Richard Feynman called the double slit the experiment that holds "the only mystery" of quantum mechanics, and described doing it one electron at a time as a thought experiment he did not expect anyone to perform. It has since been performed. Pier Giorgio Merli's group built up a pattern from single electrons in 1974; in 2013 Roger Bach and collaborators did the controlled version, opening and closing each slit with a movable mask and recording the arrivals one at a time.
What they see is the mystery in its cleanest form. Each electron strikes the screen at one place and leaves one dot — a particle's mark. But let thousands accumulate and the dots pile into bright and dark bands — a wave's interference. And if you try to settle the obvious question, which slit did each electron go through, the bands vanish; ask the question and the interference is gone. A single electron, sent through alone, somehow lands as a point while behaving as though it sampled both openings.
The contradiction is real only under one assumption: that the electron and the wave are one and the same object, so that whatever lands as a dot must itself have spanned both openings. Infinite-Dimensional Wave Theory does not grant that assumption. There is one wave, \(\Psi_\infty\), and its configuration fills the apparatus; the electron is a localized excitation of that wave. Keep the two distinct and everything fits — the dot, the bands, and a plain answer to the supposedly forbidden question: each electron goes through one slit.
The electron is a six-dimensional object
The electron is a resonance of the single wave \(\Psi_\infty\) in the \(d=6\) sector, with \(\mathbb{CP}^3\) geometry — a definite object spanning six flat, equally real spatial dimensions and moving through all six at once. We occupy three of them. The other three are not hidden away or frozen; they are ordinary spatial directions we simply do not stand in. In the interferometer the electron is not orbiting anything, so it follows a definite six-dimensional trajectory from source to screen — sharp and particular, not a smear and not a cloud.
This is the first thing the standard picture gets backward. It replaces the moving electron with a probability cloud and then calls the cloud the electron. IDWT keeps the electron a real object with a real path. What is six-dimensional about it is exactly what our instruments cannot see directly, so the part of its path we miss is forced to show up some other way.
The well binds the electron, not the wave
Two different things were being asked to be one thing. The electron is held together by its sector confinement — the well that makes it one compact object, with one mass and one charge, its structure about a femtometre across. That binding is the electron's own: it belongs to all six of its dimensions equally and travels with it, and it marks out no three of the six, because nothing in the electron marks any. What the well binds is the excitation. It does not shrink the configuration of \(\Psi_\infty\) the excitation rides — the configuration leaves the source as any free wave does and spreads as any free wave spreads, and by the panel it is broad enough to span both openings.
So "the electron is confined" and "something spans both slits" are statements about two different objects, and both are true. The confined thing is the excitation — compact, particular, the thing that will make one dot. The extended thing is the one wave's configuration. The paradox lived entirely in taking them for the same object.
The panel splits the problem in two
The three dimensions in this experiment belong to the panel, not to the electron. The panel — like the source, the screen, and every other piece of laboratory equipment — is baryonic matter, and colour confinement makes a baryonic object a \(d=3\) structure: it has structure in three dimensions and is uniform through the electron's other three, whichever three of the electron's six it stands in. The whole lab shares one set of three because its parts are built of the same matter, bound to each other. So the potential the panel presents takes the same value at every point of the three dimensions the panel does not occupy — the projection logic by which a 3D-built shield cannot contain a deeper structure — and the six-dimensional problem separates exactly along the panel's split, not along any split in the electron: in the panel's three coordinates the configuration meets the two openings the way any wave meets them; in the electron's remaining three there is nothing of the panel to meet, and that factor of the mode passes untouched, carrying the mass and the quantum numbers.
The pattern is the configuration's in the panel's coordinates, and it carries two distinct lengths. The width \(w\) of each opening sets the broad envelope — a wave squeezed through a gap fans out by \(\lambda/w\). The separation \(D\) between the openings sets the fine bands: downstream of the panel the configuration is the sum of the two openings' contributions, and their relative phase varies across a screen at distance \(L\) with spacing \(\lambda L/D\). Close one slit and that structure is gone — the envelope stays, the bands vanish — because the configuration has been reshaped, not because any electron behaved differently inside the slit that stayed open. The slit height adds nothing: the openings are uniform along it, so the pattern is too, and the bands run parallel to the slits. IDWT predicts exactly the standard pattern, here as everywhere; it moves no number.
The screen records a slice
A detector is built in our three dimensions, so it registers the electron only where its six-dimensional trajectory crosses the three directions we share. That crossing is a single place — one dot. Each electron's mark is sharp because the electron is sharp; nothing here is fuzzy. The dot is not the electron arriving "as a particle this time"; it is the one point where a definite six-dimensional path met our slice.
The pattern is what you get when those crossing points accumulate. Integrate the electron's full structure over the three sector coordinates a three-dimensional observer cannot resolve and what remains is a distribution across the screen — the three-dimensional marginal of \(|\Psi_\infty|^2\). That marginal is banded, because the six-dimensional structure it came from is, and so the dots, each one sharp and particular, pile up into bright and dark fringes. The wave behaviour and the particle behaviour are not two modes the electron switches between; they are the slice and the object it is a slice of, recorded at the same time.
Which slit? One of them, every time
Where the panel stands, the wave's amplitude survives only in the two openings, and an electron arriving at the panel crosses it the way it later meets the screen: at one place. One electron, one slit, one dot. Nothing straddles the gap, and nothing passes through both openings. The question "which slit did it take?" has an honest answer for every electron — an answer the apparatus simply never recorded.
What the question does not have is a fringe-preserving way to be asked. The bands live in the configuration spanning both openings, and the landing statistics are the marginal of that configuration — so the separation \(D\) is written into where electrons can land without any single electron having sampled both slits. Nothing needs to travel from the far slit to inform an electron passing the near one: the configuration is shaped by the whole panel before any given electron arrives, and every landing is drawn from that shape.
A which-path detector is more apparatus standing in the same three dimensions as the panel. To register a crossing it must couple to the wave at one opening, and that coupling correlates the detector with that opening's share of the configuration. In the marginal, the two shares then add as intensities rather than amplitudes: the envelope survives, the bands are gone. The measurement has not caught the electron doing anything different — it has rebuilt the configuration whose structure the bands were.
One electron at a time
The single-electron version is what makes the standard story strain hardest: with only one electron in the apparatus, there is nothing for it to interfere with. In IDWT there is nothing to strain. Each electron is a complete six-dimensional object carrying its own banded structure; its lone dot is its own crossing of our slice, and the fringes are already implicit in that one electron's marginal. The pattern does not require many electrons to talk to each other — it only requires enough crossings to fill in a distribution each of them already carries. The buildup is statistics revealing a shape, not a crowd creating one.
So nothing waits for company and nothing collapses from possibility into actuality. Every electron followed a definite path the whole way, through one slit; the screen just needs many of them before the shape of the marginal those paths share becomes visible to a three-dimensional eye.
What the experiment measures
One honest note, as elsewhere: IDWT predicts the same pattern and the same loss of fringes under which-path measurement as standard quantum mechanics. It moves no number. What it removes is the wave–particle paradox behind the number — the dot and the bands are the excitation and the configuration it rides, recorded together, not a particle that is somehow also a wave.
And the famous statement that an electron can turn up anywhere on the screen is, in this reading, not irreducible chance. The source prepares the configuration, not the electron's placement within it; where each excitation sits in that extended configuration is something a three-dimensional apparatus neither sets nor sees, and the statistics those placements produce are the marginal. How the excitation's definite path threads the configuration — its equation of motion — is an open item of the framework; the statistics that path must reproduce are not. The spread on the screen is a sharp object riding a wide configuration: wide because the configuration is wide, dotted because the electron is not.
Related reading
The Electron's Hidden Orbit — the six-dimensional electron and the three directions we cannot see.
Sector 6 — Charged Leptons — the \(\mathbb{CP}^3\) geometry the electron lives in.
The Delayed-Choice Quantum Eraser — the which-path question pushed to its strangest, with entangled pairs.
The Aharonov–Bohm Effect — another experiment where the three-dimensional slice comes up short.
Shields, Not Walls — the projection logic that separates the slit problem: a 3D-built potential is uniform in the deeper coordinates.
One Wave — why the electron is a sharp object and the cloud is only how a shallower observer sees it.
Atomic Orbits as \(\mathbb{CP}^3\) Projection — an interactive view of a six-dimensional path met by a three-dimensional slice.