Place, address and the event-ledger substrate

What Is “Here,”
and What Is “There”?

On an electron allowed to be in two places, an aether dismissed by the wrong test, and why the Schrödinger equation and ordinary movement were never properly introduced to each other — until you ask what a place actually is.

Ali Attar · Quantum Traction Theory

There is a question that has followed me since I was young, and I have never been able to put it down. It is so simple that a child asks it, and so deep that I do not think our physics has ever truly answered it. The question is this: what is “here,” and what is “there”?

It sounds almost too plain to be a real question. Here is where I am. There is where you are. We point, we agree, we move on. But press on it even slightly and it begins to come apart in your hands. When I say a thing is here, what exactly is the “here” that holds it? Is “here” a little box of space that was already waiting, empty, before the thing arrived to fill it? And if so — what is that box made of? Where did it come from? Was it there before anything was there?

But what truly began to disturb me — what turned a child’s puzzle into a lifelong unease — was the discovery, later, that physics asks an even stranger version of the same thing and then simply walks past it without flinching. Because physics tells us, with a straight face, that an electron is allowed to be “here” and “there” at the same time.

Sit with that. Not “we don’t know whether it is here or there.” Not “it is somewhere in between, and we are uncertain.” The claim is sharper and far more unsettling: the electron is both, genuinely, before we look. It is here and there at once. And when I first understood that this was not a figure of speech but the literal content of the theory, I felt the same vertigo I had felt as a child pointing at a wall and wondering what held the wall’s “where” in place.

What does it mean for one thing to be in two places? If “here” and “there” are real, separate boxes, then to be in both is to be torn — to be two. But the electron is not two; it is one. So either the electron is doing something we have no honest picture of, or — and this is the thought that took me years to take seriously — our picture of “here” and “there” was wrong from the very beginning, and the strangeness is the price we pay for that wrong picture.

The question modern physics quietly stepped around

Here is what I find almost unbelievable. This is not a small or technical matter. It is the floor of everything. Before you can speak of a force, a field, a particle, a measurement, you have already helped yourself to “here” and “there” — to a space of places where all of it is supposed to happen. And yet, somewhere along the way, physics decided to stop asking what those places are and to treat them as a free background, a stage that needs no explanation.

Newton handed us that stage: absolute space, an infinite empty grid of points, sitting there eternally whether or not anything occupied it. It was enormously useful. You could put coordinates on it, write equations, and predict the heavens. But notice what it quietly assumed — that “here” is a slot that pre-exists the thing in it. The grid is waiting in the dark, and matter merely visits.

I have come to believe that this single inherited assumption — the grid waiting in the dark — is the root of nearly every paradox that followed. Because if you believe in the pre-existing grid, then an electron that refuses to occupy a single slot looks like a miracle or a madness. It “must” be in one box; that it seems to be in two is treated as a deep and irreducible weirdness of nature, rather than as a loud signal that the box was never the right object to begin with.

And the most honest thing I can say about the standard story is that it never answers the child’s question. It refines it, dresses it, surrounds it with magnificent mathematics — and leaves it exactly where it was. We are told to compute and not to ask. My father taught me the opposite. He taught me to always ask why, and to distrust any grand structure that grows quiet precisely at its foundations.

The aether, and a handshake that proved the wrong thing

There was a time when physics did try to say what space was made of. It proposed the aether — a medium filling all of space, the “there” through which light supposedly travelled the way sound travels through air. It was an attempt, however clumsy, to give “here” and “there” a substance, a fabric, a something.

And then came the famous experiment — what I like to call the light handshake. The reasoning was simple: if the aether is a still medium and the Earth ploughs through it, then light sent along the Earth’s motion and light sent across it should return slightly out of step, like two swimmers in a river, one going with the current and one across it. Compare their arrival — let the two beams shake hands — and you would feel the “aether wind.” The experiment was done with exquisite care. And the handshake found nothing. No wind. No drift. The beams returned in step.

From that null result, physics drew a sweeping conclusion: there is no aether, and therefore space has no substance at all. Space became, once more, the empty Newtonian grid — now stripped even of its hopeful fabric, a pure nothing in which events occur.

But here is where I part ways with the textbook story, and where Quantum Traction Theory spends a great deal of its effort. The handshake ruled out the wrong aether. It tested for one very specific idea — a mechanical, material medium that things drag through, a kind of cosmic fluid with a rest frame you could measure your speed against. That idea deserved to die, and the experiment killed it cleanly. But physics then made a leap that was never justified by the experiment itself: it concluded that because that substrate does not exist, no substrate exists — that “here” and “there” are backed by literally nothing.

That leap is the quiet catastrophe. Because the moment you say space is backed by nothing, you have made “here” and “there” homeless. They float, ungrounded, defined only by coordinates we paint on the void for our own convenience. And into that homelessness, a few decades later, walked quantum mechanics — and made everything worse.

Quantum mechanics, and a friendship that never happened

When quantum mechanics arrived, it did not repair the foundation. It built another shaky new floor on top of the cracked one — but a good one: a profound lie theory — a PLT — about space. It said: do not ask where the electron is; carry a wavefunction, an amplitude spread across all the slots of the grid at once, and from it compute the chance of finding the electron here, or there, when you look. The wavefunction worked. It worked so well that we began to call quantum mechanics the most complete and successful theory in the history of human thought, with a great hidden cost:

We accepted that the electron’s reality, before measurement, is a smear of “here-ness” and “there-ness” laid over the old empty grid — the very grid we never justified. The electron is “here and there” because its amplitude is here and there. And if you ask, as a child would, but what is the amplitude — is it a real thing, a fog, a field, a possibility? — you will get many answers and no agreement. A century on, we still argue about what the wavefunction is. That is not the signature of a finished theory. It is the signature of a theory standing on a foundation it never examined.

And there is a second wound, subtler but, to me, just as telling. The Schrödinger equation — the law that governs the wavefunction — and the ordinary idea of movement were never properly introduced to each other. They do not have, as I have sometimes put it, a nice friendship.

Think of it plainly. Movement is the oldest physical idea we have: a thing goes from A to B along a path. That is the world of the Lagrangian — of least action, of trajectories, of a worldline you can draw. But the Schrödinger equation does not describe a thing moving along a path. It describes an amplitude that spreads, that lives everywhere at once, that has no single trajectory at all. That is the world of the Hamiltonian — of energy generating the evolution of a state across all positions simultaneously.

Standard physics reconciles these two only at arm’s length, with formal bridges — the classical limit, Ehrenfest’s theorem, the path integral that sums over all trajectories at once as a kind of compromise. They are stapled together by a correspondence principle, not united by a shared picture of what is going on. The worldline picture and the amplitude picture are two formalisms that both happen to predict numbers, living in an uneasy marriage with no common ancestor. The electron moving and the electron here-and-there are spoken in two different languages, and no one ever wrote the grammar that both descend from.

So when we call this our most complete theory, I cannot help asking: complete in what sense? It computes magnificently. But it cannot tell you what a place is, what an amplitude is, or why its own two great pictures — movement and spreading — do not speak to each other. These are not ornaments. They are the foundations. And a structure that is silent at its foundations is not complete; it is merely successful in one angle, which is a very different and much humbler thing.

I am far from the first to feel this unease, and one of the most fearless voices on it deserves real credit. Sir Roger Penrose has refused to be polite where almost everyone else softens the blow: he insists that quantum mechanics is not merely incomplete but wrong, and he aims the charge straight at the Schrödinger evolution itself — at the very law that is supposed to govern how the state moves. His verdict is exact and unflinching: as soon as a “significant” amount of space-time curvature is introduced, the rules of quantum linear superposition must fail. I do not adopt Penrose’s particular mechanism — he looks to gravity to break the superposition, where I look to the completed-address ledger — but I admire enormously that he was willing to walk up to the most successful equation in physics and say, plainly, that it cannot be the final word. That is the spirit my father taught me: do not bow to a thing simply because it succeeds.

The turn: a place is not a box. It is a completed event.

This is where my own road forked away from the standard one, and where the framework I have spent years building — Quantum Traction Theory — begins, not with a new force or a new particle, but with a new answer to the child’s question.

QTT refuses the grid waiting in the dark. Its founding move, which in the corpus I call the completed-address principle, says something that took me a long time to be able to state cleanly:

A place — a “here,” a “there” — is not a tiny coordinate already sitting in the darkness, waiting to be filled. A place is the name of a completed event.

The order of things is reversed, and the reversal is everything. In the old picture, the slot comes first and the happening fills it. In QTT, the happening comes first, and only when a local transaction has genuinely closed does a “place” come into existence at all. And “closed” has a precise meaning in the framework: a tick of the deepest clock has passed; an internal dial has turned through one full, legal rotation and returned; the structure’s finite capacity has actually paid for the event; and a complete bundle — a closed loop of the right amount — has been formed. Only after all of that has happened does the word “address” become legal. The place is the completed happening itself, seen from what I call the Reality-Dimension ledger. (Back in the earliest QTT program, in 2019, I gave this very handshake another name — I called it subspace — years before A5-X sharpened it into the completed-address language I use here.)

I cannot tell you how much this reframing settled in me, because it answers the thing I could not answer as a boy. There is no empty box behind “here.” “Here” is the receipt of a transaction that closed. The wall I pointed at as a child is not sitting in a pre-given location; its “where” is the running tally of countless completed events, each one a closed bundle paid for in full. Space is not a stage. Space is the bookkeeping of what has actually finished happening.

And once you hold that, the smooth, continuous space we draw on paper reveals itself as what it always was: not the deepest thing, but a coarse-grained shadow — the blurred average of an enormous ledger of completed events, the way a beach looks smooth from far away and is grains up close. The continuum is a beautiful and useful shadow. It is not the substrate. The substrate is the events.

This, by the way, is the right answer to the aether, the one the light handshake could never have touched. QTT’s substrate is not a material fluid with a rest frame — so of course no “wind” was ever found; there is nothing material to drift against. But neither is it nothing. It is a substrate of the right kind: a structured ledger of completed events, a real fabric made not of stuff but of closure. The handshake killed the mechanical aether, correctly. It said nothing whatsoever about an event-ledger substrate, because such a substrate has no wind to detect — by its very nature. Physics dismissed a fabric of one kind and wrongly concluded there was no fabric at all. QTT restores a fabric of the right kind, and with it, “here” and “there” finally get their meaning back.

The Hamiltonian framework of QTT: a real turn, not an imaginary one

Now I can come to the two pieces you really wanted me to open — the Hamiltonian and Lagrangian frameworks of QTT — because they are where the electron’s “here and there” stops being a paradox and becomes almost obvious.

Begin with the Hamiltonian side. In ordinary quantum mechanics, the law of evolution is written with the imaginary unit, the famous i — the square root of minus one — standing in the heart of the Schrödinger equation. Generations of students have been told to accept that the deepest law of nature requires an imaginary number, and almost no one is told why. It is one of those places where the theory grows quiet at exactly the spot a child would ask a question.

QTT does not write i there. In its place it writes a real geometric operation — a genuine quarter-turn, a ninety-degree rotation of the internal dial that lives at every completed address. I write it as J. And the QTT law of evolution reads, in plain shape:

J times the rate of change of the state equals the energy acting on the state.

This looks almost identical to Schrödinger’s equation — and that is the point. If you “package” the real quarter-turn J as the imaginary i, you recover standard quantum mechanics exactly, line for line. Nothing in the successful predictions is lost. But the meaning is transformed. The mysterious imaginary phase of the wavefunction is no longer a number from nowhere. It is a real rotation of a real dial. The state does not evolve by some inscrutable complex magic; it evolves by turning — and because turning is a rotation, it automatically preserves length, which is exactly the conservation of probability that quantum mechanics calls “unitarity.” In QTT it is not an axiom you must swallow; it is a geometric fact. A rotation cannot change a length. That is the whole of it.

There is more, and it matters for our question. The QTT Hamiltonian carries a finite capacity window built into it — a consequence of the framework’s principle that nothing has infinite capacity. In plain terms, the deepest structure cannot support infinitely fine detail; the very-short-wavelength extremes are gently suppressed rather than running off to infinity. The grid was never infinitely fine because there was never a grid — only events, and events come in completed, finite bundles. So the old infinities that plague the continuum picture do not arise, because the continuum was the approximation, not the truth.

What does this Hamiltonian framework say about the electron being “here and there”? It says the wavefunction — the amplitude that seems to put the electron in two places — is a projection obtained by summing over completed address events. The configuration-space amplitude is downstream of the event ledger, not the fundamental object. So “the electron is here and there” does not mean one little ball is somehow torn between two boxes on a pre-existing grid. It means the electron’s reality is a ledger of completed-address-event supports, and the “here-and-there” picture is the shadow that ledger casts when you insist on describing it in the old language of positions. The strangeness was never in the electron. It was in our demand that it live on a grid that does not exist.

The Lagrangian framework of QTT: movement as a shadow

Now the Lagrangian side — and here is where the broken friendship is finally mended.

In QTT there is a deeper Lagrangian, what I call the dial Lagrangian — a law written in the native language of the turning dial and the completed-address ledger. It is not yet the Lagrangian you learned in school. The Lagrangian you learned — the one of trajectories and least action, the one that governs movement — is, in QTT’s words, the “shadow” of the dial dynamics: what you get when you project the deep dial law down onto the ordinary laboratory world of three spatial directions and one clock. The corpus states it precisely for the deepest case: the familiar Lagrangian “remains the correct shadow of this deeper structure.” It is correct. It is just not fundamental. It is the silhouette the dial dynamics throws on the wall of the lab.

And now watch what happens to the two estranged pictures. The Hamiltonian picture — the amplitude, the spreading, the “here and there” — is one shadow of the dial dynamics. The Lagrangian picture — the worldline, the path, the movement from A to B — is another shadow of the very same dial dynamics, taken from a different projection angle. They are not two unrelated formalisms stapled together by a correspondence principle. They are two silhouettes of a single object. They are siblings. They finally have a common ancestor, and the ancestor is the real-J dial winding on the completed-address ledger.

This is why, in the ordinary theory, Schrödinger and movement never had a nice friendship: the ordinary theory only ever had the two shadows, and no knowledge of the body that cast them. Of course two shadows of an unseen body look incompatible — one stretched, one foreshortened, never quite matching. Show them the body, and the quarrel dissolves. The body is the turning dial. The spreading amplitude is the dial seen one way; the moving worldline is the dial seen another. The electron “moves” (the Lagrangian shadow) and the electron is “here and there” (the Hamiltonian shadow) for the same underlying reason, and at last you can say what that reason is.

There is even a precise place in the mathematics where the worldline shadow breaks and you are forced back to the spreading shadow — the framework calls these caustics, the points where the projection onto a single configuration loses its footing, where you can no longer pretend there is one clean path. That is not a failure. It is the body reminding you that the worldline was only ever a shadow, valid where the lighting was simple and useless where it was not. The quantum spread is what you see when the single-path silhouette can no longer be drawn.

So — what is “here,” and what is “there”?

Let me return, after all of this, to the child’s question, and answer it as plainly as I am able.

Here is not a box. There is not a box. Neither was waiting in the dark. “Here” and “there” are the names of completed transactions — closed bundles, paid in full, recorded on the Reality-Dimension ledger. The smooth space that makes us feel they are pre-existing slots is a coarse shadow of that ledger, a convenience, not the truth. The separation between “here” and “there” — the very fact of locality — is itself a projection of the separation between completed events, not a primitive fact about an empty stage.

And the electron “here and there”? It is not one thing torn across two boxes. It is a ledger of completed-address supports whose shadow, drawn in the old language, looks like a smear across positions. When a measurement happens — when an access event closes — one address is read out, one transaction is settled, and the smear we called “here and there” was simply the ledger before that settlement. There is no tearing, because there were never two boxes to be torn between. There is only the bookkeeping of closure, and the shadows it casts: the spreading amplitude on one wall, the moving worldline on another, both faithful, neither final.

I will not pretend this is a finished and proven account of the world. It is a framework, and a framework must keep earning its place against measurement, honestly, in whatever colour the data returns — that discipline matters more to me than any elegance. But I will say this, and I will say it without hedging: a framework that restores the question is worth more to me than a framework that walks past it. Modern physics, for all its staggering success, stepped around “here” and “there,” dismissed a fabric of the wrong kind and assumed there was no fabric at all, and built its most complete theory on a foundation it declined to examine. QTT walks back to that foundation and asks the child’s question again — what is a place? — and dares to answer: a place is something that happened, and finished happening, and left a record.

It began, for me, with a boy who pointed at a wall and could not say what held its “where.” I am older now, and I still point at walls. But I am no longer afraid of the question. I think the question was never the enemy. The enemy was the silence — or the fancy, technical, calculative-only answers — we built around it — and silence, my father taught me, is the one answer a real scientist is never allowed to give.