Ken S. Tucker wrote:
Ken S. Tucker wrote:
FrediFizzx wrote:
"Jay R. Yablon" wrote in message
...
| Hello to everyone:
|
| My newest paper, "General Relativity, Maxwell's Electrodynamics, and
the
| Foundations of the Quantum Theory of Gravitation and Matter," just
posted to
| ArXiV.
|
| The link is http://arxiv.org/abs/gr-qc/0511050.
|
| I would very much appreciate any comments and input you may have.

Hi Jay,

As I mentioned before; pretty fantastic! Do you think you could do a
summary of the postulates and a run down of the major features here?
FrediFizzx

Hi Fred and all...
let me try to explain that, because Jay's helped me understand the
paper,
so I'm a bit 2nd hand, and a bit off-the-cuff.

The paper is Maxwell's Equations (ME's) Super-charged.

Reviewing back to ME's and SR we note the relation of the
E and B fields in the the propagation of EMR is,

E x B = c , ( = indicates direction),

and "c" is the classical constant of the "velocity" of light in a
vacuum.

Consider E and B to be unit vectors then E x B = c = 1 in a vacuum,

and importantly E.B =0 , (scalar product).

When these equations for the propagation of light encounter a
gravitational field, a modification occurs, so that, c is not a
constant velocity. For example, the direction changes, (deflection)
the speed changes (Shapiro) and the frequency changes.

So we can re-write the transformed ME's in a g-field as

E' x B' = c' 1 AND E'.B' 0 ,

the later being crucial in the paper. That is entirely consistent
with taking an orthogonal ME relation E x B = c into a warped
spacetime, consistent with the g-field at the location of E' etc,
as a propagating EM-wave encounters a "nonorthogonal" field.

Underwriting physics is mathematics. What Jay did is to use
the "dual tensors" like

F_uv F*^uv == E.B == F_01 F*^01 = F_01 F_23

to form invariants that become E'.B' anywhere, but included a
coefficient normally marginalized in classical GR denoted,

|g_uv| = g.

such that F*^01 = F_23 / sqrt(-g), to decribe EM-fields.

The theory permits the inclusion of "magnetic monopoles"
and "negative matter", but exists fine even if those concepts
are negated.

Jay, around pg. 13, in the paper introduces what I call the
"Principle of Equilibrium", where matter reforms by the
action of potentials to tend to an entropy, by geodesics,
consistent with GR, so far as a continuum theory permits.

Recall

PRESSURE x VOLUME/ TEMPERATURE

is an invariant for an ideal gas, is firmly related to EM and
GR.

To establish an Equilibrium of the pressure, volume and
temperature when one of those are changed the paper
suggests a differential variation of the geodesics.
Tucker argues the "differential" is quantized, IOW's
the Equilibrium is obtained "inexactly".

But the paper, highlights in specific terms, how to argue
those points, and stands independant of the outcome
of those arguments.

Regards
Ken S. Tucker

I'd like to add a comment. (These comments are mine and Jay
may not necessarily agree).

The term " (E.B) sqrt(-g) " that appears in Eq.(2.35) and others
appears as a strange way to write up a geodesic equation, but
Unified Field Theories wear different coats. Let me give a quick
demo, (I'll add explanations if this is too quick)...

Begin with geodesic Eq.(2.35),

k_v = [ (E.B) sqrt(-g) ],v = [K],v = 0

k_v = K,v = 0 , K is Konstant.

Set V = E.B , V is a Velocity.

V^2 g = -K^2

Set 2p = V^2 , p = gravitational potential

2p*g = -K^2

dp g = - p dg

dp = - p dlog g = - 2*p {uv,u} dx^v

{uv,u} is a Christoffel symbol of the 2nd kind.
2nd kind = f(sqrt -1)

??? ;-)

Sue...


V = dr/ds

dp/dr = - {uv,u} U^v V

The Looks like Newton, Einstein and EM in a neat package!

What I find quite remarkable, is that a geodesic derived
from K,v=0 is expressed on the L.H.S. as "dp/dr", but the
usual from GR is expressed "dU^i/ds", which conceptually,
is quite distinct although physically very similiar.

For those reasons and more, I find [K] above to be a very
rich equation, and suggest caution in marginalizing it.
Regards
Ken S. Tucker

Ken S. Tucker wrote:
Ken S. Tucker wrote:
FrediFizzx wrote:
"Jay R. Yablon" wrote in message
...
| Hello to everyone:
|
| My newest paper, "General Relativity, Maxwell's Electrodynamics, and
the
| Foundations of the Quantum Theory of Gravitation and Matter," just
posted to
| ArXiV.
|
| The link is http://arxiv.org/abs/gr-qc/0511050.
|
| I would very much appreciate any comments and input you may have.

Hi Jay,

As I mentioned before; pretty fantastic! Do you think you could do a
summary of the postulates and a run down of the major features here?
FrediFizzx

Hi Fred and all...
let me try to explain that, because Jay's helped me understand the
paper,
so I'm a bit 2nd hand, and a bit off-the-cuff.

The paper is Maxwell's Equations (ME's) Super-charged.

Reviewing back to ME's and SR we note the relation of the
E and B fields in the the propagation of EMR is,

E x B = c , ( = indicates direction),

and "c" is the classical constant of the "velocity" of light in a
vacuum.

Consider E and B to be unit vectors then E x B = c = 1 in a vacuum,

and importantly E.B =0 , (scalar product).

When these equations for the propagation of light encounter a
gravitational field, a modification occurs, so that, c is not a
constant velocity. For example, the direction changes, (deflection)
the speed changes (Shapiro) and the frequency changes.

So we can re-write the transformed ME's in a g-field as

E' x B' = c' 1 AND E'.B' 0 ,

the later being crucial in the paper. That is entirely consistent
with taking an orthogonal ME relation E x B = c into a warped
spacetime, consistent with the g-field at the location of E' etc,
as a propagating EM-wave encounters a "nonorthogonal" field.

Underwriting physics is mathematics. What Jay did is to use
the "dual tensors" like

F_uv F*^uv == E.B == F_01 F*^01 = F_01 F_23

to form invariants that become E'.B' anywhere, but included a
coefficient normally marginalized in classical GR denoted,

|g_uv| = g.

such that F*^01 = F_23 / sqrt(-g), to decribe EM-fields.

The theory permits the inclusion of "magnetic monopoles"
and "negative matter", but exists fine even if those concepts
are negated.

Jay, around pg. 13, in the paper introduces what I call the
"Principle of Equilibrium", where matter reforms by the
action of potentials to tend to an entropy, by geodesics,
consistent with GR, so far as a continuum theory permits.

Recall

PRESSURE x VOLUME/ TEMPERATURE

is an invariant for an ideal gas, is firmly related to EM and
GR.

To establish an Equilibrium of the pressure, volume and
temperature when one of those are changed the paper
suggests a differential variation of the geodesics.
Tucker argues the "differential" is quantized, IOW's
the Equilibrium is obtained "inexactly".

But the paper, highlights in specific terms, how to argue
those points, and stands independant of the outcome
of those arguments.

Regards
Ken S. Tucker

I'd like to add a comment. (These comments are mine and Jay
may not necessarily agree).

The term " (E.B) sqrt(-g) " that appears in Eq.(2.35) and others
appears as a strange way to write up a geodesic equation, but
Unified Field Theories wear different coats. Let me give a quick
demo, (I'll add explanations if this is too quick)...

Begin with geodesic Eq.(2.35),

k_v = [ (E.B) sqrt(-g) ],v = [K],v = 0

k_v = K,v = 0 , K is Konstant.

Set V = E.B , V is a Velocity.

V^2 g = -K^2

Set 2p = V^2 , p = gravitational potential

2p*g = -K^2

dp g = - p dg

dp = - p dlog g = - 2*p {uv,u} dx^v

{uv,u} is a Christoffel symbol of the 2nd kind.

I should explain a bit more.
We can use some very compact notation and sqrt -1
to skew time a bit so we resolve why a motors current
and voltage don't indicate it's power or resolve why
the speed of light is not violated in Maxwell's near field.

OTOH we can use the same compact notation to
show painting the pyramids of Giza with 1 liter of paint
or justify the possibility we might have a pet dinosaur.

You can't simply write the compact forms and expect
your reader to imagine the rigor.

We have to call these forms "food for thought"
I am not suggesting your equations are right or wrong.
But they do seem to be assumimg quite a bit to expect
gravity to be operational at a subatomic level.

The force between two charges and the force between
two masses represents no energy exchange. So forms
that use *time* have to be viewed with a caution.

I haven't had to change the batteries in my refrigerator
magnets yet. ;-)
http://en.wikipedia.org/wiki/Triple_integral

Sue...



V = dr/ds

dp/dr = - {uv,u} U^v V

The Looks like Newton, Einstein and EM in a neat package!

What I find quite remarkable, is that a geodesic derived
from K,v=0 is expressed on the L.H.S. as "dp/dr", but the
usual from GR is expressed "dU^i/ds", which conceptually,
is quite distinct although physically very similiar.

For those reasons and more, I find [K] above to be a very
rich equation, and suggest caution in marginalizing it.
Regards
Ken S. Tucker

[more good stuff]

Then, solve for the metric, and you will
already have built into from scratch, by construction, all that we know
about QED and QCD and QWD.

so no gravitons then, but still gravity waves, I take it?

Do you feel there is a need to quantise gravity, from a "consistency"
point of view? Or until someone finds a graviton there is no need?

Well, Brendan, I have to very much suspect that there are gravitons, because
I don't see how gravitation can be exempt from energy quantization. I have
spent quite a lot of time thinking about how the energy in T^uv_;u gets
exchanged with the kappa^v.


I guess your theory is still compatible with the Higgs boson? (I know
you have alternative thoughts on mass - do you have a problem with the
Higgs?)

I do not have a problem with scalar fields operated on by the Klein Gordon
(relativistic Schrödinger) equation. I think the Higgs mechanism is the
weakest part of the standard model (and am not alone in this view), and am
always on the lookout for a "cleaner" way to generate mass which has the
same net results as the Higgs, but will also get us to Fermion masses.
See, e.g., my unpublished paper at
http://home.nycap.rr.com/jry/Papers/...n%20Masses.pdf.


Even after you have finished your current line of thought, do you think
there will still be need for a further "underlying" theory, or will you
have got everything? That is, you really will have a "theory of
everything"? (of course I speak of current knowledge, as far as we know
now. We'll ignore fundamental discoveries in the future for the
moment!). What objections do you imagine?

The work I presented here still does not tell us about weak / strong
unification, which I believe is better thought of as unification of
"isospin" and "color" internal symmetries into spin 1/2 fermions which carry
both of these internal symmetries, and which I think will go hand in hand
with leptoquark unification. The best shot I have seen to date is the
Volovik paper, section 12.2, which I have referenced in my papers. My own
take on how to improve the spin problems with Volovik's presentation (which
is the only thing I would change about it) is summarized in section 8 of my
draft paper at
http://home.nycap.rr.com/jry/Papers/...ew%20Paper.pdf, see
(8.12) and (8.13) in particular.

I also don't know what the spacetime metric will actually look like once we
have obtained real-world solutions making use of F^uv in the energy tensor
but treating F^uv according to Yang Mills rather than as strictly classical
fields. An open question for me, which gets back to your question about
gravitons, is whether by plugging in F^uv from Yang Mills via the energy
tensor at the second order in the metric, some spin 2 quanta will emerge
naturally, or whether we will still have the problem of quantum gravity to
contend with even after we have integrated QED. QCD and QWD into
gravitational theory and seen what the metrics look like.


I did not submit the earlier two papers. I DO plan to submit this new
paper, but first want to vet this paper so that I can get any of the
"kinks"
out.

Not being associated with an institution I guess means you have to pay
for publication out of personal cash, but it still seems like a good
idea that you put in the other papers as well. They are highly
relevant, and deserve a proper reference, and with full peer-review you
might get more feedback.

Thank you, and I am thinking about how to encapsulate everything into a good
journal article. The advantage of ArXiV is that I can put the details in
those papers, and then just do a referenced summary for a journal.

On the other hand my reaction to reviewer
objections is often "but the reviewer obviously hasn't even read what I
wrote!"

Well, that is true. And I feel that if these days I am not talking about
strings or something else which has a political / economic constituency
behind it, nobody will take the time to really try to understand it. Or,
they will look for the first thing they can latch onto to debunk it. And I
certainly am at a disadvantage coming from outside and taking unconventional
approaches as I do. But I believe what I am putting out these days will
eventually become recognized as fundamental; I just hope that "eventually" =
"in my lifetime" and may even = "soon." (When they find the neutral vector
boson near 2.35 TeV predicted in my monopole paper, people will have to
recognize that nature is arbitrating in my favor. If they don't find it . .
.. that's how it goes. But, I've already accounted for 60% of the NuTeV
anomaly, and can get the other 40% from weak magnetic monopoles which I am
seriously thinking needs to be shown explicitly in my next paper.)


Has Bjoern read this latest paper?

I don't think so; he and I have touched base here and there; he has a full
plate these days.


Thanks for the opportunity to discuss.

I'm only sorry I can't help you more - all those tensors make my head
swim, and I don't have the time

Appreciated. Very best to you,

Jay.


Very best,

br

Hi Sue, mostly agree with you...

Sue... wrote:
Ken S. Tucker wrote:
Ken S. Tucker wrote:
FrediFizzx wrote:
"Jay R. Yablon" wrote in message
...
| Hello to everyone:
|
| My newest paper, "General Relativity, Maxwell's Electrodynamics, and
the
| Foundations of the Quantum Theory of Gravitation and Matter," just
posted to
| ArXiV.
|
| The link is http://arxiv.org/abs/gr-qc/0511050.
|
| I would very much appreciate any comments and input you may have.

Hi Jay,

As I mentioned before; pretty fantastic! Do you think you could do a
summary of the postulates and a run down of the major features here?
FrediFizzx

Hi Fred and all...
let me try to explain that, because Jay's helped me understand the
paper,
so I'm a bit 2nd hand, and a bit off-the-cuff.

The paper is Maxwell's Equations (ME's) Super-charged.

Reviewing back to ME's and SR we note the relation of the
E and B fields in the the propagation of EMR is,

E x B = c , ( = indicates direction),

and "c" is the classical constant of the "velocity" of light in a
vacuum.

Consider E and B to be unit vectors then E x B = c = 1 in a vacuum,

and importantly E.B =0 , (scalar product).

When these equations for the propagation of light encounter a
gravitational field, a modification occurs, so that, c is not a
constant velocity. For example, the direction changes, (deflection)
the speed changes (Shapiro) and the frequency changes.

So we can re-write the transformed ME's in a g-field as

E' x B' = c' 1 AND E'.B' 0 ,

the later being crucial in the paper. That is entirely consistent
with taking an orthogonal ME relation E x B = c into a warped
spacetime, consistent with the g-field at the location of E' etc,
as a propagating EM-wave encounters a "nonorthogonal" field.

Underwriting physics is mathematics. What Jay did is to use
the "dual tensors" like

F_uv F*^uv == E.B == F_01 F*^01 = F_01 F_23

to form invariants that become E'.B' anywhere, but included a
coefficient normally marginalized in classical GR denoted,

|g_uv| = g.

such that F*^01 = F_23 / sqrt(-g), to decribe EM-fields.

The theory permits the inclusion of "magnetic monopoles"
and "negative matter", but exists fine even if those concepts
are negated.

Jay, around pg. 13, in the paper introduces what I call the
"Principle of Equilibrium", where matter reforms by the
action of potentials to tend to an entropy, by geodesics,
consistent with GR, so far as a continuum theory permits.

Recall

PRESSURE x VOLUME/ TEMPERATURE

is an invariant for an ideal gas, is firmly related to EM and
GR.

To establish an Equilibrium of the pressure, volume and
temperature when one of those are changed the paper
suggests a differential variation of the geodesics.
Tucker argues the "differential" is quantized, IOW's
the Equilibrium is obtained "inexactly".

But the paper, highlights in specific terms, how to argue
those points, and stands independant of the outcome
of those arguments.

Regards
Ken S. Tucker

I'd like to add a comment. (These comments are mine and Jay
may not necessarily agree).

The term " (E.B) sqrt(-g) " that appears in Eq.(2.35) and others
appears as a strange way to write up a geodesic equation, but
Unified Field Theories wear different coats. Let me give a quick
demo, (I'll add explanations if this is too quick)...

Begin with geodesic Eq.(2.35),

k_v = [ (E.B) sqrt(-g) ],v = [K],v = 0

k_v = K,v = 0 , K is Konstant.

Set V = E.B , V is a Velocity.

V^2 g = -K^2

Set 2p = V^2 , p = gravitational potential

2p*g = -K^2

dp g = - p dg

dp = - p dlog g = - 2*p {uv,u} dx^v

{uv,u} is a Christoffel symbol of the 2nd kind.


I should explain a bit more.
We can use some very compact notation and sqrt -1
to skew time a bit so we resolve why a motors current
and voltage don't indicate it's power or resolve why
the speed of light is not violated in Maxwell's near field.

Yes that sqrt -1 is a handy tool in Reactance, however in
the crunch I don't use it in reality. Einstein employed it
(mistakenly in IMO) in GR, and it has reached near a
biblical diety. Jay Yablon (the author), following tradition,
used it in his equations.

That's why I squared the equation, stuck the negative
on a constant and took a derivative, so that the negative
aspect of the sqrt(-g) had no physical consequences.

You can't simply write the compact forms and expect
your reader to imagine the rigor.

The invariant Jay is exploiting is surprisingly simple,
(risking making too many equations) it's just,

F_uv F*^uv = E.B sqrt(g)

(I wish I had thought of that!)

We have to call these forms "food for thought"
I am not suggesting your equations are right or wrong.
But they do seem to be assumimg quite a bit to expect
gravity to be operational at a subatomic level.

The equations should be operational anywhere EM is,
and the developement is to acquire the ability to get
a "beach head" into particle physics to determine the
relevence of GR in HEP's.

The force between two charges and the force between
two masses represents no energy exchange. So forms
that use *time* have to be viewed with a caution.

Yeah, but in view of your comment below about frig-mags,
the moon don't need batteries to keep orbiting the earth,
sounds like there both geodesic :-).

I haven't had to change the batteries in my refrigerator
magnets yet. ;-)
http://en.wikipedia.org/wiki/Triple_integral

Sue...



V = dr/ds

dp/dr = - {uv,u} U^v V

The Looks like Newton, Einstein and EM in a neat package!

What I find quite remarkable, is that a geodesic derived
from K,v=0 is expressed on the L.H.S. as "dp/dr", but the
usual from GR is expressed "dU^i/ds", which conceptually,
is quite distinct although physically very similiar.

For those reasons and more, I find [K] above to be a very
rich equation, and suggest caution in marginalizing it.
Regards
Ken S. Tucker

Ken

PS: Thanks Autumn DC for corrections.

Hi Jay and all...

Evidentially Jay and I both see different ways of defining
the reality of "absolute acceleration", as Jays defines,
supported by the majority of GRist's. (Tolman's Relativity,
Eq.(103.1)), for my part Tolman never said that f^u force is
real and thus non-zero.

Weinberg in Grav & Cosmo, Eq.(5.2.8) tends to imply the
possiblity of "absolute force" (I would say quite firmly).

While keeping opened minded, Tucker will argue for a
strict GR interpretation, but needs further study on the
Eq.(2.35), with the respect of including EM fields.
Ken

Jay R. Yablon wrote:
Hi Ken: Let me offer some thoughts on the Gedanken you lay out below, which
you and I have been discussing privately.

PART I

Let us consider the equation of motion for a charged particle in an
electromagnetic field:

(dU^u/dtau) = (e/m)U_a F^ua (1)

where e is the electric charge and m is gravitational / inertial mass, both
in units of sqrt (h-bar c) and U^u is the velocity four vector. Rather than
thrusters, let us suppose that the astronaut wears a belt with a net
electric charge (or better yet, that she IS a collection of net electric
charge e and mass m), and that an external EM field F^ua from her nearby
spacecraft is suddenly turned on so that she is given an acceleration
dU^u/dtau by virtue of carrying a charge in the EM field, and she also feels
a "force" (which I will get to in more detail momentarily).

Before the EM field is turned on and after it is turned off, she is in
geodesic free fall, and so her motion is given by the other equation of
motion we know, namely motion along a spacetime geodesic:

(dU^u/dtau) = Christoffel^u_ab U^a U^b (2)

Here she does not feel a "force," and the acceleration is determined solely
by the gravitational field as captured in Christoffel^u_ab, and does not
depend at all on whether she weighs 90 pounds or 250 pounds.

Now, the "feeling" of a force according to equation (1) comes about, I
maintain, because the "electrical mass" e is NOT equal to the inertial mass
m. If these were equal, which is to say, if the gravitational charge were
to become equal to the electrical charge, e=m, as we presume it would at GUT
energies, then equation (1) would reduce to:

(dU^u/dtau) = U_a F^ua (3)

which is more similar to (2) insofar as the acceleration is determined
solely by the EM field F^ua and does not at all depend on how much charge is
carried by the astronaut. That is, if she doubles her charge, then the
inertial resistance offered by that charge to the EM field would also
double, and her motion would thus remain the same. Just like for
gravitation. Point is, however, she would not "feel" a "force."

The sensation of a force comes about precisely because the charges of two
interactions, say, gravitational and electromagnetic, are DIFFERENT. The
gravitational mass is the inertial mass, but if the electric mass were equal
to the gravitational mass as we presume it would be at GUT energies, then
our charged astronaut would accelerate under an EM field without feeling a
force. Therefore, one of the things that happens when we break whatever
symmetry exists at GUT scale down to ordinary experience, is that the
sensation of "force" arises. That is, force itself is one of the residual
effects of breaking symmetries below the GUT scale, where e and m in
equation (1) becomes different rather than the same.

PART II

Now, consider equation (1.1) from my paper at
http://arxiv.org/abs/gr-qc/0511050. This is solely existing theory, nothing
new, based on Maxwell's second equation =0 (no magnetic charges). Consider
especially the term in the [] brackets on the right hand side of the second
line, which is equal to zero, and let's do some dimensional analysis. The
energy tensors for matter T^uv and gravitation t^uv are in dimensions of
energy density (T^00 components). Therefore, T^uv_;u and t^uv;u = kappa_v,
being differentiated with respect to a length, can be thought of as a "force
density." The term in the () on the left of the [] is the Maxwell tensor;
the term on the right of the [] is the equation of motion (1) expressed in
terms of a density of charge. The fact that these sum to zero is a precise
statement of Newton's law of action and reaction. The term on the left in
the [] expresses the density of force acting on the electromagnetic field
from a charge density in that field, the term on the right in [] expresses
the density of the force acting on the charge density in the electromagnetic
field. The fact that these sum to zero says that the force density acting
on the electromagnetic field from the charge is equal and opposite to the
force density acting on the charge from the electromagnetic field. In this
way, we have derived the equation of motion from Maxwell's second equation.
(Don't know if that precise derivation has been noticed before, but that is
not the point.)

The point is that when we express total energy conservation by T^uv_;u =
T^uv(matter)_;u + t^uv(gravitation)_;u = 0, we are asserting Newton's
principle of action and reaction as between matter and the gravitational
field. We are saying T^uv(matter)_;u = - t^uv(gravitation)_;u = -kappa^v,
action and reaction. When T^uv(matter)_;u and kappa^v are given by equation
(5.1) in http://arxiv.org/abs/gr-qc/0511050, the action and reaction is
between electromagnetic field and electromagnetic charges, and the kappa^v
thus gives us an equation of motion, expressed as a density of force, or,
alternatively, as a change in momentum density with respect to time.

But there are also energy tensors other than the Maxwell tensor and there
are gravitational kappa^v other than (5.1). For example, (5.2) through
(5.8). For each of these, the kappa^v is an equation of motion, expressed
as a density of force a.k.a. change in momentum density with respect to
time, when one is placed in the fields of the associated energy tensor.
Equation of motion in a perfect Euler adiabatic fluid, for example, is based
on the kappa^v of (5.3). In all cases, the T^uv(matter)_;u = -
t^uv(gravitation)_;u = -kappa^v expresses an action and reaction between a
type of energy tensor (field configuration) and what that field acts on.

PART III

Ken believes that there is no such thing as absolute force, which leads him
to say that kappa^v=0, always. Based on what I said in PART I above, I
believe that at GUT energies this is true, but as soon as we have an
interaction charge which is different than an inertial charge, we will end
up with absolute forces. This, however, leads to kappa^v not= 0. And
therefore, T^uv = R^uv - .5 g^uvR + delta^uv, and right into the discussion
about equilibrium which I spent some fair time on in my paper and which I am
still giving a lot of thought to.

Where it really starts to get interesting is when we ask what
T^uv(matter)_;u + t^uv(gravitation)_;u = 0 represents. For, besides the
action and reaction of two force densities, it also represents energy being
exchanged between matter and the gravitational field. Energy, we know,
comes in quantized packets. So, in one way this is not continuous, yet in
another way it is. If we have a system of energy E that absorbs a quantum
of energy delta E, then after absorption the total energy is E + delta E.
Does this system make a discrete jump up from E to E + delta E? That is, is
there a 90 degree slope at an instant of time? Is the quanta absorbed
"instantly?" NO WAY. The uncertainty principle won't permit it. delta E x
delta t = h, where h is Planck's constant and t is time. If delta E is
large, then delta t can be small, and if delta E is small, the delta t must
be larger. So, if we plot energy as a function of time, then the curve will
never jump up at 90 degrees, but will always be a smooth function of time.
So, we can use a continuous curve, even down to t=0, to represent the
accrual of energy quanta, and it is Heisenberg uncertainty which itself
gives us the smooth energy curve.

So, this plunks you into the middle of what Ken and I are batting around,
and why we are talking about absolute versus relative acceleration, and
whether kappa^v = 0 or kappa^v not= 0, and equilibrium, and what happens
when T^uv approximately= R^uv - .5 g^uvR and kappa^v approximately= 0, and
whether there is some quantum of energy principle lurking in all of this.

Jay.


This is Unified Field Theory, one needs to simultaneously
conform with GR, EM and QT.

Gedanken: An astronaut is in orbit, and is weightless,
(free-fall). Classically, that's called geodesic motion,
call that orbit geodesic "1".

She turns on her thrusters momentarily and changes orbit
to geodesic 2, again "free-fall".

In classical GR the motion in the thrust interval is regarded
as non-geodesical motion, and I think most GRist are
inclined to regard the thrust as a "real" force, and as a con-
sequence having an absolute acceleration.

Tucker OTOH maintains the Principle of General Relativity -
that no absolute acceleration can exist and thus no absolute
force either - holds in the above manuveur.

Currently I'm sitting in my chair experiencing a non-weight-
less state, and a similiar person is sitting in her chair in
Australia with an acceleration vector in the opposite direction,
yet we are at relative rest. So we cannot claim the existance
of absolute acceleration on the basis of our accelometers.

The geodesic equation merely states "absolute acceleration"
vanishes and therefore holds in the circumstance with a
nonzero accelometer reading as well.

So I argue, the difference between 2 geodesics is a geodesic.

Recall GR uses Equivalence Principle (elevator) to establish
the equivalence of inertial and gravitational accelerations as
indistinguishable so all motion is geodesical.

In tensors, a 3-velocity like U^i has an "absolute derivative",

DU^i /ds = 0 == absolute acceleration == geodesic.

That answers some of your questions in a lateral way,
but if what I wrote is agreeable we can proceed to more
detailed issues.
Regards
Ken S. Tucker

Ken S. Tucker wrote:
Hi Sue, mostly agree with you...

Sue... wrote:
Ken S. Tucker wrote:
Ken S. Tucker wrote:
FrediFizzx wrote:
"Jay R. Yablon" wrote in message
...
| Hello to everyone:
|
| My newest paper, "General Relativity, Maxwell's Electrodynamics, and
the
| Foundations of the Quantum Theory of Gravitation and Matter," just
posted to
| ArXiV.
|
| The link is http://arxiv.org/abs/gr-qc/0511050.
|
| I would very much appreciate any comments and input you may have.

Hi Jay,

As I mentioned before; pretty fantastic! Do you think you could do a
summary of the postulates and a run down of the major features here?
FrediFizzx

Hi Fred and all...
let me try to explain that, because Jay's helped me understand the
paper,
so I'm a bit 2nd hand, and a bit off-the-cuff.

The paper is Maxwell's Equations (ME's) Super-charged.

Reviewing back to ME's and SR we note the relation of the
E and B fields in the the propagation of EMR is,

E x B = c , ( = indicates direction),

and "c" is the classical constant of the "velocity" of light in a
vacuum.

Consider E and B to be unit vectors then E x B = c = 1 in a vacuum,

and importantly E.B =0 , (scalar product).

When these equations for the propagation of light encounter a
gravitational field, a modification occurs, so that, c is not a
constant velocity. For example, the direction changes, (deflection)
the speed changes (Shapiro) and the frequency changes.

So we can re-write the transformed ME's in a g-field as

E' x B' = c' 1 AND E'.B' 0 ,

the later being crucial in the paper. That is entirely consistent
with taking an orthogonal ME relation E x B = c into a warped
spacetime, consistent with the g-field at the location of E' etc,
as a propagating EM-wave encounters a "nonorthogonal" field.

Underwriting physics is mathematics. What Jay did is to use
the "dual tensors" like

F_uv F*^uv == E.B == F_01 F*^01 = F_01 F_23

to form invariants that become E'.B' anywhere, but included a
coefficient normally marginalized in classical GR denoted,

|g_uv| = g.

such that F*^01 = F_23 / sqrt(-g), to decribe EM-fields.

The theory permits the inclusion of "magnetic monopoles"
and "negative matter", but exists fine even if those concepts
are negated.

Jay, around pg. 13, in the paper introduces what I call the
"Principle of Equilibrium", where matter reforms by the
action of potentials to tend to an entropy, by geodesics,
consistent with GR, so far as a continuum theory permits.

Recall

PRESSURE x VOLUME/ TEMPERATURE

is an invariant for an ideal gas, is firmly related to EM and
GR.

To establish an Equilibrium of the pressure, volume and
temperature when one of those are changed the paper
suggests a differential variation of the geodesics.
Tucker argues the "differential" is quantized, IOW's
the Equilibrium is obtained "inexactly".

But the paper, highlights in specific terms, how to argue
those points, and stands independant of the outcome
of those arguments.

Regards
Ken S. Tucker

I'd like to add a comment. (These comments are mine and Jay
may not necessarily agree).

The term " (E.B) sqrt(-g) " that appears in Eq.(2.35) and others
appears as a strange way to write up a geodesic equation, but
Unified Field Theories wear different coats. Let me give a quick
demo, (I'll add explanations if this is too quick)...

Begin with geodesic Eq.(2.35),

k_v = [ (E.B) sqrt(-g) ],v = [K],v = 0

k_v = K,v = 0 , K is Konstant.

Set V = E.B , V is a Velocity.

V^2 g = -K^2

Set 2p = V^2 , p = gravitational potential

2p*g = -K^2

dp g = - p dg

dp = - p dlog g = - 2*p {uv,u} dx^v

{uv,u} is a Christoffel symbol of the 2nd kind.


I should explain a bit more.
We can use some very compact notation and sqrt -1
to skew time a bit so we resolve why a motors current
and voltage don't indicate it's power or resolve why
the speed of light is not violated in Maxwell's near field.

Yes that sqrt -1 is a handy tool in Reactance, however in
the crunch I don't use it in reality. Einstein employed it
(mistakenly in IMO) in GR, and it has reached near a
biblical diety. Jay Yablon (the author), following tradition,
used it in his equations.

That's why I squared the equation, stuck the negative
on a constant and took a derivative, so that the negative
aspect of the sqrt(-g) had no physical consequences.
It *seems* valid but then QED is only half crippled for
similar reaches.


You can't simply write the compact forms and expect
your reader to imagine the rigor.

The invariant Jay is exploiting is surprisingly simple,
(risking making too many equations) it's just,

F_uv F*^uv = E.B sqrt(g)

(I wish I had thought of that!)
I have to question if that is adaquate consideration
of the eps and mu of the lumps in space that we
call matter.


We have to call these forms "food for thought"
I am not suggesting your equations are right or wrong.
But they do seem to be assumimg quite a bit to expect
gravity to be operational at a subatomic level.

The equations should be operational anywhere EM is,
and the developement is to acquire the ability to get
a "beach head" into particle physics to determine the
relevence of GR in HEP's.
Again... eps and mu are lumpy because eps varies
by 1/r^2 and mu varies by 1/r^3.
Hmm... I am not sure we could have matter if that
were not true.


The force between two charges and the force between
two masses represents no energy exchange. So forms
that use *time* have to be viewed with a caution.

Yeah, but in view of your comment below about frig-mags,
the moon don't need batteries to keep orbiting the earth,
sounds like there both geodesic :-).

I suppose that is a GR way of saying the system has a
high quality factor (Q).

Sue...

I haven't had to change the batteries in my refrigerator
magnets yet. ;-)
http://en.wikipedia.org/wiki/Triple_integral

Sue...



V = dr/ds

dp/dr = - {uv,u} U^v V

The Looks like Newton, Einstein and EM in a neat package!

What I find quite remarkable, is that a geodesic derived
from K,v=0 is expressed on the L.H.S. as "dp/dr", but the
usual from GR is expressed "dU^i/ds", which conceptually,
is quite distinct although physically very similiar.

For those reasons and more, I find [K] above to be a very
rich equation, and suggest caution in marginalizing it.
Regards
Ken S. Tucker

Ken

PS: Thanks Autumn DC for corrections.

Sue... wrote: Ken S. Tucker wrote: Hi Sue, mostly agree with you...
Sue... wrote: Ken S. Tucker wrote: Ken S. Tucker wrote:
FrediFizzx wrote: "Jay R. Yablon"
wrote in message
...
| Hello to everyone:
|
| My newest paper, "General Relativity, Maxwell's Electrodynamics, and
the
| Foundations of the Quantum Theory of Gravitation and Matter," just
posted to
| ArXiV.
|
| The link is http://arxiv.org/abs/gr-qc/0511050.
|
| I would very much appreciate any comments and input you may have.

Hi Jay,

As I mentioned before; pretty fantastic! Do you think you could do a
summary of the postulates and a run down of the major features here?
FrediFizzx

Hi Fred and all...
let me try to explain that, because Jay's helped me understand the
paper,
so I'm a bit 2nd hand, and a bit off-the-cuff.

The paper is Maxwell's Equations (ME's) Super-charged.

Reviewing back to ME's and SR we note the relation of the
E and B fields in the the propagation of EMR is,

E x B = c , ( = indicates direction),

and "c" is the classical constant of the "velocity" of light in a
vacuum.

Consider E and B to be unit vectors then E x B = c = 1 in a vacuum,

Why have VELOCiTY or SPEED c be 1 unit LENGTH per 1 unit TiME, in vacu?

and importantly E.B =0 , (scalar product).

When these equations for the propagation of light encounter a
gravitational field, a modification occurs, so that, c is not a
constant velocity. For example, the direction changes, (deflection)
the speed changes (Shapiro) and the frequency changes.

So we can re-write the transformed ME's in a g-field as

E' x B' = c' 1 AND E'.B' 0 ,

the later being crucial in the paper. That is entirely consistent
with taking an orthogonal ME relation E x B = c into a warped
spacetime, consistent with the g-field at the location of E' etc,
as a propagating EM-wave encounters a "nonorthogonal" field.

Underwriting physics is mathematics. What Jay did is to use
the "dual tensors" like

F_uv F*^uv == E.B == F_01 F*^01 = F_01 F_23

to form invariants that become E'.B' anywhere, but included a
coefficient normally marginalized in classical GR denoted,

|g_uv| = g.

such that F*^01 = F_23 / sqrt(-g), to decribe EM-fields.

The theory permits the inclusion of "magnetic monopoles"
and "negative matter", but exists fine even if those concepts
are negated.

Jay, around pg. 13, in the paper introduces what I call the
"Principle of Equilibrium", where matter reforms by the
action of potentials to tend to an entropy, by geodesics,
consistent with GR, so far as a continuum theory permits.

Recall

PRESSURE x VOLUME/ TEMPERATURE

is an invariant for an ideal gas, is firmly related to EM and
GR.

To establish an Equilibrium of the pressure, volume and
temperature when one of those are changed the paper
suggests a differential variation of the geodesics.
Tucker argues the "differential" is quantized, IOW's
the Equilibrium is obtained "inexactly".

But the paper, highlights in specific terms, how to argue
those points, and stands independant of the outcome
of those arguments.

Regards
Ken S. Tucker

I'd like to add a comment. (These comments are mine and Jay
may not necessarily agree).

The term " (E.B) sqrt(-g) " that appears in Eq.(2.35) and others
appears as a strange way to write up a geodesic equation, but
Unified Field Theories wear different coats. Let me give a quick
demo, (I'll add explanations if this is too quick)...

Begin with geodesic Eq.(2.35),

k_v = [ (E.B) sqrt(-g) ],v = [K],v = 0

k_v = K,v = 0 , K is Konstant.

Set V = E.B , V is a Velocity.

V^2 g = -K^2

Set 2p = V^2 , p = gravitational potential

2p*g = -K^2

dp g = - p dg

dp = - p dlog g = - 2*p {uv,u} dx^v

{uv,u} is a Christoffel symbol of the 2nd kind.


I should explain a bit more.
We can use some very compact notation and sqrt -1
to skew time a bit so we resolve why a motors current
and voltage don't indicate it's power or resolve why
the speed of light is not violated in Maxwell's near field.

Yes that sqrt -1 is a handy tool in Reactance, however in
the crunch I don't use it in reality. Einstein employed it
(mistakenly in IMO) in GR, and it has reached near a
biblical diety. Jay Yablon (the author), following tradition,
used it in his equations.

That's why I squared the equation, stuck the negative
on a constant and took a derivative, so that the negative
aspect of the sqrt(-g) had no physical consequences.
It *seems* valid but then QED is only half crippled for
similar reaches.


You can't simply write the compact forms and expect
your reader to imagine the rigor.

The invariant Jay is exploiting is surprisingly simple,
(risking making too many equations) it's just,

F_uv F*^uv = E.B sqrt(g)

(I wish I had thought of that!)
I have to question if that is adaquate consideration
of the eps and mu of the lumps in space that we
call matter.


We have to call these forms "food for thought"
I am not suggesting your equations are right or wrong.
But they do seem to be assumimg quite a bit to expect
gravity to be operational at a subatomic level.

The equations should be operational anywhere EM is,
and the developement is to acquire the ability to get
a "beach head" into particle physics to determine the
relevence of GR in HEP's.

Again... eps and mu are lumpy because eps varies
by 1/r^2 and mu varies by 1/r^3.
Hmm... I am not sure we could have matter if that
were not true.

The Greek YAB-a-dab-a-Sue-doo, mu*eps, in SI GUESS is Uo*Eo = 1 / c^2.

$ 3*VOLUME / AREA, per DURATiON = RADiAL velocity.!!
Delta, VOLUME / surface AREA ..per second, is RADiAL velocity / 3.
Unit TRiAKiSicosa VOLUME / (surf AREA*sec) is TiP-to-TiP / 6*sec.
Unit SPHERiCAL VOLUME / (surface AREA*sec) is, DiAMETER / 6*sec.
Unit CUBiCAL VOLUME / (surface AREA*second) = EDGEside / 6*sec.
GRAViTATiONAL impulse per VOLUME; iNERTiAL impulse, per AREA.

The force between two charges and the force between
two masses represents no energy exchange.

Force x DiSTANCE = ENERGY exchange ..viewed with a CAUTiON.!!
brian a m stuckless


So forms that use *time* have to be viewed with a caution.

Sue...
I haven't had to change the batteries in my refrigerator
magnets yet. ;-)

Sue...

What I find quite remarkable, is that a geodesic derived
from K,v=0 is expressed on the L.H.S. as "dp/dr", but the
usual from GR is expressed "dU^i/ds", which conceptually,
is quite distinct although physically very similiar.

For those reasons and more, I find [K] above to be a very
rich equation, and suggest caution in marginalizing it.
Regards
Ken S. Tucker

Ken PS: Thanks Autumn DC for corrections.
New Paper: General Relativity, Maxwell's Electrodynamics,
and the Foundations of the Quantum Theory of Gravitation and Matter
(gr-qc/0511050).

$ 3*VOLUME / AREA, per DURATiON = RADiAL velocity.!!
Delta, VOLUME / surface AREA ..per second, is RADiAL velocity / 3.
Unit TRiAKiSicosa VOLUME / (surf AREA*sec) is TiP-to-TiP / 6*sec.
Unit SPHERiCAL VOLUME / (surface AREA*sec) is, DiAMETER / 6*sec.
Unit CUBiCAL VOLUME / (surface AREA*second) = EDGEside / 6*sec.
GRAViTATiONAL impulse per VOLUME; iNERTiAL impulse, per AREA.
brian a m stuckless

Sue... wrote: Ken S. Tucker wrote: Hi Sue, mostly agree with you...
Sue... wrote: Ken S. Tucker wrote: Ken S. Tucker wrote:
FrediFizzx wrote: "Jay R. Yablon"
wrote in message
...
| Hello to everyone:
|
| My newest paper, "General Relativity, Maxwell's Electrodynamics, and
the
| Foundations of the Quantum Theory of Gravitation and Matter," just
posted to
| ArXiV.
|
| The link is http://arxiv.org/abs/gr-qc/0511050.
|
| I would very much appreciate any comments and input you may have.

Hi Jay,

As I mentioned before; pretty fantastic! Do you think you could do a
summary of the postulates and a run down of the major features here?
FrediFizzx

Hi Fred and all...
let me try to explain that, because Jay's helped me understand the
paper,
so I'm a bit 2nd hand, and a bit off-the-cuff.

The paper is Maxwell's Equations (ME's) Super-charged.

Reviewing back to ME's and SR we note the relation of the
E and B fields in the the propagation of EMR is,

E x B = c , ( = indicates direction),

and "c" is the classical constant of the "velocity" of light in a
vacuum.

Consider E and B to be unit vectors then E x B = c = 1 in a vacuum,

Why have VELOCiTY or SPEED c be 1 unit LENGTH per 1 unit TiME, in vacu?

and importantly E.B =0 , (scalar product).

When these equations for the propagation of light encounter a
gravitational field, a modification occurs, so that, c is not a
constant velocity. For example, the direction changes, (deflection)
the speed changes (Shapiro) and the frequency changes.

So we can re-write the transformed ME's in a g-field as

E' x B' = c' 1 AND E'.B' 0 ,

the later being crucial in the paper. That is entirely consistent
with taking an orthogonal ME relation E x B = c into a warped
spacetime, consistent with the g-field at the location of E' etc,
as a propagating EM-wave encounters a "nonorthogonal" field.

Underwriting physics is mathematics. What Jay did is to use
the "dual tensors" like

F_uv F*^uv == E.B == F_01 F*^01 = F_01 F_23

to form invariants that become E'.B' anywhere, but included a
coefficient normally marginalized in classical GR denoted,

|g_uv| = g.

such that F*^01 = F_23 / sqrt(-g), to decribe EM-fields.

The theory permits the inclusion of "magnetic monopoles"
and "negative matter", but exists fine even if those concepts
are negated.

Jay, around pg. 13, in the paper introduces what I call the
"Principle of Equilibrium", where matter reforms by the
action of potentials to tend to an entropy, by geodesics,
consistent with GR, so far as a continuum theory permits.

Recall

PRESSURE x VOLUME/ TEMPERATURE

is an invariant for an ideal gas, is firmly related to EM and
GR.

To establish an Equilibrium of the pressure, volume and
temperature when one of those are changed the paper
suggests a differential variation of the geodesics.
Tucker argues the "differential" is quantized, IOW's
the Equilibrium is obtained "inexactly".

But the paper, highlights in specific terms, how to argue
those points, and stands independant of the outcome
of those arguments.

Regards
Ken S. Tucker

I'd like to add a comment. (These comments are mine and Jay
may not necessarily agree).

The term " (E.B) sqrt(-g) " that appears in Eq.(2.35) and others
appears as a strange way to write up a geodesic equation, but
Unified Field Theories wear different coats. Let me give a quick
demo, (I'll add explanations if this is too quick)...

Begin with geodesic Eq.(2.35),

k_v = [ (E.B) sqrt(-g) ],v = [K],v = 0

k_v = K,v = 0 , K is Konstant.

Set V = E.B , V is a Velocity.

V^2 g = -K^2

Set 2p = V^2 , p = gravitational potential

2p*g = -K^2

dp g = - p dg

dp = - p dlog g = - 2*p {uv,u} dx^v

{uv,u} is a Christoffel symbol of the 2nd kind.


I should explain a bit more.
We can use some very compact notation and sqrt -1
to skew time a bit so we resolve why a motors current
and voltage don't indicate it's power or resolve why
the speed of light is not violated in Maxwell's near field.

Yes that sqrt -1 is a handy tool in Reactance, however in
the crunch I don't use it in reality. Einstein employed it
(mistakenly in IMO) in GR, and it has reached near a
biblical diety. Jay Yablon (the author), following tradition,
used it in his equations.

That's why I squared the equation, stuck the negative
on a constant and took a derivative, so that the negative
aspect of the sqrt(-g) had no physical consequences.
It *seems* valid but then QED is only half crippled for
similar reaches.


You can't simply write the compact forms and expect
your reader to imagine the rigor.

The invariant Jay is exploiting is surprisingly simple,
(risking making too many equations) it's just,

F_uv F*^uv = E.B sqrt(g)

(I wish I had thought of that!)
I have to question if that is adaquate consideration
of the eps and mu of the lumps in space that we
call matter.


We have to call these forms "food for thought"
I am not suggesting your equations are right or wrong.
But they do seem to be assumimg quite a bit to expect
gravity to be operational at a subatomic level.

The equations should be operational anywhere EM is,
and the developement is to acquire the ability to get
a "beach head" into particle physics to determine the
relevence of GR in HEP's.

Again... eps and mu are lumpy because eps varies
by 1/r^2 and mu varies by 1/r^3.
Hmm... I am not sure we could have matter if that
were not true.

The Greek YAB-a-dab-a-Sue-doo, mu*eps, in SI GUESS is Uo*Eo = 1 / c^2.

$ 3*VOLUME / AREA, per DURATiON = RADiAL velocity.!!
Delta, VOLUME / surface AREA ..per second, is RADiAL velocity / 3.
Unit TRiAKiSicosa VOLUME / (surf AREA*sec) is TiP-to-TiP / 6*sec.
Unit SPHERiCAL VOLUME / (surface AREA*sec) is, DiAMETER / 6*sec.
Unit CUBiCAL VOLUME / (surface AREA*second) = EDGEside / 6*sec.
GRAViTATiONAL impulse per VOLUME; iNERTiAL impulse, per AREA.

The force between two charges and the force between
two masses represents no energy exchange.

Force x DiSTANCE = ENERGY exchange ..viewed with a CAUTiON.!!
brian a m stuckless


So forms that use *time* have to be viewed with a caution.

Sue...
I haven't had to change the batteries in my refrigerator
magnets yet. ;-)

Sue...

What I find quite remarkable, is that a geodesic derived
from K,v=0 is expressed on the L.H.S. as "dp/dr", but the
usual from GR is expressed "dU^i/ds", which conceptually,
is quite distinct although physically very similiar.

For those reasons and more, I find [K] above to be a very
rich equation, and suggest caution in marginalizing it.
Regards
Ken S. Tucker

Ken PS: Thanks Autumn DC for corrections.
New Paper: General Relativity, Maxwell's Electrodynamics,
and the Foundations of the Quantum Theory of Gravitation and Matter
(gr-qc/0511050).

Sue... wrote: Ken S. Tucker wrote: Hi Sue, mostly agree with you...
Sue... wrote: Ken S. Tucker wrote: Ken S. Tucker wrote:
FrediFizzx wrote: "Jay R. Yablon"
wrote in message
...
| Hello to everyone:
|
| My newest paper, "General Relativity, Maxwell's Electrodynamics, and
the
| Foundations of the Quantum Theory of Gravitation and Matter," just
posted to
| ArXiV.
|
| The link is http://arxiv.org/abs/gr-qc/0511050.
|
| I would very much appreciate any comments and input you may have.

Hi Jay,

As I mentioned before; pretty fantastic! Do you think you could do a
summary of the postulates and a run down of the major features here?
FrediFizzx

Hi Fred and all...
let me try to explain that, because Jay's helped me understand the
paper,
so I'm a bit 2nd hand, and a bit off-the-cuff.

The paper is Maxwell's Equations (ME's) Super-charged.

Reviewing back to ME's and SR we note the relation of the
E and B fields in the the propagation of EMR is,

E x B = c , ( = indicates direction),

and "c" is the classical constant of the "velocity" of light in a
vacuum.

Consider E and B to be unit vectors then E x B = c = 1 in a vacuum,

Why have VELOCiTY or SPEED c be 1 unit LENGTH per 1 unit TiME, in vacu?

and importantly E.B =0 , (scalar product).

When these equations for the propagation of light encounter a
gravitational field, a modification occurs, so that, c is not a
constant velocity. For example, the direction changes, (deflection)
the speed changes (Shapiro) and the frequency changes.

So we can re-write the transformed ME's in a g-field as

E' x B' = c' 1 AND E'.B' 0 ,

the later being crucial in the paper. That is entirely consistent
with taking an orthogonal ME relation E x B = c into a warped
spacetime, consistent with the g-field at the location of E' etc,
as a propagating EM-wave encounters a "nonorthogonal" field.

Underwriting physics is mathematics. What Jay did is to use
the "dual tensors" like

F_uv F*^uv == E.B == F_01 F*^01 = F_01 F_23

to form invariants that become E'.B' anywhere, but included a
coefficient normally marginalized in classical GR denoted,

|g_uv| = g.

such that F*^01 = F_23 / sqrt(-g), to decribe EM-fields.

The theory permits the inclusion of "magnetic monopoles"
and "negative matter", but exists fine even if those concepts
are negated.

Jay, around pg. 13, in the paper introduces what I call the
"Principle of Equilibrium", where matter reforms by the
action of potentials to tend to an entropy, by geodesics,
consistent with GR, so far as a continuum theory permits.

Recall

PRESSURE x VOLUME/ TEMPERATURE

is an invariant for an ideal gas, is firmly related to EM and
GR.

To establish an Equilibrium of the pressure, volume and
temperature when one of those are changed the paper
suggests a differential variation of the geodesics.
Tucker argues the "differential" is quantized, IOW's
the Equilibrium is obtained "inexactly".

But the paper, highlights in specific terms, how to argue
those points, and stands independant of the outcome
of those arguments.

Regards
Ken S. Tucker

I'd like to add a comment. (These comments are mine and Jay
may not necessarily agree).

The term " (E.B) sqrt(-g) " that appears in Eq.(2.35) and others
appears as a strange way to write up a geodesic equation, but
Unified Field Theories wear different coats. Let me give a quick
demo, (I'll add explanations if this is too quick)...

Begin with geodesic Eq.(2.35),

k_v = [ (E.B) sqrt(-g) ],v = [K],v = 0

k_v = K,v = 0 , K is Konstant.

Set V = E.B , V is a Velocity.

V^2 g = -K^2

Set 2p = V^2 , p = gravitational potential

2p*g = -K^2

dp g = - p dg

dp = - p dlog g = - 2*p {uv,u} dx^v

{uv,u} is a Christoffel symbol of the 2nd kind.


I should explain a bit more.
We can use some very compact notation and sqrt -1
to skew time a bit so we resolve why a motors current
and voltage don't indicate it's power or resolve why
the speed of light is not violated in Maxwell's near field.

Yes that sqrt -1 is a handy tool in Reactance, however in
the crunch I don't use it in reality. Einstein employed it
(mistakenly in IMO) in GR, and it has reached near a
biblical diety. Jay Yablon (the author), following tradition,
used it in his equations.

That's why I squared the equation, stuck the negative
on a constant and took a derivative, so that the negative
aspect of the sqrt(-g) had no physical consequences.
It *seems* valid but then QED is only half crippled for
similar reaches.


You can't simply write the compact forms and expect
your reader to imagine the rigor.

The invariant Jay is exploiting is surprisingly simple,
(risking making too many equations) it's just,

F_uv F*^uv = E.B sqrt(g)

(I wish I had thought of that!)
I have to question if that is adaquate consideration
of the eps and mu of the lumps in space that we
call matter.


We have to call these forms "food for thought"
I am not suggesting your equations are right or wrong.
But they do seem to be assumimg quite a bit to expect
gravity to be operational at a subatomic level.

The equations should be operational anywhere EM is,
and the developement is to acquire the ability to get
a "beach head" into particle physics