A Portal Special Presentation- Geometric Unity: A First Look: Difference between revisions

What about the incompatibilities between the Einstein theory of general relativity and the Dirac theory of matter? I was very struck that, if we're going to try to quantize gravity and we associate gravity with the spin-2 field \(g_{\mu \nu}\), we actually have a pretty serious problem, which is if you think about spinors, electrons, quarks, as being waves in a medium, and you think about photons as being waves in a different medium, [the] photon's medium does not depend on the existence of a metric. One-forms are defined whether or not a metric is present yet spinors are not. So if we're going to take the spin-2 \(g_{\mu \nu}\) field to be quantum mechanical, if it blinks out and does whatever the quantum does between observations, in the case of the photon, it is saying that the waves may blink out, but the ocean need not blink out. In the case of the Dirac theory, it is the ocean, the medium, in which the waves live that becomes uncertain itself. So even if you're comfortable with the quantum, to me, this becomes a bridge too far. So the question is how do we liberate the definition? How do we get the metric out from its responsibilities? It's been assigned far too many responsibilities. It is responsible for a volume form, for differential operators, it's responsible for measurement, it's responsible for being a dynamical field, part of the field content of the system.