The particles were never separated

Of all the strange results in modern physics, quantum entanglement is the one that most resists ordinary explanation. Two particles are created together and sent in opposite directions. Measure one along some direction and find its spin pointing up, then measure the other, however far away, along the same direction, and it is found pointing down. That holds every time both detectors are set the same way. But a precise pattern also holds when the detectors are tilted at different angles to each other, and that second part is the hard part.

Gloves in two boxes

Einstein suspected that nothing mysterious was going on. In 1935, with Boris Podolsky and Nathan Rosen, he argued that if no influence travels faster than light, the particles must carry their properties from the start, and quantum mechanics, which does not describe those properties, must be incomplete. The usual picture is a pair of gloves sent in two boxes: open one, find the left glove, and you know the other is the right.

In 1964 John Bell turned the question into one that experiments could answer. He proved that if particles carried pre-sorted answers, the correlations between measurements at different angles could not exceed a certain strength. A simple version, due to David Mermin, makes the point: give each pair any instructions you like for three possible detector settings, provided equal settings always give corresponding results; choose the settings at random, and the results must correspond at least five times in nine. Quantum mechanics says one time in two.

Experiments agree with quantum mechanics. They have been done with extraordinary care: in 2015 three teams, in Delft, Vienna and Boulder, each closed the two main loopholes, detection and locality, in a single experiment, and in 2018 the detector settings were chosen by about 100,000 human volunteers and, in another test, by the color of light from distant quasars, pushing back the remaining question of whether the settings could be correlated with the particles. The gloves picture is ruled out by the data.

What RSI accepts, and what it disputes

Rest-State Inversion Theory accepts the experiments completely. Bell's theorem is a mathematical proof: no theory can match these results while keeping all three of no influence faster than light between the detectors, answers fixed in advance for every measurement, and detector settings independent of those answers. One has to go.

What RSI disputes is the standard conclusion that particles must exist in indefinite states until they are measured. RSI keeps particles real and definite, and gives up the first assumption instead, as David Bohm's theory did in 1952. As a consequence, the result at one detector is not settled by its particle alone, since it can depend on what is done at the other.

Two things, not one

RSI says entanglement has two parts, and mixing them up is where the confusion comes from.

A record written at birth. When two particles are created together in the Eternal Consonance with zero total spin, the medium conserves rotation, so their spins are opposite along whatever axis both are measured. This explains why the results always correspond when both detectors are set the same way.

A live connection through the medium. The record alone is the gloves picture, and it fails at different angles. So no particle carries, on its own, a pre-written answer for every angle. A knot always has a definite position and structure, but the result at a given angle is produced when the knot, the detector and the medium interact. And the medium connects the two interactions. It is incompressible: a change in pressure anywhere is felt everywhere at once. Both particles travel through the same continuous medium, and what happens at one detector reshapes the guide of the particle at the other, instantly. This is RSI's proposed mechanism for correlations stronger than Bell's limit, playing the same role as the guiding wave in Bohm's theory.

Why you still cannot send a message

The connection is real and instantaneous, but no one can use it to signal. Each experimenter's list of results looks completely random, and neither can choose an outcome. More than that, the statistics at one detector are the same whatever setting the other experimenter chooses. The correlation is visible only when the two lists are brought together and compared, through an ordinary channel no faster than light. The medium joins the outcomes but hides the join from each observer alone.

What remains to be shown

The picture is designed to agree with every experiment, but that agreement is not yet derived. One formal step remains: showing, with the full mathematics, that the flow of this single medium produces exactly the correlations quantum mechanics predicts, reaching Bell's quantum value of 2√2, and keeps each detector's statistics independent of the other's setting. It is the most important near-term mathematical task for the theory, and an open invitation to anyone who wants to work on it.

The particles were never separated

Neither part of RSI's account requires particles to be in indefinite states, a signal faster than light, or an observer to make anything real. The particles were definite from the moment they formed, and the medium connecting them was always there. In RSI's view, the mystery in the standard account comes from leaving the medium out. If the derivation succeeds, the particles were never separated, because the medium joining them never was.