Could the Gravitational Constant G have a quantum origin?

[Lasand]

TL;DR

Does the Gravitational Constant have a quantum basis.

Could the numerical value of the Gravitational Constant G have a quantum basis?

G=(2pi x h-bar) + h/137

 

[fresh_42]

TL;DR Summary: Does the Gravitational Constant have a quantum basis.

Could the numerical value of the Gravitational Constant G have a quantum basis?

G=(2pi x h-bar) + h/137

No. This equation is a numerical coincidence in SI-units. However, the SI-units on the right differ from those on the left. The equation collapses if you choose other units, e.g., yards instead of meters and pounds instead of kilograms.

 

[mitchell porter]

According to my reading of the old papers, at the start of the 1990s, naive use of string theory was outputting a value of the gravitational constant (in string units) that was wrong by one or two orders of magnitude - which might sound like a lot, but given that these numbers can apriori range across many orders of magnitude, is somewhat promising. Ways to obtain a more accurate value were discussed (e.g. see page 18 of Dienes 1996). Then, in Witten 1996, Witten identified situations in string theory where gravitational and gauge couplings are related, and situations where they aren't. (He was able to do this, as a side effect of the recent understanding of strongly coupled strings, that included the development of M-theory.)

Speaking of string theorists, Lubos Motl posted about this subject on Quora last month.

 

[ohwilleke]

Emergent gravity seeks to explain gravity as non-fundamental, and take an approach very different than the papers Mitchell Porter references.

It wouldn't produce anything resembling the formula in the OP.

It also doesn't really derive Newton's constant, so much as it does shift it to Planck's length (which is a function of several physical constants chosen to combine in the dimension of length including Newton's constant and Planck's constant), however.

By analogy, in the Standard Model, fundamental charged fermion masses are no longer fundamental, but they are just replaced with Higgs field Yukawa's which are experimentally determined and can't be derived.

 

[arivero]

If it were possible to derive G out of h and c, should we start discussing with one is the derived and which ones are the two fundamentals?

As we stand today, with a relationship between four constants,

we consider that Planck Length is the derived one. But it is fun to consider eg that we can do path integral in terms of Planck Length, Newton Constant and Lightspeed, and forget about hbar.

 

[ohwilleke]

If it were possible to derive G out of h and c, should we start discussing with one is the derived and which ones are the two fundamentals?

As we stand today, with a relationship between four constants,
View attachment 354329
we consider that Planck Length is the derived one. But it is fun to consider eg that we can do path integral in terms of Planck Length, Newton Constant and Lightspeed, and forget about hbar.

There are also several ways to express Newton's constant in dimensionless form, like the other three coupling constants.