The Patton and Wheeler GGU-model Requirements.

Robert A. Herrmann, Ph. D.

The following are the basic requirements that Wheeler's "pregeometry" must satisfy as found in the paper presented at the 1974 Quantum Gravity Oxford Symposium. After four months of efforts, members of the mathematics and physics departments of Princeton, the foremost authorities on planet earth in this subject matter, were unable to construct a "model" that satisfied these. They even stated that they knew of no approach that would yield such a "pregeometry."

In 1979, Wheeler still thought there might be an approach that will produce such a cosmogony. And, he personally discussed a little of this with me in Aug. 1979. Please note that the word "geometry" means the 4-D spacetime geometry notions that are a generalization of the 3-D differential geometry notions of Gauss and Riemann. Further, relative to spacetime geometry, General Relativity is an analogue model for behavior that we cannot otherwise comprehend. Spacetime is not a "physical" entity.

For General Relivity, it takes a considerable amount of effort, via approximation and mathematical manipulation, to actually predict physical behavior not knowing what is the actual "physical stuff" that causes the behavior. The predictions are often relative to "comparing" paths of motion for almost massless test particles. It is interesting that Lawden in his well received book on relativity and cosmology states that relative to the General Relativity model that "Physical space then is nothing more than the aggregate of all coordinate frames" [2, p. 127] That is, modes of measurement we use to predict the behavior of such physical entities.

The Requirements.

(1) Five bits of evidence argue that geometry is as far from giving an understanding of space as elasticity is from giving a understanding of a solid. [1, p. 539]

(2) They also suggest that the basic structure is something deeper than geometry, that underlies both geometry and particles ("pregeometry"). [1, p. 539]

(3) For someday revealing this structure no perspective seems more promising than the view that it must provide the universe with a way to come into being. [1,p. 539]

(4) It brings us into closer confrontation than ever with the greatest questions on the book of physics: How did our universe come into being? And of what is it made? [1, p. 540]

(5) Tied to the paradox of the big bang and collapse is the question, what is the substance out of which the universe is made? [1, p. 543]

(6) But is it really imaginable that this deeper structure of physics should govern how the universe came into being? Is it not more reasonable to believe the converse, that the requirement that the universe should come into being governs the structure of physics? [1, p. 558]

(7) It is difficult to avoid the impression that every law of physics is "mutable" under conditions sufficiently extreme, . . . . [1, p. 568]

(8) It is difficult to believe that we can uncover this pregeometry except as we come to understand at the same time the necessity of the quantum principle, with its "observer-participator," in the construction of the world. [1, p. 575]

Relative to (6), the requirement is that, at least for our universe, "physical laws" should "emerge" from the model. They should be a byproduct of its construction.


[1] Patton, C. M and J. A. Wheeler (1975). Is physics legislated by cosmogony? in Quantum Gravity: an Oxford Symposium, Ishan, C., Penrose, R., and D. Sciama, eds, Clarendon, Oxford.

[2] Lawden, D. F., (1982) An Introuction to Tensor Calculus, Relativity and Cosmology, (3rd Edition), John Wiley \& Sons, New York.