"As far as the laws of mathematics refer to reality, they are not
certain, as far as they are certain, they do not refer to reality." Einstein

Waldyr is a fine mathematician and scholar no doubt. The problem is that
his critiques are very hard to read for the average theoretical
physicist who uses math tricks more like the Alchymsts used chemistry.

Waldyr swats flies with sledgehammers.

I have a simple idea for example. It is, using Cartan's ideas

Local curved space-time's metric tetrad field e^a is analogous to the
superfluid velocity field. In an over-simplified toy model with only one
Goldstone phase Theta (not really enough but it shows the essential point)

e^a = eu^adx^u

e = e^a&a

u is in curved base space

a is in tangent fiber space

e = I + B

B = 0 globally means zero curvature

B ~ (hG/c^3)^1/2d(Theta)

The analogy here is to

v = (h/m)d(theta) in superfluid helium

This is a PHYSICAL IDEA! - analogy to Bohm's pilot wave guidance constraint.

D = d + W/\

W = spin connection

T = De = 0 zero torsion 2-form

Therefore,

dB^a + W^ab/\(I^a + B^a) = 0

since dI^a = 0

Therefore, in this zero torsion field limit the 6 spin connection
1-forms W^ab are constrained by the 4 curved tetrad 1-forms B^a.

R = DW = curvature 2-form

Bianchi identities

DR = 0

OK here I am on shaky ground - correct it if you can

Problem: How to write Einstein's source field equation in this Cartan
notation?

Note that

R^a^b = - R^b^a

R = R^a^buvdx^u/\dx^v&a&b

Ruv = R^a^buv&a&b = Rvu

Guv = Ruv - (1/2)Rguv


On Jul 7, 2006, at 12:20 PM, Jack Sarfatti wrote:

There is good mathematics that is not relevant to physics - M theory may
be an example - too soon to tell.

Key physical ideas are largely independent of mathematical "proofs".

Take key ideas like

1. The speed of light in vacuum is the highest possible speed of objects.

2. Gravity is the curvature of 4D space-time.

3. Mass is equivalent to energy.

4. Energy is nonlocal in curved space-time.

6. Energy is quantized.

7. Circulation is quantized in a superfluid.

8. Magnetic flux is quantized in Type II superconductors.

9. Dark energy is an anti-gravity repulsive cosmic field.

10. gravity "g-force" is locally equivalent to the inertial force of an
accelerating local non-inertial frame.

Let's start with those. All of the above have physical meaning
independent of math formalisms in terms of operational procedures (PW
Bridgman). Also there do exist formalisms of different degrees of rigor
that correspond to them. Indeed, several different formalism can
describe the same physical statement.

e.g. 2

I. Einstein's orginal tensors

II Cartan's tetrads

III Cartan's exterior differential forms

Of course there are relationships, formal transformations among the
different formalisms.


On Jul 7, 2006, at 11:41 AM, Arkadiusz Jadczyk wrote:


Waldyr is a mathematician with
different standards of "rigor" than ALL theoretical physicists.

That is incorrect.

ark