Some discussion of the Reciprocal Cosmology concept: messy bits, alternatives, and inspirations. This page is an informal “brain dump” intended to stimulate ideas, not a settled or peer-reviewed model.
From: Alan Carter
Is Infall Real?
I’m not that attached to the “infall” notion. It is appealing because it keeps us in an Einstein/Minkowski-style universe where the work done on expansion models might be adjusted to fit a contraction model. We might even be able to keep a rough “12 billion years since things started happening” intuition because the data are typically pre-processed assuming a scaling metric.
However, as one astute person pointed out, we may not need infall at all. We can do just as well with a scaling notion, at least in most of the model. I’m not sure how we would handle inertia in a universe where objects are “just getting bigger,” but it may be workable if we keep the time oscillation.
A major puzzle still to be sorted is how geometry would impose a speed limit in “hyperspace” that yields the light-speed limit we observe. It is easy to say “without the speed limit, nothing would happen,” but the question remains: can we derive the speed limit from an elegant geometry?
It also helps to think of the process as an “explosion backwards” rather than as infall. An explosion backwards is coordinated by a common cause. As infall, we lack a reason for the coordination; there is no obvious reason why everything would be “falling” together. This is where Mach’s Principle seems to fall out in r3.
There is still work to do: staring into space and trying to get a geometry that fits. But I think the deadlock is broken. Early-stage theories are fragile. With each step that survives contact with basic constraints, the odds of long-term survival improve. And whatever we end up with, despite having to map to the tensors in GR, I suspect the working geometry will be close to Euclidean in spirit, as what we have currently.
Gross Evidence
Spiral galaxies are entertaining things. Pretty, aren’t they? There is a recurring claim (and controversy) that spiral structure is not straightforward to reproduce from gravity alone in simplified models, and that “dark matter where you put it” does not automatically yield spiral arm patterns. If so, it may be worth exploring alternative ways to frame the same observations.
In r3, the increased “expansion” rate is treated as greater redshift, interpreted as a faster explosion backwards. As an explosion backwards, the universe does not need to be gravitationally closed in the usual sense; it can rely on coordinated trajectories. In that framing, a low-mass universe could still “slam together” on coordinated paths irrespective of gravitational closure.
Back to spiral galaxies: although the anecdote is that you cannot “cook them up” from gravity alone, I know one way to make that shape very easily. Roll up a length of paper into a tight cylinder, and let it unroll. The resulting pattern is a simple spiral.
Oscillating Photons
The modeling of massive particles as pairs of oscillating photons came from a remarkable book: Information Mechanics by F. W. Kantor (John Wiley, 1977), ISBN 0-471-02968-8 (see p. 43+). It is his “Photon Particle Representation,” but modified so that the oscillation occurs along the time axis. What this modification does to the rigor of Kantor’s work, I do not know. It is a kludge to fit.
Block Universe
Here is a thought experiment that aims to show how much we live in a block universe where events are fixed in spacetime. It starts with the traditional demonstration in GR that there is no such thing as simultaneous action across reference frames. Arrange Einstein, Lorentz, Newton, and a pair of intergalactic ammo dumps as follows:
Einstein Bar Lorentz
Dump A Newton Dump B
Newton sends a signal to both dumps. When the signals arrive, the dumps explode. The situation is symmetric with respect to Newton, so he sees two flashes occurring at the same time. For Einstein, the light from Dump A reaches him before the light from Dump B, so he sees the flash sequence A, then B. Lorentz sees sequence B, then A. Since nothing can travel faster than light, the time we see a thing happening is the time when it is happening for us, so we conclude there is no frame-invariant notion of simultaneity. That is the usual demonstration.
Now continue by allowing Einstein and Lorentz to travel through shared space until they reach the Bar (which can be anywhere). They tell their tales, and then look at each other in shock. They both believe they inhabit a universe that stays self-consistent.
Einstein saw A before B, so in his account, A is a precondition for B (in the sense that by the time he observed B, he had already observed A). But Lorentz saw B first. If both accounts are part of a single consistent spacetime, then (so the argument goes) each observer’s “second event” must already be fixed in the overall structure, because for the other observer it was the “first.” The observers still must behave as if the future is uncertain (insurance policies included) because it is uncertain to them, but the spacetime picture implies the events are “already there.”
GR is also trusted operationally in everyday technology. GPS timing needs relativistic effects accounted for in order to maintain accuracy. NASA notes that relativity is critical to GPS accuracy because clock rates differ under gravity and motion.
Yet in over 100 years, the newspapers have rarely roared, “Einstein confirms: fate exists!”
Speakable and Unspeakable
One way I have tried to test the thinking is to bear it in mind while reading Speakable and Unspeakable in Quantum Mechanics by J. S. Bell (Cambridge University Press, 1993), ISBN 0-521-33495-0 (hard) or 0-521-36869-3 (paper). Bell’s thinking is clear, rigorous, and often very funny. He made significant contributions to the field and looks honestly at unanswered questions. r3 seems (to me) to address several of the problems Bell poses, though that claim itself needs careful scrutiny.
Gravity and Binding Energy
One speculative claim here is that with the Ghost Not and Reciprocal Cosmology in hand, it may be possible to reinterpret certain historical “mystical” statements as crude attempts to describe patterns that are otherwise hard to express. Whether a reader sees any correlation will depend on what they have previously tried to read into those sources. This is not offered as evidence, only as a possible heuristic for generating analogies.
There is also a fully “re-creative arrow” explanation as well as the “creative arrow” explanation (which is intended to be causal in the new paradigm and not “supernatural”). For example, if they were free of the Ghost Not, able to see spiral galaxies and do fractal mathematics, the Pythagoreans might have stumbled onto useful intuitions. We can borrow ideas without borrowing the framing.
One specific mapping problem remains. Somehow, we have to get the photons to oscillate past each other, to bind instead of flying away. These photons are close together. We also have to sort out the gravitational/scaling issues. When photons are bound, they make massive particles. Massive particles produce gravity. I suspect we should look for binding to emerge from geometry in a way analogous to how gravity produces a black hole where light cannot escape. We should expect this from the detailed geometry. Call it “Pythagoras’ Conjecture,” perhaps.
Alan Carter wrote:
From: Charles Kendrick
Is it the case that for any reference frame X, where two events A and B appear to happen in the order (A, B), that there is necessarily a reference frame Y in which they appear to happen in the order (B, A)?
And if not, then maybe only a sliding window of determinism is implied?
What I’m saying is this: if Einstein’s “true sequence” is A then B, and Lorentz’s “true sequence” is B then A, then because they inhabit the same universe (which remains self-consistent), the inverted experiences mean that both second events are predetermined, because for the other observer they were first events. They cannot know that the second events are predetermined, of course. They still must act as if the future is uncertain, because it is uncertain for them. But for the universe, it is not. It is all there already.