Abstract:

Quantum field theory on curved spacetime (QFT-CST) postulates that it makes sense in certain regimes to treat the geometry of spacetime as classical while treating the matter that geometry couples with as quantum fields.  The form of that coupling is defined by the semi-classical Einstein field equation (SCEFE), equating a classical geometrical structure, the Einstein tensor, with the expectation value of the stress-energy tensor (considered as a quantum operator).  There are, however, many serious, unresolved technical and conceptual problems with this framework about even such basic issues as ist physical consistency.  In this talk, I plan to canvass those problems and briefly discuss how serious they are, and then conclude by treating three of them in more detail.  1. Some straightforward attempts to draw physically significant conclusions from the union of quantum field theory and general relativity fail miserably (the computation of the cosmological constant from vacuum fluctuations), so why should we trust these methods in their prediction of other phenomena such as Hawking radiation?  2. Given the form of the semi-classical Einstein field equation, classical geometry couples with quantum effects in the Riemann tensor associated only with Ricci but not Weyl curvature: can one even consistently define a Riemann tensor that is ``part quantum, part classical''?  3. Is there a compelling justification for the form of the semi-classical Einstein field equation, in particular why classical geometry should couple with the *expectation value* of the quantum stress-energy tensor operator?