truly separate. When we say two particles interact, we picture two distinct objects closing a distance and touching. That picture has no place here. There are not two things. There is one wave, and an "interaction" is just the shape that wave takes where two of its ripples live in the same region.
Take the electron and the tau. The electron is a six-dimensional object — a resonance of \(\Psi_\infty\) in the \(d=6\) sector, real across all six of its dimensions. The tau is a ten-dimensional object, real across ten. The electron's six dimensions are the first six of the tau's ten; the tau has four the electron does not. When the two interact — an event that lives in the full ten dimensions, the larger of the two — the electron does not reach up into those four extra dimensions, and it does not travel there. There is nothing for it to cross. It is already a feature of the one wave those four dimensions belong to. It was never a separate object sitting outside them, waiting to be connected.
"The electron interacts with the tau" is one wave's structure seen at two depths. It is not a meeting of two travelers.
The cloud is relative to depth
The other habit — the fuzzy cloud — falls to the same fact, and the connection between them is the heart of it.
We sit at three dimensions. When we look at an electron, we cannot resolve the three dimensions of it that lie outside our three. The honest thing to do with what we cannot resolve is to average over it — to add up the electron's activity across those three directions and keep only what is left in ours. What is left is a diffuse smear in three-dimensional space: the "electron cloud" of chemistry. But the electron was never a cloud. It is a definite six-dimensional object at every moment. The smear is not in the electron; it is in our viewing. It is the price of looking at a six-dimensional thing from three dimensions.
Now run the exact same operation one level up. From the electron's own six-dimensional vantage, the tau's four deeper dimensions cannot be resolved either — so they too get averaged over, and the tau's activity in them appears, to the electron, as a smear of precisely the same kind. The electron sees a fuzzy tau for the same reason we see a fuzzy electron: each is looking at an object that extends past its own depth.
So the cloud is not a fundamental property of anything. It is relative to the depth of the observer. Every particle is a sharp, definite object in its own dimensions, and a smeared cloud to anything that resolves fewer of them. Fuzziness is the signature of looking from below — never a fact about the thing itself.
Already there
These two answers are the same answer. The electron does not reach into the tau's four extra dimensions because it is already there — already a feature of the one wave that fills all ten. And from the electron's six-dimensional side, those four dimensions it shares nothing with are simply averaged out, appearing as the same smear we meet whenever we look past our own depth. Being "already there" and "seeing a smear" are the inside and the outside of one situation: a single wave, resolved to different depths by whatever is doing the looking.
This is why the framework keeps insisting there is no real separation between sectors. The sectors are not six different spaces with particles passing messages between them. They are six depths into one space, and the particles are one wave's ripples at those depths. What looks like an interaction between two objects, and what looks like a fuzzy probability cloud, are both just what a single sharp wave looks like when the observer cannot reach as deep as the wave extends.
No privileged observer, no fundamental fuzziness
Three dimensions are not special. We average over the electron's deeper directions; the electron averages over the tau's; nothing about three is the true floor of reality — it is only where we happen to stand. There is no fundamental fuzziness waiting at the bottom of things, and no smallest separate objects. There is one wave, sharp and definite across all its dimensions, and a hierarchy of observers each resolving it down to their own depth and meeting a cloud beyond it.
The fuzz was never in the world. It was in the distance between the depth of the looker and the depth of the looked-at. Close that distance — see the wave at its own dimension — and there is one definite thing, with nothing separate in it and nothing smeared about it.