Would a Quantum Theory of Gravity dispense with the Inverse....

[sderamus]

Square law?

i raise this question because of recently reading some QM, and realizing that for significantly short periods of time, it becomes hard to detect the mathematical patterns. E.g. in the double slit experiment, the standard pattern doesn’t appear after just a few photons. It takes many photons for the pattern to emerge. This is of course due to the statistical nature of the experiment itself. But this got me wondering about a quantum theory of gravity and whether one might have trouble discerning the inverse square law from an object that is very far away except over a long period of time, possibly years even. To what extent can we truly say we are in the gravitational field of a red dwarf on the other side of the galaxy if the gravitational force is mediated by gravitons and we are only intermittently exchanging them?

Of course the field is always there. But if it’s so weak as to be immeasurable then how could we ever determine that it follows an inverse square law?

Thanks!

 

[sophiecentaur]

Of course the field is always there. But if it’s so weak as to be immeasurable then how could we ever determine that it follows an inverse square law?

The linearity of these things has to be assumed. In reality, later experiments have always (?) justified the ISL idea.

 

[dreens]

A quantum theory of gravity would be unlikely to mess with the ISL at long distances. Generally speaking, quantum theories behave classically at long enough length-scales and low enough energy scales. However, it would be much more likely to mess with ISL at short distances.

With a quick google scholar search I pulled up this paper discussing various experiments and what they tell us about the possibility of a short-range modification to the ISL:

A review of short-range gravity experiments in the LHC era

It appears from the abstract that the length range on which gravity could be modified has been confined to smaller than 23 microns.

Typically, quantum theories are expected to introduce a modification to the ISL, or rather to the gravitational potential energy one starts with prior to differentiating to get the ISL, that is of the Yukawa type:
V(r) = (GMm/r)*(1+e^(-r/L))

So that the behavior is normal for r >> L, but becomes modified otherwise. L often has some expected relation to the mass of the graviton or other appropriate gauge boson. The paper I linked has more discussion of all this if you have access.

Cheers,
Dave

 

[Mister T]

General relativity, confirmed by observation, tells us that the inverse square law is an approximation. A relativistic quantum theory of gravity will not change this, but it will tell us additional information about the limits of the validity of the inverse square law.