I found my copy of L&L's Electrodynamics of Continuous Media - tricky stuff.
I will have more to say on why my eq 8 for the gravity field in materials in Woodward's paper is completely justified because of similar arguments Landau & Lifshitz's make for the D and H electromagnetic fields in moving conductors and dielectrics.
Basic rule of thumb is you keep the covariant form of the equations while changing the constituitive parameters.
Yes, E and B are the exterior vacuum applied EM fields independent of the material structure
D and H are the interior material forms depending on induced polarization (charge separations from E) as well as magnetic moment couplings to B
the energy densities are E.D and B.H.
For example, starting in vacuum with its bare permittivity and permeability, the field tensor for D & H in the material is same as it would be in vacuum using the modified lumped parameter "dressed" permittivity and permeability - even though the speed of light is slower in the material, so strictly speaking it is not invariant as it is in vacuum as proved by the Cerenkov effect.
e.g. for moving dielectrics for exterior measurements by inertial observers outside the dielectric (in contrast to Maxwell nano-demons inside the dielectric clamped to its lattice or moving SLOWLY v/c << 1 Galilean relativity) through it)
"to ensure relativistic invariance ... it is necessary that the components of the vectors D and H should be transformed exactly as the components of a four-tensor similar to" the one for E and B in vacuum section 76 of L&L ED of continuous media
i.e. a simple charge renormalization of sorts. I do the same thing in my eq 8 keeping Einstein's gravity field equation formally covariant inside the meta-material in the same way that Landau and Lifshitz do for Maxwell's EM field equation inside a dielectric that can be in motion relative to an exterior observer.
So what I have done in eq 8 is very plausible and definitely Popper falsifiable. Vague handwaving appeals to "background independence" are definitely specious at this early stage in the game of unexplored physics.
Again - there is no group velocity for near coherent EM fields because they do not obey an f = f(k) dispersion relation unlike coherent far fields.
coherent near induction fields (e.g. Tesla's playground) are Glauber states of virtual photons of all four polarizations with one gauge constraint.
coherent far radiation fields (lasers, masers) are Glauber states of real photons of only two transverse polarizations (for zero rest mass).
changing the subject
F = dA
dF = 0 is for Faraday induction and no real magnetic monopole - it is topological independent of the material structures
d*F = *J is Ampere's law and Gauss's law including the interiors of materials
i.e. *F uses induced D and H fields not the bare vacuum E and B fields.
d is the Cartan exterior derivative in globally flat Minkowski spacetime of 1905 Einstein special relativity
d^2*F = d*J = 0 is LOCAL conservation of electric current densities.
Maxwell's EM field coupled to Einstein's curved spacetime gravity field is gotten by universal minimal coupling (i.e. the strong equivalence principle) that
d is replaced by D the covariant exterior derivative
D = d + Spin Connection 1-form
Einstein's curvature 2-form is
R = D(Spin Connection)
S = spin connection
Maxwell's EM equations coupled to gravity are simply
F' = DA = dA + S/\A
DF' = 0
i.e.
d(S/\A) + S/\dA + S/\S/\A = 0
D*F' = *J
D*J = 0 i.e. local conservation of electric current densities in curved spacetime.
On Aug 4, 2011, at 11:19 AM, X wrote:
I don't honestly see a distinction between the Higgs field in the Standard Model, and the gravinertial field in Mach's Principle.
That's because you have no understanding of the pre-requisite mathematics beyond vague informal plain English metaphors of pop books and internet posts. It does not matter how high your IQ is if you can't speak the language - in this case applied mathematics. Start by reading Roger Penrose's "The Road to Reality."
OK test yourself
1) What are the equations for the Higgs field in the standard model?
2) What are the premises for that model?
3) What are the equations for the gravi-inertial field in Mach's principle?
4) What are the premises for it?
5) What is the relation of it to Einstein's general relativity?
The Higgs field comes out of the standard model in Special Relativity, there is no gravity in it at all.
In other words, are your words above not even wrong malapropisms?
Test yourself. I am not trying to insult you or anyone else. I am only acting as any hard-core physics professor would in an elite university (like Cornell, UCSD, UCB, Cal Tech ....) would do - at least in the 1950's and 60's before political correctness took over.
Both are universal.
Inertial pseudo-forces are contingent artifacts of the acceleration of the small detector that forms the local frame of reference.
Newton's universal gravity force per unit test particle is actually, in Einstein's terms of curved spacetime, simply the covariant acceleration needed to keep the detector "static" fixed in space relative to the static spherically symmetric mass curving the spacetime. This is shown in Hawking's picture
The post-inflation Higgs and Goldstone smooth coherent c-number ODLRO vacuum fields are the amplitudes and phases of condensates of virtual massless lepton and quark particle-antiparticle pairs and their induced virtual photons, massless W mesons and massless gluons that give rest masses to real leptons and quarks as well as real W mesons at high energies.
There is no connection at all to Newton's "gravity force" that is a contingent low energy emergent inertial pseudo-force corresponding to a very particular arbitrary convenient choice - since we are stuck on the surface of hard rock.
The only objective c-number gravity fields are the tetrads e^I and spin connections w^I^J for the geodesic local inertial frames (LIFs) in curved spacetime and the curvature tensor fields derived from them.
Both are said to give matter its mass or mass its inertia, depending upon your choice of phrase. In either case, what Jim is talking about is manipulating a non-zero field in order to temporarily fluctuate the mass caused by the field.
This is hogwash. The gravi-inertial field PROPERLY DEFINED in battle-tested Einstein GR, has nothing whatsoever to do with creating the invariant rest mass of elementary particles. That's pure bunkum.
If one wanted to presume inertia was an intrinsic property of mass, as it sounded Jean-Luc was doing the other day, then Higgs bosons would not need the Higgs field to have mass. Seems the Standard model is saying this isn't so.
Just trying to be clear on this for myself--I don't see a distinction with a difference here, between what the Standard Model says about the Higgs field, and what Mach, Sciama, Woodward, etc. say about the origins of inertia. In the Standard Model, a universal, non-zero field gives the Higgs its mass. I think what we have here is the history of the Standard Model is in accord with what Mach was saying well before and in fact is requiring once again that Mach was right, same as GR requires Mach was right.
On Thu, Aug 4, 2011 at 2:05 PM, Jack Sarfatti <
On Aug 4, 2011, at 10:39 AM, Paul Zielinski <
> So you're saying that the Higgs mechanism doesn't actually require or predict the existence of a detectable Higgs boson?
Right can u see an isolated Cooper pair boson in empty space outside the crystal lattice?
>
> Then why all the hoopla about the search for the "God particle"?
Some models predict it like pulling a helium atom out of a superfluid helium 4 condensate.
There is a lot of leeway Spontaneous breakdown of vacuum solution symmetries of the underlying local Lagrange field equations that keep the symmetries is very general.
U can break Lorentz group as well as general covariance group in the solutions just like U1 breaks in a superconductor.
>
> On 8/4/2011 9:41 AM, JACK SARFATTI wrote:
>> Z's remark below is a common misconception based on the fact that many physicists do not properly understand the physical meaning of the distinction between real and virtual particles and spontaneous symmetry breaking.
>>
>> The Higgs field that gives the small rest masses to leptons and quarks is macroquantum off-diagonal order of the density matrix of virtual particles inside the vacuum. It does not even require that there be a real Higgs boson, though there might be. If the off-diagonal order ODLRO is a Bose-Einstein condensate of Higgs Goldstone bosons possibly one will see it. However, that is not the only alternative. The difference is seen in the case of the BCS superconductor. There, the ODLRO is a Bose-Einstein condensate of Cooper-Pairs, but you never see an isolated Cooper pair outside of the condensate, because the Cooper pair of electrons is bound by crystal vibrations - VIRTUAL phonons. The vacuum Higgs field may be similar, e.g. "Cooper pairs" of virtual quarks. If they are virtual quark-antiquark pairs they will be virtual mesons.
>>
>> In short the constituents of a virtual Bose-Einstein condensate do not need to exist as isolated real particles, though they might. Whether they do or not depends on other details of the dynamics.
>>
>> On Aug 4, 2011, at 8:59 AM, Paul Zielinski wrote:
>>
>>> If CERN can't produce convincing evidence for the existence of the Higgs boson, I will begin to suspect that
>>> the Standard Model is also a Ponzi scheme.
>>>
>>> On 8/4/2011 8:56 AM, .... wrote:
>>>> Feynman thought that string theory was something which physicists could
>>>> immerse themselves in which was interesting, engaging, beautiful, and
>>>> ultimately useless. It's a ponzi scheme to the extent that it keeps them
>>>> employed but will never actually produce anything worthwhile. If Feynman
>>>> knew what he was talking about. Lee Smolin's book, "The Trouble with
>>>> Physics" discusses this and other related questions.
>>>>
>>>> PSB, Ph.D.
>>>>