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Gravity and Action from the Evolution of a Complex Manifold

Posted 5 months ago

POSTED BY: Donald Airey
4 Replies

In 1687, Newton hung a bucket of water from a twisted rope and let it spin. At first the bucket turned but the water stayed flat. Then the water caught up, spun with the bucket, and climbed the walls. Newton stared at that curve and asked the question that has haunted physics ever since: rotating relative to what? Not the bucket — the water curves precisely when it moves with the bucket. Newton's answer: space itself. Mach's rebuttal, two centuries later: there is no "space itself" — the water spins relative to the distant stars, and in an empty universe, spinning would mean nothing at all.

You'd think Einstein settled this. He didn't. General relativity isn't a description of our universe — it's a rulebook for building universes. Curvature on one side of the field equation, matter-energy on the other, and all the rulebook demands is that they balance. In 1949, Gödel showed how permissive that is: he built a universe with rotation twisted into spacetime itself — sourced by nothing more exotic than ordinary dust — and it balanced perfectly. In Gödel's universe, the bucket answer comes out backwards: a bucket at rest relative to every star in the cosmos still gets curved water. Ask GR what the bucket does, and it predicts both outcomes.

PME is not a rulebook, but a single universe, already written. One of its postulates is a universal clock — a single time shared by every point on the manifold. That matters because every Gödel-style universe, in any theory, requires time to be tangled: no consistent global "now" slicing through the cosmos. That tangling is what cosmic rotation means, mathematically. But in PME the temporal structure is the exact differential of one global evolution parameter, so a consistent now exists automatically, everywhere, always. A rotating universe isn't forbidden in PME — it's unwritable. The door Gödel walked through was never built into this house.

So the bucket finally gets one answer. There is exactly one standard of "not rotating" — the homogeneous background field — and the water climbs if and only if it spins relative to it. Even in a universe emptied of everything but the bucket. Newton was right, and PME returns his answer not as an interpretation but as a prediction the theory cannot avoid — something GR structurally cannot do.

This is a better absolute stage than Newton's. His was an invisible container that pushed matter around while remaining untouchable. PME's background evolves, carries a finite acceleration budget that every rotating body must draw against — tying each local spin to the universe's total inertial content — and is observed: every supernova distance in the Pantheon+ Hubble diagram is, in PME, an integral of that universal clock over billions of years. Newton's stage — but dynamical, on a budget, and visible in the data.

PME answers the oldest question in dynamics; GR shrugs. Your rebuttals are welcome.

POSTED BY: Donald Airey

PME Manifold

This is your universe. The red line indicates the current age of the universe at 14.5 billion years. The surface of this manifold is closed and this universe will return to the same singularity from which it came in 505 billion years. The universe started expanding at a rate of $3.15\times 10^8\,m\,s^{-1}$, it is currently expanding at a rate of $2.99\times 10^8 \,m\,s^{-1}$ under a uniform deceleration of $3.67\times 10^{-11} m\,s^{-2}$.

POSTED BY: Donald Airey

Your universe is lumpy, open, causally disconnected (Horizon Problem), has causal paradoxes (Goedel Time Travel Theorem), and singularities (Penrose Singularity Theorem).

My universe is perfectly smooth, closed, causally connected, doesn't allow paradoxes and has a finite acceleration budget that doesn't allow for unconstrained collapse.

POSTED BY: Donald Airey

This bilocal construction doesn't merely permit a minimum action as a postulate — it demands one, because there's no well-defined continuum to fall back on. Quantization isn't bolted on after the fact; it's baked into the geometry from the start.

POSTED BY: Donald Airey
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