ABSTRACT
Question Doesn’t this global time, measuring the expansion of the universe, contrast with the idea of time in relativity theory? As you have explained, isn’t time supposed to be a subjective parameter that a particular observer may use to express the physical laws, in one reference frame or another, with different corresponding measures? Reply Yes, I agree that there is a contrast here. But if the theory of relativity is indeed one of our abstract laws of nature, and a cosmological model, that disagrees with it, such as the RobertsonWalker model, turns out to be empirically correct, then this model could only be taken as a mathematical approximation for a more general description that is indeed covariant-i.e. where there would not be an absolute (global) time measure that is the same in all possible reference frames. This is in the same sense that Newton’s ‘action-at-adistance’ concept-implying that the attraction of the Sun to the Earth is only a function of their mutual separation-must be rejected when Einstein’s field theory is accepted. This is in spite of the fact that Newton’s equations are valid as a good mathematical approximation in the domain of experimentation where the predictions of the newtonian theory are in good agreement with the empirical data. Question Were you saying that the ‘big bang’ model in cosmology is not compatible with the theory of general relativity? Reply Yes, I believe that this is basically true. If the theory of relativity, and its revolutionary interpretation of space and time, are taken to be the starting point for a theory of cosmology, then the big bang model cannot represent a true theory that is compatible in an exact sense with this theory —because it is not covariant. That is, it entails an absolute time axis-called ‘cosmic time’—whereby all time measures may be made with respect to an absolute origin of time, which is the beginning of the universe-the time when it all started! This is clearly incompatible with the concept of time as a subjective parameter, dependent on the reference frame from which it is measured. Of course, it is opposite to the spirit of science to claim that any theory will ever show itself to be absolutely true! As scientists, we are supposed to probe predictions of a theory as far as we can. If contradictions and inconsistencies appear along the way, then the theory must be altered or, if necessary, abandoned. But so long as we are investigating the full set of implications of the theory of general relativity, it must be recognized that it does imply the necessity of a cosmological model that does not single out any special time axis, even though, from our particular platform in the universe, we observe that the galaxies of the night sky seem to be moving away from us, in the course of (our) time measure. Thus, I do not believe that general
relativity applied to cosmology can, in principle, be compatible with the present-day cosmological model of the big bang. Question Will the cosmology based on general relativity come from a better determination of the solutions of Einstein’s tensor field equations? Reply Not necessarily. Einstein’s tensor equations are not the most general representation of his theory of general relativity. As we have discussed earlier, it can be shown that the symmetry aspects of general relativity require that there must be 16 field relationships at each spacetime point, while Einstein’s equations are only 10 field relations at each space-time point. Einstein was fully aware that his tensor field equations were not the final, most general expression for his theory. In his Autobiographical Notes, he made the following comment about his tensor field expression for his theory5.
