on new AJL paper, vsusy and causality

Thomas Larsson wrote:

"In the AJL model, the gauge is already fixed;they formulate the
action in terms of diff-invariant edge lengths rather than the
metric, there is a privileged time direction, etc. Since their
model only contains gauge-invariant quantities, there are no
diffeomorphism constraints left, and thus no need for ghosts."

Hi Thomas, I think you have misunderstood what I wrote and so before I
read the AJL or Bert Schroer papers let us try to clarify what we are
talking about and to make sure that we are considering the same
concepts.

Despite the particularities of the specific BV approach to vsusy, it
is the case that vsusy is an essential part of the origin of
perturbative finiteness of BF theory, and it helps with the algebraic
renormalization of topological YM theory, and vsusy may have a role in
constructing physical observables in addition to perhaps being the
symmetric origin for the IR safety of topologically massive YM theory
in Landau gauge.

Well, at least this is more established for CS theory defined on an
arbitrary space-time three-manifold for Landau gauge choice in which
vsusy is a renormalizable local supersymmetry which derives
perturbative (UV) finiteness at all orders [1].

It is also interesting to note that YM field configurations on 3 and 4
dimensional manifolds generate an effective Riemann-Cartan (in certain
models, Riemann) geometry on a space (or spacetime) and vice versa,
i.e. R-C geometry can yield YM gauge fields. The YM equations can
perhaps be written without the use of any metric on an arbitrary
smooth manifold [2].

However, the new AJL paper may also be intriguing because coframe
models can have the problem of allowing the existence of non-physical
modes such as ghosts or tachyons [e.g. references 18 and 19 in
gr-qc/0111087].

Anyways, the first question I would like to ask before reading this
new AJL paper is if their approach is compatible with the Ashtekar
action?

I ask because the vsusy of 4d Einstein gravity (in the Palantini first
order formalism) is compatible with the Ashtekar action and may be
compatible with any other actions if such actions have the vierbein
and connection as independent variables and have invariance under
_active_ diffeomorphisms, i.e. diffeos which act on dynamical fields
only, IOW, act quantum mechanically on field operators - the vierbein,
connection and matter fields [hep-th/0005011].

"Causality seems to be the whole point with the AJL approach -
lack of causality, i.e. singular metrics, is explicitly thrown
out."

Here we are thinking of different notions of "causality" which I will
now start attempting to clarify. Also, before discussing the AJL paper
further we might want to consider the important conundrum I ask about
at the bottom of this post.

1) For some as yet unknown and hypothetical reason, it might turn out
to be the case that theorists, e.g. either string theorists, LQG
theorists or discretized gravity theorists, will uncover what seems to
be a reasonable theory of QG but then for decades not be able to
figure out how to make the theory compatible with what we already know
to exist here at the everyday low energy scale.

However, let us presume, for this discussion at least, that a good
theory of QG should be inherently compatible with various low energy
phenomena and then consider the following:

1) Various quantum phenomena have already been demonstrated to be
"noncausal" both theoretically and sometimes even experimentally. I
have been looking at some of this literature recently and so far,
except for the one very important condrum I ask about below, the term
"noncausal" means only that there is no discernable and meaningful
dependence upon causality which is different from the idea that there
is some kind of explicit violation of Einstein causality via
superluminal signals.

For instance, experiments with TmYAG crystals have shown that
stimulated photon ehoes (SPEs) can exist in the noncausal direction
[3], and separate experiments have shown that the phase and energy of
a photon pulse can travel faster than c, the speed of light in a
vacuum, but there does not (yet, anyways) seem to be meaningful
information transmitted via superluminal signals due to cancellation
of such potential superluminal signals because of complicated
diffraction and diffusion effects [4].

3) However, now consider the important conundrum:

Suppose that one definition of the presence of "acausality" would be
the existence of uncertainty which is clearly non-statistical (or
non-probabilistic). Well, this is what happens in the photon
experiment decsribed in this brief four page paper [quant-ph/0102109],
yet there are no superluminal communications necssarily entailed !

Furthermore, also consider this paper [quant-ph/9802056] about
acausality in QED which shows that it is theoretically possible for
there to be acausal behavior for photons in both time-like and/or
space-like directions.

Thomas, since you are from Scandinavia you should heed what the Prince
of Denmark once said and also do not forget about ghosts :-)

"I will tell you why; so shall my anticipation precede your discovery,
...."

Hamlet, Act II, Scene 3

I will post more later about noncausality and acausality, but in the
meantime I will demonstrate the existence of acausality by correctly
anticipating what you, Thomas, will write in reply to this post before
you have even started typing on your keyboard !-)


[1] "Local Supersymmetry of the Chern-Simons theory and finiteness",
C. Lucchesi, O. Piguet, Nucl Phys B 381 (1992) 281-300.

[2] "Induced Geometry: Riemann-Cartan from Yang-Mills", Y. Obukhov,
D. Ivaneko Festschrift, JMS, v5 (1995) pp1-20.

[3] "Nutational Stimulated Photon Echoes", Optics Letters, v27(iss
13) (2002), pp.1156-58.

[4] J.J. Carey et al., Phys Rev Lett, v84(no7) (2000), p.1431.