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22 December 2011: KEK - The mechanism that explains why our universe was born with 3 dimensions: a 40-year-old puzzle of superstring theory solved by supercomputer
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From: JACK SARFATTI <firstname.lastname@example.org>Date: January 23, 2011 1:24:11 PM PSTTo: michael ibison <email@example.com>
Subject: Re: why doesn't light just go on forever?
1) Remember retarded light falling into a black hole is blue shifted for static LNIFs just outside the horizon. The infinite redshift is for retarded light leaving a static LNIF emitter just outside the event horizon. It is not clear if light emitted by a geodesic LIF emitter falling through the horizon will be similarly redshifted because the LIF metric is approximately Minkowski not g00 = 1 - rs/r. That is, the LIF signal should be same as the static LNIF at r ---> infinity. It is not correct to use the g00 = 1 - rs/r metric representation for any devices that are not static hovering. The Pound-Rebka experiment for example is done with static LNIF detectors clamped to the Harvard Tower. On the other hand we have the GPS satellites which in free orbit should correspond to r --> infinity. Therefore, the question is whether the accuracy and precision of the GPS redshift corrections can detect the difference between r = position of satellite and "infinity"?
Suppose the satellite is twice the distance from the center of Earth to the Earth's surface where the approximately static LNIF ground detector is.
1/f(r)(1 - rs/r)^1/2 = 1/f(2r)(1 - rs/2r)^1/2
f(2r)/f(r) = (1 - rs/r)^1/2/(1 - rs/2r)^1/2
rs/r << 1
f(2r)/f(r) ~ (1 - rs/2r)/(1 - rs/4r) ~ (1 - rs/2r)(1 + rs/4r) ~ 1 - rs/2r + rs/4r ~ 1 - rs/4r
vs 1 - rs/2r if we use r --> infinity for the satellite
note that rs ~ .4cm
& r ~ 6x 10^8 cm
rs/r ~ (2/3)10^-9
for a visible light signal the gravity redshift is of order 10^-9 10^15 Hz ~ megaHz
so the issue is can these fractions be unambiguously detected? It would seem so.
Again the problem is, does the free-float GPS detector see the static LNIF metric or the LIF metric? The equivalence principle says the latter. What is seen depends on a transaction between both the sender and receiver detectors.
2) We can never see retarded light from our future horizon - unlike the black hole situation. Is the dark energy advanced Unruh radiation from our future horizon at temperature T ~ c^2/\^1/2?
Following Lenny Susskind - each BIT on the horizon is nonlocally smeared over the entire horizon from our POV. The Stephan-Boltzmann law gives Poynting flux ~ T^4 ~ /\^2 per BIT, but the number of BITS is N ~ 1/Lp^2/\ which gives the observed
dark energy density ~ N/\^2 ~ hc/\/Lp^2
On Jan 23, 2011, at 12:09 PM, JACK SARFATTI wrote:1) the apparent conflict between the local gauge principle and the Wheeler-Feynman light cone limited advanced-retarded idea needs clarification I agree.I mean the issue of dynamically independent vector fields to mediate forces between spinor fields.
2) The conformal singularity is an artifact of a solution of Guv + /\guv = 0. Therefore it cannot be fundamental to the problem of deriving that law of nature.
3) Hoyle and Narlikar do assert that in the de Sitter /\ > 0 solution that the total absorber condition is obeyed so we need to see if their argument is correct.
4) I am hopeful about my real electron-positron plasma idea from the blue-shift Unruh effect high temperature at our observer-dependent future event horizon.
On Jan 23, 2011, at 9:19 AM, michael ibison wrote:
On Sat, Jan 22, 2011 at 10:50 PM, JACK SARFATTI <firstname.lastname@example.org> wrote:
At first I mean only that EM radiation is a change in the state of the gravitational background. That conclusion seems forced after considering the effect of the future conformal singularity AND the observed fact of retarded radiation. These two are compatible only if the radiation can be re-interpreted a reduction in a negative energy field. The only candidate is gravitation.I don't quite understand your verbal argument below on first reading, but my question is, what does it mean that gravity is fundamentally electromagnetic?How do you get Einstein's field equations
Guv + kTuv = 0
Maxwell's EM field equations?
dF = 0
d*F = *J
How do you get a metric field guv from them in Minkowski spacetime?
Or do you mean something else?
EM is the local gauge field of an internal compact U1 group that is not universal for uncharged fields.
Gravity is the local gauge field of an external non-compact universal group, e.g. T4 for a start.
What does this mean for the relationship between the two?
I guess you could take the view that gravity is more fundamental than EM if you wish, so my statement about which is more the fundamental is premature.
Regarding the invariances of EM and GR, I would point out that an EM theory that fits the above description, i.e. with a compliant conformal singularity acting as an effective mirror, plus the re-interpretation of radiation I suggested, means that it is possible to construct a direct action version of EM i.e. with no genuine field degrees of freedom consistent with the observation of radiation - just as Wheeler and Feynman had hoped. The direct action version is not mandated by this reasoning, but it would surely be favored over field theory by William of Ockham.
With no fields, the U1 gauge invariance loses its meaning. Starting from direct action, one is free to manufacture fields to carry the forces in order to facilitate the mathematics, provided of course one does not accidentally introduce additional degrees of freedom (associated with vacuum solutions). If one does so, then those fields must respect U1 invariance.
Perhaps if direct action EM were somehow to underpin gravity, then the resulting theory would likewise be direct action, along the lines of Regge Calculus perhaps. If so, if the tetrad could in principle be eliminated from the theory, then, just as for U1 in EM the associated invarainces would loose their meaning.
This is not to imply the above moves us any closer to identifying the conjectured relationship between EM and GR. All it means is that I would not start by trying to construct a theory exhibiting diffeomorphism covariance.
- MichaelOn Jan 22, 2011, at 8:29 PM, michael ibison wrote:
On Sat, Jan 22, 2011 at 5:39 PM, JACK SARFATTI <email@example.com> wrote:
If you believe the reasoning that leads to the boundary condition at the singularity (frankly I can so no other option) then Cosmology provides a mirror - not an absorber - at the future conformal singularity.OK thanks
On Jan 22, 2011, at 12:35 PM, michael ibison wrote:Jack:
A few notes of clarification in response to your recent exchanges.
The calculation I did was not purely classical.
I looked at the evolution of the Dirac wavefunction as it crossed the conformal singularity.
True, I did treat the EM fields classically, but the outcome for the EM fields would have been the same if they had been quantized.
In a sense the fields do continue across the singularity 'forever'. But the constraint that the Friedmann equation is obeyed means that the post singularity evolution must mirror the pre-singularity evolution up to a certain set of discrete symmetries. This turns out to be enough to make the singularity look like a time-like magnetic mirror in the coordinate system I analyzed. In other coordinate representations of the de Sitter asymptotic future, the singularity has a different structure and the set of discrete symmetries are correspondingly different with corresponding consequences for the property of the mirror.
An outcome of this - if correct - is that discrete local symmetries (C P T Mass) are related to the global topology as implied by the particular choice of coordinate system to represent the singularity.Fine, but does that tell us anything about total absorber condition?
As I point out in the paper, this has observable consequences unrelated to direct action versus field theory debate. Roughly, the effect of the mirror is to invert the W/F argument and leads to the conclusion that the natural Green's function is advanced, not retarded. By natural I mean automatically consistent with the mirror condition, requiring no additional complimentary-function terms.
Though this would seem to be in direct conflict with the observation of (predominantly) retarded radiation there is a way to achieve agreement as follows:
1. Presume that matter is electromagnetically bound i.e. inter-particle interaction energies are generally negative.
2. Re-interpret the increase of field energy diverging on the future oriented cone (normally associated with radiation) as a reduction in the negative binding energy of the matter.
Retarded EM radiation from a source is therefore re-intepreted as annihilation of negative energy on the advanced cone of that source.
I argue on the paper that the only way to allow for pair annihilation (the maximum radiation possible from a source) is to identify the negative background energy with (Cosmological) gravitation. And so I see no way to reconcile theory with observation unless gravity is fundamentally electromagnetic.
Saturday, January 22, 2011
On Jan 22, 2011, at 11:15 AM, Paul Zielinski wrote:On Sat, Jan 22, 2011 at 1:11 AM, JACK SARFATTI <firstname.lastname@example.org> wrote:
On Jan 21, 2011, at 11:18 PM, Paul Zielinski wrote:
On Fri, Jan 21, 2011 at 7:23 PM, JACK SARFATTI <email@example.com> wrote:
all that shows is that your intuition detached from the mathematical machinery leads you to wrong hunches.On Jan 21, 2011, at 6:53 PM, Paul Zielinski wrote:
If their "physical part" LC^ represents a "true" physical quantity, why would it not be generally
covariant in GTR? Given that GTR is a generally covariant theory?
It's a question. A perfectly reasonable one in my view.
What is the point of general covariance if physical quantities are not generally covariant?
General covariance is simply the local gauge invariance of the translation group T4(x).
Mathematically this is just a fancy recipe for generating GCTs. It's not at all clear to me that such local
invariance has any more meaning than that in gauge gravity.
The local gauge principle is an organizing meta-principle that unifies and works. Also it give physical meaning to GCTs when combined with the equivalence principle as the computation of invariants by locally coincident Alice and Bob each independently in arbitrary motion measuring the same observables. SR is restricted to inertial motions and constant acceleration hyperbolic motion (Rindler horizons & maybe extended to special conformal boosts).
Locally gauging SR with T4 ---> T4(x) gives 1916 GR.
However, the INDUCED spin 1 vector tetrad gravity fields e^I are fundamental with guv spin 2 fields as secondary. Nick's problem why no spin 1 & spin 0 in addition to spin 2 still needs a good answer of course.
In terms of reference frames, doesn't this simply mean that the observer's velocity is allowed to vary from point to point in spacetime?No. It means that and a lot more. The coincident observers also can have, acceleration, jerk, snap, crackle, pop, i.e. D^nx^u(Alice, Bob ...)/ds^n =/= 0 for all n.
Physically it corresponds to locally coincident frame transformations between Alice and Bob each of which is on any world line that need not be geodesic, but can be.
I think you should say here that it is the invariance of tensor quantities under such transformations.It's COVARIANCE not INVARIANCE. Invariants can be constructed by contractions of COVARIANTS.
e.g. in non-Abelian gauge fields SU2 & SU3, unlike the U1 Maxwell electrodynamics the curvature 2-form F^a is not invariant, but is covariant
F^a = dA^a + f^abcA^b/\A^c
[A^b,A^c] = fa^b^cA^a
F^a ---> F^a' = G^a'aF^a
This is COVARIANCE not INVARIANCE (U1 is a degenerate case exception).
G^a'a is a matrix irrep of G (Lie gauge group of relevant frame transformations).
when the gauge connection Cartan 1-form transforms inhomogeneously (not a G-tensor)
A^a --> A^a' = G^a'aA^a + G^bc'G^a'b,c'
In gravity G is a universal space-time symmetry group for all actions of all physical fields including their couplings. This is the EEP in most fundamental form.
But if "physical" quantities (e.g., LC^) are not invariant under such transformations, what is the point of general covariance?
As far as I can see calling GCTs "gauge transformations" based on a superficial analogy with internal parameter gauge theory
doesn't change anything.
The intrinsic induced pure gravity fields are the four tetrads e^I that form a Lorentz group 4-vector hence spin 1.
Well this is tricky. It is the tetrad *transformations* e^u_a that represent the Einstein field. Such transformation take
you from a coordinate LNIF basis to an LIF orthonormal non-coordinate tetrad basis. Thus the e^u_a pick up both
the intrinsic geometry *and* the coordinate representation of the LNIF
Of course the e^u_a and the e^a_u can also be treated as the components of the LNIF coordinate basis vectors in the tetrad
basis, and vice versa, but that is another matter.
Each e^I is generally INVARIANT i.e. scalar under GCTs T4(x).
Right. Local Lorentz frames and LLTs are represented by orthonormal tetrad basis vectors in this model, while we
are free to apply arbitrary GCTs in the local frames. I think it is this subtlety of the tetrad model that has led Chen
and Zhu astray as to their attempted decomposition of the LC connection into physical and "spurious" parts in the
context of plain vanilla GTR (coordinate frame model).
What they appear to have done is extract the first order variation of the metric g_uv from the part that encodes the
Riemann curvature, attributing such first order variation in its entirety to the choice of coordinates. If so then the
entire paper is misconceived IMO.
The LC connection is not gauge invariant nor even gauge covariant - that's an effect of the equivalence principle that Newton's "gravity force" is a chimera - 100% inertial force from the acceleration of the detector in curved spacetime.
Of course and no one is saying that it is. We are talking about the "physical part" LC^ that Chen and Zhu claim
to have extracted from LC, after removiing what they call the "spurious" part LC_ that according to them simply reflects
the choice of coordinates.But that choice is also physical though not intrinsic. Its physical because its a state of motion of a detector - ultimately at the operational level where the hard rubber hits the ground of experience.
My point is that if their "physical part" LC^ is not a covariant quantity, then its intrinsic value likewise depends on
the choice of coordinates. This makes no sense to me. Not only that, but they claim to be able to derive a tensor
vacuum stress-energy density from such a quantity. Since the whole problem with the Einstein and various other
stress-energy pseudotensors is precisely that they are not covariant quantities, what exactly *is* the point of their
paper?It depends what you mean by "physical". Arbitrary concomitant g-forces are observables even though they are are not tensor covariants or part of the intrinsic curvature geometry, which is 100% geodesic deviations.
It's not clear to me whether Chen and Zhu are saying this must be the case in gauge gravity, or in the GTR,
or both. Their reasoning strikes me as obscure.
What happens in local gauging of a rigid group G to a local group G(x) is that the induced compensating connection A Cartan 1-form (principle bundle etc) needed to keep the extended action of the source matter field (associated bundle etx) invariant can never be a tensor relative to G(x). That's in the very definition of local gauging'.
You're talking here about a connection. Of course, everyone knows that. If the connection itself is a tensor, then you
don't get a covariant derivative. A connection has to be non-covariant. In order to correct for curved coordinate artifacts
in partial derivatives, it has do depend non-tensorially on the coordinates.
But Chen and Xhu said they were going to remove the coordinate dependent part LC_ from the LC connection to get
their "physical part" LC^. If so, then why is the resulting LC^ not a covariant quantity?
And if it isn't, how does it help with the construction of a vacuum stress-energy tensor?
Clear as mud.
All you can hope for is covariance of the "field" 2-form, i.e. the 2-form A-covariant derivative of itself is a tensor under G(x).
D = d + A/\
Jack, no one is saying that connections are tensors. Please.
But A/\A = 0 for U1(x)
a = 1
A/\A =/= 0
a = 1,2,3
a = 1,2,3,4,5,6,7,8
In general A/\A -> fbc^aA^b/\A^c
i.e. F^a = DA^a = dA^a + fbc^aA^b/\A^c
[A^b,A^c] = f^abcA^c
In the special case G(x) -> U1(x) the field 2-form F = dA is actually invariant, but not so for SU2(x) & SU3(x)
If G(x) has the representation U(G(x)) then
A -> A' = UAU^-1 + dUU^-1
F --> F' = UFU^-1
Now for Einstein's GR G(x) -> T4(x)
and the induced A is NOT the spin 2 Christoffel symbol etc. but the non-trivial TETRAD set.
I guess you mean the tetrad *transformations*, starting from an LNIF coordinate basis.
The induced A clearly depends on the initial coordinates and on the geometry in the general
the internal index a is replaced by the Lorentz group index I (J,K etc).
The induced gravity spin 1 tetrad connection is A^I analog to A^a (Yang-Mills)
I = 0, 1, 2, 3
the relation to the spin 2 Christoffel symbol is very indirect and complicated.
OK fine but beside the point. No one is arguing that a connection is a tensor. As far as I know
no one ever has.
Exactly what is Chen and Zhu's so-called "geometric part" LC_ ? Do you know?And how do Chen and Zhu propose to derive a vacuum stress-energy *tensor* from LC^ if
LC^ is not itself covariant? How can non-covariant LC^ be a solution to the GR energy
Doesn't make sense.