The old homepage address has ceased to work again. As I have told, I learned too late that the web hotel owner is a criminal. It is quite possible that he receives "encouragement" from some finnish academic people who have done during these 35 years all they can to silence me. Thinking in a novel way in Finland is really dangerous activity! It turned out impossible to get any contact with this fellow to get the right to forward the visitors from the old address to the new one (which by the way differs from the old one only by replacement of ".com" with ".fi").

I am sorry for inconvenience. The situation should change in January.

## 4 comments:

Dear Matti,

About equivalence principle in TGD:

I try to write what I understand, maybe wrong and ask some questions:

In TGD super-symplectic algebra acting at imbedding space and Super Kac-Moody algebra acting on light-like 3-surfaces. The Lagrangian with respect to the corresponding symmetries gives us inertial and gravitaional 4-momentum respectively. You assign the inertial 4-momentum to Imbedding space and the gravitaional 4-momentum to the light like 3-surfaces in it.

At quantum Level, there are infinite 4-momentums for both. Hence for simplification (also it is needed because we see the world classical ;-)) lets go to classical level. TGD say there is one inertial 4-momentum associated with Imbedding space and one gravitational 4-momentum associated with the 3-surface.

But we assign inertial 4-momentum to an object(3-surface) in classical mechanic with respect to the symmetry of translation. It seems for me that some transformation of the 3-surface that act on CM degrees of freedom of it in Minkowskian space-time must gives the inertial 4-momentum.

What is my misunderstanding?

Your interpretation of gravitational mass to something associated with internal degrees of freedom of 3-surface in Imbedding space looks interesting. I try to understand it gradually too)

What is physical intuition of EP in TGD for other forces? I try to say what does it seems for me for a theory that generalized EP for electromagnetic force:

There must be two charges in this picture!: inertial charge and ordinary electric charge.

Ordinary electric charge appears in Coulomb's law. What is inertial Charge? But just inertial mass is body's resistance to being accelerated by every force containing electromagnetic force.

May be you say in TGD EP is only for color quantum number and gravitation. This means there is also inertial nuclear strong charge in TGD?

I wait intensively for your answers ;-).

Continuation….

B. Consider classical situation

1. Kahler action gives rise to (only) inertial four-momentum as classical conserved charges assignable to translations by Noether's theorem. Classical ( four-momentum is always assignable to 3-surface and its components correspond to translations of M^4 and are in one-one correspondence with Minkowski coordinates. It can be regarded as M^4 vector and thus also imbedding space vector.

2. Can one identify gravitational momentum classically or does it correspond to super-conformal momentum as very cautiously suggested above? Or do classical field equations for preferred extremals imply that the inertial four momentum density defined by Kahler action is expressible as a superposition of terms corresponding to Einstein tensor and cosmological term or its generalization.

a) The condition that the energy momentum tensor associated with Kahler action has vanishing covariant divergence is very natural and satisfied for known preferred extremals. This condition is very powerful and is satisfied if Einstein equations with cosmological term are satisfied. The vanishing of trace of Kahler energy momentum tensor implies is that curvature scalar is constant and expressible in terms of cosmological constant. If Lambda vanishes, curvature scalar vanishes.

b) A more general possibility is that cosmological term is replaced by a combination of several projection operators to space-time surface instead of metric alone. Coefficients could even depend on position but satisfying consistency conditions guaranteeing that the energy momentum tensor is divergencenceless.

Concerning your comment about the possibility of inertial em charge. I am not sure about whether this makes sense: the reason is that electroweak charges do not correspond to isometries of imbedding space. One can assign em charge with Super-conformal representations ("gravitational em charge"?). There is however a complete analogy between color charges and four-momenta inspires the question whether one can assign to color charges also gravitational variants. Generalization of Einstein's equations would indeed imply this kind of correspondence for preferred extremals.

Dear Matti,

So Thanks. there is no problem if you see there is one comment of you hear in the blog because I received both of your comments in my mail.

As you said too "Classical four-momentum is always assignable to 3-surface and its components correspond to translations of M^4 "

But why in other hand Classical four-momentum(inertial four-momentum) is correspond to symplectic transformations of the whole of deltaM4*CP2 and not just on the 3-surface in M4(or preciser just on the 3-surface in deltaM4*CP2)?

Dear Hamed,

I have explained this in blog posting. Quantum classical correspondence is the principle. The conserved Noetherian four-momentum, which is classical *should be equal* to quantal four-momentum popping up automatically in the representations of super-conformal algebra.

I do not know whether preferred extremal property (Bohr orbitology) forced by general coordinate invariance implies this or not!

There is second problem: should I have both inertial and gravitational momentum at quantum and classical level? Or should classical Noether momentum be identified as inertial momentum and quantal four-momentum as gravitational: this would reduce EP to quantum classical correspondence.

This would simplify the situation dramatically but p-adic mass calculations might exclude this interpretation. Also the possibility of coset representations and analogs of Einstein's equations suggest that q-classical correspondence and EP are independent principles.

Concerning your question. Symplectic transformations act at the level of imbedding space just as Poincare and colour symmetries. This makes it natural to assign inertial momentum to them. Kac-Moody algebra acts at the level of light-like 3-surfaces and therefore gravitational moment is naturally assigned to it.

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