BurtJordaan » October 19th, 2019, 7:18 am wrote:socrat44 » 19 Oct 2019, 12:30 wrote: Newton's gravity ( inverse square law): 1/r^2 , M/r^2, Mass-zero: r=0, F=0

Can massless-graviton have energy ?

Yes, just like a massless photon carries energy, E=hf, the

Planck-Einstein relation.

But:

https://en.wikipedia.org/wiki/Graviton wrote:While gravitons are presumed to be massless, they would still carry energy, as does any other quantum particle. Photon energy and gluon energy are also carried by massless particles. It is unclear which variables might determine graviton energy, the amount of energy carried by a single graviton.

Graviton

There is no complete quantum field theory of gravitons . . .

the graviton is a massless state of a fundamental string. . . .

If it exists, the graviton is expected to be massless because

the gravitational force is very long range and appears to propagate

at the speed of light.

Additionally, it can be shown that any massless spin-2 field would give rise to a force indistinguishable from gravitation, because a massless spin-2 field would couple to the stress–energy tensor in the same way that gravitational interactions do. This result suggests that, if a massless spin-2 particle is discovered, it must be the graviton.

Theory

In the classical limit, a successful theory of gravitons would reduce to general relativity, which itself reduces to Newton's law of gravitation in the weak-field limit.

Gravitons in speculative theories

String theory predicts the existence of gravitons and their well-defined interactions. A graviton in perturbative string theory is a closed string in a very particular low-energy vibrational state. The scattering of gravitons in string theory can also be computed from the correlation functions in conformal field theory, as dictated by the AdS/CFT correspondence, or from matrix theory.[citation needed]

A feature of gravitons in string theory is that, as closed strings without endpoints, they would not be bound to branes and could move freely between them. If we live on a brane (as hypothesized by brane theories), this "leakage" of gravitons from the brane into higher-dimensional space could explain why gravitation is such a weak force, and gravitons from other branes adjacent to our own could provide a potential explanation for dark matter. However, if gravitons were to move completely freely between branes, this would dilute gravity too much, causing a violation of Newton's inverse-square law. To combat this, Lisa Randall found that a three-brane (such as ours) would have a gravitational pull of its own, preventing gravitons from drifting freely, possibly resulting in the diluted gravity we observe, while roughly maintaining Newton's inverse square law.[12] See brane cosmology.

A theory by Ahmed Farag Ali and Saurya Das adds quantum mechanical corrections (using Bohm trajectories) to general relativistic geodesics. If gravitons are given a small but non-zero mass, it could explain the cosmological constant without need for dark energy and solve the smallness problem.[13] The theory received an Honorable Mention in the 2014 Essay Competition of the Gravity Research Foundation for explaining the smallness of cosmological constant.[14] Also the theory received an Honorable Mention in the 2015 Essay Competition of the Gravity Research Foundation for naturally explaining the observed large-scale homogeneity and isotropy of the universe due to the proposed quantum corrections.

Difficulties and outstanding issues

Most theories containing gravitons suffer from severe problems.

Attempts to extend the Standard Model or other quantum field theories

by adding gravitons run into serious theoretical difficulties at energies close to or above the Planck scale.

This is because of infinities arising due to quantum effects; technically, gravitation is not renormalizable.

Since classical general relativity and quantum mechanics seem to be

incompatible at such energies, from a theoretical point of view,

this situation is not tenable.

One possible solution is to replace particles with strings.

String theories are quantum theories of gravity in the sense that they

reduce to classical general relativity plus field theory at low energies,

but are fully quantum mechanical, contain a graviton, and are thought

to be mathematically consistent.

https://en.wikipedia.org/wiki/Graviton