What's so hard about Quantum Gravity ?

[Widdekind]

According to QM, a particle of mass m is associated w/ a spatially extended (normalized) Wave Function [math]\psi(\vec{r})[/math]. At any given point in space, that WF corresponds to a Mass Density of [math]m \; \psi^{*}(\vec{r}) \; \psi(\vec{r})[/math]; an Energy Density of [math]\psi^{*}(\vec{r}) \; \hat{E} \psi(\vec{r})[/math] (where [math]\hat{E} = i \hbar \frac{\partial}{\partial t}[/math] is the Energy Operator); and a Momentum Density of [math]\psi^{*}(\vec{r}) \; \vec{p} \psi(\vec{r})[/math] (where [math]\vec{p} = - i \hbar \vec{\nabla}[/math] is the Momentum Operator).

 

These well-defined spatial quantities, all of real values, could be plugged straight into the Stress-Energy Tensor of GR. Likewise, the Metric (e.g. Schwarzschild Metric) could be used to adjust the time & space derivatives in those above Operators.

 

Also, given GR's Mass-Energy Equivalence, how come the Rest Energy doesn't appear as an Operator ([math]m \; c^{2} \bullet[/math]) in the Hamiltonian Operator in QM ??

Edited September 19, 2009 by Widdekind