Thursday, July 28, 2005

Epistle and Response

Lubos Motl has both exceeded and confounded my expectations by producing an extensive and (mostly) polite response to Lee Smolin’s article discussed below. His response is partly positive in that he seems to accept that background independence might be a good thing, but he also has plenty of objections to the “relativistic” program of Leibniz and Smolin. Unfortunately, his response demonstrates his tendency to create and demolish strawmen instead of the real arguements.

First a point of philosophy: He doesn’t like Leibniz’s principle of “the identity of the indiscernible.”

On the other hand, Leibniz's "identity of the indiscernible" - which says that the objects with the same properties must be identified - is technically wrong in all theories we've been using in the last 300 years. If two objects/states A,B are related by a global symmetry transformation, they have the same properties but they must still be considered as two distinct objects (configurations or states in the Hilbert space) - two objects that are not equal (=) - otherwise the mathematics would break down.
I have very little idea what Lubos is talking about here, but it’s not recognizable as Leibniz’s principle. In fact, a central pillar of quantum statistics, and a profound difference from the classical case, is the idea that states that differ only by the interchange of otherwise identical particles are in fact the same state. Smolin doesn’t use the phrase “global symmetry” in his paper and I don’t see how it’s relevant here.

Also, adds Prof. Motl:
Obviously, not all physicists share my viewpoint that the verifiable truth is more important than the philosophical prejudices.

I think most physicists do share that viewpoint, and the viewpoint that philosophical ideas are heuristic guides to physics, not gold standards against which we can test our theories. Nature has too often confounded our sincerest philosophical prejudices.

The Cartesian coordinates, for example, look more fundamental than the angle between a bucket, Mercury, and a Mercedes, so why shouldn't we use them?

The answer Lubos, as you know very well, is that we should use them when they work, for example on a sheet of paper, but not when they don’t, as on the surface of the Earth, say, or in curved spacetime.

Mach’s Principle

Mach’s principle is a major battleground for our protagonists. Smolin notes that General Relativity is Machian only if the spatial topology is compact, that is, finite but unbounded. Lubos ignores this distinction and launches a rambling attack claiming GR is not Machian.
But eventually, General Relativity had killed Mach's principle.

Mach's principle has not only been challenged: it became one of the weird prejudices that often leads you to wrong conclusions. Mach's principle was the main reason why so many people in the 1960s thought that the gravitational waves could not exist in GR; they thought that all such solutions always had to be pure gauge which means that they could be transformed into flat space by a coordinate transformation.
This is an example of the unfortunately frequent and invalid rhetorical technique of our author. The fact that some misguided persons misinterpreted GR and Mach’s principle to come to a false conclusion is not a valid argument against either. The real argument against Mach’s principle is that it doesn’t work when we have boundary conditions – of course we don’t know if this is true of the actual universe or not.
An attempt to revive Mach's principle means to argue that the gravitational waves do not exist.

This is simply not true.

Motl seems to be under the impression that Smolin is claiming that diffeomorphism invariance is not a gauge symmetry. Motl: “It is definitely a misunderstanding to assign the diffeomorphism invariance with a philosophically deeper role than the Yang-Mills symmetry has, for example. Both of them are local symmetries - redundancies of the description.”

In fact, Smolin explicitly recognizes this fact, and it this very redundancy of description that leads him to seek background independent, in this case gauge invariant quantization.

That's all I have time or energy for right now, but maybe more later if I have the time.