The expanding universe / by Sir Arthur Eddington.

  • Eddington, Arthur Stanley, Sir, 1882-1944.
Date:
1940
Catalogue details

Licence: In copyright

Credit: The expanding universe / by Sir Arthur Eddington. Source: Wellcome Collection.

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    number of degrees of freedom, say n. In this simplified form “ the rest of the universe ” comes into the equa¬ tion of the hydrogen atom through the quantity R. I think we must expect that the numbers N and n will also occur in the equation, as a memorandum of the substitution of a space with n degrees of freedom for a universe with N degrees of freedom. For four-dimen¬ sional space-time the number n is found to be 10. We shall lose sight of it for the time being, but it will turn up later. Having decided that N and R will enter into the co¬ efficients of the equation of the hydrogen atom, we next inquire in what kind of association they will occur. The factor N, of course, arises from adding together equal contributions from each of the particles or wave- systems; the question is, What is the nature of the con¬ tributions to be added and how do they contain R? I do not profess to have achieved the necessary physical insight to settle the question. It will no doubt be much more satisfactory when we have a picture in which we can, as it were, see these entities adding themselves to¬ gether, just as we can see a hundred centimetres adding themselves to form a metre. But when this kind of insight fails, we are not without a guide. As conduct may be guided by ethics or by “ good form,” so this kind of investigation can be guided by physical insight or by analytical form. Both wave-mechanics and rela¬ tivity theory are very strict on good form. Only cer¬ tain kinds of entities are allowed to be added together. To add anything else would be a solecism. “ It isn’t done.” In relativity theory the only things that are additive are action-invariants.1 The action-invariant contain¬ ing R is the Gaussian curvature, which is proportional 1 Other tensors may only be added if they are at the same point of space—a condition which is obviously not fulfilled here.