"First we polish off some batches of political dispatches ..." Gondoliers G&S
12:45 PM and I am still in pajamas answering e-mails - looks like Nick Herbert has come up with a practical non-local signaling device? Is the "quantum compound" beyond orthodox QM?
On Oct 23, 2007, at 12:35 PM, Paul Zielinski wrote:
Jack Sarfatti wrote:
"equivalence principle" has several meanings.
If you read Norton's paper you will see that Einstein's and Pauli's versions are quite different.
I doubt it. I bet Einstein was fully aware of Pauli's version before Pauli.
Formally it is the tetrad idea as in the Rovelli quotes you sent to Kiehn.
If the principle is restricted to uniform acceleration and static homogeneous fields, then that should be
reflected in the mathematical model.
Wrong. It's obviously not restricted like that. Red Herring. False premise.
"g-force" is always locally indistinguishable from Newton's common sense notion as "weight"! This is independent of local curvature field R^a^b.
Einstein's GR eliminates "gravity force in the inertial frame" as in Newton's picture where
V(gravity) = - c^2rs/r
f(gravity) = - dV(gravity)dr
in the GIF
In Einstein 1916 GR
f(gravity) = - dV(gravity)dr is the "inertial force" in the LNIF (Local Non-Inertial Frame) that you need using a non-gravity force to stand still in the R^a^b =/= 0 curvature field. This is a contingent arbitrary conventional choice. The world line of this "shell observer" is not timelike geodesic in the R^a^B =/= 0 curved spacetime.
See new Wheeler & Taylor "Black Holes" for a high school level discussion of this point e.g. "shell observers" (LNIF).
Now you can be in a rocket ship in flat Minkowski space-time R^a^b = 0 and apply your rocket engine in an arbitrary manner - that will be locally equivalent to being in some dynamical gravity field in some LNIF -it need not be a static uniform field. There can be local gravity waves passing through the LNIF detector for example.
g-force criterion only applies to the Center of Mass (COM) not to relative tidal coordinates. If you are weightless then you know you are on a timelike geodesic and it does not matter what the local curvature R^a^b is. If you feel weight = g-force then you know you are not on a timelike geodesic no matter what local R^a^b is. You can, ALSO, choose to measure R^a^b independently - but that does not violate equivalence principle that only applies to COMs and to a small enough LIF or LNIF whose detector cannot measure the geodesic deviations.
zero g-force LIF <-> non-zero g-forceLNIF at same P local coincidence
a lot of confusion sets in about "gravity force" = "weight" in non-inertial frames that should not be confused with curvature.
Curvature is second order, coordinate metric gradient is first order. Of course these are not the same and
can be varied independently.
Yes, and therefore, when the questions are properly posed the paradox vanishes.
However, all other things being equal, if in GR you vary the curvature R^u_vwl =/= 0 around a source then you also vary the metric gradients g_uv, w, and such variation of the metric gradients has *nothing at all to do with any observer's world line*.
False. When you do that you change the pattern of geodesic world lines both null and timelike.
Basically in those discussions the static hovering frames are tacitly meant as when one writes
g00 = 1 - rs/r = - 1/grr
rs/r < 1
so for example
g ~ c^2rs/r^2
is what you need in an off-geodesic LNIF that stands still, as it were, in the curved spacetime in that simplest of metrics.
Yes, and if as Einstein suggested a uniform frame acceleration field is in essence not different from a static homogeneous field,
That's only a special situation - the underlying idea is general.
What Einstein did in above is to say that a local constant inertial g-force g per unit mass is AS IF one is in a static frame with a Newtonian potential energy per unit mass V = -gz .
In Newton's theory the static frame is Minkowski geodesic GIF, however in Einstein's GMD the same static frame is off-geodesic (in curved spacetime) LNIF where e.g.
g00 = 1 + 2V for a special static LNIF detector
This paradigm shift is oft overlooked in pop informal discussions - even in some text books.
g00 = 1 + 2V
is perfectly general for a non-rotating dynamic source
g ~ - (1/2)dg00/dr
V need not be gz
then the definition of the gravitational field is made relative to an observer's world line, i.e., dependent on the observer's frame of reference, and the "weight" then has only contingent meaning. If, on the other hand, the objective physical gravitational field is not the same physically speaking as any frame acceleration field, then the weight assumes absolute objective physical meaning.
Your words here do not mean anything to my way of thinking. g-force is 100% contingent always. You have garbled different meanings of "gravitational field"
R^a^b = "gravitational field 1"
g-force = "gravitational field 2"
"weight" = g-force = 0 in REST LIFs & REST GIFS on timelike geodesics (relative to whatever R^A^B might be) is universally true in both 1905 SR & 1916 GR
g-force =/= 0 in REST LNIFs & REST GNIFS is universally true in both 1905 SR & 1916 GR
In REST FRAMEs the detector measures itself, as it were, in a kind of Godelian self-reference.
R^a^b 's value is completely irrelevant. You can measure it independently from the above.
On Oct 22, 2007, at 6:48 PM, Paul Zielinski wrote:
If Einstein's equivalence principle is the cornerstone, then I think it's important to be clear about what it actually is and what parts of it can still be considered valid in the 1916 theory.
It looks to me that the tetrad model is built around Einstein's version of the principle as presented very clearly by Einstein himself in 1916, and not Pauli's.
Einstein's version, unlike Pauli's, refers to uniform frame acceleration in a Minkowski spacetime.
No, it's more general, i.e. Pauli's. Look what Einstein says informally is not all that he had in mind.
But Einstein was consistent on this to the end of his life. Read Norton.
Maybe one day.
In the 1916 quote Einstein is very clear: a uniformly accelerating frame is physically completely the same in essence as a non-accelerating frame equipped with a static homogeneous gravitational field.
This is garbled. "non-accelerating frame" in Newton's paradigm is an "accelerating frame" in Einstein's paradigm, hence the semantic confusion. A static shell frame in curved space-time is an accelerating off-geodesic LNIF frame! It's acceleration is precisely
g = - c^2rs/r^2
the LNIF needs to accelerate to stand still in curved spacetime. This is counter-intuitive to "common sense".
When we stand still on Earth, we are accelerating relative to the local GMD curvature R^a^b =/= 0 field. That's why we feel weight from the electrical Van der Waals reaction forces in the ground. Bernie Haisch got that part right in his otherwise over simplistic "EM ZPF origin of inertia" model.
If the tetrad model is based on this version, then you need to understand that in order to understand the
meaning of the tetrad model in GR.
Weight as gravity force (Newton's sense) is always an inertial force in a LNIF off-geodesic independent of the local curvature until and unless you contingently arbitrarily specify the static "shell" (Wheeler) frame which does not always exist. All inertial forces pushing test particles off timelike geodesics require non-gravity forces to create them.
True, given Einstein's 1916 version of the equivalence principle.
That's the one. If it ain't broke don't fix it.
However, in addition to this Mickey Mouse stuff
So you agree that the Einstein principle is "Mickey Mouse stuff"?
How about "Alice in Wonderland"!
I made a nice picture of quark forces today all from Sakharov's zero point energy induced gravity that is strong on short scale in 3D space - none of this extra-dimensional nonsense needed for this experimental problem - enough of excess mathematical baggage!
OK. No unseen higher spatial dimensions folded up 10^500 ways? No hypergeometric oregami?
Excess formal baggage. Keep it simple Stupid!, though not simpler than is possible. ;-)
Remember Feynman's "a beautiful theory is murdered by an ugly fact" - see Lee Smolin's "The Trouble With Physics" for examples.
Was he talking about GR? :-)
No, he is talking about superstring/M-theory.
Imagine two point monopole defects connected by a string "vortex" defect". By "defect" I mean Goldstone phase singularities (Michael Berry's term) in the several real Higgs fields of the vacuum. The "cores" of the point defects (the quarks) are spherically symmetric with uniform negative zero point energy density giving the induced Sakharov gravity potential energy per unit mass of
V(monopole quark) = -c^2(r/Lp*)^2
out to the coherence "annealing" length within which the quark force per unit mass is
f(UV) ~ c^2r/Lp*^2 -> 0 as r = distance between two point defects -> 0
this is UV "asymptotic freedom"
In the opposite IR limit of "confinement" assume that the zero point energy density in the line vortex core falls off as 1/Lp*r
f(IR) ~ c^2/Lp*
similar to the cosmic dark energy repulsion (but of different sign)
g(accelerating universe) ~ cH ~ 1 nanometer/sec^2 - same as Pioneer anomaly, but in opposite direction?
Note the UNIFORM large-scale dark energy density corresponds to /\zpf ~ 1/(Hubble radius)^2
i.e. V(cosmic) ~ c^2r^2/(Hubble)^2
~ c^2r/(Hubble)^2 ~ c^2/(Hubble) on large scale
compare to the IR quark force of similar origin c^2/Lp*
Newton saw the equivalence of the falling apple to the motion of the planets.
Sarfatti saw the equivalence of the quark force to the accelerating universe!
Looks interesting -- but beware of mathematical red herrings!
There is very little math here beyond high school level. It's the physical ideas that are important.
Supersymmetry? Extra dimensions? we don't need no damn supersymmetries and extra dimensions! ;-)
(well maybe we do :-))
I mean for example, locally gauging 10-parameter Poincare group gives curvature and torsion GMD fields with an extra 6 dynamical degrees of freedom, i.e.
FOUR tetrads e^a and SIX dynamically independent of tetrads spin connections S^a^b = - S^b^a. The latter SIX form a 6D fiber - Shipov's "oriented point" manifold that sure looks like a primitive Calabi-Yau sort of space.
Now if we locally gauge Penrose's 15 parameter twistor conformal group then there are even more GMD fields that both Tony Smith & Carlos Castro seem to get? This then, according to Castro, gives a new kind of UV/IR duality in which
g(UV Pioneer Anomaly) = cH = c^2/(Hubble radius) ~ 1 nanometer/sec^2 on short UV scale = c^2/R (below)
mod sign (attractive to center of Sun)
i.e. dark matter shell /\zpf = -H/cr
just like IR quark force is
g(IR quark) = c^2/Lp*
Lp* ~ 1 fermi
/\zpf(IR quark) = -1/Lp*r
this is QUARK CONFINEMENT!
Then in UV limit
g(UV quark) = c^2r/Lp*^2
/\zpf(UV quark) = - 1/2Lp*^2
this is QUARK ASYMPTOTIC FREEDOM!
Note, for accelerating universe on IR cosmic scale
/\zpf(dark energy) = + (H/c)^2
Vzpf(dark energy) = -c^2(1/2)/\zpf(dark energy)R^2
g(dark energy) = H^2R = c^2/R ~ 1 nanometer/sec^2 - same number mod sign as NASA Pioneer anomalous acceleration, but pointing opposite direction to center of sun? In case of cosmology, think of a flat infinite rubber sheet in accelerating expansion same in all directions at each point of the sheet.
c/H ~ R
Area of future de Sitter WORLD HOLOGRAM horizon is NLp^2 = 4piR^2
N = Bekenstein c-bits ~ 10^122
N^1/2 ~ 10^61
R ~ 10^61 10^-33 ~ 10^28 cm
&R = (Lp^2R)^1/3 = N^1/6Lp ~ 1 fermi = size of Lp* quantum gravity "foam" bubble.