One of the hot topics in physics, and this one is what I'm really interested in, is the application of QFT to systems with a classical field like gravity as a background. Here's a post by John Baez on quantum corrections to Newton's law of gravity.
V = -Gm[sub:32sgszzr]1[/sub:32sgszzr]m[sub:32sgszzr]2[/sub:32sgszzr]/r { 1 - (3G(m[sub:32sgszzr]1[/sub:32sgszzr]+ m[sub:32sgszzr]2[/sub:32sgszzr])/(rc[sup:32sgszzr]2[/sup:32sgszzr]) - 41G?/(10?r[sup:32sgszzr]2[/sup:32sgszzr]r[sup:32sgszzr]3[/sup:32sgszzr]) + ...}
Notice: the first term is regular Newton's law; the second is the GR correction to Newton's law - which gives correctly the term in the anomalous rate of precession of the perihelion of Mercury's orbit; and the third term gives the 1[sup:32sgszzr]st[/sup:32sgszzr] quantum correction to Newton's law- it contains ?, Planck's reduced constant.
Link: https://plus.google.com/u/0/11766301541 ... 7iC8XYhubZ (https://plus.google.com/u/0/117663015413546257905/posts/87iC8XYhubZ#117663015413546257905/posts/87iC8XYhubZ)
Shouldn't -Gm[sub:3k4vmyuu]1[/sub:3k4vmyuu]m[sub:3k4vmyuu]2[/sub:3k4vmyuu]/r be -G(m[sub:3k4vmyuu]1[/sub:3k4vmyuu]m[sub:3k4vmyuu]2[/sub:3k4vmyuu])/r
Quote from: "Sal1981"Shouldn't -Gm[sub:17n65nbf]1[/sub:17n65nbf]m[sub:17n65nbf]2[/sub:17n65nbf]/r be -G(m[sub:17n65nbf]1[/sub:17n65nbf]m[sub:17n65nbf]2[/sub:17n65nbf])/r
No, :twisted:
Or shouldn't be F=G (m1m2/r^2). If not, explain why not. :-? Solitary
Quote from: "Solitary"Or shouldn't be F=G (m1m2/r^2). If not, explain why not. :-? Solitary
That's the force F, what I have in the OP is the potential, V.
:wink:
A simpler version of the Quantum correction to Newton's law in this paper:
Quantum power correction to Newton's law (//http://arxiv.org/pdf/gr-qc/0207118.pdf)
Quote from: "josephpalazzo"Quote from: "Solitary"Or shouldn't be F=G (m1m2/r^2). If not, explain why not. :-? Solitary
That's the force F, what I have in the OP is the potential, V.
:wink:
OK! :wink: :-D Solitary
A more detail calculation on the op is found here:
PERTURBATIVE QUANTUM GRAVITY AND NEWTON'S LAW ON A FLAT ROBERTSON-WALKER BACKGROUND (//http://arxiv.org/pdf/gr-qc/9801028v1.pdf)
This paper is longer, but gives a more comprehensive conclusion on the state of where we are on this topic. Have a good read.