Potential energy explains the so-called GR effect on satellite clocks
mlut...@wanadoo.fr
indeed:
GR formula:
(dt(s)/dt(e))^2 = (1-2M/Rs)-v(s)^2)/(1-2M/Re-v(e)^2)
M = G*Mearth/c^2 and v(s)^2 corresponds to (v(s)/c)^2,
thus to G*Mearth/c^2*Rs or M/2Rs
N.B.:
Rs is the orbital radius of the satellite and Re is the Earth radius
After simplification, one gets
dt(s)/dt(e) = 1 - M/Rs - v(s)^2/2 + M/Re + v(e)^2/2
= 1 - M/Rs - M/2Rs + M/Re + v(e)^2/2
= 1 - 3M/2Rs + M/Re + v(e)^2/2
Ignoring v(e)^2/2 because of the Earth oblateness, one is left with
dt(s)/dt(e) = 1 + M*(1/Re - 3/2Rs) = 1 + shift
Notice that the shift is 0 when Rs = 3Re/2, meaning that a clock
situated on the satellite orbiting at such distance Rs from the Earth
center and a clock situated on Earth will tick at the same rate.
If the satellite were *at rest* at a distance Rs from the Earth
center (v(s)=0), we would have a *pure* GR effect given by
dt(s)/dt(e) = 1 + M * (1/Re - 1/Rs) = 1 + shift(GR)
Such GR formula can easily be derived from the potential energy formula
Ep = m(ph) * gm * (Rs-Re), where
gm = G * Mearth / (Rs * Re)
m(ph) = hNu(s)/c^2 (m(ph) = "mass" of a photon of initial frequency
Nu(s))
Thus Ep = (hNu(s)/c^2) * (G * Mearth / (Rs * Re) * (Rs-Re)
= hNu(s) * (GMearth/c^2) * (1/Re - 1/Rs)
As the photon adds Ep to its initial energy hNu(s), its
energy at the ground level (at the distance Re from the Earth center)
becomes
hNu(e) = hNu(s) + hNu(s) * (GMearth/c^2) * (1/Re - 1/Rs)
After simplfication, one gets
Nu(e)/Nu(s) = 1 + (G*Mearth/c^2) * (1/Re - 1/Rs), which is equivalent
to
the GR formula dt(s)/dt(e) = 1 + M*(1/Re - 1/Rs)
To take into account the SR effect due to the orbital velocity v(s) of
the
satellite, one has to multiply Nu(e)/Nu(s) by sqrt(1-v(s)^2/c^2), where
v(s)^2/c^2 = G*Mearth/Rs*c^2. Then Nu(e)/Nu(s) becomes, after replacing
G*Mearth/c^2 by M,
(1 + M(1/Re - 1/Rs)) * sqrt(1 - M/Rs), or about
(1 + M(1/Re - 1/Rs)) * (1 - M/2Rs) =
1 + M(1/Re - 1/Rs) - M/2Rs - a negligible term
The "global" formula is thus
Nu(e)/Nu(s) = 1 + M(1/Re - 1/Rs - 1/2Rs)
= 1 + M(1/Re - 3/2Rs), which is equivalent to the GR
formula
dt(s)/dt(e) = 1 + M(1/Re - 3/2Rs)
Marcel Luttgens
Areader
6 millimeters from the center of mass. That's a
reeeeeaaaaaaallllllyyyyyy low orbit.
Dirk Van de moortel
<mlut...@wanadoo.fr> wrote in message news:1137067782.1...@z14g2000cwz.googlegroups.com...
> Potential energy explains the so-called GR effect on satellite clocks,
> indeed:
>
> GR formula:
>
> (dt(s)/dt(e))^2 = (1-2M/Rs)-v(s)^2)/(1-2M/Re-v(e)^2)
>
> M = G*Mearth/c^2 and v(s)^2 corresponds to (v(s)/c)^2,
> thus to G*Mearth/c^2*Rs or M/2Rs
>
> N.B.:
> Rs is the orbital radius of the satellite and Re is the Earth radius
>
> After simplification, one gets
That is not a simplification.
It is a first order *approximation*.
>
> dt(s)/dt(e) = 1 - M/Rs - v(s)^2/2 + M/Re + v(e)^2/2
> = 1 - M/Rs - M/2Rs + M/Re + v(e)^2/2
> = 1 - 3M/2Rs + M/Re + v(e)^2/2
>
> Ignoring v(e)^2/2 because of the Earth oblateness, one is left with
Perhaps you haven't understood what you are doing here,
or you don't properly express what you mean, despite what
I explained to you in
http://groups.google.com/group/sci.physics.relativity/msg/208be9a5598a3424
If you ignore v(e), and still continue treating Re as "*the*
Earth radius", then you actually *ignore* the Earth oblateness,
and when you ignore something, you certainly can't use it as a
*reason*, so your phrase "*because* of the Earth oblateness"
is misplaced.
I don't know where you copied this from, but apart from the fact
that photons are modelled to have no mass, not even if "mass"
is scare quoted, you have indeed reproduced the first order
approximation of an effect that is very simply and naturally
modeled by general relativity.
Alas, you used special relativity in your derivation. Since you
obviously don't accept (nor understand) special relativity (as
witnessed by your entire website), according to yourself, your
derivation must be invalid.
Therefore, according to you, your demonstration that "Potential
energy explains the so-called GR effect on satellite clocks",
is useless.
Dirk Vdm
mlut...@wanadoo.fr
Quibbler!
I demonstrated that GR can be replaced by a formula based on
classical mechanics (potential energy of a photon of
pseudo-mass hNu/c^2) and the SR effect due to the orbital velocity
of the satellite.
> Alas, you used special relativity in your derivation. Since you
> obviously don't accept (nor understand) special relativity (as
> witnessed by your entire website), according to yourself, your
> derivation must be invalid.
I always accepted the "time slowing" effect predicted by SR
and similar theories like LET.
> Therefore, according to you, your demonstration that "Potential
> energy explains the so-called GR effect on satellite clocks",
> is useless.
>
> Dirk Vdm
Marcel Luttgens
benutzer
mlut...@wanadoo.fr wrote:
> Potential energy explains the so-called GR effect on satellite clocks,
> indeed:
thanks, maybe you could explain what tha many simbols stands for
Dirk Van de moortel
<mlut...@wanadoo.fr> wrote in message news:1137160701.6...@g44g2000cwa.googlegroups.com...
Sloppy slobberer.
You demonstrated that *one very special first order approximation
of one GR expression, which itself is only a crude approximation*
(dt(s)/dt(e))^2 = (1-2M/Rs)-v(s)^2)/(1-2M/Re-v(e)^2)
can be produced by modelling photons with non zero "pseudomass",
and an effect of special relativity that, according to your website and
posting history, is complete nonsense.
>
> > Alas, you used special relativity in your derivation. Since you
> > obviously don't accept (nor understand) special relativity (as
> > witnessed by your entire website), according to yourself, your
> > derivation must be invalid.
>
> I always accepted the "time slowing" effect predicted by SR
> and similar theories like LET.
Perhaps you could have a look at your own website and
to your posting history on this newsgroup some day:
There is no length contraction, by M. Luttgens:
http://perso.wanadoo.fr/mluttgens/mmx.htm
"Sapere Aude": Refutations of SR, by G. Walton:
http://perso.wanadoo.fr/mluttgens/sapere.htm
The Lorentz transformation (LT) are false, by M. Luttgens:
http://perso.wanadoo.fr/mluttgens/LTfalse.htm
Mathematical Error in the Lorentz Transformation, by Paul Marmet:
http://www.newtonphysics.on.ca/Lorentz/lorentz.html
The Twin paradox falsifies SR:
http://perso.wanadoo.fr/mluttgens/twinpdx1.htm
It seems that you don't quite understand what you have on your
website :-)
>
> > Therefore, according to you, your demonstration that "Potential
> > energy explains the so-called GR effect on satellite clocks",
> > is useless.
Perhaps I should have added that the logic probably
would escape you - as it always has and always will.
Dirk Vdm
Ken S. Tucker
Marcel, from what I understand your quite right,
((Dinky Vd is fuckin you over, he's admitted to
suffer from OCD, Obessive Compulsive Disorder,
a serious kook needing meds))
The time *rate* of clocks in between separate CS's
is in proportion to their relative potential energies.
For example, Planck's "h" must be invariant, therefore
dE = h * df
where dE is the potential and df the frequency difference
between two clocks rate of time.
In my view that's a very important contact between QT
and GR confirmed by the Pound-Rebka experiment.
Weinberg in G&C pg.84 details the math clearly.
Regards
Ken
Dirk Van de moortel
"Ken S. Tucker" <dyna...@vianet.on.ca> wrote in message news:1137247332....@g44g2000cwa.googlegroups.com...
[snip]
> > > Alas, you used special relativity in your derivation. Since you
> > > obviously don't accept (nor understand) special relativity (as
> > > witnessed by your entire website), according to yourself, your
> > > derivation must be invalid.
> >
> > I always accepted the "time slowing" effect predicted by SR
> > and similar theories like LET.
> >
> > > Therefore, according to you, your demonstration that "Potential
> > > energy explains the so-called GR effect on satellite clocks",
> > > is useless.
> > >
> > > Dirk Vdm
> >
> > Marcel Luttgens
>
> Marcel, from what I understand your quite right,
The problem is, Ken, that Marcel does not think that he
is right to begin with. You see, according to Marcel:
There is no length contraction, by M. Luttgens:
http://perso.wanadoo.fr/mluttgens/mmx.htm
"Sapere Aude": Refutations of SR, by G. Walton:
http://perso.wanadoo.fr/mluttgens/sapere.htm
The Lorentz transformation (LT) are false, by M. Luttgens:
http://perso.wanadoo.fr/mluttgens/LTfalse.htm
Mathematical Error in the Lorentz Transformation, by Paul Marmet:
http://www.newtonphysics.on.ca/Lorentz/lorentz.html
The Twin paradox falsifies SR:
http://perso.wanadoo.fr/mluttgens/twinpdx1.htm
So, clearly Marcel has a severy consistency and logic
problem.
As I said a few days ago, before you give a comment
to something, it might be a good idea to find out what
was written first. Of course that only works if you're
sober.
Dirk Vdm