Hawking singularities

Though Stephen Hawking seems to have moved on from singularity theory in his latest book (http://www.dnaindia.com/lifestyle/review_the-christian-propaganda-in-stephen-hawkings-work_1495047), there is one point about singularities which still needs to be clarified, since even the Large Hadronic Collider website confounds a singularity with a moment of creation.

Hawking\'s Grand Design


The question is what sort of singularity? Most physicists think of a singularity as a Robertson-Walker singularity, or a point of infinite mass-density.

There are three key points to notice here.

A Robertson-Walker singularity is readily avoidable, if the cosmos rotates, for example. The whole point of Hawking’s singularity theory was to try to show that a singularity (or a true beginning of time, or creation) is somehow inevitable.

Second, to achieve this agenda, Hawking redefined the term  ’singularity’ in such an abstract way, that it need not even be a point of infinite density but only an infinity that arises because of a shock wave, for example. That is, what one might meet at a singularity maybe just a firecracker and not the Christian God. (A shock wave corresponds to a discontinuity in the second derivative of the metric tensor, a shell of matter to a discontinuity in the first derivative, and a gravitational screen to a discontinuity in the metric tensor.) The infinites here arise because one differentiates a discontinuous function.

Now that is a very old-fashioned definition of the derivative to use, which arose from Newton’s confusion about fluxions, and his inability to understand the Indian calculus. Calculus students are indoctrinated that a discontinuous function is not differentiable. At a later stage, some students are taught that discontinous functions can be differentiated using the (distinct) theories of Sobolev or Schwartz, or Mikusinski.

Formal mathematics being metaphysics, discontinuous functions are differentiable or not, exactly as one pleases (or exactly as it pleases some authoritative Western mathematicians).

Now both definitions of the derivative do not work for the equations of physics (the one because discontinuous functions are not differentiable, and the other because the equations of physics are nonlinear and Schwartz distributions cannot be multiplied or convolved). It is possible to get around this as well, but it requires empirical inputs into mathematics as I have pointed out. (See my paper, “Distributional Matter Tensors in Relativity,” from the days when I still believed in formal mathematics; arxiv.org:0804.1998.)

The point is that the “laws of physics” (i.e. the equations of general relativity) need NOT break down at a singularity (whether infinite matter density or a shock wave).

So, confounding a singularity with a moment of creation, or a beginning of time, as most physicists still seem to do, is just another piece of evidence of how physics is influenced by theology coming down from the Crusading times of Aquinas, who said exactly the same thing in his Summa Theologica (that laws of physics break down at the moment of creation).


Leave a Reply