What is "present time" in physics?

Post by Richard Hachel
The problem of relativity is the understanding of the notion of present
time, that is to say the notion of simultaneity (which should not be
confused with the notion of chronotropy).
Is there on the planet Fomalhaut IV, a princess Alexandra who lives
there, at the same time as me; me who is here on earth?
That is to say in the same present moment?
It must be said that yes, since whatever procedure of universal
synchronization I adopt, whether mine or that of Albert Einstein, there
is necessarily a LABEL, and only one, to characterize the existence of
Alexandra simultaneous with mine.
But according to the method of "synchronization of present time", we
will not have the same label.
Einstein uses procedure M, Hachel procedure H.
Procedure M is the most practical, procedure H is the most true.
Procedure M is the most practical, because it derives from the
synchronization of the present time on a point M placed very far away in
an imaginary fourth dimension, and at an equal distance from all the
points constituting our universe. This gives an abstract universal time,
but very useful, where the notion of universal present time is flat, and
reciprocal. If A exists at the same time as B for M, then B exists at
the same time as A for M. It is very practical.
Procedure H proposed by Richard Hachel is less practical, but truer. It
is less practical, because the notion of symmetry of the present time
will not be absolute. But it is truer, physically more accurate, and
more beautiful. It will remain eternally true experimentally, and
eternally more beautiful philosophically. What could be more beautiful
than saying to a child: "This horse in this meadow, this moon in the
sky, this galaxy in this telescope, you see them instantly, as they are
today, live-live".
What is uglier than human thought, which thinks it is intelligent,
even though it is full of stupid mockery, conceptual imbecilities,
simply because it can say, as all morons say: "The speed of light is c,
we know it, we have measured it, experimented with it, and we get
3.10^8m/s".
This is the most stupid reflection in the history of humanity, proposed
by mocking morons (Python, John Baez) who think they are funny and
intelligent, authorized mockers, but who have not understood anything
about the notion of universal anisochrony and the two possible ways in
which we can (or even MUST be able to) synchronize the clocks of the
universe.
R.H.

The (physical) space-time is a (mathematical) coordinate space, and
the (physical) Space-Time is the continuous manifold of the field number
formalism of QM combined with the inertial-systems'
differential-system GR, where according to Einstein the GR is
a differential-system parameterized by a "the time", and in
QM the time-reversibility has never been falsified, with the
time-ordering of the path-integral being pretty much classical,
a "clock hypothesis" is not un-usual, that with respect to a
coordinate space, yet there's only a forward-pointing ray of time,
between zero and one a vector field over the entirety of Space-Time,
that in deep space in absolute vacuum at absolute zero equals one.

Clocks either slow or meet, ....

That "there are no closed time-like curves" and "time reversibility
has never been falsified" then as with regards to null geodesics
and any usual ideas about using the time-like as simply an extra
"Fourth Dimension" for only mathematical extrapolation, has that
physically it might as well just be considered "the gradient" as
with regards to "t" everywhere universally parameterizing the
differential-system and time-ordering of GR and QM.

This sort of theory can for example reduce functional freedom
from 10^120 to approximately 1, while that "time dilation plus
length contraction equals space contraction" is simply enough
as of the FitzGeraldian and associated considerations of the
Heaviside and Larmour with respect to Lorentz, while in QM
there are both low-energy and high-energy supersymmetry, as
whether "virtual" particles are just another model of continuum
dynamics.

I.e., all one theory, all one manifold, all one t.

The d'Espagnat on a model philosopher's model physicist's
model philosophy's model physics, "objective realism",
with Broglie-Bohm and Aspect-like extra-locality, as
with regards to "anti-realist model physics", helps
explore then why making for a clock hypothesis and
a "the time" as Einstein does in "Out of My Later Years",
why curved space-time is just a model in the Cartesian
for "space contraction" then that though its consideration
as a "Fourth Dimension" asks a bit much of a simple numerical
resource of a mathematical/physical continuum, continuous
manifold.

What time is now?

The Starmaker

2024-09-05 05:46:10 UTC

The (physical) space-time is a (mathematical) coordinate space, and
the (physical) Space-Time is the continuous manifold of the field number
formalism of QM combined with the inertial-systems'
differential-system GR, where according to Einstein the GR is
a differential-system parameterized by a "the time", and in
QM the time-reversibility has never been falsified, with the
time-ordering of the path-integral being pretty much classical,
a "clock hypothesis" is not un-usual, that with respect to a
coordinate space, yet there's only a forward-pointing ray of time,
between zero and one a vector field over the entirety of Space-Time,
that in deep space in absolute vacuum at absolute zero equals one.
Clocks either slow or meet, ....
That "there are no closed time-like curves" and "time reversibility
has never been falsified" then as with regards to null geodesics
and any usual ideas about using the time-like as simply an extra
"Fourth Dimension" for only mathematical extrapolation, has that
physically it might as well just be considered "the gradient" as
with regards to "t" everywhere universally parameterizing the
differential-system and time-ordering of GR and QM.
This sort of theory can for example reduce functional freedom
from 10^120 to approximately 1, while that "time dilation plus
length contraction equals space contraction" is simply enough
as of the FitzGeraldian and associated considerations of the
Heaviside and Larmour with respect to Lorentz, while in QM
there are both low-energy and high-energy supersymmetry, as
whether "virtual" particles are just another model of continuum
dynamics.
I.e., all one theory, all one manifold, all one t.
The d'Espagnat on a model philosopher's model physicist's
model philosophy's model physics, "objective realism",
with Broglie-Bohm and Aspect-like extra-locality, as
with regards to "anti-realist model physics", helps
explore then why making for a clock hypothesis and
a "the time" as Einstein does in "Out of My Later Years",
why curved space-time is just a model in the Cartesian
for "space contraction" then that though its consideration
as a "Fourth Dimension" asks a bit much of a simple numerical
resource of a mathematical/physical continuum, continuous
manifold.
What time is now?

Now here or now, or here and now??? where? here? now? is it here now?

--
The Starmaker -- To question the unquestionable, ask the unaskable,
to think the unthinkable, mention the unmentionable, say the unsayable,
and challenge the unchallengeable.

The Starmaker

2024-09-05 16:40:59 UTC

The (physical) space-time is a (mathematical) coordinate space, and
the (physical) Space-Time is the continuous manifold of the field number
formalism of QM combined with the inertial-systems'
differential-system GR, where according to Einstein the GR is
a differential-system parameterized by a "the time", and in
QM the time-reversibility has never been falsified, with the
time-ordering of the path-integral being pretty much classical,
a "clock hypothesis" is not un-usual, that with respect to a
coordinate space, yet there's only a forward-pointing ray of time,
between zero and one a vector field over the entirety of Space-Time,
that in deep space in absolute vacuum at absolute zero equals one.
Clocks either slow or meet, ....
That "there are no closed time-like curves" and "time reversibility
has never been falsified" then as with regards to null geodesics
and any usual ideas about using the time-like as simply an extra
"Fourth Dimension" for only mathematical extrapolation, has that
physically it might as well just be considered "the gradient" as
with regards to "t" everywhere universally parameterizing the
differential-system and time-ordering of GR and QM.
This sort of theory can for example reduce functional freedom
from 10^120 to approximately 1, while that "time dilation plus
length contraction equals space contraction" is simply enough
as of the FitzGeraldian and associated considerations of the
Heaviside and Larmour with respect to Lorentz, while in QM
there are both low-energy and high-energy supersymmetry, as
whether "virtual" particles are just another model of continuum
dynamics.
I.e., all one theory, all one manifold, all one t.
The d'Espagnat on a model philosopher's model physicist's
model philosophy's model physics, "objective realism",
with Broglie-Bohm and Aspect-like extra-locality, as
with regards to "anti-realist model physics", helps
explore then why making for a clock hypothesis and
a "the time" as Einstein does in "Out of My Later Years",
why curved space-time is just a model in the Cartesian
for "space contraction" then that though its consideration
as a "Fourth Dimension" asks a bit much of a simple numerical
resource of a mathematical/physical continuum, continuous
manifold.
What time is now?

Now here or now, or here and now??? where? here? now? is it here now?

The question nobody wants to ask is..Where is Now? and

where is Here?

Is Here and Now the same place or are they two different places?

Here

Now

--
The Starmaker -- To question the unquestionable, ask the unaskable,
to think the unthinkable, mention the unmentionable, say the unsayable,
and challenge the unchallengeable.

Ross Finlayson

2024-09-05 19:44:50 UTC

The (physical) space-time is a (mathematical) coordinate space, and
the (physical) Space-Time is the continuous manifold of the field number
formalism of QM combined with the inertial-systems'
differential-system GR, where according to Einstein the GR is
a differential-system parameterized by a "the time", and in
QM the time-reversibility has never been falsified, with the
time-ordering of the path-integral being pretty much classical,
a "clock hypothesis" is not un-usual, that with respect to a
coordinate space, yet there's only a forward-pointing ray of time,
between zero and one a vector field over the entirety of Space-Time,
that in deep space in absolute vacuum at absolute zero equals one.
Clocks either slow or meet, ....
That "there are no closed time-like curves" and "time reversibility
has never been falsified" then as with regards to null geodesics
and any usual ideas about using the time-like as simply an extra
"Fourth Dimension" for only mathematical extrapolation, has that
physically it might as well just be considered "the gradient" as
with regards to "t" everywhere universally parameterizing the
differential-system and time-ordering of GR and QM.
This sort of theory can for example reduce functional freedom
from 10^120 to approximately 1, while that "time dilation plus
length contraction equals space contraction" is simply enough
as of the FitzGeraldian and associated considerations of the
Heaviside and Larmour with respect to Lorentz, while in QM
there are both low-energy and high-energy supersymmetry, as
whether "virtual" particles are just another model of continuum
dynamics.
I.e., all one theory, all one manifold, all one t.
The d'Espagnat on a model philosopher's model physicist's
model philosophy's model physics, "objective realism",
with Broglie-Bohm and Aspect-like extra-locality, as
with regards to "anti-realist model physics", helps
explore then why making for a clock hypothesis and
a "the time" as Einstein does in "Out of My Later Years",
why curved space-time is just a model in the Cartesian
for "space contraction" then that though its consideration
as a "Fourth Dimension" asks a bit much of a simple numerical
resource of a mathematical/physical continuum, continuous
manifold.
What time is now?

Now here or now, or here and now??? where? here? now? is it here now?

The question nobody wants to ask is..Where is Now? and
where is Here?
Is Here and Now the same place or are they two different places?
Here
Now

"Do you know who ...?" "Yeah"

The Starmaker

2024-09-06 21:58:07 UTC

The (physical) space-time is a (mathematical) coordinate space, and
the (physical) Space-Time is the continuous manifold of the field number
formalism of QM combined with the inertial-systems'
differential-system GR, where according to Einstein the GR is
a differential-system parameterized by a "the time", and in
QM the time-reversibility has never been falsified, with the
time-ordering of the path-integral being pretty much classical,
a "clock hypothesis" is not un-usual, that with respect to a
coordinate space, yet there's only a forward-pointing ray of time,
between zero and one a vector field over the entirety of Space-Time,
that in deep space in absolute vacuum at absolute zero equals one.
Clocks either slow or meet, ....
That "there are no closed time-like curves" and "time reversibility
has never been falsified" then as with regards to null geodesics
and any usual ideas about using the time-like as simply an extra
"Fourth Dimension" for only mathematical extrapolation, has that
physically it might as well just be considered "the gradient" as
with regards to "t" everywhere universally parameterizing the
differential-system and time-ordering of GR and QM.
This sort of theory can for example reduce functional freedom
from 10^120 to approximately 1, while that "time dilation plus
length contraction equals space contraction" is simply enough
as of the FitzGeraldian and associated considerations of the
Heaviside and Larmour with respect to Lorentz, while in QM
there are both low-energy and high-energy supersymmetry, as
whether "virtual" particles are just another model of continuum
dynamics.
I.e., all one theory, all one manifold, all one t.
The d'Espagnat on a model philosopher's model physicist's
model philosophy's model physics, "objective realism",
with Broglie-Bohm and Aspect-like extra-locality, as
with regards to "anti-realist model physics", helps
explore then why making for a clock hypothesis and
a "the time" as Einstein does in "Out of My Later Years",
why curved space-time is just a model in the Cartesian
for "space contraction" then that though its consideration
as a "Fourth Dimension" asks a bit much of a simple numerical
resource of a mathematical/physical continuum, continuous
manifold.
What time is now?

Now here or now, or here and now??? where? here? now? is it here now?

The question nobody wants to ask is..Where is Now? and
where is Here?
Is Here and Now the same place or are they two different places?
Here
Now

"Do you know who ...?" "Yeah"

I know it's Now everywhere, but is Here and Now Here or is Here
everywhere, or over there or

Here, There.. Everywhere?

What time is it Here, and what time is it over there, is Here here? Is
there here?

--
The Starmaker -- To question the unquestionable, ask the unaskable,
to think the unthinkable, mention the unmentionable, say the unsayable,
and challenge the unchallengeable.

Ross Finlayson

2024-09-07 00:07:42 UTC

The (physical) space-time is a (mathematical) coordinate space, and
the (physical) Space-Time is the continuous manifold of the field number
formalism of QM combined with the inertial-systems'
differential-system GR, where according to Einstein the GR is
a differential-system parameterized by a "the time", and in
QM the time-reversibility has never been falsified, with the
time-ordering of the path-integral being pretty much classical,
a "clock hypothesis" is not un-usual, that with respect to a
coordinate space, yet there's only a forward-pointing ray of time,
between zero and one a vector field over the entirety of Space-Time,
that in deep space in absolute vacuum at absolute zero equals one.
Clocks either slow or meet, ....
That "there are no closed time-like curves" and "time reversibility
has never been falsified" then as with regards to null geodesics
and any usual ideas about using the time-like as simply an extra
"Fourth Dimension" for only mathematical extrapolation, has that
physically it might as well just be considered "the gradient" as
with regards to "t" everywhere universally parameterizing the
differential-system and time-ordering of GR and QM.
This sort of theory can for example reduce functional freedom
from 10^120 to approximately 1, while that "time dilation plus
length contraction equals space contraction" is simply enough
as of the FitzGeraldian and associated considerations of the
Heaviside and Larmour with respect to Lorentz, while in QM
there are both low-energy and high-energy supersymmetry, as
whether "virtual" particles are just another model of continuum
dynamics.
I.e., all one theory, all one manifold, all one t.
The d'Espagnat on a model philosopher's model physicist's
model philosophy's model physics, "objective realism",
with Broglie-Bohm and Aspect-like extra-locality, as
with regards to "anti-realist model physics", helps
explore then why making for a clock hypothesis and
a "the time" as Einstein does in "Out of My Later Years",
why curved space-time is just a model in the Cartesian
for "space contraction" then that though its consideration
as a "Fourth Dimension" asks a bit much of a simple numerical
resource of a mathematical/physical continuum, continuous
manifold.
What time is now?

Now here or now, or here and now??? where? here? now? is it here now?

The question nobody wants to ask is..Where is Now? and
where is Here?
Is Here and Now the same place or are they two different places?
Here
Now

"Do you know who ...?" "Yeah"

I know it's Now everywhere, but is Here and Now Here or is Here
everywhere, or over there or
Here, There.. Everywhere?
What time is it Here, and what time is it over there, is Here here? Is
there here?

The idea of space contraction is still "Lorentzian" while it must
still explain both length contraction and time dilation, which get
arrived at according to both cosmological constant and L-principle
and mass-energy equivalency, according to light-speed being the
metered propagation of information, that the propagation of information
is free, while metered, in terms of these establishing any reason
why there's not otherwise just plain universal-time, at all.

The idea is that there's FitzGerald, sitting next to Heaviside and
Faraday and Larmour, a bit separately from Maxwell, yet as well all
involved in E&M and the fields of potential, among a sort of tetrad
of quantities, like electron/proton neutron/photon, charge/mass
rest/motion and these kinds of things, in sum-of-histories
sum-of-potentials.

FitzGerald makes for a different Lorentzian than Maxwell and Einstein
respectively, who make Lorentzians, as with regards to dx+dy+dz, -dt,
and ds with regards to the metric, or for the Laplacian so related,
dx^2+dy^2+dx^2, -dy, squared, and ds, squared, and that being zero.

This way, what results is that the linear is Galilean again,
and, the rotational, is free and independent itself, while
yet both are Lorentzian, so that space-contraction, means
nothing to objects in their orbits moving linearly, and
makes for clock-slowing for objects moving circularly in
their orbits.

So, you don't have to care what time it is and can assume it's
the same everywhere, except with regards to coming and going
from quite distinct orbits and trajectories, that basically
appear mostly classical while when they meet and part can show
that the object having entered and left a free rotational slowed
then met and demonstrates space contraction centrally and inwardly,
while the object in linear motion plain departed and exhibits
space-contraction in its own space-frame and space-frame?

Or, you care, then can have what looks like a continuous space-time
manifold again be re-attaching a FitzGeraldian (and Galilean) while
still Lorentzian interpretation, for linear motion and kinetics,
and rotational motion and kinematics, distinctly.

When you look into Larmour forces then Faraday then Compton effect
and so on, this is sort of the super-classical and non-linear which
is sort of what theoretical physicists need to equip their model
philosophy with if they'd care to get past the usual plain fluid
model of electricity, which while correct and all "classically",
ends up not sufficing more "thoroughly".

For example, look into the 20 or more other lettered fields
of electrical and electromagnetic potential besides B, D, and E,
since at least the fin de siecle or Heaviside who have us the
telegrapher's equation, Faraday, and Larmour. Then FitzGerald
is for your space contraction, while of course other usual sorts
of Lorentzians like Maxwell's and Einstein's have their own bits,
as related to various particulars, in the dynamics.

I.e. if you give Lorentzians then the rest of Relativity Theory
has nothing else to say about it, at all.

Ross Finlayson

2024-09-07 03:53:32 UTC

Post by Richard Hachel
The problem of relativity is the understanding of the notion of present
time, that is to say the notion of simultaneity (which should not be
confused with the notion of chronotropy).
Is there on the planet Fomalhaut IV, a princess Alexandra who lives
there, at the same time as me; me who is here on earth?
That is to say in the same present moment?
It must be said that yes, since whatever procedure of universal
synchronization I adopt, whether mine or that of Albert Einstein, there
is necessarily a LABEL, and only one, to characterize the existence of
Alexandra simultaneous with mine.
But according to the method of "synchronization of present time", we
will not have the same label.
Einstein uses procedure M, Hachel procedure H.
Procedure M is the most practical, procedure H is the most true.
Procedure M is the most practical, because it derives from the
synchronization of the present time on a point M placed very far away in
an imaginary fourth dimension, and at an equal distance from all the
points constituting our universe. This gives an abstract
universal time,
but very useful, where the notion of universal present time is flat, and
reciprocal. If A exists at the same time as B for M, then B exists at
the same time as A for M. It is very practical.
Procedure H proposed by Richard Hachel is less practical, but truer. It
is less practical, because the notion of symmetry of the present time
will not be absolute. But it is truer, physically more accurate, and
more beautiful. It will remain eternally true experimentally, and
eternally more beautiful philosophically. What could be more beautiful
than saying to a child: "This horse in this meadow, this moon in the
sky, this galaxy in this telescope, you see them instantly, as they are
today, live-live".
What is uglier than human thought, which thinks it is intelligent,
even though it is full of stupid mockery, conceptual imbecilities,
simply because it can say, as all morons say: "The speed of light is c,
we know it, we have measured it, experimented with it, and we get
3.10^8m/s".
This is the most stupid reflection in the history of humanity, proposed
by mocking morons (Python, John Baez) who think they are funny and
intelligent, authorized mockers, but who have not understood anything
about the notion of universal anisochrony and the two possible ways in
which we can (or even MUST be able to) synchronize the clocks of the
universe.
R.H.

The (physical) space-time is a (mathematical) coordinate space, and
the (physical) Space-Time is the continuous manifold of the field number
formalism of QM combined with the inertial-systems'
differential-system GR, where according to Einstein the GR is
a differential-system parameterized by a "the time", and in
QM the time-reversibility has never been falsified, with the
time-ordering of the path-integral being pretty much classical,
a "clock hypothesis" is not un-usual, that with respect to a
coordinate space, yet there's only a forward-pointing ray of time,
between zero and one a vector field over the entirety of Space-Time,
that in deep space in absolute vacuum at absolute zero equals one.
Clocks either slow or meet, ....
That "there are no closed time-like curves" and "time reversibility
has never been falsified" then as with regards to null geodesics
and any usual ideas about using the time-like as simply an extra
"Fourth Dimension" for only mathematical extrapolation, has that
physically it might as well just be considered "the gradient" as
with regards to "t" everywhere universally parameterizing the
differential-system and time-ordering of GR and QM.
This sort of theory can for example reduce functional freedom
from 10^120 to approximately 1, while that "time dilation plus
length contraction equals space contraction" is simply enough
as of the FitzGeraldian and associated considerations of the
Heaviside and Larmour with respect to Lorentz, while in QM
there are both low-energy and high-energy supersymmetry, as
whether "virtual" particles are just another model of continuum
dynamics.
I.e., all one theory, all one manifold, all one t.
The d'Espagnat on a model philosopher's model physicist's
model philosophy's model physics, "objective realism",
with Broglie-Bohm and Aspect-like extra-locality, as
with regards to "anti-realist model physics", helps
explore then why making for a clock hypothesis and
a "the time" as Einstein does in "Out of My Later Years",
why curved space-time is just a model in the Cartesian
for "space contraction" then that though its consideration
as a "Fourth Dimension" asks a bit much of a simple numerical
resource of a mathematical/physical continuum, continuous
manifold.
What time is now?

Now here or now, or here and now??? where? here? now? is it here now?

The question nobody wants to ask is..Where is Now? and
where is Here?
Is Here and Now the same place or are they two different places?
Here
Now

"Do you know who ...?" "Yeah"

I know it's Now everywhere, but is Here and Now Here or is Here
everywhere, or over there or
Here, There.. Everywhere?
What time is it Here, and what time is it over there, is Here here? Is
there here?

The idea of space contraction is still "Lorentzian" while it must
still explain both length contraction and time dilation, which get
arrived at according to both cosmological constant and L-principle
and mass-energy equivalency, according to light-speed being the
metered propagation of information, that the propagation of information
is free, while metered, in terms of these establishing any reason
why there's not otherwise just plain universal-time, at all.
The idea is that there's FitzGerald, sitting next to Heaviside and
Faraday and Larmour, a bit separately from Maxwell, yet as well all
involved in E&M and the fields of potential, among a sort of tetrad
of quantities, like electron/proton neutron/photon, charge/mass
rest/motion and these kinds of things, in sum-of-histories
sum-of-potentials.
FitzGerald makes for a different Lorentzian than Maxwell and Einstein
respectively, who make Lorentzians, as with regards to dx+dy+dz, -dt,
and ds with regards to the metric, or for the Laplacian so related,
dx^2+dy^2+dx^2, -dy, squared, and ds, squared, and that being zero.
This way, what results is that the linear is Galilean again,
and, the rotational, is free and independent itself, while
yet both are Lorentzian, so that space-contraction, means
nothing to objects in their orbits moving linearly, and
makes for clock-slowing for objects moving circularly in
their orbits.
So, you don't have to care what time it is and can assume it's
the same everywhere, except with regards to coming and going
from quite distinct orbits and trajectories, that basically
appear mostly classical while when they meet and part can show
that the object having entered and left a free rotational slowed
then met and demonstrates space contraction centrally and inwardly,
while the object in linear motion plain departed and exhibits
space-contraction in its own space-frame and space-frame?
Or, you care, then can have what looks like a continuous space-time
manifold again be re-attaching a FitzGeraldian (and Galilean) while
still Lorentzian interpretation, for linear motion and kinetics,
and rotational motion and kinematics, distinctly.
When you look into Larmour forces then Faraday then Compton effect
and so on, this is sort of the super-classical and non-linear which
is sort of what theoretical physicists need to equip their model
philosophy with if they'd care to get past the usual plain fluid
model of electricity, which while correct and all "classically",
ends up not sufficing more "thoroughly".
For example, look into the 20 or more other lettered fields
of electrical and electromagnetic potential besides B, D, and E,
since at least the fin de siecle or Heaviside who have us the
telegrapher's equation, Faraday, and Larmour. Then FitzGerald
is for your space contraction, while of course other usual sorts
of Lorentzians like Maxwell's and Einstein's have their own bits,
as related to various particulars, in the dynamics.
I.e. if you give Lorentzians then the rest of Relativity Theory
has nothing else to say about it, at all.

Larmor, rather.

"Quasilinear theory of Brillouin resonances
in rotating magnetized plasmas"

"It is, however, shown that the Landau and cyclotron resonance
conditions which classically describe resonant energy–momentum exchange
between waves and particles are no longer valid in a rotating magnetized
plasma column. In this case a new resonance
condition which involves a resonant matching between the wave frequency,
the cyclotron frequency modified by inertial effects and the harmonics
of the guiding centre rotation is identified."
-- Rax, Guerolt, Fisch

Nienhuis appears to have an industry in "Faraday rotation".

"Brillouin" and "resonance theory" for that matter is
sort of usual when wave mechanics just won't do.

"... the first successful application of rotating non-neutral plasmas
was the magnetron microwave source theorized by Brillouin (1945)."

"While quasilinear radial transport has been studied
within the framework of non-neutral plasmas confinement deploying a
so-called ‘rotating wall technique’ (Eggleston & O’Neil 1999; Kiwamoto,
Soga & Aoki 2005), these studies were restricted to electrostatic modes.
Finite Larmor radius effects were also neglected
as an infinite magnetic field was assumed. Lastly, although inertial
effects are central to equilibria in Brillouin configurations, these
studies neglected inertial effects so that the resonance condition is
limited to the axial Doppler-shifted resonance between the plasma
rotation and the wave frequency. These restrictions are removed in the
present paper."

"Brillouin modes ...".

"In summary, the first term on the right-hand side of (8.8) corresponds
to a change of the moment of inertia of the particle as a result of the
quasilinear radial drift and Larmor radius evolution."

Of course you can read this for yourself and make of it what it is.

"Although angular momentum exchange between a wave and a rotating plasma
is of importance both to astrophysics (Goldreich & Julian 1969; Julian
1973; Ferrière 2006) and laboratory plasmas (Kostyukov et al. 2002;
Shvets, Fisch & Rax 2002; Thaury et al. 2013), a kinetic model of this
interaction had to our knowledge never been proposed."

"Appendix A. The SAM and OAM of a vector field Consider a wave field
A(r) exp jωt. The identification of (i) linear momentum, (ii) SAM
and (iii) OAM eigenstates can be guided by the analysis of the
transformation properties of the wave under translations and rotations."

"The next step is to consider a Fourier decomposition of the O(V)
oscillating Vlasov terms."

Refers to a GARETZ , B.A. 1981 Angular Doppler effect. J. Opt. Soc. Am.
71 (5), 609

GOUGH , W. 1986 The angular momentum of radiation. Eur. J. Phys. 7 (2),
81–87.

RAX , J.M. 1992 Compton harmonic resonances, stochastic instabilities,
quasilinear diffusion, and collisionless damping with
ultra-high-intensity laser waves. Phys. Fluids B 4 (12), 3962–3972.

RAX , J.-M. & GUEROULT , R. 2021 Faraday–Fresnel rotation and splitting
of orbital angular momentum carrying waves in a rotating plasma. J.
Plasma Phys. 87 (5), 905870507.

("... we use the usual rule <Re[a(u)]Re[b(u)]>_u
= Re[a(u)b^∗(u)]/2 ...".)

https://en.wikipedia.org/wiki/Vlasov_equation

https://en.wikipedia.org/wiki/Levi-Civita_connection

Reintroduces "parallel transport", even "teleparallelism".

https://en.wikipedia.org/wiki/Parallel_transport
https://en.wikipedia.org/wiki/Teleparallelism

Anyways you just come up with Lorentzians for
the propagation equations and that's Relativity.

Right about now

Ross Finlayson

2024-09-07 16:51:27 UTC

The (physical) space-time is a (mathematical) coordinate space, and
the (physical) Space-Time is the continuous manifold of the field number
formalism of QM combined with the inertial-systems'
differential-system GR, where according to Einstein the GR is
a differential-system parameterized by a "the time", and in
QM the time-reversibility has never been falsified, with the
time-ordering of the path-integral being pretty much classical,
a "clock hypothesis" is not un-usual, that with respect to a
coordinate space, yet there's only a forward-pointing ray of time,
between zero and one a vector field over the entirety of Space-Time,
that in deep space in absolute vacuum at absolute zero equals one.
Clocks either slow or meet, ....
That "there are no closed time-like curves" and "time reversibility
has never been falsified" then as with regards to null geodesics
and any usual ideas about using the time-like as simply an extra
"Fourth Dimension" for only mathematical extrapolation, has that
physically it might as well just be considered "the gradient" as
with regards to "t" everywhere universally parameterizing the
differential-system and time-ordering of GR and QM.
This sort of theory can for example reduce functional freedom
from 10^120 to approximately 1, while that "time dilation plus
length contraction equals space contraction" is simply enough
as of the FitzGeraldian and associated considerations of the
Heaviside and Larmour with respect to Lorentz, while in QM
there are both low-energy and high-energy supersymmetry, as
whether "virtual" particles are just another model of continuum
dynamics.
I.e., all one theory, all one manifold, all one t.
The d'Espagnat on a model philosopher's model physicist's
model philosophy's model physics, "objective realism",
with Broglie-Bohm and Aspect-like extra-locality, as
with regards to "anti-realist model physics", helps
explore then why making for a clock hypothesis and
a "the time" as Einstein does in "Out of My Later Years",
why curved space-time is just a model in the Cartesian
for "space contraction" then that though its consideration
as a "Fourth Dimension" asks a bit much of a simple numerical
resource of a mathematical/physical continuum, continuous
manifold.
What time is now?

Now here or now, or here and now??? where? here? now? is it here now?

The question nobody wants to ask is..Where is Now? and
where is Here?
Is Here and Now the same place or are they two different places?
Here
Now

"Do you know who ...?" "Yeah"

I know it's Now everywhere, but is Here and Now Here or is Here
everywhere, or over there or
Here, There.. Everywhere?
What time is it Here, and what time is it over there, is Here here? Is
there here?

The idea of space contraction is still "Lorentzian" while it must
still explain both length contraction and time dilation, which get
arrived at according to both cosmological constant and L-principle
and mass-energy equivalency, according to light-speed being the
metered propagation of information, that the propagation of information
is free, while metered, in terms of these establishing any reason
why there's not otherwise just plain universal-time, at all.
The idea is that there's FitzGerald, sitting next to Heaviside and
Faraday and Larmour, a bit separately from Maxwell, yet as well all
involved in E&M and the fields of potential, among a sort of tetrad
of quantities, like electron/proton neutron/photon, charge/mass
rest/motion and these kinds of things, in sum-of-histories
sum-of-potentials.
FitzGerald makes for a different Lorentzian than Maxwell and Einstein
respectively, who make Lorentzians, as with regards to dx+dy+dz, -dt,
and ds with regards to the metric, or for the Laplacian so related,
dx^2+dy^2+dx^2, -dy, squared, and ds, squared, and that being zero.
This way, what results is that the linear is Galilean again,
and, the rotational, is free and independent itself, while
yet both are Lorentzian, so that space-contraction, means
nothing to objects in their orbits moving linearly, and
makes for clock-slowing for objects moving circularly in
their orbits.
So, you don't have to care what time it is and can assume it's
the same everywhere, except with regards to coming and going
from quite distinct orbits and trajectories, that basically
appear mostly classical while when they meet and part can show
that the object having entered and left a free rotational slowed
then met and demonstrates space contraction centrally and inwardly,
while the object in linear motion plain departed and exhibits
space-contraction in its own space-frame and space-frame?
Or, you care, then can have what looks like a continuous space-time
manifold again be re-attaching a FitzGeraldian (and Galilean) while
still Lorentzian interpretation, for linear motion and kinetics,
and rotational motion and kinematics, distinctly.
When you look into Larmour forces then Faraday then Compton effect
and so on, this is sort of the super-classical and non-linear which
is sort of what theoretical physicists need to equip their model
philosophy with if they'd care to get past the usual plain fluid
model of electricity, which while correct and all "classically",
ends up not sufficing more "thoroughly".
For example, look into the 20 or more other lettered fields
of electrical and electromagnetic potential besides B, D, and E,
since at least the fin de siecle or Heaviside who have us the
telegrapher's equation, Faraday, and Larmour. Then FitzGerald
is for your space contraction, while of course other usual sorts
of Lorentzians like Maxwell's and Einstein's have their own bits,
as related to various particulars, in the dynamics.
I.e. if you give Lorentzians then the rest of Relativity Theory
has nothing else to say about it, at all.

Larmor, rather.
"Quasilinear theory of Brillouin resonances
in rotating magnetized plasmas"
"It is, however, shown that the Landau and cyclotron resonance
conditions which classically describe resonant energy–momentum exchange
between waves and particles are no longer valid in a rotating magnetized
plasma column. In this case a new resonance
condition which involves a resonant matching between the wave frequency,
the cyclotron frequency modified by inertial effects and the harmonics
of the guiding centre rotation is identified."
-- Rax, Guerolt, Fisch
Nienhuis appears to have an industry in "Faraday rotation".
"Brillouin" and "resonance theory" for that matter is
sort of usual when wave mechanics just won't do.
"... the first successful application of rotating non-neutral plasmas
was the magnetron microwave source theorized by Brillouin (1945)."
"While quasilinear radial transport has been studied
within the framework of non-neutral plasmas confinement deploying a
so-called ‘rotating wall technique’ (Eggleston & O’Neil 1999; Kiwamoto,
Soga & Aoki 2005), these studies were restricted to electrostatic modes.
Finite Larmor radius effects were also neglected
as an infinite magnetic field was assumed. Lastly, although inertial
effects are central to equilibria in Brillouin configurations, these
studies neglected inertial effects so that the resonance condition is
limited to the axial Doppler-shifted resonance between the plasma
rotation and the wave frequency. These restrictions are removed in the
present paper."
"Brillouin modes ...".
"In summary, the first term on the right-hand side of (8.8) corresponds
to a change of the moment of inertia of the particle as a result of the
quasilinear radial drift and Larmor radius evolution."
Of course you can read this for yourself and make of it what it is.
"Although angular momentum exchange between a wave and a rotating plasma
is of importance both to astrophysics (Goldreich & Julian 1969; Julian
1973; Ferrière 2006) and laboratory plasmas (Kostyukov et al. 2002;
Shvets, Fisch & Rax 2002; Thaury et al. 2013), a kinetic model of this
interaction had to our knowledge never been proposed."
"Appendix A. The SAM and OAM of a vector field Consider a wave field
A(r) exp jωt. The identification of (i) linear momentum, (ii) SAM
and (iii) OAM eigenstates can be guided by the analysis of the
transformation properties of the wave under translations and rotations."
"The next step is to consider a Fourier decomposition of the O(V)
oscillating Vlasov terms."
Refers to a GARETZ , B.A. 1981 Angular Doppler effect. J. Opt. Soc. Am.
71 (5), 609
GOUGH , W. 1986 The angular momentum of radiation. Eur. J. Phys. 7 (2),
81–87.
RAX , J.M. 1992 Compton harmonic resonances, stochastic instabilities,
quasilinear diffusion, and collisionless damping with
ultra-high-intensity laser waves. Phys. Fluids B 4 (12), 3962–3972.
RAX , J.-M. & GUEROULT , R. 2021 Faraday–Fresnel rotation and splitting
of orbital angular momentum carrying waves in a rotating plasma. J.
Plasma Phys. 87 (5), 905870507.
("... we use the usual rule <Re[a(u)]Re[b(u)]>_u
= Re[a(u)b^∗(u)]/2 ...".)
https://en.wikipedia.org/wiki/Vlasov_equation
https://en.wikipedia.org/wiki/Levi-Civita_connection
Reintroduces "parallel transport", even "teleparallelism".
https://en.wikipedia.org/wiki/Parallel_transport
https://en.wikipedia.org/wiki/Teleparallelism
Anyways you just come up with Lorentzians for
the propagation equations and that's Relativity.
Right about now

"In classical electrodynamics, problems are typically divided into two
classes:

Problems in which the charge and current sources of fields are specified
and the fields are calculated, and

The reverse situation, problems in which the fields are specified and
the motion of particles are calculated."

-- https://en.wikipedia.org/wiki/Abraham%E2%80%93Lorentz_force#Background

"The reason for this is twofold:

Neglect of the "self-fields" usually leads to answers that are accurate
enough for many applications, and
Inclusion of self-fields leads to problems in physics such as
renormalization, some of which are still unsolved, that relate to the
very nature of matter and energy.

These conceptual problems created by self-fields are highlighted in a
standard graduate text. [Jackson]

The difficulties presented by this problem touch one of the most
fundamental aspects of physics, the nature of the elementary particle.
Although partial solutions, workable within limited areas, can be given,
the basic problem remains unsolved. One might hope that the transition
from classical to quantum-mechanical treatments would remove the
difficulties. While there is still hope that this may eventually occur,
the present quantum-mechanical discussions are beset with even more
elaborate troubles than the classical ones. It is one of the triumphs of
comparatively recent years (~ 1948–1950) that the concepts of Lorentz
covariance and gauge invariance were exploited sufficiently cleverly to
circumvent these difficulties in quantum electrodynamics and so allow
the calculation of very small radiative effects to extremely high
precision, in full agreement with experiment. From a fundamental point
of view, however, the difficulties remain. "

Or, "QED is sort of a propitious lie".

Anyways for _classical_ motion and "zero-eth laws" of motion,
then getting into things like "the infinitely-many higher orders
of acceleration, which are formally non-zero", helps reflect
for example that while Born's "Restless Universe" has nowhere
that v = 0, at the same time it results that nowhere are any
of the infinitely-many higher orders of acceleration zero!
What results in changes that Born is both contradicted and
in the Mach-ian confirmed!

(This is usually enough that "the potential fields are the
real fields" and "it's, sum-of-histories, and, sum-of-potentials".)

You know why renormalization is such a problem for physics?
Because "normalization" is really "de-normalization".

So, for space-contraction and the linear and rotational being
different at all, makes for that it's simple that Lorentzians
are given, and it's a gauge theory, and that objects moving
linearly are, ..., "mostly space" and carry their space-frames
and frame-spaces with them, while, objects moving rotationally
are both free and focal as it were, with space-contraction on
the in-side.

All this "abstract physics", absent even a notion of the
infinitely-many higher orders of acceleration all formally
non-zero while each yet vanishing, has that mathematics _owes_
physics why this is so so that philosophers and physicists like
d'Espagnat can equip model philosopher's model physicists' like
Einstein's with enough mental apparatus of the true super-classical
to arrive at the true centrifugal and fulfill things like
"the zero-eth laws of motion", which are slightly yet only
so much more so involved than otherwise the first few.

According to Einstein in "Out of My Later Years",
the "present time" is what is called "the time",
and usually pronounced "thee" to indicate that
moreso than trivial, it's proper, the definite article.

The Starmaker

2024-09-07 17:05:36 UTC

The (physical) space-time is a (mathematical) coordinate space, and
the (physical) Space-Time is the continuous manifold of the field number
formalism of QM combined with the inertial-systems'
differential-system GR, where according to Einstein the GR is
a differential-system parameterized by a "the time", and in
QM the time-reversibility has never been falsified, with the
time-ordering of the path-integral being pretty much classical,
a "clock hypothesis" is not un-usual, that with respect to a
coordinate space, yet there's only a forward-pointing ray of time,
between zero and one a vector field over the entirety of Space-Time,
that in deep space in absolute vacuum at absolute zero equals one.
Clocks either slow or meet, ....
That "there are no closed time-like curves" and "time reversibility
has never been falsified" then as with regards to null geodesics
and any usual ideas about using the time-like as simply an extra
"Fourth Dimension" for only mathematical extrapolation, has that
physically it might as well just be considered "the gradient" as
with regards to "t" everywhere universally parameterizing the
differential-system and time-ordering of GR and QM.
This sort of theory can for example reduce functional freedom
from 10^120 to approximately 1, while that "time dilation plus
length contraction equals space contraction" is simply enough
as of the FitzGeraldian and associated considerations of the
Heaviside and Larmour with respect to Lorentz, while in QM
there are both low-energy and high-energy supersymmetry, as
whether "virtual" particles are just another model of continuum
dynamics.
I.e., all one theory, all one manifold, all one t.
The d'Espagnat on a model philosopher's model physicist's
model philosophy's model physics, "objective realism",
with Broglie-Bohm and Aspect-like extra-locality, as
with regards to "anti-realist model physics", helps
explore then why making for a clock hypothesis and
a "the time" as Einstein does in "Out of My Later Years",
why curved space-time is just a model in the Cartesian
for "space contraction" then that though its consideration
as a "Fourth Dimension" asks a bit much of a simple numerical
resource of a mathematical/physical continuum, continuous
manifold.
What time is now?

Now here or now, or here and now??? where? here? now? is it here now?

The question nobody wants to ask is..Where is Now? and
where is Here?
Is Here and Now the same place or are they two different places?
Here
Now

"Do you know who ...?" "Yeah"

I know it's Now everywhere, but is Here and Now Here or is Here
everywhere, or over there or
Here, There.. Everywhere?
What time is it Here, and what time is it over there, is Here here? Is
there here?

The idea of space contraction is still "Lorentzian" while it must
still explain both length contraction and time dilation, which get
arrived at according to both cosmological constant and L-principle
and mass-energy equivalency, according to light-speed being the
metered propagation of information, that the propagation of information
is free, while metered, in terms of these establishing any reason
why there's not otherwise just plain universal-time, at all.
The idea is that there's FitzGerald, sitting next to Heaviside and
Faraday and Larmour, a bit separately from Maxwell, yet as well all
involved in E&M and the fields of potential, among a sort of tetrad
of quantities, like electron/proton neutron/photon, charge/mass
rest/motion and these kinds of things, in sum-of-histories
sum-of-potentials.
FitzGerald makes for a different Lorentzian than Maxwell and Einstein
respectively, who make Lorentzians, as with regards to dx+dy+dz, -dt,
and ds with regards to the metric, or for the Laplacian so related,
dx^2+dy^2+dx^2, -dy, squared, and ds, squared, and that being zero.
This way, what results is that the linear is Galilean again,
and, the rotational, is free and independent itself, while
yet both are Lorentzian, so that space-contraction, means
nothing to objects in their orbits moving linearly, and
makes for clock-slowing for objects moving circularly in
their orbits.
So, you don't have to care what time it is and can assume it's
the same everywhere, except with regards to coming and going
from quite distinct orbits and trajectories, that basically
appear mostly classical while when they meet and part can show
that the object having entered and left a free rotational slowed
then met and demonstrates space contraction centrally and inwardly,
while the object in linear motion plain departed and exhibits
space-contraction in its own space-frame and space-frame?
Or, you care, then can have what looks like a continuous space-time
manifold again be re-attaching a FitzGeraldian (and Galilean) while
still Lorentzian interpretation, for linear motion and kinetics,
and rotational motion and kinematics, distinctly.
When you look into Larmour forces then Faraday then Compton effect
and so on, this is sort of the super-classical and non-linear which
is sort of what theoretical physicists need to equip their model
philosophy with if they'd care to get past the usual plain fluid
model of electricity, which while correct and all "classically",
ends up not sufficing more "thoroughly".
For example, look into the 20 or more other lettered fields
of electrical and electromagnetic potential besides B, D, and E,
since at least the fin de siecle or Heaviside who have us the
telegrapher's equation, Faraday, and Larmour. Then FitzGerald
is for your space contraction, while of course other usual sorts
of Lorentzians like Maxwell's and Einstein's have their own bits,
as related to various particulars, in the dynamics.
I.e. if you give Lorentzians then the rest of Relativity Theory
has nothing else to say about it, at all.

Larmor, rather.
"Quasilinear theory of Brillouin resonances
in rotating magnetized plasmas"
"It is, however, shown that the Landau and cyclotron resonance
conditions which classically describe resonant energy–momentum exchange
between waves and particles are no longer valid in a rotating magnetized
plasma column. In this case a new resonance
condition which involves a resonant matching between the wave frequency,
the cyclotron frequency modified by inertial effects and the harmonics
of the guiding centre rotation is identified."
-- Rax, Guerolt, Fisch
Nienhuis appears to have an industry in "Faraday rotation".
"Brillouin" and "resonance theory" for that matter is
sort of usual when wave mechanics just won't do.
"... the first successful application of rotating non-neutral plasmas
was the magnetron microwave source theorized by Brillouin (1945)."
"While quasilinear radial transport has been studied
within the framework of non-neutral plasmas confinement deploying a
so-called ‘rotating wall technique’ (Eggleston & O’Neil 1999; Kiwamoto,
Soga & Aoki 2005), these studies were restricted to electrostatic modes.
Finite Larmor radius effects were also neglected
as an infinite magnetic field was assumed. Lastly, although inertial
effects are central to equilibria in Brillouin configurations, these
studies neglected inertial effects so that the resonance condition is
limited to the axial Doppler-shifted resonance between the plasma
rotation and the wave frequency. These restrictions are removed in the
present paper."
"Brillouin modes ...".
"In summary, the first term on the right-hand side of (8.8) corresponds
to a change of the moment of inertia of the particle as a result of the
quasilinear radial drift and Larmor radius evolution."
Of course you can read this for yourself and make of it what it is.
"Although angular momentum exchange between a wave and a rotating plasma
is of importance both to astrophysics (Goldreich & Julian 1969; Julian
1973; Ferrière 2006) and laboratory plasmas (Kostyukov et al. 2002;
Shvets, Fisch & Rax 2002; Thaury et al. 2013), a kinetic model of this
interaction had to our knowledge never been proposed."
"Appendix A. The SAM and OAM of a vector field Consider a wave field
A(r) exp jωt. The identification of (i) linear momentum, (ii) SAM
and (iii) OAM eigenstates can be guided by the analysis of the
transformation properties of the wave under translations and rotations."
"The next step is to consider a Fourier decomposition of the O(V)
oscillating Vlasov terms."
Refers to a GARETZ , B.A. 1981 Angular Doppler effect. J. Opt. Soc. Am.
71 (5), 609
GOUGH , W. 1986 The angular momentum of radiation. Eur. J. Phys. 7 (2),
81–87.
RAX , J.M. 1992 Compton harmonic resonances, stochastic instabilities,
quasilinear diffusion, and collisionless damping with
ultra-high-intensity laser waves. Phys. Fluids B 4 (12), 3962–3972.
RAX , J.-M. & GUEROULT , R. 2021 Faraday–Fresnel rotation and splitting
of orbital angular momentum carrying waves in a rotating plasma. J.
Plasma Phys. 87 (5), 905870507.
("... we use the usual rule <Re[a(u)]Re[b(u)]>_u
= Re[a(u)b^∗(u)]/2 ...".)
https://en.wikipedia.org/wiki/Vlasov_equation
https://en.wikipedia.org/wiki/Levi-Civita_connection
Reintroduces "parallel transport", even "teleparallelism".
https://en.wikipedia.org/wiki/Parallel_transport
https://en.wikipedia.org/wiki/Teleparallelism
Anyways you just come up with Lorentzians for
the propagation equations and that's Relativity.
Right about now

"In classical electrodynamics, problems are typically divided into two
Problems in which the charge and current sources of fields are specified
and the fields are calculated, and
The reverse situation, problems in which the fields are specified and
the motion of particles are calculated."
-- https://en.wikipedia.org/wiki/Abraham%E2%80%93Lorentz_force#Background
Neglect of the "self-fields" usually leads to answers that are accurate
enough for many applications, and
Inclusion of self-fields leads to problems in physics such as
renormalization, some of which are still unsolved, that relate to the
very nature of matter and energy.
These conceptual problems created by self-fields are highlighted in a
standard graduate text. [Jackson]
The difficulties presented by this problem touch one of the most
fundamental aspects of physics, the nature of the elementary particle.
Although partial solutions, workable within limited areas, can be given,
the basic problem remains unsolved. One might hope that the transition
from classical to quantum-mechanical treatments would remove the
difficulties. While there is still hope that this may eventually occur,
the present quantum-mechanical discussions are beset with even more
elaborate troubles than the classical ones. It is one of the triumphs of
comparatively recent years (~ 1948–1950) that the concepts of Lorentz
covariance and gauge invariance were exploited sufficiently cleverly to
circumvent these difficulties in quantum electrodynamics and so allow
the calculation of very small radiative effects to extremely high
precision, in full agreement with experiment. From a fundamental point
of view, however, the difficulties remain. "
Or, "QED is sort of a propitious lie".
Anyways for _classical_ motion and "zero-eth laws" of motion,
then getting into things like "the infinitely-many higher orders
of acceleration, which are formally non-zero", helps reflect
for example that while Born's "Restless Universe" has nowhere
that v = 0, at the same time it results that nowhere are any
of the infinitely-many higher orders of acceleration zero!
What results in changes that Born is both contradicted and
in the Mach-ian confirmed!
(This is usually enough that "the potential fields are the
real fields" and "it's, sum-of-histories, and, sum-of-potentials".)
You know why renormalization is such a problem for physics?
Because "normalization" is really "de-normalization".
So, for space-contraction and the linear and rotational being
different at all, makes for that it's simple that Lorentzians
are given, and it's a gauge theory, and that objects moving
linearly are, ..., "mostly space" and carry their space-frames
and frame-spaces with them, while, objects moving rotationally
are both free and focal as it were, with space-contraction on
the in-side.
All this "abstract physics", absent even a notion of the
infinitely-many higher orders of acceleration all formally
non-zero while each yet vanishing, has that mathematics _owes_
physics why this is so so that philosophers and physicists like
d'Espagnat can equip model philosopher's model physicists' like
Einstein's with enough mental apparatus of the true super-classical
to arrive at the true centrifugal and fulfill things like
"the zero-eth laws of motion", which are slightly yet only
so much more so involved than otherwise the first few.
According to Einstein in "Out of My Later Years",
the "present time" is what is called "the time",
and usually pronounced "thee" to indicate that
moreso than trivial, it's proper, the definite article.

The "present time" in einstein's mind is 'what time is it there?'

The NOW time is the time it is ...Now.

Since Now is everywhere...'"What time it it now?" can also mean, not
here, there but everywhere.

What time is it Everywhere, Now?

Not, 'what time do you have?' since you means there.

What time is it Everywhere, Now?

Your 'clocks' do not apply.

Because you all have the wrong time...now.

--
The Starmaker -- To question the unquestionable, ask the unaskable,
to think the unthinkable, mention the unmentionable, say the unsayable,
and challenge the unchallengeable.

Ross Finlayson

2024-09-07 17:34:13 UTC

The (physical) space-time is a (mathematical) coordinate space, and
the (physical) Space-Time is the continuous manifold of the field number
formalism of QM combined with the inertial-systems'
differential-system GR, where according to Einstein the GR is
a differential-system parameterized by a "the time", and in
QM the time-reversibility has never been falsified, with the
time-ordering of the path-integral being pretty much classical,
a "clock hypothesis" is not un-usual, that with respect to a
coordinate space, yet there's only a forward-pointing ray of time,
between zero and one a vector field over the entirety of Space-Time,
that in deep space in absolute vacuum at absolute zero equals one.
Clocks either slow or meet, ....
That "there are no closed time-like curves" and "time reversibility
has never been falsified" then as with regards to null geodesics
and any usual ideas about using the time-like as simply an extra
"Fourth Dimension" for only mathematical extrapolation, has that
physically it might as well just be considered "the gradient" as
with regards to "t" everywhere universally parameterizing the
differential-system and time-ordering of GR and QM.
This sort of theory can for example reduce functional freedom
from 10^120 to approximately 1, while that "time dilation plus
length contraction equals space contraction" is simply enough
as of the FitzGeraldian and associated considerations of the
Heaviside and Larmour with respect to Lorentz, while in QM
there are both low-energy and high-energy supersymmetry, as
whether "virtual" particles are just another model of continuum
dynamics.
I.e., all one theory, all one manifold, all one t.
The d'Espagnat on a model philosopher's model physicist's
model philosophy's model physics, "objective realism",
with Broglie-Bohm and Aspect-like extra-locality, as
with regards to "anti-realist model physics", helps
explore then why making for a clock hypothesis and
a "the time" as Einstein does in "Out of My Later Years",
why curved space-time is just a model in the Cartesian
for "space contraction" then that though its consideration
as a "Fourth Dimension" asks a bit much of a simple numerical
resource of a mathematical/physical continuum, continuous
manifold.
What time is now?

Now here or now, or here and now??? where? here? now? is it here now?

The question nobody wants to ask is..Where is Now? and
where is Here?
Is Here and Now the same place or are they two different places?
Here
Now

"Do you know who ...?" "Yeah"

I know it's Now everywhere, but is Here and Now Here or is Here
everywhere, or over there or
Here, There.. Everywhere?
What time is it Here, and what time is it over there, is Here here? Is
there here?

The idea of space contraction is still "Lorentzian" while it must
still explain both length contraction and time dilation, which get
arrived at according to both cosmological constant and L-principle
and mass-energy equivalency, according to light-speed being the
metered propagation of information, that the propagation of information
is free, while metered, in terms of these establishing any reason
why there's not otherwise just plain universal-time, at all.
The idea is that there's FitzGerald, sitting next to Heaviside and
Faraday and Larmour, a bit separately from Maxwell, yet as well all
involved in E&M and the fields of potential, among a sort of tetrad
of quantities, like electron/proton neutron/photon, charge/mass
rest/motion and these kinds of things, in sum-of-histories
sum-of-potentials.
FitzGerald makes for a different Lorentzian than Maxwell and Einstein
respectively, who make Lorentzians, as with regards to dx+dy+dz, -dt,
and ds with regards to the metric, or for the Laplacian so related,
dx^2+dy^2+dx^2, -dy, squared, and ds, squared, and that being zero.
This way, what results is that the linear is Galilean again,
and, the rotational, is free and independent itself, while
yet both are Lorentzian, so that space-contraction, means
nothing to objects in their orbits moving linearly, and
makes for clock-slowing for objects moving circularly in
their orbits.
So, you don't have to care what time it is and can assume it's
the same everywhere, except with regards to coming and going
from quite distinct orbits and trajectories, that basically
appear mostly classical while when they meet and part can show
that the object having entered and left a free rotational slowed
then met and demonstrates space contraction centrally and inwardly,
while the object in linear motion plain departed and exhibits
space-contraction in its own space-frame and space-frame?
Or, you care, then can have what looks like a continuous space-time
manifold again be re-attaching a FitzGeraldian (and Galilean) while
still Lorentzian interpretation, for linear motion and kinetics,
and rotational motion and kinematics, distinctly.
When you look into Larmour forces then Faraday then Compton effect
and so on, this is sort of the super-classical and non-linear which
is sort of what theoretical physicists need to equip their model
philosophy with if they'd care to get past the usual plain fluid
model of electricity, which while correct and all "classically",
ends up not sufficing more "thoroughly".
For example, look into the 20 or more other lettered fields
of electrical and electromagnetic potential besides B, D, and E,
since at least the fin de siecle or Heaviside who have us the
telegrapher's equation, Faraday, and Larmour. Then FitzGerald
is for your space contraction, while of course other usual sorts
of Lorentzians like Maxwell's and Einstein's have their own bits,
as related to various particulars, in the dynamics.
I.e. if you give Lorentzians then the rest of Relativity Theory
has nothing else to say about it, at all.

Larmor, rather.
"Quasilinear theory of Brillouin resonances
in rotating magnetized plasmas"
"It is, however, shown that the Landau and cyclotron resonance
conditions which classically describe resonant energy–momentum exchange
between waves and particles are no longer valid in a rotating magnetized
plasma column. In this case a new resonance
condition which involves a resonant matching between the wave frequency,
the cyclotron frequency modified by inertial effects and the harmonics
of the guiding centre rotation is identified."
-- Rax, Guerolt, Fisch
Nienhuis appears to have an industry in "Faraday rotation".
"Brillouin" and "resonance theory" for that matter is
sort of usual when wave mechanics just won't do.
"... the first successful application of rotating non-neutral plasmas
was the magnetron microwave source theorized by Brillouin (1945)."
"While quasilinear radial transport has been studied
within the framework of non-neutral plasmas confinement deploying a
so-called ‘rotating wall technique’ (Eggleston & O’Neil 1999; Kiwamoto,
Soga & Aoki 2005), these studies were restricted to electrostatic modes.
Finite Larmor radius effects were also neglected
as an infinite magnetic field was assumed. Lastly, although inertial
effects are central to equilibria in Brillouin configurations, these
studies neglected inertial effects so that the resonance condition is
limited to the axial Doppler-shifted resonance between the plasma
rotation and the wave frequency. These restrictions are removed in the
present paper."
"Brillouin modes ...".
"In summary, the first term on the right-hand side of (8.8) corresponds
to a change of the moment of inertia of the particle as a result of the
quasilinear radial drift and Larmor radius evolution."
Of course you can read this for yourself and make of it what it is.
"Although angular momentum exchange between a wave and a rotating plasma
is of importance both to astrophysics (Goldreich & Julian 1969; Julian
1973; Ferrière 2006) and laboratory plasmas (Kostyukov et al. 2002;
Shvets, Fisch & Rax 2002; Thaury et al. 2013), a kinetic model of this
interaction had to our knowledge never been proposed."
"Appendix A. The SAM and OAM of a vector field Consider a wave field
A(r) exp jωt. The identification of (i) linear momentum, (ii) SAM
and (iii) OAM eigenstates can be guided by the analysis of the
transformation properties of the wave under translations and rotations."
"The next step is to consider a Fourier decomposition of the O(V)
oscillating Vlasov terms."
Refers to a GARETZ , B.A. 1981 Angular Doppler effect. J. Opt. Soc. Am.
71 (5), 609
GOUGH , W. 1986 The angular momentum of radiation. Eur. J. Phys. 7 (2),
81–87.
RAX , J.M. 1992 Compton harmonic resonances, stochastic instabilities,
quasilinear diffusion, and collisionless damping with
ultra-high-intensity laser waves. Phys. Fluids B 4 (12), 3962–3972.
RAX , J.-M. & GUEROULT , R. 2021 Faraday–Fresnel rotation and splitting
of orbital angular momentum carrying waves in a rotating plasma. J.
Plasma Phys. 87 (5), 905870507.
("... we use the usual rule <Re[a(u)]Re[b(u)]>_u
= Re[a(u)b^∗(u)]/2 ...".)
https://en.wikipedia.org/wiki/Vlasov_equation
https://en.wikipedia.org/wiki/Levi-Civita_connection
Reintroduces "parallel transport", even "teleparallelism".
https://en.wikipedia.org/wiki/Parallel_transport
https://en.wikipedia.org/wiki/Teleparallelism
Anyways you just come up with Lorentzians for
the propagation equations and that's Relativity.
Right about now

The "present time" in einstein's mind is 'what time is it there?'
The NOW time is the time it is ...Now.
Since Now is everywhere...'"What time it it now?" can also mean, not
here, there but everywhere.
What time is it Everywhere, Now?
Not, 'what time do you have?' since you means there.
What time is it Everywhere, Now?
Your 'clocks' do not apply.
Because you all have the wrong time...now.

Meh, the "naive Einstein" and "two observers, limited by light speed",
is just Doppler is all.

What happens is that given a model of curved space time,
people naturally make that any non-zero curve would
eventually diverge and even make a discontinuous space-time.
Then they need to be regularly disabused that there are
no closed time-like curves.

It's like, "naive Einstein" is early in his career,
"wiser Einstein" is later, fine. Then, Einstein's train
is the most usual milieu of his thought experiments or
devices, gedanken or ansaetzen. So, have you ever
been on a moving train and noticed it's different
going forward and backward? How about a bus, any
moving overall medium where it's easier to go to
the back than the front, this is called "fictitious"
while it's very much so. If you get a cheap cup of
coffee in a styrofoam cup from the commissary car
and set it in the aisle, it will eventually tip,
spill, and spill to the back.

Then, that "Einstein's train is perfectly still",
isn't saying much. Also it never is.

Einstein's later works are a lot more Mach-ian,
and, one of his big efforts is trying to figure
out for the centrally symmetric, which these days
is reflected in theories like "infinite dimensional
gravity", which aims to make for a d'Alembertian,
making these things continuous again, when, naively,
they go everywhere without getting anywhere.

So, in a world like today's where GR and QM result
being 120 orders of magnitude apart from each other
and pointing in the opposite directions and where
gravity can't exist in the theory at all because it
cannot be free lunch, and there's thusly nothing to
either bend or straighten space-time the supposed
geodesy, then it's much simpler where gravity is
just a Mach-ian gradient fall-gravity, and where
GR is rehabilitated for linear and rotational variously,
and QM the quantum mechanics makes for continuum mechanics,
again, which may be neatly "super-classical continuum
mechanics, all fields of potential sum-of-histories
sum-of-potentials, which is classical in the limit again,
or as rather that the classical is as to that".

Otherwise you just got sub-fields getting farther and
farther apart, not a "foundations".

The Starmaker

2024-09-07 17:34:39 UTC

The (physical) space-time is a (mathematical) coordinate space, and
the (physical) Space-Time is the continuous manifold of the field number
formalism of QM combined with the inertial-systems'
differential-system GR, where according to Einstein the GR is
a differential-system parameterized by a "the time", and in
QM the time-reversibility has never been falsified, with the
time-ordering of the path-integral being pretty much classical,
a "clock hypothesis" is not un-usual, that with respect to a
coordinate space, yet there's only a forward-pointing ray of time,
between zero and one a vector field over the entirety of Space-Time,
that in deep space in absolute vacuum at absolute zero equals one.
Clocks either slow or meet, ....
That "there are no closed time-like curves" and "time reversibility
has never been falsified" then as with regards to null geodesics
and any usual ideas about using the time-like as simply an extra
"Fourth Dimension" for only mathematical extrapolation, has that
physically it might as well just be considered "the gradient" as
with regards to "t" everywhere universally parameterizing the
differential-system and time-ordering of GR and QM.
This sort of theory can for example reduce functional freedom
from 10^120 to approximately 1, while that "time dilation plus
length contraction equals space contraction" is simply enough
as of the FitzGeraldian and associated considerations of the
Heaviside and Larmour with respect to Lorentz, while in QM
there are both low-energy and high-energy supersymmetry, as
whether "virtual" particles are just another model of continuum
dynamics.
I.e., all one theory, all one manifold, all one t.
The d'Espagnat on a model philosopher's model physicist's
model philosophy's model physics, "objective realism",
with Broglie-Bohm and Aspect-like extra-locality, as
with regards to "anti-realist model physics", helps
explore then why making for a clock hypothesis and
a "the time" as Einstein does in "Out of My Later Years",
why curved space-time is just a model in the Cartesian
for "space contraction" then that though its consideration
as a "Fourth Dimension" asks a bit much of a simple numerical
resource of a mathematical/physical continuum, continuous
manifold.
What time is now?

Now here or now, or here and now??? where? here? now? is it here now?

The question nobody wants to ask is..Where is Now? and
where is Here?
Is Here and Now the same place or are they two different places?
Here
Now

"Do you know who ...?" "Yeah"

I know it's Now everywhere, but is Here and Now Here or is Here
everywhere, or over there or
Here, There.. Everywhere?
What time is it Here, and what time is it over there, is Here here? Is
there here?

The idea of space contraction is still "Lorentzian" while it must
still explain both length contraction and time dilation, which get
arrived at according to both cosmological constant and L-principle
and mass-energy equivalency, according to light-speed being the
metered propagation of information, that the propagation of information
is free, while metered, in terms of these establishing any reason
why there's not otherwise just plain universal-time, at all.
The idea is that there's FitzGerald, sitting next to Heaviside and
Faraday and Larmour, a bit separately from Maxwell, yet as well all
involved in E&M and the fields of potential, among a sort of tetrad
of quantities, like electron/proton neutron/photon, charge/mass
rest/motion and these kinds of things, in sum-of-histories
sum-of-potentials.
FitzGerald makes for a different Lorentzian than Maxwell and Einstein
respectively, who make Lorentzians, as with regards to dx+dy+dz, -dt,
and ds with regards to the metric, or for the Laplacian so related,
dx^2+dy^2+dx^2, -dy, squared, and ds, squared, and that being zero.
This way, what results is that the linear is Galilean again,
and, the rotational, is free and independent itself, while
yet both are Lorentzian, so that space-contraction, means
nothing to objects in their orbits moving linearly, and
makes for clock-slowing for objects moving circularly in
their orbits.
So, you don't have to care what time it is and can assume it's
the same everywhere, except with regards to coming and going
from quite distinct orbits and trajectories, that basically
appear mostly classical while when they meet and part can show
that the object having entered and left a free rotational slowed
then met and demonstrates space contraction centrally and inwardly,
while the object in linear motion plain departed and exhibits
space-contraction in its own space-frame and space-frame?
Or, you care, then can have what looks like a continuous space-time
manifold again be re-attaching a FitzGeraldian (and Galilean) while
still Lorentzian interpretation, for linear motion and kinetics,
and rotational motion and kinematics, distinctly.
When you look into Larmour forces then Faraday then Compton effect
and so on, this is sort of the super-classical and non-linear which
is sort of what theoretical physicists need to equip their model
philosophy with if they'd care to get past the usual plain fluid
model of electricity, which while correct and all "classically",
ends up not sufficing more "thoroughly".
For example, look into the 20 or more other lettered fields
of electrical and electromagnetic potential besides B, D, and E,
since at least the fin de siecle or Heaviside who have us the
telegrapher's equation, Faraday, and Larmour. Then FitzGerald
is for your space contraction, while of course other usual sorts
of Lorentzians like Maxwell's and Einstein's have their own bits,
as related to various particulars, in the dynamics.
I.e. if you give Lorentzians then the rest of Relativity Theory
has nothing else to say about it, at all.

Larmor, rather.
"Quasilinear theory of Brillouin resonances
in rotating magnetized plasmas"
"It is, however, shown that the Landau and cyclotron resonance
conditions which classically describe resonant energy–momentum exchange
between waves and particles are no longer valid in a rotating magnetized
plasma column. In this case a new resonance
condition which involves a resonant matching between the wave frequency,
the cyclotron frequency modified by inertial effects and the harmonics
of the guiding centre rotation is identified."
-- Rax, Guerolt, Fisch
Nienhuis appears to have an industry in "Faraday rotation".
"Brillouin" and "resonance theory" for that matter is
sort of usual when wave mechanics just won't do.
"... the first successful application of rotating non-neutral plasmas
was the magnetron microwave source theorized by Brillouin (1945)."
"While quasilinear radial transport has been studied
within the framework of non-neutral plasmas confinement deploying a
so-called ‘rotating wall technique’ (Eggleston & O’Neil 1999; Kiwamoto,
Soga & Aoki 2005), these studies were restricted to electrostatic modes.
Finite Larmor radius effects were also neglected
as an infinite magnetic field was assumed. Lastly, although inertial
effects are central to equilibria in Brillouin configurations, these
studies neglected inertial effects so that the resonance condition is
limited to the axial Doppler-shifted resonance between the plasma
rotation and the wave frequency. These restrictions are removed in the
present paper."
"Brillouin modes ...".
"In summary, the first term on the right-hand side of (8.8) corresponds
to a change of the moment of inertia of the particle as a result of the
quasilinear radial drift and Larmor radius evolution."
Of course you can read this for yourself and make of it what it is.
"Although angular momentum exchange between a wave and a rotating plasma
is of importance both to astrophysics (Goldreich & Julian 1969; Julian
1973; Ferrière 2006) and laboratory plasmas (Kostyukov et al. 2002;
Shvets, Fisch & Rax 2002; Thaury et al. 2013), a kinetic model of this
interaction had to our knowledge never been proposed."
"Appendix A. The SAM and OAM of a vector field Consider a wave field
A(r) exp jωt. The identification of (i) linear momentum, (ii) SAM
and (iii) OAM eigenstates can be guided by the analysis of the
transformation properties of the wave under translations and rotations."
"The next step is to consider a Fourier decomposition of the O(V)
oscillating Vlasov terms."
Refers to a GARETZ , B.A. 1981 Angular Doppler effect. J. Opt. Soc. Am.
71 (5), 609
GOUGH , W. 1986 The angular momentum of radiation. Eur. J. Phys. 7 (2),
81–87.
RAX , J.M. 1992 Compton harmonic resonances, stochastic instabilities,
quasilinear diffusion, and collisionless damping with
ultra-high-intensity laser waves. Phys. Fluids B 4 (12), 3962–3972.
RAX , J.-M. & GUEROULT , R. 2021 Faraday–Fresnel rotation and splitting
of orbital angular momentum carrying waves in a rotating plasma. J.
Plasma Phys. 87 (5), 905870507.
("... we use the usual rule <Re[a(u)]Re[b(u)]>_u
= Re[a(u)b^∗(u)]/2 ...".)
https://en.wikipedia.org/wiki/Vlasov_equation
https://en.wikipedia.org/wiki/Levi-Civita_connection
Reintroduces "parallel transport", even "teleparallelism".
https://en.wikipedia.org/wiki/Parallel_transport
https://en.wikipedia.org/wiki/Teleparallelism
Anyways you just come up with Lorentzians for
the propagation equations and that's Relativity.
Right about now

Eisnein's "present time" refers to here or there time, not everywhere
time.

--
The Starmaker -- To question the unquestionable, ask the unaskable,
to think the unthinkable, mention the unmentionable, say the unsayable,
and challenge the unchallengeable.

Ross Finlayson

2024-09-07 17:53:17 UTC

The (physical) space-time is a (mathematical) coordinate space, and
the (physical) Space-Time is the continuous manifold of the field number
formalism of QM combined with the inertial-systems'
differential-system GR, where according to Einstein the GR is
a differential-system parameterized by a "the time", and in
QM the time-reversibility has never been falsified, with the
time-ordering of the path-integral being pretty much classical,
a "clock hypothesis" is not un-usual, that with respect to a
coordinate space, yet there's only a forward-pointing ray of time,
between zero and one a vector field over the entirety of Space-Time,
that in deep space in absolute vacuum at absolute zero equals one.
Clocks either slow or meet, ....
That "there are no closed time-like curves" and "time reversibility
has never been falsified" then as with regards to null geodesics
and any usual ideas about using the time-like as simply an extra
"Fourth Dimension" for only mathematical extrapolation, has that
physically it might as well just be considered "the gradient" as
with regards to "t" everywhere universally parameterizing the
differential-system and time-ordering of GR and QM.
This sort of theory can for example reduce functional freedom
from 10^120 to approximately 1, while that "time dilation plus
length contraction equals space contraction" is simply enough
as of the FitzGeraldian and associated considerations of the
Heaviside and Larmour with respect to Lorentz, while in QM
there are both low-energy and high-energy supersymmetry, as
whether "virtual" particles are just another model of continuum
dynamics.
I.e., all one theory, all one manifold, all one t.
The d'Espagnat on a model philosopher's model physicist's
model philosophy's model physics, "objective realism",
with Broglie-Bohm and Aspect-like extra-locality, as
with regards to "anti-realist model physics", helps
explore then why making for a clock hypothesis and
a "the time" as Einstein does in "Out of My Later Years",
why curved space-time is just a model in the Cartesian
for "space contraction" then that though its consideration
as a "Fourth Dimension" asks a bit much of a simple numerical
resource of a mathematical/physical continuum, continuous
manifold.
What time is now?

Now here or now, or here and now??? where? here? now? is it here now?

The question nobody wants to ask is..Where is Now? and
where is Here?
Is Here and Now the same place or are they two different places?
Here
Now

"Do you know who ...?" "Yeah"

I know it's Now everywhere, but is Here and Now Here or is Here
everywhere, or over there or
Here, There.. Everywhere?
What time is it Here, and what time is it over there, is Here here? Is
there here?

The idea of space contraction is still "Lorentzian" while it must
still explain both length contraction and time dilation, which get
arrived at according to both cosmological constant and L-principle
and mass-energy equivalency, according to light-speed being the
metered propagation of information, that the propagation of information
is free, while metered, in terms of these establishing any reason
why there's not otherwise just plain universal-time, at all.
The idea is that there's FitzGerald, sitting next to Heaviside and
Faraday and Larmour, a bit separately from Maxwell, yet as well all
involved in E&M and the fields of potential, among a sort of tetrad
of quantities, like electron/proton neutron/photon, charge/mass
rest/motion and these kinds of things, in sum-of-histories
sum-of-potentials.
FitzGerald makes for a different Lorentzian than Maxwell and Einstein
respectively, who make Lorentzians, as with regards to dx+dy+dz, -dt,
and ds with regards to the metric, or for the Laplacian so related,
dx^2+dy^2+dx^2, -dy, squared, and ds, squared, and that being zero.
This way, what results is that the linear is Galilean again,
and, the rotational, is free and independent itself, while
yet both are Lorentzian, so that space-contraction, means
nothing to objects in their orbits moving linearly, and
makes for clock-slowing for objects moving circularly in
their orbits.
So, you don't have to care what time it is and can assume it's
the same everywhere, except with regards to coming and going
from quite distinct orbits and trajectories, that basically
appear mostly classical while when they meet and part can show
that the object having entered and left a free rotational slowed
then met and demonstrates space contraction centrally and inwardly,
while the object in linear motion plain departed and exhibits
space-contraction in its own space-frame and space-frame?
Or, you care, then can have what looks like a continuous space-time
manifold again be re-attaching a FitzGeraldian (and Galilean) while
still Lorentzian interpretation, for linear motion and kinetics,
and rotational motion and kinematics, distinctly.
When you look into Larmour forces then Faraday then Compton effect
and so on, this is sort of the super-classical and non-linear which
is sort of what theoretical physicists need to equip their model
philosophy with if they'd care to get past the usual plain fluid
model of electricity, which while correct and all "classically",
ends up not sufficing more "thoroughly".
For example, look into the 20 or more other lettered fields
of electrical and electromagnetic potential besides B, D, and E,
since at least the fin de siecle or Heaviside who have us the
telegrapher's equation, Faraday, and Larmour. Then FitzGerald
is for your space contraction, while of course other usual sorts
of Lorentzians like Maxwell's and Einstein's have their own bits,
as related to various particulars, in the dynamics.
I.e. if you give Lorentzians then the rest of Relativity Theory
has nothing else to say about it, at all.

Larmor, rather.
"Quasilinear theory of Brillouin resonances
in rotating magnetized plasmas"
"It is, however, shown that the Landau and cyclotron resonance
conditions which classically describe resonant energy–momentum exchange
between waves and particles are no longer valid in a rotating magnetized
plasma column. In this case a new resonance
condition which involves a resonant matching between the wave frequency,
the cyclotron frequency modified by inertial effects and the harmonics
of the guiding centre rotation is identified."
-- Rax, Guerolt, Fisch
Nienhuis appears to have an industry in "Faraday rotation".
"Brillouin" and "resonance theory" for that matter is
sort of usual when wave mechanics just won't do.
"... the first successful application of rotating non-neutral plasmas
was the magnetron microwave source theorized by Brillouin (1945)."
"While quasilinear radial transport has been studied
within the framework of non-neutral plasmas confinement deploying a
so-called ‘rotating wall technique’ (Eggleston & O’Neil 1999; Kiwamoto,
Soga & Aoki 2005), these studies were restricted to electrostatic modes.
Finite Larmor radius effects were also neglected
as an infinite magnetic field was assumed. Lastly, although inertial
effects are central to equilibria in Brillouin configurations, these
studies neglected inertial effects so that the resonance condition is
limited to the axial Doppler-shifted resonance between the plasma
rotation and the wave frequency. These restrictions are removed in the
present paper."
"Brillouin modes ...".
"In summary, the first term on the right-hand side of (8.8) corresponds
to a change of the moment of inertia of the particle as a result of the
quasilinear radial drift and Larmor radius evolution."
Of course you can read this for yourself and make of it what it is.
"Although angular momentum exchange between a wave and a rotating plasma
is of importance both to astrophysics (Goldreich & Julian 1969; Julian
1973; Ferrière 2006) and laboratory plasmas (Kostyukov et al. 2002;
Shvets, Fisch & Rax 2002; Thaury et al. 2013), a kinetic model of this
interaction had to our knowledge never been proposed."
"Appendix A. The SAM and OAM of a vector field Consider a wave field
A(r) exp jωt. The identification of (i) linear momentum, (ii) SAM
and (iii) OAM eigenstates can be guided by the analysis of the
transformation properties of the wave under translations and rotations."
"The next step is to consider a Fourier decomposition of the O(V)
oscillating Vlasov terms."
Refers to a GARETZ , B.A. 1981 Angular Doppler effect. J. Opt. Soc. Am.
71 (5), 609
GOUGH , W. 1986 The angular momentum of radiation. Eur. J. Phys. 7 (2),
81–87.
RAX , J.M. 1992 Compton harmonic resonances, stochastic instabilities,
quasilinear diffusion, and collisionless damping with
ultra-high-intensity laser waves. Phys. Fluids B 4 (12), 3962–3972.
RAX , J.-M. & GUEROULT , R. 2021 Faraday–Fresnel rotation and splitting
of orbital angular momentum carrying waves in a rotating plasma. J.
Plasma Phys. 87 (5), 905870507.
("... we use the usual rule <Re[a(u)]Re[b(u)]>_u
= Re[a(u)b^∗(u)]/2 ...".)
https://en.wikipedia.org/wiki/Vlasov_equation
https://en.wikipedia.org/wiki/Levi-Civita_connection
Reintroduces "parallel transport", even "teleparallelism".
https://en.wikipedia.org/wiki/Parallel_transport
https://en.wikipedia.org/wiki/Teleparallelism
Anyways you just come up with Lorentzians for
the propagation equations and that's Relativity.
Right about now

Eisnein's "present time" refers to here or there time, not everywhere
time.

You know how it is.

It's like "Einstein: what's the apparent force
of gravity", and he's like, "it's whatever the
field-lines of it are, the only field lines we have
are space-time's field-lines, it's space-time's
field-lines". Then, it's like "Einstein: what is
it right now", and he's like "whatever it is right
not is whatever it is right now", and it's like,
"Einstein, what is it going to be", and it's like,
"it's going to be whatever it's going to be and
then it's going to be what it is", and it's like,
"Einstein, how is that added up", and he's like,
"you know, it's Newtonian in the limit".

Then it's like, "Einstein, how about fall-gravity",
and he's like, "well yeah, fall-gravity's the only
thing that makes sense but everyone makes
non-sense of it".

So, it's like, "Einstein, what's gravity", and
it's like, "gravity is down: straight down".

And it's like "Einstein, are they ever going to learn",
and it's like "not if they don't".

'As you can read from 'Out of My Later Years'
I establish a model of a model physicist as for
and after a model of a model philosopher and
that it's so that a model physicist is limited to
his model of physics and that's the way it is
and unless you widen his world by mathematical
philosophy to equip him with super-classical
mathematics then the super-classical models of
physics we ponder won't be making much sense".

And it's like "Einstein, can we ever learn" and he's
like "provide Lorentzians and as far as Relativity's
concerned that's the word".

Then, most people try to "expand" the theory and
it's like "shouldn't you figure out the zero-eth laws
before adding new ones".

So, "now" is just "sum-of-histories sum-of-potentials",
which a principle of least action, and a gradient,
always forward, universally parameterizing the
entire differential-system that Einstein calls
Relativity, the wiser Einstein.

Ross Finlayson

2024-09-08 19:04:12 UTC