• [deleted]

  • Post #61

Dear Cristi,

I read your essay yesterday, and apologize once more for not reading it earlier. It is very technical and interesting. I did not check your equations.

Lawrence Crowell and I are also working on GUT's/ TOE's. Lawrence has a 26/27-dimensional TOE framework that looks promising, but needs a lot of work. I have a 12-dimensional geometrical TOE that may be an intermediate simplification of his ideas. Your model does not directly appeal to extra dimensions, but I suspect that your effective Lagrangian implies an unseen Hyperspace with new dimensions/ degrees of freedom.

You threw me off by calling it "Marblewood" because you did not discuss either marble or wooden quantities in detail, but your overall scheme is an effective GUT, and thus "Marble-wood". Peter Van Gaalen and I have had some conversations about marble and wooden quantities on his essay blog site. Using different arguments from mine, Peter also arrived at a multi-dimensional model. I don't know if the difference between marble and wooden is the difference between Abelian vs. non-Abelian Lie algebras, or if it is the difference between quantities with a fundamentally Spacetime origin vs. those with a Hyperspace origin.

Your Principle of Integral Interactions is a very key assumption. Fundamentally, this is the way that my 12-dimensional TOE works - we either have an interaction or not - it makes no sense to have a half-interaction. And although I agree that this is where Quantum Mechanics defies the Classical World and our classical Common Sense, we must be certain that this assumption is QM-compatible.

Equation 13 is an interesting effective GUT, but it seems 'forced' in the sense that if other dimensions exist, if other gauge, scalar or tensor forces exist, then we must enter new effective Lagrangians or curvatures by hand. Being a forced effective GUT, it cannot help predict which parts of the puzzle might be undiscovered.

Still, your approach is interesting, and you might want to read the three above essays.

Good luck with your research!

Ray Munroe

Thank you, Ray.

I called it "marblewood" because I propose an interpretation for the "wooden" part of Einstein's equation. The "marble" part is the curvature part, it is spacetime geometry, which Einstein considered perfect. The "wood" part is the energy tensor, which is very different in quantum field theory, incompatible with the general relativity. Reinterpreting the quantum field theory in terms of classical gauge fields is the way I propose to unite the two.

There may be another sense in which "marble" and "wood" are tried to be unified, by seeing gravity on equal footing with the other forces. I think that gravity is sourced by the other forces, and they are not on equal footing. As an analogy, a vector is not on equal footing with its norm, yet they are unified. Spacetime and internal degrees of freedom should not mix. Therefore, I am not concerned with the curvature of the "internal dimensions". I consider the standard model forces as gauge forces, and the 4-dimensional spacetime is the basis manifold of the gauge bundle of the standard model. Of course, this bundle is itself a manifold, with extra dimensions, and with its own curvature, while the base spacetime is a factor manifold under the action of the gauge group. I consider this only a reformulation which adds nothing to the gauge theoretical approach, that's why I am not concerned with its curvature or how to curl its extra dimensions to make them unobservable.

As for the other approaches, which try to unify the standard model forces, many of them are compatible with mine. I used the standard model, but other GUTs which try to unify the SM forces can work as well, such as the ones based on SU(5), SO(10), Spin(10), etc. The main compatibility requirement for these GUTs with my approach is the non-mixing of the spacetime dimensions with the internal degrees of freedom.

Good luck with your research too!

Cristi Stoica