He may not have framed them, at least for publication, but it is hard to
believe that he did not at least speculate about them. Among Newton’s
substantial mathematical achievements was the development of calculus
(which was also developed independently by Gottfried Leibniz). The de-
velopment of Newtonian gravitation in contemporary textbooks is in-
variably phrased in terms of calculus, as it is so clearly the correct
mathematical tool for expressing the results. Interestingly enough, New-
ton used calculus sparingly in his Principia; the great majority of his re-
sults were developed using only Euclidean geometry. Newton’s ability to
use geometry was extraordinary, and it is impossible to believe that once
he had expressed the gravitational force between two bodies as varying
inversely with the square of the distance between them, he did not specu-
late upon the connection between this fact and geometry. The fact that
the surface area of a sphere is a multiple of the square of the radius was
known to the Greek geometers, and if there is a finite amount of “gravita-
tional stuff ” emanating from a material body, that gravitational stuff
must be spread out over the surface of an expanding sphere. The exist-
ence of such gravitational stuff emanating from material bodies in an
expanding sphere would explain the inverse square law of gravitation,
and surely Newton must have had some thoughts along these lines.Another Gap in Another Table
The Standard Model is not an equation, but a table. There is a gap in the
Standard Model, a particle that fits in perfectly but has not yet been ob-
served. Just as Mendeleyev’s organization of the elements led him to pre-
dict missing elements and their properties, the gap in the Standard Model
cries out to be filled by a boson that transmits the gravitational force (as
the other bosons transmit the other forces). This hypothetical particle is
known as the graviton.
Gravitons are in some respects a natural way to explain Newton’s in-
verse square law of gravity. Electromagnetism is also a force in which the
strength of the attraction or repulsion varies as the inverse square of the
distance between electromagnetic particles, and the reason is that pho-
tons spread out over the surface of the expanding sphere (expanding at
the speed of light) whose center is the source of the emission. If the same
number of photons are spread out over two spheres, and the larger has a
radius three times the radius of the smaller, the larger sphere has a sur-
face area nine times as large as the surface area of the smaller sphere.
Assuming that the same number of photons are used to cover the surface
of the sphere, the photon density (which is a measure of the strength of
Space and Time: Is That All There Is? 145