Dear Rajan,

   I didn't read your papers but your question suggest me that you use quite badly the basic concepts of general relativity and quantum field theory. The Ricci tensor is a contraction of the Riemann tensor which is zero for flat metric as usually is used in Dirac equations and obviously, within the context of general relativity and using the equivalence principle the inertial mass must be zero too. If you find that this happens perhaps you could try to understand where is your mistake.

Dear Daniel,

Although inertial mass may be zero at zero point, gradient tensor won't be zero, as suggested by articles on zero point field theory. In my question, I amn't implying about inertial mass. You are generally correct about the Ricci tensor being a contraction of the Riemann tensor which for a flat metric is zero.

I'm sorry about not stating these explicitly in my question. Hope you will agree about the main theme about nonzero aspects of zero point energy and the zero point field, esp. gradient nature of the field. Of course, the rotational tensor will be zero at zero point, considering zero value of the inertial mass.  Hence please appreciate my point and not that I am trying to use basic concepts of general theory and quantum field any other way than being all consistent with these fundamentals.

Thank you with your comments. Please clarify with any further details to get all these ironed out.

  If by inertia tensor you mean moment of inertia tensor, then Ricci tensor or Einstein's tensor haven't any relation with it. These tensors are only related with translations and never with rotations.

Thank you.

Daniel

The relations between the Ricci tensor, Einstein tensor, translations and rotations are very subtle. I would suggest that it is too simplistic to state that “These tensors are only related with translations and never with rotations”. Inertia comes into this in a non-trivial way too.

Inertial effects appear when one takes measurements in a non-holonomic frame. This is not allowed in Newtonian gravitational theory – in that, measurements are always made in inertial frames. Einstein considered non-inertial frames of reference in his development of General Relativity. However, it is based on the metric for the chosen coordinate system – a curvilinear system if the spacetime is curved. The coordinate basis for this system at a given point can be related to any chosen frame basis at that point using a general linear transformation. This can be decomposed into a pseudo-orthogonal factor (a “spacetime rotation”) and a non-pseudo-orthogonal factor. The pseudo-orthogonal factor relates a holonomic frame basis to the frame basis (which in general is non- holonomic). However, this factor does not contribute to the metric – that is determined entirely by the other factor.

The equivalence principle in GR means that one cannot truly separate inertial and gravitational effects in that framework. To do so, one needs to use the Teleparallel Equivalent of General Relativity (TEGR). This utilises the Weitzenböck connection rather than the Levi-Civita connection of GR. The Weitzenböck connection is based on the transformation matrix relating the coordinate basis to the frame basis – including the spacetime rotation factor.

The Ricci and Einstein tensors can be defined either in terms of the Levi-Civita connection or in terms of the Weitzenböck connection – thus I would contend that it is too simplistic to state that they have nothing to do with rotations.

More detail on all of this, as well as the relation between frame transformations in TEGR and translations, can be found in a combination of the notes I have just published on this site:

http://bit.ly/2DQstl0

and the following articles:

https://www.researchgate.net/publication/23503583_Inertia_and_gravitation_in_teleparallel_gravity

https://www.researchgate.net/publication/231513385_Lorentz_Connections_and_Gravitation.

https://www.researchgate.net/publication/1968868_Torsion_as_Alternative_to_Curvature_in_the_Description_of_Gravitation

https://arxiv.org/pdf/1303.3897v1.pdf

as well as in my recent post here:

https://www.researchgate.net/post/Is_the_non_locality_of_the_gravitational_energy_a_serious_problem_for_General_Relativity_GRT

(the one which starts with Christmas wishes).

Rajan

I’m not sure that I’ll be able to give you a very comprehensive answer to your question. This is partly because I’m quite rusty on quantum field theory, having concentrated on geometric field theories and their symmetries in recent years. It’s also because it seems to relate to quantum field theory in curved spacetime, which is not something I’ve really got to grips with, and from my limited experience I suspect is a bit of a niche area with relatively few experts. If it goes beyond this into the actual quantisation of gravity, then nobody will have definite answers for you, as there is no quantum field theory of gravity in four dimensions which has yet gained widespread acceptance.

However, I might be able to point you towards some useful resources.

If I’m to do this, I’d like a clearer understanding of the terms you use. Firstly, please explain “at zero point”. If the words “zero point energy” come up, I understand by that the energy of the quantum vacuum – quantum fluctuations around the true vacuum with no on-shell particles. But I’m not clear about what you mean by “at zero point” in this context.

Similarly, if you could clarify what you mean by “inertia” or “the inertia tensor”, that would be helpful.

By the way, I'm intending to modified my notes cited above to become an early section of the first paper I'll be submitting for publication in nearly a decade. Any challenge on their contents or constructive criticism is therefore welcome.

Thank you with your explanations. Term "zero point" refers to zero point field emanation per my working papers @RESEARCHGATE. Like you have mentioned there are lot of subtle aspects associating to that. Presently my mathematical analysis extends beyond to new metric mathematics, that will be able to answer questions regarding all these. I am hoping to have international conference where presentations & discussions about these can proceed. Essentially I am quantum relativistic scientist presently. At zero point a vacuum "micro_white_hole" states seem to happen linking to "micro_black_hole" states that form eternal circuity feeding one another to generate Higgs mechanism aether vacuum field, according to my mathematical metric physics quantum relativity analyses. One of the critical proofs will be detection of micro_black_hole @LHC, if possible.

Hence this subject is quite complex. However, the question of inertia and/or inertia tensor will refer to Helmholtz mathematical theorem fields, that are perhaps mathematical equivalent of principle of least action in physics - they are prime principle on which everything else are derivable. Of course specifically the inertia tensor will refer to quasi- static condition at zero point where rotational field & torque are zero, however nonzero gradient field manifesting as an inertial tensor can occur. In order words, inertia not a zero and that may be why zero point energy exists. Proof of all that are a project of the future leading to grand unified theory of everything.