In the Mind's Eye

Steven Weinberg, whom I had the privilege to know when I was a graduate student, is an atheist. He believes the vast weight of evidence gathered from 300 years of science since Newton points to the inescapable conclusion that God, as Jews, Christians, Muslims, or anyone else might conceive of God, does not exist.

Prof. Weinberg shares the 1979 Nobel Prize in physics with Abdus Salaam and Sheldon Glashow for their key contributions to what has become the "Standard Model" of elementary particle theory and cosmology, namely their unification of the electromagnetic and weak-nuclear forces. As such, Weinberg is eminently qualified to write the three-volume graduate level text, The Quantum Theory of Fields. As if this were not enough, he writes with a grace and clarity that make it a relative delight to read what, in lesser hands, can be a tedious subject. It is a "must read," if you are a theoretical physicist. Short of that, however, there is still a revelation in it that I must tell you about.

To begin, Weinberg admits that we believe that Quantum Field Theory (QFT) is only an approximation to a more exact theory that may grow out of current attempts at String Theory. Therefore, he emphasizes those aspects of QFT that he thinks will stand the test of time, and will continue to be features of a more advanced theory. The most fundamental of those aspects is symmetry — the way the properties of a particle stay the same (or not) under certain transformations of space-time. These transformations are rotations (spinning around), translations (standing at different places) and boosts (which are shifts to a frame of reference that is moving at a high, but constant, velocity). Together, these transformations are called the inhomogeneous Lorentz group.

Now there are a number of mathematical ways to represent the Lorentz group. Any set of symbols and rules to manipulate them will do, provided that the symbols and rules behave the same way the Lorentz group does. Those representations, that cannot be decomposed into subgroups that also represent the Lorentz group, are called irreducible representations of the Lorentz group.

And now the point of all this mumbo-jumbo: Weinberg writes on page 63 of Volume I, "It is natural to identify the states of a specific particle type with the components of a representation of the inhomogeneous Lorentz group which is irreducible...."

I'm stunned by that statement. What it means is that the irreducible representations of the basic symmetries of our universe give rise to the possibilities of all the sub-atomic particles, and thus to all the matter, in the universe. This is the closest thing you are ever likely to see to a Platonic Form in actual existence and effect.

In case you skipped that part of the college experience, the ancient Greek philosopher, Plato, a student of Socrates, believed that things existed in reality only because their ideal, perfect Forms existed in the realm of the mind. For example, a circle could be drawn on the ground only because of the existence of the ideal Form of a circle in the mind.

Now we know that Platonic Forms are hogwash, because our minds are not powerful enough to make anything exist, just by thinking. One can think very clearly of things that do not and cannot exist, and even draw pictures of them, like the art of M. C. Escher. And yet, there it is — the irreducible representations of the inhomogeneous Lorentz group are the Forms of elementary particles, and thus, of all matter that exists.

To me, it begs the question: In whose mind can the irreducible representations of the inhomogeneous Lorentz group give rise to reality? This is probably as close as theoretical physics has ever come to postulating the existence of God, and we have been brought here by an atheist.

Who knows? God may have planned it that way, just for the irony.

I'd rather listen to Tom Lehrer's "Lobachevsky."