Arnold gave the reference but I'll add some speculative thoughts. The

scalar component of the geometric gauge defines the mass scale and

reciprocally the proper-time scale at each point in space-time.

We can express this in several different ways.

- The standard method is to allow the gravitational constant G to

become a variable.

- One might also consider variation of hbar which relates mass and

proper-time units.

- I also think allowing the cosmological constant to be a variable is

another equivalent way of manifesting this scalar gauge field.

These choices are ways of picking the gauge condition. They are each

ways of fixing the scale of space-time units to some empirical

phenomenon. We specifically like to scale units such that the mass of

elementary particles and the speed of light and Plank's constant are

fixed over space and time. The existance of massive particles and

hence fundamental units of space and time (e.g. the Bohr radius or

Compton wavelength or Plank radius) breaks the scaling gauge symmetry.

But consider this. The Higgs boson is postulated to be a spin-zero

quantum. One might speculate (somewhat wildly) that the Higgs boson

*is* the scalar graviton.

The first difficulty with this proposition is that the Higgs is massive

unlike the scalar gravitational field of Brans-Dicke theory. But the

Higgs mass is due to self interaction in the quantum theory. We may

incorporate into this speculation the explaination that this quantum

theoretical self-generating mass is exactly what condenses the more

general Brans-Dicke theory to the standard Einstein theory (with

cosmological constant).

Such speculation would require a electro-weak-gravitational unified

theory to formulate rigorously and thence to test. That is unless

there are more obvious reasons to reject this notion. I'm not

currently well read enough to see where this speculation would fall

flat immediately. My intuition tells me that mass is the charge

associated with the scalar gauge and so the Higgs mechanism by which

particles aquire mass should relate intimately with scalar gravitation.

But this is only an intuitive guess and I would not be shocked if

someone comes up with (or has already come up with) an obvious reason

these two theorized gauge fields should not be identified.

Hmmmm....

Regards,

James