The Quantum Structure of Space and Time (293 pages)

158 The Quantum Structure of Space and Time

(2) leads to the dispersion relation

_- E mc+kexp(_) irE =o

C (3)

giving the quantization condition

(4)

nc

E

r=-r (n an integer)

which shows that T is an integer multiple of the Compton wavelength of the electron,
so is of order m.

This elementary argument giving the scale of the retardation parameter r f c is
striking. Note that the real part of the equation gives

E = mc2 + (-l)n-lkc (5)

so that the constant k will have to be extremely small.

Analysis of exp(-rD) raises many challenging problems which are related to
the mixing of positive and negative energy states. On the other hand the equation

makes sense on a curved background. Coupling the Dirac operator to other gauge

fields can be treated in a similar way, though a gravitational counterpart presents

further problems.

I finish by simply asking whether these ideas have any relevance to string theory

or M-theory. In particular is the initial data problem for retarded equations related

in some way to quantum theory?

My purpose is not to make any claims but to stimulate thoughtt

Bibliography

[l] C.K. Raju, Time: Towards a Consistent Theory, Kluwer Academic,

Dordrecht, (1994) Fundamental Theories of Physics, Vol. 65.

t I am grateful to the participants of the Solvay Conference for a number of cogent

and constructive criticisms.