> In response to a previous email

Will an antisymmetric part of the connection do the latter?

> Jack said

> I specifically focussed on detailed local field patterns. For example, path

> of a

> light beam in flat space-time is not same as in curved space time. An extreme

> example is a trapped surface in curved space time.

> *

> Kiehn responds

> The path of a light beam (normal field to a characteristic surface) in a

> gravitational field is a solution to the equations of Maxwell, subject to the

> constraint that the eikonal and the null line element are the same.

> The equations of Maxwell involving the E,B and D,H fields remain the same

> independent from the constraint. The solutions depend upon the constraints,

> especially the characteristic solutions upon which the field amplitudes can

> be discontinuous.

> *

> Jack said:

> Certainly what you say at the abstract global bare bones topological level is

> true, but physicists find phenomena at the more concrete connection and metric

> levels that add flesh to the bones. So we are talking past each other.

> Einstein's

> GR is a local metric theory of gravity for example.

> *

> Kiehn responds:

> A metric based theory of constitutive equations (a la Misner, et. al.) can be

> used to explain bi- refringence and Fresnel - Fizeau effects. It does not

> explain Faraday rotation nor Optical Activity.

>

Please point to your URLS with more details on this. In this case you mean

> More than that , such an assumption indicates that the speed of an

> electromagnetic signal propagating away from you is always the same as the

> speed of a signal propagating towards you. This incorrect dogma, I guess,

> dates back to Einstein. It is based upon assumptions about constitutive

> constraints.

constraints as part of the structure of the physical vacuum I presume. That is,

the metric properties as a kind of constraint.

>

This seems to be a significant remark with many implications.

> It is not true that the speed of light is the same in all directions, nor is

> it true that the Faraday effect and Optical Activity are "similar" concepts.

> Such dogma has been preached by Jacksonian EM enthusiasts for almost 3

> generations, now, and it is not correct.

> *

>

OK so you are saying this is more than theory.

> Theoretical solutions to Maxwell's E,B,D,H equations indicate that a

> combination of Optical Activity and Faraday phenomena produce Quaternion wave

> solutions for the singular surfaces or characteristics.

> The propagation speeds are different in different directions!

> These results were used by my student Virgil Sanders and myself to construct

> a dual polarized ring laser. The experiments justified the assertion that

> speed of light is not the same in different directions and led to several

> patents and industrial secrets.

>

Why not?

> The dual polarized ring laser uses an optical cavity which is the same for

> both directions of signal propagation. Yet when the system is rotated, and

> beams in opposite directions are extracted and mixed on a non-linear diode,

> the result is a beat signal (not a spatial phase component, but a time phase

> component) depending on the rotation rate of the apparatus.

> This phenomena is related to, but is not the same as, the Sagnac effect

> (which is a spatial phase effect)

> The theory for this work appears in the physical review,

> Phys Rev A, 43 , (1991) p. 5665

> but a download is available in pdf format at

> http://www22.pair.com/csdc/pdf/timerev.pdf

> I knew these results in 1975.

> *

> Jack said

> These would be constitutive constraints on the quantum vacuum, i.e.

> polarization

> of virtual electron-positron pairs etc.

> *

> Kiehn responds

> I am not empathetic with such an approach.

>

This should connect to Kleinert's 1-dim defect picture of general relativity which

> *

> Jack said

> The physical vacuum is "media" in your sense because of quantum effects.

> *

> Kiehn responds

> I would prefer to say: "because of creation of topological defects created by

> non-zero values of the Poincare deformation invariants". I call these

> defects topological spin and topological torsion. Although the values of

> integrals of these defects are rational, it is not certain that this means

> "quantum mechanics". I personally believe the conjecture is valid, but the

> idea remains a conjecture.

>

> *

also comes up in Ashtekar's nonperturbative approach to quantum gravity. 1-dim as

"strings" in a rough sense.

>

What are the implications of what you just said for the distinction between near

> Kiehn said

> > I do object to the statements that state that Classical EM theory (the PDE's

> > of Maxwell Faraday and the PDEs of Maxwell Ampere) are metric and connection

> > dependent. It is an error to say that the PDE's of Maxwell-Faraday are not

> > preserved in form with respect to Galilean transforms,

> *

> Jack said

> You mean like most of the mainstream physics text books say in motivating

> Einstein's special relativity?

> *

> Kiehn responds

> Absolutely correct. A defect of dogmatic teaching without thinking. Look at

> the 3 line proof.

> 1. Maxwell's equations are tensor equations

> 2. All tensor equations are covariant in form with respect to

> diffeomorphisms.

> 3. The Galilean transformation ( as well as many many others) is a

> diffeomorphism.

> *

> Kiehn continued

> > or any other diffeomorphism.

> > What is not preserved are the characteristics of the PDE's, that is the

> point

> > sets upon which analytic continuation fails.

> > The constitutive equations can be metric dependent, but the Maxwell

> equations

> > as PDE,s are not metric dependent.

and far fields? Given a partial differential equation of second order in two

variables for simplicity (1 + 1 "string" space-time), following #8 of Sommerfeld's

"Partial Differential Equations", one gets to a determinant. The issue is whether

the determinant vanishes. The characteristics are two families of curves (advanced

and retarded potentials) for every point on which the determinant vanishes. Near

field seems to be a boundary curve for initial conditions that is not along a

characteristic. Far field radiation is when the curve is along a characteristic.

>

OK

> *

> Jack said

> Important distinction generally overlooked in the text books?

> *

> Kiehn responds

> Absolutely correct. Mostly do to the use of Jackson's EM textbook in the USA.

> Arnold Sommerfeld did not teach EM theory this way.

>

> Jack continues

> If I take a spherically symmetric set of electric field lines coming from a

> point

> charge, then make a Lorentz boost in a given direction, the equipotentials

> will

> pancake flattening along direction of the boosts and of course there will

> also be

> a magnetic field. Yes, there are frame invariants like FuvF^u^v. Is that what

> you

> mean? The invariants?

> *

> Kiehn responds

> The two Poincare invariants are closed integrals of (E dot B)and integrals of

> (B dot H - D dot E) - (A dot J - rho phi) over a space time volume. (note

> the factor of 1/2 is missing) These even dimensional integrals are

> invariants of all evolutionary processes that can be described by singly

> parameterized vector fields. When zero, the closed integrals of A^F and A^G

> (topological torsion and topological spin) are also deformation invariants.

> I know of no text books that discuss these issues.

> *

> Kiehn continues

> > Radiation propagates along characteric normal fields generated by the

> > eikonal, which is the point set upon which solutions to Maxwell Field

> > equations (PDE's) admit discontinuities. (Read Fock, Luneberg, Klein and

> Kaye)

> *

> Jack asks

> which, the GR book?

> *

> Kiehn responds

> "Space Time and Gravitation" by Fock

> This concept of characteristics has nothing to do with connection,

> explicitly, as far as I know.

> But I may be naive on this point.

> *

> Jack says

> But in a classical vacuum (not quantum) D = E outside the charge itself.

> *

> Kiehn says

> No

> D = epsilon E

> D is a contravariant tensor density,

> E is a covariant tensor.

>

I suspect that this because they assume the standard symmetric Levi Civita

> Kiehn continues

>

> > Certainly it can be valid that under constraint assumptions the metric and

> > connections may be influential. Recall that the only linear transformation

> > set that preserves the discontinuity eikonal solutions is the Lorentz

> > equivalence class. Note that the Schwarzschild solution is not "Lorentz

> > invariant". However, recall that the fractional Moebius projective

> > transformations also preserve the eikonal discontinuity solutions. A signal

> > is not described by all wave solutions; it is described by that special

> > class of waves which represent propagating discontinuities. Einstein never

> > precisely defined a "signal". Fock did.

> *

> Jack says

> I agree this is an important point that is ignored in mainstream courses.

> Where is

> it in Jackson?

>

> *

> Kiehn responds

> It is not in JACKSON. That is why Jackson's text should not be used to teach

> classical EM theory.

> Kiehn continues

> > The topological properties of the electromagnetic field need not be

> > conserved, and indeed are not conserved when either of the two Poincare

> > "invariants" are not zero.

> > Parity is violated when the topological torsion has a non-zero divergence.

> >

> *

> Jack says

> Again none of this is well known in physics text books today - or am I wrong

> about

> that?

> *

> Kiehn responds.

> Absolutely correct.

> --------

> Kiehn continues

> > I disagree emphatically, for F-dA = 0 generates the Faraday induction law as

> > a universal statement, independent of metric, connection, the number of

> > dimensions, or position in the universe.

> > I find this universality to be very interesting.

> *

> Jack asks

> Indeed. Are you implying that Corum is not paying enough attention to this

> distinction?

> *

> Kiehn responds

> Absolutely correct again.

>

> >

> > *

> Jack said

>

> We are apparently not talking about same thing here. Just look at Maxwell

> field

> theory in a curved metric. In Einstein's theory GR the distance between to

> nearby

> points is invariant and that's how gravity happens according to mainstream

> physics. The covariant derivative in the sense I mean is the way Misner

> Thorne and

> Wheeler "Gravitation" adapt Maxwell's flat space-time theory via the

> equivalence

> principle with minimal coupling i.e. changing partial derivatives , to

> covariant

> derivatives ; (for symmetric Levi-Civita connection) done explicitly in 22.4

> eqs.

> 22.17 - 22.22) pp 568-570. That's what I meant. Surely, you do not dispute

> that?

> *

> Kiehn responds.

> Yes I do contest this approach.

> The Misner Wheeler case is a special case of constraints, and implies that

> Faraday effects and Optical Activity effects are excluded by the constraint

> assumptions.

connection. So you may be arguing for the nonsymmetric connection classical

unified field theory that Einstein was working on in his later years.

> The speed of light is the same in both directions.

Something like this may happen in M-theory as well because the antisymmetric

> But with a rotating ring laser I find that light signals experimentally do

> not propagate with the same speed in the left handed vs right handed

> directions.

> *

connection is in it.

>

OK important distinction I agree.

> Jack asks

> However, will a nonsymmetric connection simulate analogs to piezo

> electricity?

> *

> Kiehn responds

> I do not know the answer, but I suspect that if the EM potential 1-form A is

> 1 component of a connection based constraint, then the topological torsion of

> that 1-form and the corresponding Cartan torsion of the assumed connection

> will express some difference between left handed and right handed

> polarizations. The more important problem is how the constraint affects

> propagation direction.

> *

> Sarfatti says

> Beginning to sound like Salam's strong short range gravity L*. Of course,

> none of

> what you say above is well known. You do not find it in Misner Thorne &

> Wheeler

> for example. There is no "Pfaff" in the index. So this is your own original

> research I presume?

> *

> Kiehn responds (in reference to the 4 forces)

> Yes

> But it has been (ignored) in the literature for a long time.

> Kiehn, R. M., 1975, "Submersive equivalence classes for metric fields", Lett.

> al Nuovo Cimento 14, p. 308.

> Kiehn, R. M., (1975a), "A Geometric model for supersymmetry", Lett. al Nuovo

> Cimento 12, p. 300.

>

> *

> Jaclk says

> No, for one thing Corum uses precisely that equation to explain the Sagnac

> effect

> for rotating interferometers and that Sagnac effect is on Bo Lehnert's list of

> actually observed related electrodynamic anomalies.

> *

> Kiehn responds

> I have some experimental and theoretical experience with rotating dual

> polarized ring lasers, that cause me to have a different viewpoint. The work

> is related to the Sagnac effect in the frequency domain, not in the wave

> number domain.

>

But physically are these interpenetrating parallel realities of some kind? This is

>

> *

> Jack comments (related to multiple components)

>

> Like two universes floating in hyperspace perhaps as in Kaku's book? I think

> Ch

> 10.

> *

> Kiehn responds

> No, two bounded universes in the same space time domain would perhaps be more

> to the point that I make. Physicists with their insistance on functional

> forms for unique descriptions of "physical systems" miss the opportunities of

> systems with separated non-unique multiple components. These multiple

> components do not have to be in "other dimensions". Consider the sun and the

> earth. Two bounded physical systems. There is not a single parametric

> functional map from space time to describe both objects. However, there is a

> single implicit surface such that the zero set describes the two balls (both

> in the same space time arena and not in higher dimensions.)

what Vallee has been suggesting. The "implicit surface" is simply another way to

formulate hyperspace I suspect.

>

Oh yes. I knew that but did not not remember it was called "Cayley Hamilton".

> > Kiehn continues

> > Consider any dimension N

> > Construct the homgeneous 1-form, and its Jacobian matrix.

> > The similarity invariants are of degree 1, 2, 3, 4, 5,....

> > and are computed via the Cayley Hamilton theorem.

> *

> Jack says

> Which I have forgotten and which most physicists probably do not know. :-)

> *

> Kiehn responds

> The Cayley Hamilton theorem says that any square matrix M of n x n terms

> satisfies a polynomial expression of degree n. The coefficients of the

> polynomial are similarity invariants of the matrix and remain the same if the

> matrix is transformed to Mprime= T M T^-1, for any T.

>

Have you written any pedagogical URLs on this?

> The coefficients appear as the mean curvature, Gauss curvature, etc in

> differential geometry, and for complex matrices form the basis for the Chern

> numbers so vital to Witten type research.

>

Nice. :-)

> For the matrix associated with the 3D Gibbs function in thermodynamics, the

> points upon which the Gauss curvature (second similarity invariant) vanishes

> corresponds to the spinodal line (phase transitions). When both the Gauss

> curvature and the mean curvature vanish, the system is at the critical point.

> This implies that all 3 dimensional systems have an analogue as a Van der

> Waals gas.

> see

> http://www22.pair.com/csdc/pdf/vwgas.pdf

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