On Feb 8, 2014, at 1:23 AM, "jfwoodward@juno.com" wrote:
For those of you who are trying to figure out what Jack and Paul are arguing about, sometimes on this list again, the basic issue, put simply, is whether gravitational fields are present in spatially flat spacetimes. Jack says no. That non-vanishing spatial curvature must be present if gravity is present.
JS: Jim is muddling my position.
1) Real gravity fields must have curvature.
2) Artificial gravity fields exist without curvature.
3) Einstein's Equivalence Principle (EEP) is: imagine you are inside an elevator with no windows.
Situation A: Elevator is standing still on surface of Earth. The reaction force (radially inward) of your body down on the scale is your weight
W = (your inertia in kg)10 meters per sec^2
Your inertia is
m = E/c^2
E is your total energy in Joules
c = 3 x 10^8 meters/sec^2
In Einstein's GR you have an upward net non-zero off-geodesic proper tensor acceleration (radially outward) g = DV/dt = 10 meters per sec^2 in order to stand still (hovering static LNIF) in the Earth's curvature field. Your world line is not a geodesic of the Earth's curvature field.
V = 0 and dV/dt = 0 in the hovering static LNIF
g = - {LNIF}V0^2 = + GMEarthr/r^3 radially outward
The action-reaction pair of electrical contact forces of Newton's third law is LOCAL having no astrological magic influence from the distant stars. It is caused by local U1 electromagnetic gauge invariance + quantum field theory.
WHEELER-FEYNMAN RADIATION REACTION IS NOT IN PLAY HERE - THERE IS NO RADIATION.
dP/dt = 0 P = total charge momentum + EM field momentum
= mV + (e/c)A
From quantum field theory, the local U1 gauge transformation is simply mostly the exchange of a near field spacelike virtual photon between the charge e of inertia m and the EM field A coincident with the charge.
The dominating Feynman diagram is >---|
> = electron world line
--- = virtual spacelike photon world line
| = Glauber macro-quantum coherent state of virtual photons order parameter describing the near field A
A is exactly like the Bose-Einstein condensate reservoir in superfluid helium it is also analogous to the Higgs vacuum field - these are all examples of spontaneous broken continuous symmetry groups of the dynamical action.
note subject of my PhD was "Local Gauge Invariance in the Theory of Superfluids" 1969 UCR
Formally the internal symmetry local U1 gauge transformation is
mV -> mV' = mV + hGradS
S = quantum phase of the charge's information BIT field.
A -> A' = A - (hc/e)GradS
Therefore, the total canonical momentum P of the Hamiltonian for minimal QED coupling is GAUGE INVARIANT
P -> P' = mV + hGradS + (e/c)A - hGradS = P
dP/dt = 0
The formal U1 internal symmetry local gauge transformation actually describes the transfer of a virtual photon from the classical near EM field to the charge and vice versa! It's a quantum field virtual dynamical process in space-time and it obviously implements Newton's 3rd Law that the total momentum of the system of interest is LOCALLY CONSERVED.
Change in momentum of charge + change in momentum of near field = 0
The radially outward real force pushing the charge off a timelike geodesic is
F = hGradS/&t
The radially inward real reaction force of the charge back on the source of the near field A is
- F = -hGradS/&t
this radially inward reaction force causes the pointer of the scale to show weight.
&E&t < h for virtual photon (Heisenberg uncertainty principle)
Situation B: the elevator is properly accelerating at 10 meters per sec^2 in any direction in flat empty spacetime.
The observer inside the elevator cannot tell whether he is out in empty space or sitting still on surface of Earth.
We assume of course that he has no windows and no tidal curvature measuring capability.
Therefore, subject to these conditions one cannot distinguish artificial non-tidal gravity defined as the Levi-Civita connection from the non-tidal gravity field associated with tidal curvature.
JW: Paul says yes. That spatially flat spacetime does not preclude the presence of gravity. That Paul is right should be obvious from the fact that general relativity is predicated on the assumption that in sufficiently small regions of spacetime, the Minkowski metric (spatially flat) applies.
JS: Jim, you have totally muddled two different meanings of the ambiguous term "gravitational field". Also you are dead wrong. You have made a very elementary error.
Your "the Minkowski metric (spatially flat) applies"
The Minkowski metric is flat in the 4D sense, not only in the 3D sense.
Your argument here is a non sequitur
"Non sequitur (Latin for "it does not follow"), in formal logic, is an argument in which its conclusion does not follow from its premises.[1] In a non sequitur, the conclusion could be either true or false, but the argument is fallacious because there is a disconnection between the premise and the conclusion. All invalid arguments are special cases of non sequitur. The term has special applicability in law, having a formal legal definition. Many types of known non sequitur argument forms have been classified into many different types of logical fallacies." wiki
JW: It is also the boundary condition in the Schwartschild solution of Einstein's equations.
JS: Schwarzschild, also it's another non sequitur red herring.
JW: And in critical cosmic matter density cosmologies, spatial flatness obtains in the presence of black hole horizon strength gravity. The problem for Jack (and other "modernists") is that if you allow that, the WMAP results give back Mach's principle as a simple prediction of general relativity.
JS: I challenge you to give a mathematical model that WMAP proves Mach's Principle.
You do not need Mach to have k = 0 in the FRW metric.
JW: Do not expect closure on this any time soon. :-)
The importance of gyroscopes for the construction of real LIFs[i]
“Local inertial frames have a fundamental role in Einstein geometrodynamics. The spatial axes of a local inertial frame along the world line of a freely falling observer are mathematically defined using Fermi-Walker transport (eq. 3.4.25); that is, along … her geodesic they are defined using parallel transport. These axes are physically realized with gyroscopes. … The most advanced gyroscopes … measure the very tiny effect due to the gravimagnetic field of the Earth: the ‘dragging of inertial frames,’ that is, the precession of the gyroscopes by the Earth’s angular momentum, which in orbit, is of the order of a few tens of milliarcseconds/year. There are two main types of gyroscopes … mechanical and optical. The optical gyroscopes … are usually built with optical fibers or with ring lasers.” (6.12)
Fermi-Walker Transport, De Sitter (Geodetic)&Lense-Thirring Effects
For weak gravity fields in the first Einstein 20^{th} Century correction to Newton’s 17^{th} century gravity theory: S^{a} is a spacelike 4-vector outside its local light cone that describes the spin of the test gyroscope about its rotation axis. The test gyroscope travels along a timelike worldline x^{a} (s) with tangent vector u^{a}. S^{a}u_{a} = 0 and the equation for Fermi-Walker transport is
S^{a}_{;}_{b}u^{b} = u^{a} (a^{b}S_{b}) = u^{a}(u^{b}_{;}_{g}u^{g}S_{b}) (3.4.25)
Where a semi-colon “;” always stands for the covariant partial derivative with respect to the Levi-Civita connection that describes fictitious forces on the test gyroscope that are, in reality, real forces on the detector measuring the motion of the gyro. Repeated upper and lower indices are summed through 0,1,2,3. The local observable objectively real proper acceleration first-rank tensor directly measured by accelerometers clamped to the center of mass of the test gyro is
a^{b} = u^{b}_{;}_{g}u^{g}
If the arbitrary timelike world line of the center of mass of the test gyro (remember LIFs have three of them forming a spacelike triad base frame) is a geodesic, then, by definition, the proper acceleration tensor a^{b} = 0. Therefore,
S^{a}_{;}_{b}u^{b} = 0
This is the equation for Fermi-Walker transport.
“A mechanical gyroscope is … made of a wheel-like rotor, torque-free to a substantial level, whose spin determines the axis of a local, nonrotating frame. Due to very tiny general relativistic effects … that is, the ‘dragging of inertial frames’ and the geodetic precession, this spin direction may differ from a direction fixed in ‘inertial space’ that may be defined by a telescope always pointing toward the same distant galaxy assumed to be fixed with respect to some asymptotic quasi-inertial frame (see 4.8).”
Inertial Navigation From ICBMs to Starships
“Mechanical gyroscopes are based on the principle of conservation of angular momentum of an isolated system … with no external forces and torques. … the spinning rotor maintains its direction fixed in ‘space’ (apart from dragging effects as Earth rotates but, however, a vector with general orientation, fixed with respect to the laboratory walls, describes a circle on the celestial sphere in 24 hours, a spinning rotor … describes a circle with respect to the laboratory walls in 24 hours … In a moving laboratory, using three ‘inertial sensors’, that is, three gyroscopes to determine three fixed directions (apart from relativistic effects…) plus three accelerometers to measure linear accelerations and a clock (and possibly three gravity gradiometers to correct for torques due to gravity gradients, one can determine the position of the moving laboratory with respect to its initial position. This can be done by a simple integration of the accelerations measured by the three accelerometers along the three fixed directions determined by the gyroscopes [held by gimbals]. Position can thus be determined solely by measurements internal to the [starship] laboratory … a priori independently of external information is called ‘inertial navigation’ … an onboard computer integrates the accelerations … one is able to find velocity, attitude, and position of the object.”
The word “acceleration” here means off-geodesic proper tensor acceleration not the old Newtonian kinematic acceleration measured by Doppler radar in Einstein’s somewhat misleading popular “happiest thought quote” I discussed earlier whose Siren’s song that has shipwrecked many a wannabe physicist-philosopher Flying Dutchman searching for Ithaca. However, for a starship in free float on a timelike geodesic we can dispense with the gyroscopes to preserve “direction.” “Instead one may use gradiometers …”
“The needs of air navigation have generated a powerful drive for a compact, light weight gyroscopic compass of high accuracy … Today, optical gyros have displaced the mechanical gyro … A wave-guide is bent into a circle. A beam splitter takes light from a laser and sends it round the circle in two opposite directions. Where the beams reunite, interference between them gives rise to wave crests and troughs. If the wave-guide sits on a turning platform, the wave crests reveal the rotation of the platform or the airplane that carries it.
While mechanical gyroscopes are based on the principle of conservation of angular momentum, optical gyroscopes (really optical rotation sensors) are essentially based on the principle of the constancy of the speed of light c in every inertial frame. Therefore, in a rotating circuit and relative to the {LNIF} observers moving with it, the round trip travel time of light depends on the sense of propagation of light with respect to the circuit angular velocity relative to a local inertial frame.” [LIF]
From the general connection of continuous Lie groups[ii] of symmetries of closed dynamical systems to conserved local currents and global “charges” that form the group’s non-commuting Lie algebra[iii], we conclude that the operation of the gyroscope corresponds to the three rotational symmetries of Einstein’s 1905 special relativity’s Poincare group. Therefore, the Sagnac effect[iv] basis of the optical gyros correspond to the three Lorentz boosts of that same Poincare group that formally express the constancy of the speed of light in inertial frames. Newton’s action-reaction third law comes from the three space translation symmetry’s conservation of linear momentum and the conservation of energy comes from the time translation symmetry – if these symmetries are not broken. Does the accelerometer’s operation depend on the Rindler boosts of constant proper accelerating hyperbolic world lines of test particles? These are outside of the Poincare group requiring Roger Penrose’s twistor conformal group.[v] The Poincare group is a subgroup of the conformal group that also includes dilations.
On Oct 8, 2013, at 2:36 PM, jack <jacksarfatti@gmail.com> wrote:
"Einstein continues by pointing out how things fare better in GR:
By the way, physical space possesses reality according to the general theory of relativity, too, but not an independent one; for its properties are completely determined by matter. Space is incorporated into the causal nexus without playing a one-sided role in the causal chain.
The second half of the first sentence is also striking, as Einstein had previously recognised that Mach’s principle only holds for certain solutions of the Einstein field equations, not for all of them — but of course, at the time he considered those solutions for which it held as the only physically relevant ones. At any rate, we here see the complete position which would first be presented in the 1921 Princeton lectures: in Newtonian mechanics space acts without being acted upon, while in general relativity it interacts."
For twenty years I have made the same point for quantum theory.
Signal nonlocality happens when the matter beables and their quantum information mental pilot waves obey the very same AR action reaction principle. This opens Pandora's Box.
See Lecture 8 of http://www.tcm.phy.cam.ac.uk/~mdt26/pilot_waves.html
Sent from my iPad"As we mentioned in section 3.3 above, Norton argued in 1999 that AR was in the back of Einstein’s mind well before 1920, and indeed formed the stimulus of his original Machian tendencies. Here is a further quote from Norton’s study:
This view of the deficiency of earlier theories [their violating the action–reaction principle] and general relativity’s achievement is not one that grew in the wake of Einstein’s disenchantment with Mach’s principle. Rather, it was present even in his earliest writings beneath the concerns for the relative motion of bodies and the observability of causes.78
Next year the eclipse is supposed to show whether light rays are bent by the sun, whether, in other words, the fundamental assumption of the equivalence between ac- celeration of the frame of reference on the one hand and the gravitational field on the
79Einstein [1913], p.1260-1261.
80It is true that Einstein rejected his own 1912 scalar field theory (mentioned footnote 32 above) when he discovered that it failed to satisfy Newton’s third law of motion concerning action–reaction. But this is a case of the existence of both action and reaction, which happen not to be equal and opposite, thus giving rise to an unacceptable force-free accelerative phenomenon. As we stressed in section 2, AR is not be to be conflated with Newton’s third law, which is a much stronger constraint on the way bodies act on each other.
Einstein is explicit in regard to the claim that gravitation is an interaction, with the clarification that the interaction is said to be mediated by gμν. The outcome, incidentally, is a revised description of the 1916 thought experiment of the two rotating spheres:
'Mr. Reichenb ̈acher misunderstood my considerations regarding two celestial bodies rotating with respect to one another. One of these bodies is rotating in the sense of Newtonian Mechanics, and thus flattened by centrifugal effects, the other is not. This is what the inhabitants would measure with rigid rods, tell each other about it, and then ask themselves about the real cause of the different behaviour of the celestial bodies. (This has nothing to do with Lorentz contraction.) Newton answered this question by declaring absolute space real, with respect to which one but not the other allegedly rotates. I myself am of the Machian opinion, which in the language of relativity theory can be put in the following way: All masses of the world together determine the gμν- field, which is, judged from the first celestial body, a different one than judged from the second one; for the motion of the masses producing the gμν-field differ significantly. Inertia is, in my opinion, a (mediated) interaction between the masses of the world in the same sense as those effects which in Newtonian theory are considered as gravitational effects.'
To summarise, it seems fair to say that Einstein did not need a variant of the action–reaction principle as a reason to adopt the relativity of inertia in 1913. His strong belief in the equivalence between gravity and inertia, together with his retention of the Newtonian tenet that gravity is an interaction between bodies, could be seen as reason enough.85 Furthermore, it is the pairing of the equivalence principle and the principle of the relativity of inertia, together with the principle of relativity, that Einstein mentions repeatedly up until 1920 as the cornerstones of GR, whereas AR only really takes centre stage in 1920 in the correspondence with Schlick and in subsequent publications. For these reasons, we are inclined to believe that the 1920 correspondence brought out a watershed in Einstein’s thinking, marking an unprecedented shift in Einstein’s interpretation of the superiority of GR over preceding theories of space-time: its superiority now rested on satisfaction of the action–reaction principle, rather than implementation of Mach’s original analysis of inertia.
Einstein’s frequent references to GR’s vindication of the action–reaction principle in the years following his 1921 Princeton lectures have been noted in a number of studies.86 A particularly telling quotation is from a letter Einstein wrote a year before his death to Georg Jaffe:
'You consider the transition to special relativity as the most essential thought of relativity, not the transition to general relativity. I consider the reverse to be correct. I see the most essential thing in the overcoming of the inertial system, a thing which acts upon all processes, but undergoes no reaction. The concept is in principle no better than that of the centre of the universe in Aristotelian physics.87'
For Einstein, the glory of GR rested partly on its alleged superiority to preceding theories of space-time which involve absolute structure. His 1924 essay “On the ether” contains a particularly clear denunciation of Newtonian mechanics in terms of its violation of AR.88 But caution should be exercised when extrapolating backwards, as it were, in the history of physics. It doesn’t automatically follow from the fact that GR satisfies AR, that NM and SR don’t, as we mentioned in section 1 above. To repeat, Einstein was content in his 1905 development of SR to explicitly borrow the inertial frames from NM, without any fretting about the correct metaphysics of action. Of course, if AR is to be respected in these theories, inertia must be taken as a brute fact, a position advocated, in different ways, by Schlick and others, as we have seen. Such a position is surely defensible in the context of these theories.
The two epigrammatic Einstein quotations cited at the beginning of this essay underscore how Einstein’s thinking changed between 1905 and 1913, and again between 1913 and 1924. In the years 1912 and 1913, when Mach’s influence on him may have been greatest, Einstein had convinced himself that the phenomenon of inertia required a causal explanation, while regarding as absurd the notion of immaterial space acting as such a cause. By 1924, he was stressing that the metric field in GR is as real and efficacious as the electromagnetic field, and in particular could indeed be seen as the origin of inertia. (But it is worth stressing here that Einstein did not view GR as furnishing a geometric explanation of gravitational phenomena; he continued to reject the notion of space, or space-time, as providing the cause of inertia.89)
Nowadays, acceptance of Einstein’s 1924 claim should be seen to rest not simply on the nature of gμν and its geodesics, but rather on the so-called geodesic theorem, which demonstrates that the form of Einstein’s field equations, along, it must be noted, with other plausible universal assumptions about matter fields, imply that the world-lines of test particles are time-like geodesics as defined by the metric field.90 Note that the theorem deals with an idealisation; it states that extended, but truly freely-falling bodies only approximately move inertially.91 In fact, it is a subject worthy of investigation as to whether the details of the theorem are strictly consistent with Einstein’s insistence that a violation of AR holds in theories with absolute space-time structure.92 But such an investigation must be pursued elsewhere. It is our hope that in the present essay, some further light has been shed on the circumstances which led Einstein to bring to the fore the role of the action–reaction principle in his new theory of gravity.
83Einstein [1920a].
84Einstein [1921] p. 12 see also Vol.7, Doc. 31 CPAE for a similar statement from December 1919 / January 1920. 85Compare Norton [1989b], p. 24: “[I]t was natural for expect that the extended theory, which dealt with general gravitational effects, would explain the observed disposition of inertial frames of reference in terms of the matter distribution of the universe. For the structure that determined this disposition would behave in many aspects like a traditional gravitational field and therefore be strongly influenced by any motion of its sources, the masses of the universe.”
On Oct 8, 2013, at 1:54 PM, Jack <jacksarfatti@gmail.com> wrote:
Sent from my iPhone
On Oct 8, 2013, at 1:45 PM, Max Comess <mcomess@gmail.com> wrote:[Add more about details relating to stargates (e.g. metrics, exotic matter requirements, etc), why is this approach different from previous wormhole literature? Also, is there a particular experimental approach you suggest pursuing, or any experimental work that has already been done to validate your hypothesis?]
Obviously i will
"Gravitational field is the manifestation of space-time translational (T4) gauge symmetry, which enables gravitational interaction to be unified with the strong and the electroweak interactions. Such a total-unified model is based on a generalized Yang-Mills framework in flat space-time."I have said this for many years now.
Note that the total energy of the gravity field has this Q problem suggesting gravity as a "More is different" (P.W. Anderson) low-energy emergent field from a spontaneous broken vacuum symmetry at the Alpha Moment of Inflation (zero conformal time & zero comoving distance in Tamara Davis’s Fig 1.1 c) from false to true vacuum in the above picture.
On the other hand gravity is also induced by localizing the universal global gauge (De Sitter - Poincare group) - so how do we merge these two ideas from different levels?
One model is G = O(9) spontaneously breaks to H = O(8) giving 8 Goldstone post-inflation condensates whose quantized vibrations are the massless SU3 QCD gluons via an analytic continuation of non-compact O(9)/O(8) to compact SU3?
This model has 28 Higgs-like massive bosons - not to be confused with the single electro-weak Higgs allegedly now found at LHC from G = U1xSU2 ---> H = U1 where the three massless W bosons of SU2 essentially absorb the three massless Goldstone bosons leaving only the single massive Higgs boson in this simplest of models.
28 + 8 = 36 = 9x8/2 = number of spacetime charges in string theory type O(9) spacelike sub-group of string theory O(1,9) with 6 extra space dimensions.O(9) is for the spacelike slices of O(1,9) used in superstring theory