It’s good to focus on “General Relativity” and Cosmology without the cloak of mathematics gone wild and unsupervised, indeed.

Anything having to do with “General Relativity” has a lot of extremely debatable philosophy hidden below a thick carpet of computations. Abuse of philosophically unsupervised spacetime leads one to believe in time machines, wormholes, and similar absurdities. A recent discovery such as Dark Energy (ever expanding space faster than previously anticipated), and a not so recent one, Dark Matter, show one has to be extremely careful.

Einstein equation of “General Relativity” (GR) is basically Curvature = Mass-Energy. Einstein long observed that the left hand side of the equation was built of mathematical beauty, and the right hand side of a murky mud of a mess. The discovery of Dark Matter proved him prophetic about that. (BTW, I know perfectly well that, stricto sensu, it’s the Ricci tensor, derived from the full Curvature tensor on the left…)

First a philosophical trap: “General Relativity” (GR) is a misnomer. It’s not clear what’s being generalized. GR is certainly a theory of the relationship between gravity and local space-times (the Theory of Relativity of space and time which *Poincaré* named that way in 1904).

Einstein was initially motivated to explain inertia according to the Newton-Mach observation that the distant stars seemed to endow matter with inertia (because if matter rotates relative to distant stars, a centrifugal force appears).

That way, he failed, as Kurt Goedel produced spacetime models which rotated wildly without local consequences. Frame dragging exists nevertheless, and is crucial to GPS. So GR has local consequences.

Neither Poincaré nor Einstein liked the concept of “spacetime”.

A question has naturally come up: if space expands, how come we don’t? An answer to this has been the raisin bread model of the expanding universe.

As *Sabine Hossenfelder*, a theoretical physicist in Quantum Gravity and High energy physics puts it: *“In cosmology, too, it helps to first clarify what it is we measure. We don’t measure the size of space between galaxies — how would we do that? We measure the light that comes from distant galaxies. And it turns out to be systematically red-shifted regardless of where we look. A simple way to describe this — a space-time slicing that makes calculations and interpretations easy — is that space between the galaxies expands.”*

However, the entire area is contentious. The usual snap-back of haughty physicist keen to deny any brains worth noticing to the Commons, is to say that all those who don’t understand the mathematics at hand should shut up.

That’s a disingenuous answer, as NOBODY understands fully the mathematics at hand (those with snappy rejoinders know this, but they enjoy their power maliciously).

An example of the non-universality of the notion of expanding space is the following exact quote from Physics Nobel Laureate Steven Weinberg, author, among many other things, such as the Weinberg-Salam model of the electroweak interaction, of the most famous textbook on the subject, “Gravitation and Cosmology”: *“…how is it possible for space, which is utterly empty, to expand? How can nothing expand? The answer is: space does not expand. Cosmologists sometimes talk about expanding space, but they should know better”*

Well, they don’t.

Reference https://www.physicsforums.com/threads/raisin-bread-model-of-space-time.901290/

Personally, I think that both space and time are local concepts (as long as one does not add to consideration the Quantum theory, as it was created, post 1923, by De Broglie, and after 1924, by the Copenhagen School). Local space and local time are united by the speed of light, c, through naturally ubiquitous light clocks. Space and time are measured locally (although Poincaré proposed a slow motion to move synchronized clocks around, and Einstein copied and published that mechanism, verbatim, as he had with E = m c²).

It has been proposed that the redshift of cosmological photons, and its attribution, 100%, to the expansion of spacetime, is a proof of the expanding “spacetime”. One must say that this statement is the core of present cosmology. And anybody looking down on the idea will not be viewed as serious by famous physicists. However just saying something does not prove it. Especially when the conclusion seems to be the hypothesis.

Lorentz- Poincaré Local Space and Time theory was experimentally provable (electromagnetism proved it).

But where is the proof that the universe is like an expanding dough, spacetime, with galactic raisin grains in it? Just waving the notion that the atomic force is 10⁴⁰ the gravitation force at a small scale does not seem compelling to me. It’s rather a question of range: gravitation is much longer range, although, much weaker. Thus the geodesic deviations due to gravitation show up at a very great distance, whereas those due to atomic and molecular force cause enormous geodesic deviations, but only at very short range. We are these enormous local deviations, larger by 10⁴⁰ locally.

Yet, even this more precise argument smacks of hand waving. Why? Because a theory of local forces as curvatures, although posited by Riemann in 1865, and the foundation of GR, still does not exist (that’s one thing string theory was trying to achieve, and failed). Gravitation remains the only force that is tautologically equivalent to a curved space theory.

Quantum Physics has provided that theoretical spacetime with a nonlocal causal architecture (through Quantum Entanglement). However that “causality” although geometric, is non metric (and thus manifests itself with no geodesic deviation, no force).

Einstein, after a debate on nonlocality imparted by the Quantum, with the Austrian philosopher Karl Popper, attracted the world’s attention on that problem in 1935, with his famous EPR paper. There Einstein denounced the way the “spooky action at a distance” affected distant “elements of reality”. Since then, the spookiness at a distance has been amply confirmed (and enables to encrypt space communications while knowing 100% whether they have been breached, as a Chinese satellite recently showed). Nonlocal effects show unambiguously that the metric (of “spacetime”) does not capture all the geometry (an notion which may surprise physicists, but not those mathematicians who have studied the foundations of their field).

This Quantum architecture has led, so far, to no prophecy, let alone theory, by established physicist. Entangled Quantum architecture is actually not part of the General Relativistic raisin cake model (or any GR model). However, I will venture to say one can view it as predicting Dark matter, at the very least. It’s just a question of baking something more sophisticated than raisin bread.

Patrice Ayme