On Feb 21, 2012, at 1:32 PM, Paul Zielinski wrote:
On 2/21/2012 10:00, JACK SARFATTI wrote:
I was only talking about light rays in free space of course - not refraction of light by lenses etc in materials from multiple scatterings off mainly electrons. Yes, in the usual sense the inertia of light is infinite classically in general relativity in vacuum. If one uses Newton's picture, and considers GM(sun)E(light)/c^2r, one will get orbits for light rays in flat Euclidean space. As I recall this Newtonian calculation is off by a factor of 2.
Z: But if the energy of a photon is given by E = hv, and according to SR m = E/c^2, then how can m be infinite?
JS: That's my point. You are garbling Newton and Einstein again - mixing Apples with Oranges getting paradoxes from mingling different paradigms. I think Jim also has fallen into this quagmire. Of course it's very common and hard not to do. It's the same confusion in the unification of the electro-weak-strong forces with gravity.
In Newton's classical picture, you can use for the zero mass quantum m = E/c^2 where E = pc and you get pretty close to the correct GR answers within a factor of 2 or so for WEAK GRAVITY CURVATURE FIELDS, slow motions. Of course, the test particle mass cancels out of the gravity orbit equation if dm/dt = 0, which may not be the case here because of the gravity redshift. That is, for each photon in the light beam E = hf changes at different gravity potentials causing the bending of light in Newton's picture? However, again classically in vacuum -I am not talking about refraction of light by lenses etc or diffraction, i.e. only in the geometrical optics short-wave UV limit relative to radii of curvature, the effective inertia of light is "infinite" because there is no way to push it off a null geodesic. Actually, if you include the weak force, light has some weak charge as I recall - mixture of Z and photon in the Salam-Weinberg theory, so maybe if there was some external macro-quantum coherent W,Z weak near field you could push it off a null geodesic.
Again that's quantum field theory and the classical guv(LNIF) metric picture may simply breakdown there since gravity is probably an emergent low energy macro-quantum coherent effective field similar to the order parameters of superconductivity. Indeed, a set of Higgs-Goldstone amplitude - phase Glauber states of virtual massless Goldstone and massive Higgs bosons inside the post-inflation vacuum give the tetrads e^I and the spin-connections S^I^J and with them Einstein's GR as an emergent space-time theory that has perhaps no meaning on the level of a fermi and less? Sort of like looking for Young's modulus inside the unit cell of a space crystal (spontaneously broken continuous T3 group translational symmetry).
Z: And if the weak equivalence principle holds, wouldn't that imply that the active gravitational mass of each photon is also infinite?
JS: Again, you come up with a paradox by being inconsistent garbling Einstein with Newton.
For Newton everything is consistent with the real photon having a finite inertia M = E/c^2 and E = pc
For Einstein classical rays of light (geometric optics limit) are on null geodesics whose shape is determined by Tuv(matter) sources. No quantum theory there and also no weak forces. Light carries weak charge - but not in Einstein's 1916 GR of course.
So for Einstein's classical GR the notion of inertia as resistance against a push off a geodesic has no meaning for light. Or you could say, that the inertia of light is infinite there. On the other hand since Newton's 2nd law for OFF-GEODESIC world lines is
F = DP/ds
D is the Levi-Civita connection etc.
F and P are 4-vectors both under GCT4 and SO1,3 groups.
P^2 = (E/c^2)^2 - P^2 = 0
You could say that for light F = 0 always. Then the issue of the inertia of light simply does not come up in Einstein's theory. It's perfectly finite in Newton's theory, but it does not give the correct predictions, though it is not off by much in the appropriate limiting cases.
Z: Doesn't add up. What's wrong with this picture?
JS: I just answered that.
There are many objections to Jim's picture.
1) He uses cosmological metric parameters locally at a scale they do not apply.
Z: Yes but Jim has a separate argument for local phi based on the EP and non-localizability.
JS: I find his argument unintelligible. How can phi = c^2 locally and phi also be a wave traveling at c?
Also in LIFs c is always a constant the same constant.
And in the rotating disk LNIF c is same as in the LIF for a TWO-WAY ROUND TRIP rim-to-rim time of flight measurement for zero rotational "jerk" of the disk. However, the Sagnac effect with ring laser interferometers shows a rotational fringe shift CW =/= CCW corresponding to the one-way doublet in the local speed of light in the rotating LNIF. Irwin Shapiro long distance radar slowing of speed of light by large masses is a completely different kind of experiment.
Z: I don't understand his argument for local phi, but he does have one.
JS: It's obviously wrong in my opinion.
2) He assumes a static Newtonian gravity potential
phi/c^2 = GM/c^2R = 1
where E = Mc^2 is the total mass-energy of the universe
A = R^2 is the area of a horizon infinite redshift surrounding surface of the interior bulk volume
Our universe has two such horizons, one in our past and one in our future.
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Tamara Davis PhD Fig 1.1c modified
Z: Not only that but he argues this from the Einstein EP and non-localizability of gravitational energy-momentum,
which as far as I can see lead you to precisely the opposite conclusions -- namely that there is no local frame
invariant phi in GR!
JS: Alice in Wonderland.
Z: And even if there were a covariant local vacuum energy-momentum density in GR, phi on its own would still not
be GCT invariant, since it would then be only one component of a tensor quantity, which could *not* be invariant
under GCTs -- for purely mathematical reasons.
JS: Right.
Z: So Jim seems to be mixing up Sciama's semi-Newtonian toy model with GR and trying to have it both ways. I think
he needs to look much more closely at the correspondence relationship between Newtonian phi and the metric
components g_uv of GR.
JS: Exactly. Only the future horizon works.
In fact M is a monotonic increasing function of cosmic time that approaches a constant value de Sitter metric asymptotically, and R does increase in proportion to keep phi = c^2. However, it makes no sense to think of this cosmological scale phi as some kind of local gravity potential that obeys a wave equation and that causes mass fluctuations in a engine of some kind in his laboratory. To me that's magical thinking - astrology.
I don't know if Jim is seeing anything real that may be useful for propulsion. I doubt it. However, if there is a real effect in his device I am sure it will have a mundane local explanation without invoking the old classical ambiguous notion of Mach.
Z: OK.
JS: 3) in addition there is a lot of confusion in terminology around fictitious "inertial forces".
Z: There certainly is.
JS: I always mean the frame acceleration in the Levi-Civita connection by that term.
Z: OK.
JS: There is a clear cut distinction between real and fictitious forces.
Z: There is? Didn't we see that there is a gray area in which a force is not real, but it models the effects of underlying inertial effects that are themselves real and objective?
JS: No, you are not understanding what I have written. Like Bohr's version of quantum theory (Copenhagen) Einstein's GR has a measurement theory. I remember David Bohm talking about this at Birkbeck College London 1971 when I was there for several months.
Einstein's 1916 GR is about COINCIDENT LOCAL OBSERVERS measuring the same events and comparing their data by the computation of invariant numbers the same for ALL of them. That is LOCAL OBJECTIVE REALITY out there. It's Plato's Theory of Ideas in the sense of Roger Penrose.
Einstein's 1905 SR is about observers in GLOBAL INERTIAL FRAMES only doing the same thing, but they don't have to be coincident fundamentally.
The local tetrad/spin-connection --> tensor --> entangled spinor/entangled twistor laws (field equations) are covariant of the same algebraic form for all of these coincident observers independent of their world lines, geodesic or not, rotating or not. The lowest energy stable solutions of these field equations with initial & final boundary conditions need not respect all the symmetries of the local field equations and their global dynamical actions. For example, Frank Wilczek's "time crystals" as the latest, that in this context would be Hagen Kleinert's "world crystal lattice" in 4D and David Finkelstein's "chronons."
GR per-se has THREE INTER-TWINED symmetry groups for LOCALLY COINCIDENT observer-detector-frames of reference.
I. Tetrads: LNIF <---> LIF
2. SO1,3: LIF < ---> LIF' local Minkowski metric nIJ(LIF)
3. GCT4(x): LNIF <---> LNIF' local curvilinear metric guv(LNIF)
ds^2 = guv(LNIF)e^ue^v = nIJ(LIF)e^Ie^J
Finally the internal fiber groups
4. U1, SU2, SU3 all locally gauged with induced boson fields of electromagnetism, weak and strong forces.
Einstein's 1916 gravity field is simply the induced boson field from localizing the rigid Poincare group T4*SO(1,3) and ad hoc putting in constraint of zero torsion.
If the force is real, then an accelerometer clamped to the object in question will show a non-zero pointer reading.
Z: I think here you are confusing the reality of the applied force with the reality of inertial reaction *treated* as a force. Two different animals.
JS: I'm not confusing anything. The confusion is all yours.
You have two extended particles - the observed test particle and the tiny detector measuring the motion of the test particle.
NEITHER ARE Tuv SOURCES of the gravity curvature field if any. This works also in Minkowski space time, which is why Tuv and Mach's Principle are irrelevant to the basic idea - measurement theory.
Each particle has a still tinier accelerometer clamped to it.
The pointer of the accelerometer stays at zero on a timelike geodesic where there is no rotation about the center of mass of the possibly extended particle - either one.
The pointer of the accelerometer moves off zero on a timelike NON-geodesic where there may also be rotation about the center of mass of the possibly particle - either one.
Newton's 2nd law of motion for the observed test particle is then (suppressing indices)
D(detector)P(test particle)/ds = F(test particle)
D with the Levi-Civita connection is a property of the DETECTOR not the test particle!
When D =/= d, then there is another force F(detector) where
D(detector)P(detector)/ds = F'(detector)
no connection between F and F'.
All the fictitious inertial Coriolis, centrifugal, Newton's gravity force -GM(Tuv source)/r per unit test particle m are CONTINGENT properties of the DETECTOR.
Indeed, Newton's gravity force F(m) = - GMm/r^2 = mg(r) is simply a description of the STATIC LNIF, e.g. clamped to M's surface.
The accelerometer clamped to the observer who in turn is clamped to M's surface has a pointer that moves to -GMm/r^2.
If the test particle is freely falling on a timelike geodesic of the Earth's field its accelerometer pointer stays on the "zero" - no g force.
All fictitious forces on the observed test particle fail to cause the local accelerometer pointer to move. However, the clamped constraint on the detector will cause its accelerometer pointer to move. All real EM weak strong forces on the test particle will cause its accelerometer to move off "zero."
When we look at Baron Munchausen in free fall his local accelerometer's pointer sits at zero. Ours stationary on Earth's surface moves off zero (we are standing on a scale). Therefore, the real electrical reaction force of the rock beneath us pushes us off a timelike geodesic.
Z: Only in combination with the inertia of the Earth. It is the inertia of the Earth that is really pushing on the rock, *mediated* by the electrical forces.
JS: Clear as mud. It's Earth's Tuv tensor field that makes the dominant Ruvwl curvature tensor field that then demands
F = - GMm/r^2 for the static LNIF
More precisely the formula is
F = - (1 - 2GM/c^2r)^-1/2GMm/r^2
Z: Both the Earth and the rock want to move along geodesics. What creates the phenomenon of "weight:" in GR is the geodesic *deviation*.
JS: No, you are wrong Z. You garble "geodesic deviation" with pushing a single test particle off its geodesic. Two completely different procedures. Indeed, this is the root cause of your persistent confusion about a non-zeor tensor hidden inside the Levi Civita connection! You have been fooled by superficial similarity of the nouns in the informal language.
Geodesic deviation is the relative apparent kinematic acceleration between two neighboring geodesic test particles neither of which experience g-force.
Newton's 2nd law in contrast is completely different operationally - a non-gravity force pushes one test particle off its timelike geodesic.
INERTIA in Einstein's GR is really only a property of motion on timelike world lines. It's measurable only on non-geodesic timelike world lines.
Z: The inertia of the Earth overcomes the much smaller inertia of the rock -- all *mediated* by your electrical forces.
JS: We are really accelerating in place in curved spacetime - that's Einstein's picture.
Z: By "really" I think you must mean "dynamically". This has nothing to do with *kinematical* frame acceleration.
JS: Clear as mud. Real acceleration is what accelerometers measure. Real time is what clocks measure. Etc. LNIFs really accelerate.
Z: Einstein failed to sufficiently emphasize the distinction between kinematical and dynamical acceleration that holds in GR.
JS: Therefore, Newton's "real gravity force" is in fact 100% fictitious inertial force just like the Coriolis-Centrifugal forces are.
Z: NOT OK.
JS: I know that you are profoundly confused on that for the reasons I gave above, but I don't expect that your mental block on this hobby horse will allow you to properly process what I am telling you. ;-) Consequently I will not comment further on your remarks below that are based on your wrong premise in my opinion. Let other readers decide who they agree with.
Z: The gravitational deformation of the geodesics of the rock -- which in GR is an objective (i.e. frame invariant) phenomenon -- is what underlies Newton's gravitational force. It is the gravitational deformation of the geidesics that acts like a force. So Newton's gravitational force is NOT "100% fictitious", like Coriolis forces, since it models an underlying objective phenomenon. Coriolis forces in contrast are pure kinematical frame acceleration artifacts that do not point to any underlying objective physical phenomenon. Coriolis forces really are "100% fictitious".
JS: Consequently, any attempt to explain Newton's gravity force by Mach's Principle is wrong-headed it seems to me because all inertial forces are frozen historical accidents - contingencies, or intelligently contrived experiments with spaceships etc
Z: Jack I think you are still confusing 100% kinameatical artifacts (truly fictitious) with force models for underlying objective inertial effects. Two different animals. Inertial effects are kinematically frame invariant in GR. It is essential to distinguish between dynamical and kinematical frames in discussions of GR. Otherwise there will be endless confusion generated by illegitimate punning.
JS: Einstein's theory explains gravity as the total geodesic pattern (null and timelike primarily) with curvature as geodesic deviation relative tipping of neighboring light cones.
Z: Right. Objective gravitational deformation of the geodesics, the effects of which are modeled as a gravity force in Newtonian physics.
JS: Newton's gravity force in flat space with absolute time is a chimera not at all relevant to Einstein's curved spacetime theory of gravity.
Z: Except by correspondence.
Jim's theory simply confounds the two qualitatively different pictures of Newton and Einstein.
Z: I have to agree that it does seem that Jim is mixing up the Newtonian and Einsteinian pictures of the gravitational potential and trying to have things both ways.
On Feb 21, 2012, at 3:51 AM, qraal01 wrote:
A useful gedankenexperiment perhaps, but boxes and mirrors have inertia - photons don't reflect from photons.
Right only at really high energies where the virtual electron-positrons come into play - a very tiny effect in most cases.
Idealisations sometimes strip away too much. Yet the idea that inertia has something to do with massless sub-units in a confined repetitive pattern doesn't seem to fit Machian inertia either and makes inertia a local phenomena rather than something caused by global constraints.
Right again. It's from the Higgs field and QCD confinement in my opinion.
Sent from my iPad
On 21/02/2012, at 10:09 AM, "
Imagine a box with perfectly reflecting walls filled with photons. You try to "push" the box off of its geodesic. How much force must you apply to achieve some prestated acceleration?
When I scanned the traffic earlier in the day, I must say I was not encouraged that anything I said last night had made any impression. Later traffic is more encouraging. But talk of the issues I left unaddressed last night would be premature at best. So I'll stay out of the discussion, for a while at least. . . .
---------- Original Message ----------
From: Paul Zielinski To: qraal01 Subject: Re: Who's on first?
Date: Mon, 20 Feb 2012 23:04:10 -0800
Right one even could argue that they have infinite inertia since they
cannot be accelerate away from null geodesics.
Yes, I said that several times.
Maybe we should say that photons have momentum, but that the concept of
inertia doesn't apply.
Tricky point.
However, not really relevant to what I was talking about which was the
meaning of "inertial reaction" of material bodies
with reference to Newton's third law of motion.
Again, Newton's 3rd law is strictly a LOCAL effect from translational invariance --> momentum conservation in the small between pairs of objects - no need for Mach's principle. Formally it's from the general Tuv^,v(matter) = 0
On 2/20/2012 22:36, qraal01 wrote:
I tend to agree with Jack on this one. It's hard to imagine how "inertia" applies conceptually to photons, which never accelerate, but are always instantaneously at c. They definitely have momentum, but what inertia and inertial reaction could possibly describe phenomenologically about photons...?
Sent from my iPad
On 21/02/2012, at 3:29 PM, Paul Zielinski wrote:
You wrote,
"The photon has no inertia in the sense of rest mass."
I would say simply that photons have inertia, but zero rest mass.
You can do that in Newton's picture as I suggested above. You don't however get the precisely correct answer - off by a factor of 2 as I recall because Newton does not have the 3p pressure term in the Poisson equation.
(energy density + 3 pressure)
for light w = pressure/energy density = 1/3
The whole point here is to decide on what picture to use Newton or Einstein and then stay consistently within the rules of each picture. Jim is mixing the two and coming up with absurdities in my opinion.
Debate with Zielinski on Einstein's General Relativity 2-21-12
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- Category: Jack Sarfatti Blog
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