This reply is to Sue as well.

Jay R. Yablon wrote:
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".

Hi Ken:

Please explain as clearly as possible what you are seeing here. I would
agree that in principle, matter must exchange energy with the gravitational
field in discrete "packets" not continuously. Planck's delta E = n h-bar
frequency.

But, you seem to think that this quantization actually emerges out of the
"Principle of Equilibrium" and might be cranked out of the equations already
in the paper. How?

Because I replied by email to Jay I'll post this for Sue and all.

Jay has these equations,

k_v = K,v = 0 (k=kappa).

K=sqrt(-g) E.B = scalar.

I think Jay and I agree to the above.

Here's what Tucker further argues,

Use "$" for an integral and get,

$ K,v dx^v = $ dK = K = $ k_v dx^v ,

proving the constant of integration of $ k_v dx^v = K.

Is that agreeable?

Ok then, let 2 distinct geodesics "A" and "B" exist,

k_v = k(A)_v - k(B)_v

A
$ k_v dx^v = K as a minimum
B

K appears as the quantized input (difference) to move from
one geodesic to another. For example going from geodesic
A=B=C needs 2K etc... nK, n = integer.

It would be fantastic if these results can self-quantize the energy
exchanges between matter and gravitational field.
Jay.

Well Tucker reads that in,

k_v = K,v = 0

as his interpretation. Physically a particle in freefall
moving along geodesic "A" according to k(A)_v =0
is struck by a photon that varies it's geodesic by a
quantized amount, (discontinuous quantity), I find to
be K, resulting in a new geodesic k(B)_v.

There is precedent. Planck's invariant constant "h" is
in relative units, (ergs x seconds).

So I suggest (conjecture) the constant

K=sqrt(-g) E.B

(is on a similiar footing as Planck's "h") , which I currently
interperate as an "invariant constant of energy density".
Regards
Ken S. Tucker

Ken S. Tucker wrote:
This reply is to Sue as well.

Jay R. Yablon wrote:
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".

Hi Ken:

Please explain as clearly as possible what you are seeing here. I would
agree that in principle, matter must exchange energy with the gravitational
field in discrete "packets" not continuously. Planck's delta E = n h-bar
frequency.

But, you seem to think that this quantization actually emerges out of the
"Principle of Equilibrium" and might be cranked out of the equations already
in the paper. How?

Because I replied by email to Jay I'll post this for Sue and all.

Jay has these equations,

k_v = K,v = 0 (k=kappa).

K=sqrt(-g) E.B = scalar.

I think Jay and I agree to the above.

Here's what Tucker further argues,

Use "$" for an integral and get,

$ K,v dx^v = $ dK = K = $ k_v dx^v ,

proving the constant of integration of $ k_v dx^v = K.

Is that agreeable?

Ok then, let 2 distinct geodesics "A" and "B" exist,

k_v = k(A)_v - k(B)_v

A
$ k_v dx^v = K as a minimum
B

K appears as the quantized input (difference) to move from
one geodesic to another. For example going from geodesic
A=B=C needs 2K etc... nK, n = integer.

It would be fantastic if these results can self-quantize the energy
exchanges between matter and gravitational field.
Jay.

Well Tucker reads that in,

k_v = K,v = 0

as his interpretation. Physically a particle in freefall
moving along geodesic "A" according to k(A)_v =0
is struck by a photon that varies it's geodesic by a
quantized amount, (discontinuous quantity), I find to
be K, resulting in a new geodesic k(B)_v.

There is precedent. Planck's invariant constant "h" is
in relative units, (ergs x seconds).

So I suggest (conjecture) the constant

K=sqrt(-g) E.B

(is on a similiar footing as Planck's "h") , which I currently
interperate as an "invariant constant of energy density".
Regards
Ken S. Tucker

OK. KenST. Your method seeks to produce standard atomic
quanta. I don't see the mechanism which I described as capable
of that. Your method may be useful where you are focused on
sub atomic structure but I will be watching with interest how
it deals with long-range electrically neutral forces.

Jay's strategy of wringing all you can out of empirical data might
dictate use of your method be limited to subatomic scales.
I haven't found any *convincing* work where forces resulting
from macro scale ensembles are well represented with standard
atomic quanta but I did find a few *unconvincing* attempts.

Where large ensembles are involved, some means of
'broadcasting' to all parts of the ensemble, how its energy
' differs from standard quanta'
seems necessary to the mechanism.

This is where I saw application for Jay's magnetic monopoles.
They, of course, are not real, but come into existence
to accomodate the size of the ensemble, as defined.

A macro ensemble is not going to seek a new equilibrium
point simply because we redefine its size so I have to
echo some puzzlement about this. Perhaps your work
is assuming a quantized 3d+1t space?

Regards,
Sue...

Sue... wrote:
Ken S. Tucker wrote:
This reply is to Sue as well.

Jay R. Yablon wrote:
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".

Hi Ken:

Please explain as clearly as possible what you are seeing here. I would
agree that in principle, matter must exchange energy with the gravitational
field in discrete "packets" not continuously. Planck's delta E = n h-bar
frequency.

But, you seem to think that this quantization actually emerges out of the
"Principle of Equilibrium" and might be cranked out of the equations already
in the paper. How?

Because I replied by email to Jay I'll post this for Sue and all.

Jay has these equations,

k_v = K,v = 0 (k=kappa).

K=sqrt(-g) E.B = scalar.

I think Jay and I agree to the above.

Here's what Tucker further argues,

Use "$" for an integral and get,

$ K,v dx^v = $ dK = K = $ k_v dx^v ,

proving the constant of integration of $ k_v dx^v = K.

Is that agreeable?

Ok then, let 2 distinct geodesics "A" and "B" exist,

k_v = k(A)_v - k(B)_v

A
$ k_v dx^v = K as a minimum
B

K appears as the quantized input (difference) to move from
one geodesic to another. For example going from geodesic
A=B=C needs 2K etc... nK, n = integer.

It would be fantastic if these results can self-quantize the energy
exchanges between matter and gravitational field.
Jay.

Well Tucker reads that in,

k_v = K,v = 0

as his interpretation. Physically a particle in freefall
moving along geodesic "A" according to k(A)_v =0
is struck by a photon that varies it's geodesic by a
quantized amount, (discontinuous quantity), I find to
be K, resulting in a new geodesic k(B)_v.

There is precedent. Planck's invariant constant "h" is
in relative units, (ergs x seconds).

So I suggest (conjecture) the constant

K=sqrt(-g) E.B

(is on a similiar footing as Planck's "h") , which I currently
interperate as an "invariant constant of energy density".
Regards
Ken S. Tucker

OK. KenST. Your method seeks to produce standard atomic
quanta. I don't see the mechanism which I described as capable
of that. Your method may be useful where you are focused on
sub atomic structure but I will be watching with interest how
it deals with long-range electrically neutral forces.

Jay's strategy of wringing all you can out of empirical data might
dictate use of your method be limited to subatomic scales.
I haven't found any *convincing* work where forces resulting
from macro scale ensembles are well represented with standard
atomic quanta but I did find a few *unconvincing* attempts.

Where large ensembles are involved, some means of
'broadcasting' to all parts of the ensemble, how its energy
' differs from standard quanta'
seems necessary to the mechanism.

This is where I saw application for Jay's magnetic monopoles.
They, of course, are not real, but come into existence
to accomodate the size of the ensemble, as defined.

A macro ensemble is not going to seek a new equilibrium
point simply because we redefine its size so I have to
echo some puzzlement about this. Perhaps your work
is assuming a quantized 3d+1t space?

Regards,
Sue...

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

"Sue..." wrote in message
oups.com...
|
| Ken S. Tucker wrote:
| This reply is to Sue as well.
|
| Jay R. Yablon wrote:
| 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".
|
| Hi Ken:
|
| Please explain as clearly as possible what you are seeing here. I
would
| agree that in principle, matter must exchange energy with the
gravitational
| field in discrete "packets" not continuously. Planck's delta E =
n h-bar
| frequency.
|
| But, you seem to think that this quantization actually emerges out
of the
| "Principle of Equilibrium" and might be cranked out of the
equations already
| in the paper. How?
|
| Because I replied by email to Jay I'll post this for Sue and all.
|
| Jay has these equations,
|
| k_v = K,v = 0 (k=kappa).
|
| K=sqrt(-g) E.B = scalar.
|
| I think Jay and I agree to the above.
|
| Here's what Tucker further argues,
|
| Use "$" for an integral and get,
|
| $ K,v dx^v = $ dK = K = $ k_v dx^v ,
|
| proving the constant of integration of $ k_v dx^v = K.
|
| Is that agreeable?
|
| Ok then, let 2 distinct geodesics "A" and "B" exist,
|
| k_v = k(A)_v - k(B)_v
|
| A
| $ k_v dx^v = K as a minimum
| B
|
| K appears as the quantized input (difference) to move from
| one geodesic to another. For example going from geodesic
| A=B=C needs 2K etc... nK, n = integer.
|
| It would be fantastic if these results can self-quantize the
energy
| exchanges between matter and gravitational field.
| Jay.
|
| Well Tucker reads that in,
|
| k_v = K,v = 0
|
| as his interpretation. Physically a particle in freefall
| moving along geodesic "A" according to k(A)_v =0
| is struck by a photon that varies it's geodesic by a
| quantized amount, (discontinuous quantity), I find to
| be K, resulting in a new geodesic k(B)_v.
|
| There is precedent. Planck's invariant constant "h" is
| in relative units, (ergs x seconds).
|
| So I suggest (conjecture) the constant
|
| K=sqrt(-g) E.B
|
| (is on a similiar footing as Planck's "h") , which I currently
| interperate as an "invariant constant of energy density".
| Regards
| Ken S. Tucker
|
| OK. KenST. Your method seeks to produce standard atomic
| quanta. I don't see the mechanism which I described as capable
| of that. Your method may be useful where you are focused on
| sub atomic structure but I will be watching with interest how
| it deals with long-range electrically neutral forces.

Key words; "long-range electrically neutral". How do we know that is
true to the level of gravity ~ 10^-42? We simply don't have the
experimental capability to see if an object really is truely
electrically neutral. But what I think is more important is putting EM
in the same framework as GR. Spacetime is curved or "tilted" way more
by EM than by "neutral" matter wrt other charges. Very easy to imagine
this with the quantum "vacuum" as a medium as Volovik proposes. More
difficult to make it all work out mathematically.

FrediFizzx

http://www.vacuum-physics.com/QVC/qu...uum_charge.pdf
or postscript
http://www.vacuum-physics.com/QVC/qu...cuum_charge.ps

http://www.vacuum-physics.com

FrediFizzx wrote:
"Sue..." wrote in message
oups.com...
|
| Ken S. Tucker wrote:
| This reply is to Sue as well.
|
| Jay R. Yablon wrote:
| 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".
|
| Hi Ken:
|
| Please explain as clearly as possible what you are seeing here. I
would
| agree that in principle, matter must exchange energy with the
gravitational
| field in discrete "packets" not continuously. Planck's delta E =
n h-bar
| frequency.
|
| But, you seem to think that this quantization actually emerges out
of the
| "Principle of Equilibrium" and might be cranked out of the
equations already
| in the paper. How?
|
| Because I replied by email to Jay I'll post this for Sue and all.
|
| Jay has these equations,
|
| k_v = K,v = 0 (k=kappa).
|
| K=sqrt(-g) E.B = scalar.
|
| I think Jay and I agree to the above.
|
| Here's what Tucker further argues,
|
| Use "$" for an integral and get,
|
| $ K,v dx^v = $ dK = K = $ k_v dx^v ,
|
| proving the constant of integration of $ k_v dx^v = K.
|
| Is that agreeable?
|
| Ok then, let 2 distinct geodesics "A" and "B" exist,
|
| k_v = k(A)_v - k(B)_v
|
| A
| $ k_v dx^v = K as a minimum
| B
|
| K appears as the quantized input (difference) to move from
| one geodesic to another. For example going from geodesic
| A=B=C needs 2K etc... nK, n = integer.
|
| It would be fantastic if these results can self-quantize the
energy
| exchanges between matter and gravitational field.
| Jay.
|
| Well Tucker reads that in,
|
| k_v = K,v = 0
|
| as his interpretation. Physically a particle in freefall
| moving along geodesic "A" according to k(A)_v =0
| is struck by a photon that varies it's geodesic by a
| quantized amount, (discontinuous quantity), I find to
| be K, resulting in a new geodesic k(B)_v.
|
| There is precedent. Planck's invariant constant "h" is
| in relative units, (ergs x seconds).
|
| So I suggest (conjecture) the constant
|
| K=sqrt(-g) E.B
|
| (is on a similiar footing as Planck's "h") , which I currently
| interperate as an "invariant constant of energy density".
| Regards
| Ken S. Tucker
|
| OK. KenST. Your method seeks to produce standard atomic
| quanta. I don't see the mechanism which I described as capable
| of that. Your method may be useful where you are focused on
| sub atomic structure but I will be watching with interest how
| it deals with long-range electrically neutral forces.

Key words; "long-range electrically neutral". How do we know that is
true to the level of gravity ~ 10^-42? We simply don't have the
experimental capability to see if an object really is truely
electrically neutral. But what I think is more important is putting EM
in the same framework as GR. Spacetime is curved or "tilted" way more
by EM than by "neutral" matter wrt other charges. Very easy to imagine
this with the quantum "vacuum" as a medium as Volovik proposes. More
difficult to make it all work out mathematically.

FrediFizzx

http://www.vacuum-physics.com/QVC/qu...uum_charge.pdf
or postscript
http://www.vacuum-physics.com/QVC/qu...cuum_charge.ps

http://www.vacuum-physics.com

FrediFizzx wrote:
"Sue..." wrote in message
oups.com...
|
| Ken S. Tucker wrote:
| This reply is to Sue as well.
|
| Jay R. Yablon wrote:
| 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".
|
| Hi Ken:
|
| Please explain as clearly as possible what you are seeing here. I
would
| agree that in principle, matter must exchange energy with the
gravitational
| field in discrete "packets" not continuously. Planck's delta E =
n h-bar
| frequency.
|
| But, you seem to think that this quantization actually emerges out
of the
| "Principle of Equilibrium" and might be cranked out of the
equations already
| in the paper. How?
|
| Because I replied by email to Jay I'll post this for Sue and all.
|
| Jay has these equations,
|
| k_v = K,v = 0 (k=kappa).
|
| K=sqrt(-g) E.B = scalar.
|
| I think Jay and I agree to the above.
|
| Here's what Tucker further argues,
|
| Use "$" for an integral and get,
|
| $ K,v dx^v = $ dK = K = $ k_v dx^v ,
|
| proving the constant of integration of $ k_v dx^v = K.
|
| Is that agreeable?
|
| Ok then, let 2 distinct geodesics "A" and "B" exist,
|
| k_v = k(A)_v - k(B)_v
|
| A
| $ k_v dx^v = K as a minimum
| B
|
| K appears as the quantized input (difference) to move from
| one geodesic to another. For example going from geodesic
| A=B=C needs 2K etc... nK, n = integer.
|
| It would be fantastic if these results can self-quantize the
energy
| exchanges between matter and gravitational field.
| Jay.
|
| Well Tucker reads that in,
|
| k_v = K,v = 0
|
| as his interpretation. Physically a particle in freefall
| moving along geodesic "A" according to k(A)_v =0
| is struck by a photon that varies it's geodesic by a
| quantized amount, (discontinuous quantity), I find to
| be K, resulting in a new geodesic k(B)_v.
|
| There is precedent. Planck's invariant constant "h" is
| in relative units, (ergs x seconds).
|
| So I suggest (conjecture) the constant
|
| K=sqrt(-g) E.B
|
| (is on a similiar footing as Planck's "h") , which I currently
| interperate as an "invariant constant of energy density".
| Regards
| Ken S. Tucker
|
| OK. KenST. Your method seeks to produce standard atomic
| quanta. I don't see the mechanism which I described as capable
| of that. Your method may be useful where you are focused on
| sub atomic structure but I will be watching with interest how
| it deals with long-range electrically neutral forces.

Key words; "long-range electrically neutral". How do we know that is
true to the level of gravity ~ 10^-42? We simply don't have the
experimental capability to see if an object really is truely
electrically neutral. But what I think is more important is putting EM
in the same framework as GR. Spacetime is curved or "tilted" way more
by EM than by "neutral" matter wrt other charges. Very easy to imagine
this with the quantum "vacuum" as a medium as Volovik proposes. More
difficult to make it all work out mathematically.

OOps. Sorry for empty post. (some say all mine are) )
I'll have to respond to Tensor-Tucker separately after I decrypt
his post.

You are experssing a PoV that KenST caused me to doubt when
he pointed out how London forces operate. Your argurment about
measurement limitations in comparing Coulomb vs. gravitaional forces
cuts both ways.

You are imbuing a charge with a unique longrange force responsible
for gravity and inertia. I certainly can't disprove that and it is a
popular
concept.

I am considering that gravity is only operative for macro atomic
ensembles.

But I agree "more important is putting EM in the same
framework as GR."

One or the the other paradigms has to bend a bit for that to
happen.

Where you say:
Spacetime is curved or "tilted" way more by EM than by
"neutral" matter wrt other charges.

Faraday rotation and optical tweezers come to mind.

I want to try and think about this in several other gauges
so nicely provided by JD Jackson. The insight might change
someones way of thinking. Or more likely drive us all closer
to Dingle's old haunt.

Regards,
Sue...







FrediFizzx

http://www.vacuum-physics.com/QVC/qu...uum_charge.pdf
or postscript
http://www.vacuum-physics.com/QVC/qu...cuum_charge.ps

http://www.vacuum-physics.com

Ken S. Tucker wrote:
snip for Gedanken comments

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.

She burned fuel and exerted a force between her ship
and some exhaust gas. This seems a recipe for acceleration.


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.

Her friend is in a chair on the earth's surface too but holding
a vibratiing reed accelerometer whose frequency was measured
at a point between the moon and earth. It is oscillating at
a lower frequency than when in outer space so is
indicating some acceleration. The earth's gravity perhaps?


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

She says the weights on her vibrating reed followed
straight lines when near the moon. She says they never
follow straight lines near gravitational masses so they
are loosing energy by trying to make the earth wiggle.
(Hypefine Cs transitions behave similarly on GPS clocks)


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

UH OH...
That could be a meaningless geodesic (to me anyway)
unless we resolve the above issues. The vibrating reed in
freefall is the trickiest to visualize.

I believe I said that right? Whether in orbit, or bound for
Davy Jones locker the weights are following a curved
path in 3d +1t space, therefore are loosing energy.

They can only follow straight paths somewhere near the moon.

Whew! That was close!
I almost got to the part with tensors. )

Sue...


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

I should point out:
I am not arguing against the equivalence principle, I am
arguing against something about the freefall gedankens
we ?say? exemplifies it.... and also the interchange of
clocks and acceleration in the Schwartzchild solution.

Quantitativtly they are small issues but lead to singularities
and infinities at extremes.

Sue...


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

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

Jay R. Yablon wrote:
snip

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.

Yes...DIFFERENT.
Very small or low energy ensembles haven't much coupling
efficiency so that result seems a little disconcerting. However
tiny ensembles are difficult weigh on earth. I know of no experiment
that proves they can't be different.
If electromagnetism is signaling spatially and gravity/inertia is
signaling temporally, then nature is making good use of the
bandwidth.

Sue...

snip