, which is to account for gravitation, is neither spherical nor homogeneous nor homaloidal. This law represents a heterogeneous species of curvature; indeed, were the curvature spherical, it could never account for gravitation.
Starting from his mistaken premises, our philosopher soon falls into further confusion. After telling us (p. 224) that the supposedly spherical law of curvature,
, is able to account for gravitation, and for all the gravitational effects predicted by Einstein, he next informs us (p. 485) that this law cannot be the law of gravitation in the real world because the space round the sun is never completely empty, but is filled with tenuous cosmic matter, electromagnetic fields, and light waves. This casual presence of matter and electromagnetic fields would (always according to Broad) modify the law of spherical curvature,
, causing it to become heterogeneous. But all these statements are utterly erroneous, since, as we have said, even in an ideally empty space-time, the law of curvature,
, round the sun would still be heterogeneous, quite apart from the minute superadded effects that might be occasioned by a casual matter distribution. In other words, the heterogeneity is essential, not accidental.
We now come to the Professor’s philosophical conclusions. He notes that this passage from a space-time which is spherical and homogeneous in a gravitational field to one which is heterogeneous is brought about by the casual presence of matter round the sun. Einstein never stresses this point which Broad has brought to light, whence Broad concludes that this important transition from homogeneity to heterogeneity has been “slurred over.” As a philosopher he deprecates this loose treatment, pointing out that a totally new conception of space is involved, one that should be submitted to careful philosophical scrutiny.