Geometrodynamics
GENERAL RELATIVITY |
---|
Geometrodynamics |
1916 – |
The geometrodynamics ("GMD") research project was started in around ~1960 by the physicist John Archibald Wheeler. Wheeler's stated ambition with geometrodynamics was to try to base all of physics on the geometry of spacetime, and continue a project started by Clifford and Einstein. While Einstein's general theory was regarded as a success in its modelling of inertia and gravity (and was arguably already a geometrodynamic theory), there were other frontiers for the theory – could we model particles as stable features in the gravitational field? Could we model other fields, such as the electromagnetic field, as some sort of additional dimension or twist or distortion in the gravitational field?
Wheeler set about exploring what could be done with geometry.
“ | "There is nothing in the world except empty curved space. Matter, charge, electromagnetism, and other fields are only manifestations of the bending of space. Physics is geometry. | ” |
— John Archibald Wheeler, 1962 |
Experimental concepts:
Wheeler's main successes in geometrodynamics were conceptual:
- "mass without mass"
- In 1960, we already had the concept of a kugelblitz – a "ball of light" in which a momentary concentration of electromagnetic energy could become so intense that it could form its own event horizon and become gravitationally self-trapped. Wheeler took the idea and replaced EM energy with gravitational energy (gravity-waves), to try to produce a persistent object with a static-looking gravitational field, although the interior of the horizon contained nothing but curvature – a geon. The geon concept didn't seem to work particularly well, but it produced a talking-point.
- "charge without charge"
- If we created a wormhole in such a way that lines of electric charge passed into one of the mouths and back into normal space from the other, then these lines would be trapped by the geometry of space, and the two mouths would seem to an observer to be the origins of the fieldlines, with one mouth seeming to be the source of a positive electric charge, and the other appearing to be the source of a positive electric charge. However, the existence of these two charges would be an illusion created by scale-dependent topology – if we dived into the "negative" mouth in an attempt to find the source of the charge, we would find ourselves exiting back into normal space at the other mouth, where the same fieldlines exited, but now presenting their "other ends" to the universe, and appearing to represent a positive electric charge.
- When viewed with lower-resolution equipment, the region would appear to be singly-connected and containing two electrically-charged particles, but when explored at smaller scales, the region would be revealed to be doubly-connected and particle-free.
Geometrodynamics and Advanced General Relativity
Advanced General Relativity is also technically a geometrodynamic theory, and takes Clifford's "all physics is curvature" concept, referenced by Wheeler, quite literally. Logically, therefore, we would expect Wheeler's project to have either produced AGR, or produced an argument against AGR. The fact that this didn't seem to happen may be due to Wheeler's personality.
Wheeler was an odd mixture of would-be revolutionary and establishment figure. While some other American theoretical physicists in the 1960s slobbed around in teeshirts and jeans, Wheeler wore a suit, and had a habit of posing for publicity photos in front of pictures or statues of Einstein. While he spent much of his later career trying to come up with revolutionary concepts (with cool attention-grabbing names and slogans), he doesn't seem to have been quite so keen on overturning existing theory - his attitude seems to have been that revolutions should happen, but they should be properly organised and managed by the appropriate officially-assigned personnel. In short, while Wheeler wanted to come up with radical new ways of looking at the equations that governed the universe and hopefully extending them, he didn't seem to be so keen on changing the ones that we already had.
Wheeler said that his own personal motto – which he said that he lived by – was never ask a question until you know the answer
.
Wheeler, post-GMD
With the Cliffordian approach leading (apparently inevitably) to non-SR equations, Wheeler apparently either rejected this option, or was never able, for psychological reasons, to see it, and in the early 1970s, he backed away form the idea of physics being constructed from warped and twisted space, and increasingly focused instead on the subject of pregeometry. Pregeometry assumed a causal network and deeper set of rules that was responsible for creating both quantum mechanics and the metric of spacetime. If GR could not recreate or be reconciled with quantum effects, then perhaps this was because it was not supposed to create quantum effects - QM and classical effects might both be sibling emergent behaviours originating in some more primal level of physics, as-yet undiscovered.
Wheeler then went on to promote the idea of physics as pure information theory (It from Bit
)., which became influential in encouraging attempts to describe black hole horizon behaviour in terms of entropy and information-content – but which again appeared to side with QM and contradict GR1960.
Notes
AGR might also in some sense be thought of as "pregeometric" in the sense that instead of starting out with definitions of the shape of space and time (as in SR), or going straight to the derivation of a rigorous set of equations describing the shape of spacetime (as in GR), it focuses first on deriving a set of rules that any emergent theory would need to satisfy. However, where Wheeler's pregeometric explorations focused more on constructing the rules for a more abstract underlying level of reality (that might then be able to spawn both QM and GR1960), AGR bases many of its concepts on more mundane observerspace principles closer to experience, and reengineers general relativity in a way that appears to make it dual with quantum mechanics.