In quantum mechanics, the vacuum of space is not a vacuum; rather, it is field with virtual particles, such as the graviton. Light passing through this field of virtual particles is refracted, just as it is when passing through water or any medium.
The graviton, being the essence of gravitational force, would interact with (or slow down) those particles with greater gravitational potential. With mass directly proportional to energy, as expressed in e=mc2, photons of higher energy have greater gravitational potential than lower-energy photons -- as if they "weigh" more.
The highest-energy photons would therefore travel through space more slowly than lower-energy photons. (This does not violate the constancy of the speed of light, for light travels at the same speed only in an absolute vacuum.) To detect the very slight difference in photon speed, one needs an extremely distant source emitting extremely high-energy photons: that is, the gamma ray burst.
sol2 said:I was looking for some method that would help me discern the nature of this quantum geometry, yet it has revealled a non communitive geometry for thinking, so this begins a new road.
It must be recognized tha LQG does not recognize the graviton, yet strings does. So looking to SR I see where LQG is basing its bets?
I hope this falls in line with your post.
humanino said:I can't help much. I want to say that I picture Connes' work as very much more fundamental than anything else that has been done for decades.
(...)
Unfortunately : I do understand some of string theories or LQG, and I do have Connes' book, and began it. But I preferred to postpone this reading, because it is way more mathematical than everything else, and will require me full-time attention.
Alejandro said:During my travel, I have remembered a related point: Dixmier trace has
a kind of scale invariance; this was remarked in the French version of the
book of Alain Connes, but de-emphatised in the english one. I will try to
think along this line.
Strings in non-commutative qft are one-dimensional objects that behave as fundamental building blocks of the theory. They are extended objects, similar to particles in regular qft, but with a finite length instead of a point-like structure. These strings are thought to be responsible for the interactions between particles in the theory.
Unlike particles in regular qft, strings in non-commutative qft do not have a definite position in space and time. This is because the coordinates in non-commutative space are non-commutative, meaning they do not commute with each other. As a result, the concept of a point in space becomes fuzzy and strings are needed to describe the interactions between particles.
Non-commutativity is a fundamental property of space in non-commutative qft. It arises from the uncertainty principle, where the position and momentum of a particle cannot be known simultaneously with arbitrary precision. This leads to a non-commutative relation between the coordinates in space, which has important implications for the behavior of particles and strings in the theory.
At present, there is no direct experimental evidence for the existence of strings in non-commutative qft. However, some theoretical models predict that strings may have observable effects at very high energies, such as in particle accelerators, or in the early universe. More research is needed to verify these predictions and potentially observe strings in experiments.
Non-commutative qft is a framework for describing the behavior of particles and strings in a non-commutative space. It is closely related to string theory, which is a theory that attempts to unify all of the fundamental forces of nature, including gravity. Some string theories also incorporate non-commutativity, making them a promising avenue for exploring the connections between these two theories.