Re: Jack Sarfatti bio

On May 14, 8:31 pm, markw...@xxxxxxxxx wrote:
You might be heading in the same direction, but from an entirely
different starting point -- but one that's got problems. For one, with
the I's in the definition of the tetrad, you're still trying to have
it both ways and inject a semblance of translation invariance in
curved spacetimes. There is none.

Rather, you should be looking at the more general notion of affine
spaces and affine connections. This is where you begin to find a
natural correspondence.

When you start bringing in the M matrix and the various other
constructs associated with it (your novel contributions), ultimately
what you're doing or what you're going to end up doing is landing in
the same spot that Sardanashvily's already gotten to. That is, you
started from a somewhat problematic point of departure, took a turn on
your path, and ended up landing right in the middle of a confluence
with the gauge gravitation idea, which already has a perfectly sound
starting point. Hence, the need to systematically compare notes.

One of the major elements in Sardanashvily's treatment of mechanics
(which comes straight out of the mathematical community) is the more
general notion of a "connection". A connection is not just for gauge
theory, but is a more general object that lives on a jet bundle.
Moreover, when the latter is related to an already-existing gauge-
theoretic connection, then it has a decomposition into it plus a
"soldering form". Ultimately, the tetrads come out of soldering forms
for affine connections. At least, that's my understanding of it.

Sardanashvily's goldstone phases come about through the breaking of
the general frame bundle's GL(4) symmetry group to the SL(2,C) group
associated with fermions' local frames. That's enough to give you the
spin coefficients -- but not the tetrad.

The dimensions of GL(4) and SL(2,C) are 16 and 6. The symmetry
breaking entails vacuum sectors associated with the quotient group
GL(4)/SL(2,C) (10 dimensions, isomorphic to S_3 x R^7, in fact). This
is where the tetrad lives. They're the Goldstone phases of the broken
symmetry brought about by the fermions' frames.

Sardanashvily's papers and books has a large number of Hehl
references, though I'm not entirely sure what the relation of the two
is. He also seems to be caught up in the same general "clique" that I
think may be centered on the 1979 Lecture Notes in Physics 107. It's
probably out of there that the whole "covariant Hamiltonian" and
"polysymplectic" trends begun.

The more notable feature of this extra element, that should
particularly interest you, is that it does not require the 3+1
decomposition of spacetime! That is, it's not only fully GR-
compatible, but provides a natural starting point for anyone who wants
to further study all matters related to achronal spacetimes, or
spacetimes with causal anomalies (e.g. closed timelike curves). The
"covariant Hamiltonian" approach is general enough to accommodate
this.

Sardanashvily stays within the more rigid confines of globally
hyperbolic spacetimes, however (in part, because there's already a
well-known representation theorem that relates more general spacetimes
to these).

You've got a PhD in Physics. However, the subtleties that are brought
out by the jet bundle formalism and all matters related requires a
deeper probing into the Mathematical issues; and this is probably
where the greater focus may need to lie for a while. This is a
language problem that's endemic to Math and Physics and it's serving
as an obstacle to real progress in Physics.

there may be language difficulties
but it seems more and more are overcoming them every day

i would even say there are not two languages separated here
but at least 12 and likely many more

bundle field theory is not excruciatingly unreachable
many can attain fluency by their late twenties
and understand the translation
of symmetry breaking higgs production
in quotient bundles of the principle
over the symmetries broken

but just because many could understand
does not mean many do understand
because there are many other interesting things in this world

there are many approaches to quantum gravity
that explore higgs-like mechanisms

the higgs mechanism has always been intimate
to explanations of matter and mass
and it has been a regular source of quantum gravity speculation

h dehnen, h frommert, and associates
showed that any excited higgs field
can be viewed as mediating a scalar gravitational interaction
but their mechanism gave a massive (yukawa) form

v alan kostelecky and others have interesting papers
on the spontaneous breaking of lorentz and cpt symmetries
which are also generated by a typical gamma matrix term
that can be found in extended standard models and string theory

in particular
lorentz violation may provide a mechanism
for a massless graviton
and naturally seem to describe some of the features
of dark matter and dark energy
and the cosmological constant

similarly
gasperini, hehl, and sardanashvily
have shown the emergence of various gravities
with actions coupling to
torsion
curvature
and other connection-derived terms

all of these authors approach these ideas
from slightly different geometric or interactionist/group formalisms
often several different ones per author

scalar
linear and quadratic poincare
metric affine
....

but higgs mechanisms are not the only "natural" approach

similar to the reason for investigating higgs gravity
the zeropoint field has been interpreted as generating inertia
and there have been a few attempts at
zeropoint effects that generate gravity

additionally
there is the holographic programme
seeking to explain the surface terms in the hilbert action
in terms of a fundamental description of information

there are also a number of purely geometric approaches
when one alters the geometry sufficiently
as is found in the torsion theories
or extensions of the work by obukhov and others
exploring the relationships between gravity and spin
( which have influence the spin-network programme
and other more mainstream approaches )

there is a desire to make gravity emergent

the whole point is of course
to avoid the divergences and ontological difficulties
of direct quantisation of the metric field

barcelo, visser, and liberati
have proven a very general result
that linearising a classical scalar field
( or indeed any hyperbolic second-order equation )
can always be interpreted as a lorentzian geometry
affecting particle propagation as gravity

so these emergence results are very general

((((((..)))))))

this background of working theories
helps give some placement to sarfatti's approach

now
he would have more insight into his approach
than any reconstruction that could be attempted
but it is always instructive to try

his expositions have suggested that a primary motivation is
geometrical
he has been closely following shipov's work on torsion
and exploring its relation to various quantisation programmes
and the geometry is certainly central to his mathematical formalism

but there are other currents present

he has also pointed a number of times over the recent years
to distinctions between the higgs mechanicsm
and zero point mechanisms of inertia

in particular he has stressed that
differences of fundamental scales in the theories
the equivalence principle
the nonlocal nature of gravity at asymptotic infinity
and the holographic principle
strongly suggest the zeropoint mechanism is ruled out

interestingly
he has taken some of the mathematical insights
of what are unacceptable features of these
directly into his current working form
explicitly avoiding those issues through a foundation in holography

and of course
as is common with jack
he has many other directions he is attempting to reinterpret
inside the kernel of his new formalism

much still appears in flux
with some crystallisations and subsequent return to fluidity
as facts and derivations drive new speculations

so i wouldn't be too quick to place sarfatti in sardanashvily's camp
just as i wouldn't be too quick to put sarfatti in 't hooft's camp

they may share progenitors
( as we all do )
but they have their own unique directions

i also wouldn't be too quick to any given geometric intuition
is the more "correct" approach
as humanity has repeatedly been shown wrong here
and geometry is one of the big underspecifications
in modern speculation

our universe could operate on pointless geometries
for all we know

well anyways
it looks like my lunchtime is almost over so i'll cut this short
but i just wanted to make one last observation

despite its now obvious ramifications
in hypergeometric systems and general algebraic geometry
it took candelas, de la ossa, green, and parkes
coming from a physics background
to discover mirror symmetry

i think much mathematics comes from such physical intuitions
( despite some recent threads claiming more damage than good )

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar

.

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