[c517402]

"untreatable infinities in calculations of particle interactions due to the possibility of point particles coming arbitrarily close to each other." This is actually very misleading. As mentioned in other comments, QED has "infinities in calculations of particle interactions due to the possibility of point particles coming arbitrarily close to each other," but these are treated via renormalization. QED (Quantum ElectroDynamics) is the QFT (Quantum Field Theory) based on Maxwells equations of Electromagnetism. Maxwells equations are linear partial differential equations and when converted to a quantized form, via QFT, the infinities can be dealt with by Renormalization. Einstein's General Relativity equations are non-linear partial differential equations and when converted to a quantized form, via QFT, the infinities cannot be dealt with by Renormalization. The quote makes it sound like classical point particles "coming arbitrarily close" is the problem with quantizing gravity(General Relativity), but the same problem exists in QED and yet QED yields a viable theory through Renormalization. The real difference is that Maxwell's equations are linear and Einstein's equations are non-linear. OTOH, the non-linearities in Einstein's equations do not become important until the particles are very close.

So, IMHO the quote is correct but misleading.