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Chalky
Feb 12, 2012, 6:43:00 PM2/12/12
to
If I recall correctly, some time ago I read an article (now lost or
mislaid), and written by Steve Carlip (I think), where he explained
how the mathematics mean that the direction of gravitational
attraction is, in effect, projected forward in time to point to the
position in space of the gravitating body now......Or, was that just
the direction in space, as opposed to both direction and distance?
Can anyone advise me on whether I recall correctly, and/or provide the
appropriate on-line reference?
[[Mod. note -- You might be thinking of
http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html
which in turn cites the beautiful paper
S. Carlip
"Aberration and the Speed of Gravity"
Phys. Lett. A267 (2000) 81-87
http://arxiv.org/abs/gr-qc/9909087
-- jt]]
As I understand matters, it would be nonsensical to additionally claim
that the direction of acceleration is towards the spacetime location
of the gravitating body now, for two reasons:
firstly, because acceleration is understood to take place in the
conventional direction of time's arrow, and, secondly, for
acceleration to take place without the passage of time would be
oxymoronic.
[[Mod. note --
In a curved spacetime there's no generic notion of the direction
"towards" a distant event. In any case, a body (gravitating or not)
doesn't occupy a single event; rather, it follows a *worldline* in
spacetime.
-- jt]]
mislaid), and written by Steve Carlip (I think), where he explained
how the mathematics mean that the direction of gravitational
attraction is, in effect, projected forward in time to point to the
position in space of the gravitating body now......Or, was that just
the direction in space, as opposed to both direction and distance?
Can anyone advise me on whether I recall correctly, and/or provide the
appropriate on-line reference?
[[Mod. note -- You might be thinking of
http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html
which in turn cites the beautiful paper
S. Carlip
"Aberration and the Speed of Gravity"
Phys. Lett. A267 (2000) 81-87
http://arxiv.org/abs/gr-qc/9909087
-- jt]]
As I understand matters, it would be nonsensical to additionally claim
that the direction of acceleration is towards the spacetime location
of the gravitating body now, for two reasons:
firstly, because acceleration is understood to take place in the
conventional direction of time's arrow, and, secondly, for
acceleration to take place without the passage of time would be
oxymoronic.
[[Mod. note --
In a curved spacetime there's no generic notion of the direction
"towards" a distant event. In any case, a body (gravitating or not)
doesn't occupy a single event; rather, it follows a *worldline* in
spacetime.
-- jt]]
Phillip Helbig---undress to reply
Feb 17, 2012, 5:35:55 AM2/17/12
to
In article
<798628db-633f-434f...@c21g2000yqi.googlegroups.com>,
particles move in the gravitational field of other particles do NOT have
to take into account the speed of gravity. In effect, taking the speed
of gravity into account AND the fact that the particles will have moved
to new positions by the time the "gravity arrives" cancel to first (and
maybe higher---I'm not sure) order. Thus, one can do the calculation
with much less overhead and get, to a useful approximation, the same
results as with a proper calculation.
<798628db-633f-434f...@c21g2000yqi.googlegroups.com>,
Chalky <chalk...@bleachboys.co.uk> writes:
> If I recall correctly, some time ago I read an article (now lost or
> mislaid), and written by Steve Carlip (I think), where he explained
> how the mathematics mean that the direction of gravitational
> attraction is, in effect, projected forward in time to point to the
> position in space of the gravitating body now......Or, was that just
> the direction in space, as opposed to both direction and distance?
>
> Can anyone advise me on whether I recall correctly, and/or provide the
> appropriate on-line reference?
>
> [[Mod. note -- You might be thinking of
> http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html
> which in turn cites the beautiful paper
> S. Carlip
> "Aberration and the Speed of Gravity"
> Phys. Lett. A267 (2000) 81-87
> http://arxiv.org/abs/gr-qc/9909087
> -- jt]]
Note that this means that N-body simulations which calculate how
> If I recall correctly, some time ago I read an article (now lost or
> mislaid), and written by Steve Carlip (I think), where he explained
> how the mathematics mean that the direction of gravitational
> attraction is, in effect, projected forward in time to point to the
> position in space of the gravitating body now......Or, was that just
> the direction in space, as opposed to both direction and distance?
>
> Can anyone advise me on whether I recall correctly, and/or provide the
> appropriate on-line reference?
>
> [[Mod. note -- You might be thinking of
> http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html
> which in turn cites the beautiful paper
> S. Carlip
> "Aberration and the Speed of Gravity"
> Phys. Lett. A267 (2000) 81-87
> http://arxiv.org/abs/gr-qc/9909087
> -- jt]]
particles move in the gravitational field of other particles do NOT have
to take into account the speed of gravity. In effect, taking the speed
of gravity into account AND the fact that the particles will have moved
to new positions by the time the "gravity arrives" cancel to first (and
maybe higher---I'm not sure) order. Thus, one can do the calculation
with much less overhead and get, to a useful approximation, the same
results as with a proper calculation.
Chalky
Feb 21, 2012, 3:14:25 AM2/21/12
to
On Feb 12, 11:43=A0pm, Chalky <chalkys...@bleachboys.co.uk> wrote:
> If I recall correctly, some time ago I read an article (now lost or
> mislaid), and written by Steve Carlip (I think), where he explained
> how the mathematics mean that the direction of gravitational
> attraction is, in effect, projected forward in time to point to the
> position in space of the gravitating body now......Or, was that just
> the direction in space, as opposed to both direction and distance?
>
> Can anyone advise me on whether I recall correctly, and/or provide the
> appropriate on-line reference?
>
> [[Mod. note -- You might be thinking of
> =A0http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html
> If I recall correctly, some time ago I read an article (now lost or
> mislaid), and written by Steve Carlip (I think), where he explained
> how the mathematics mean that the direction of gravitational
> attraction is, in effect, projected forward in time to point to the
> position in space of the gravitating body now......Or, was that just
> the direction in space, as opposed to both direction and distance?
>
> Can anyone advise me on whether I recall correctly, and/or provide the
> appropriate on-line reference?
>
> [[Mod. note -- You might be thinking of
> which in turn cites the beautiful paper
> =A0 S. Carlip
> =A0 "Aberration and the Speed of Gravity"
> =A0 Phys. Lett. A267 (2000) 81-87
> =A0http://arxiv.org/abs/gr-qc/9909087
> -- jt]]
>
Yes, this probably was the material I needed to refresh my memory on.
However, reference [18] to R. J. Low, Class. Quantum Grav. 16 (1999)
543., on page 5 of the paper, seems unfamiliar.
Is Carlip actually claiming here that Cox has succeeded in rigorously
disproving the advanced solution to Einstein's field equation, for the
speed of gravity?
Chalky
Feb 21, 2012, 4:01:54 AM2/21/12
to
On Feb 21, 8:14=A0am, Chalky <chalkys...@bleachboys.co.uk> wrote:
> > =3DA0 "Aberration and the Speed of Gravity"
> > =3DA0 Phys. Lett. A267 (2000) 81-87
> > =3DA0http://arxiv.org/abs/gr-qc/9909087
Yes, this probably was the material I needed to refresh my memory on.
However, reference [18] to R. J. Low, Class. Quantum Grav. 16 (1999)
543., on page 5 of the _arXiv copy of the_ paper, seems unfamiliar.
Is Carlip actually claiming here that _Low_ has succeeded in
> On Feb 12, 11:43=3DA0pm, Chalky <chalkys...@bleachboys.co.uk> wrote:
>
>
>
>
>
>
>
>
>
> > If I recall correctly, some time ago I read an article (now lost or
> > mislaid), and written by Steve Carlip (I think), where he explained
> > how the mathematics mean that the direction of gravitational
> > attraction is, in effect, projected forward in time to point to the
> > position in space of the gravitating body now......Or, was that just
> > the direction in space, as opposed to both direction and distance?
>
> > Can anyone advise me on whether I recall correctly, and/or provide the
> > appropriate on-line reference?
>
> > [[Mod. note -- You might be thinking of
> > =3DA0http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.htm=
>
>
>
>
>
>
>
>
>
> > If I recall correctly, some time ago I read an article (now lost or
> > mislaid), and written by Steve Carlip (I think), where he explained
> > how the mathematics mean that the direction of gravitational
> > attraction is, in effect, projected forward in time to point to the
> > position in space of the gravitating body now......Or, was that just
> > the direction in space, as opposed to both direction and distance?
>
> > Can anyone advise me on whether I recall correctly, and/or provide the
> > appropriate on-line reference?
>
> > [[Mod. note -- You might be thinking of
l
> > which in turn cites the beautiful paper
> > =3DA0 S. Carlip
> > which in turn cites the beautiful paper
> > =3DA0 "Aberration and the Speed of Gravity"
> > =3DA0 Phys. Lett. A267 (2000) 81-87
> > =3DA0http://arxiv.org/abs/gr-qc/9909087
> > -- jt]]
>
> Yes, this probably was the material I needed to refresh my memory on.
>
> However, reference [18] to R. J. Low, Class. Quantum Grav. 16 (1999)
> 543., on page 5 of the paper, seems unfamiliar.
>
> Is Carlip actually claiming here that Cox has succeeded in rigorously
> disproving the advanced solution to Einstein's field equation, for the
> speed of gravity?
My previous posting contained two minor errors, so here goes again:
>
> Yes, this probably was the material I needed to refresh my memory on.
>
> However, reference [18] to R. J. Low, Class. Quantum Grav. 16 (1999)
> 543., on page 5 of the paper, seems unfamiliar.
>
> Is Carlip actually claiming here that Cox has succeeded in rigorously
> disproving the advanced solution to Einstein's field equation, for the
> speed of gravity?
Yes, this probably was the material I needed to refresh my memory on.
However, reference [18] to R. J. Low, Class. Quantum Grav. 16 (1999)
Is Carlip actually claiming here that _Low_ has succeeded in
carlip...@physics.ucdavis.edu
Mar 3, 2012, 3:21:24 AM3/3/12
to
Chalky <chalk...@bleachboys.co.uk> wrote:
[...]
trajectory of light is determined by your distribution of matter and
you're asking what happens if you wiggle the matter. Low answers
this with a clever trick.
Low assumes a globally hyperbolic spacetime, so the past and future
are completely determined by data on a Cauchy surface. He chooses
an initial surface, and (arbitrary) initial data that he propagates
both forward and backward in time to get the full spacetime. He then
asks what happens if he changes the data on the initial surface in a
small region S. He shows that the change propagates no faster than
the speed of light in the sense that the future geometry does not
change outside the causal future -- essentially the forward light
cone -- of the region S.
This has nothing in particular to do with advanced or retarded
solutions. You could time-reverse the same argument and say that
the advanced solution propagates backwards no faster than light.
You can find Low's paper at http://arxiv.org/abs/gr-qc/9812067.
Steve Carlip
[...]
> However, reference [18] to R. J. Low, Class. Quantum Grav. 16 (1999)
> 543., on page 5 of the _arXiv copy of the_ paper, seems unfamiliar.
> Is Carlip actually claiming here that _Low_ has succeeded in
> rigorously disproving the advanced solution to Einstein's field
> equation, for the speed of gravity?
It's tricky to say what you mean by "faster than light" when the
> 543., on page 5 of the _arXiv copy of the_ paper, seems unfamiliar.
> Is Carlip actually claiming here that _Low_ has succeeded in
> rigorously disproving the advanced solution to Einstein's field
> equation, for the speed of gravity?
trajectory of light is determined by your distribution of matter and
you're asking what happens if you wiggle the matter. Low answers
this with a clever trick.
Low assumes a globally hyperbolic spacetime, so the past and future
are completely determined by data on a Cauchy surface. He chooses
an initial surface, and (arbitrary) initial data that he propagates
both forward and backward in time to get the full spacetime. He then
asks what happens if he changes the data on the initial surface in a
small region S. He shows that the change propagates no faster than
the speed of light in the sense that the future geometry does not
change outside the causal future -- essentially the forward light
cone -- of the region S.
This has nothing in particular to do with advanced or retarded
solutions. You could time-reverse the same argument and say that
the advanced solution propagates backwards no faster than light.
You can find Low's paper at http://arxiv.org/abs/gr-qc/9812067.
Steve Carlip
Chalky
Mar 7, 2012, 9:04:48 PM3/7/12
to
On Mar 3, 8:21 am, carlip-nos...@physics.ucdavis.edu wrote:
Thank you for your considered and clear response.
Yes, it is also tricky to say whether an advanced solution would be
"faster" than a retarded solution, in that an advanced solution would
have negative speed (distance of travel/ time taken for travel). It
would thus be difficult (or impossible) to argue that -1 is greater
than +1. This is why I raised the query. However, you have answered
that query succinctly and unambiguously, and with more authority than
I could probably manage myself. This is appreciated.
Chalky.
Yes, it is also tricky to say whether an advanced solution would be
"faster" than a retarded solution, in that an advanced solution would
have negative speed (distance of travel/ time taken for travel). It
would thus be difficult (or impossible) to argue that -1 is greater
than +1. This is why I raised the query. However, you have answered
that query succinctly and unambiguously, and with more authority than
I could probably manage myself. This is appreciated.
Chalky.
Norbert Dragon
May 5, 2012, 12:38:57 PM5/5/12
to
* carlip...@physics.ucdavis.edu writes:
> Low assumes a globally hyperbolic spacetime, so the past and future
> are completely determined by data on a Cauchy surface. He chooses
> an initial surface, and (arbitrary) initial data that he propagates
> both forward and backward in time to get the full spacetime. He then
> asks what happens if he changes the data on the initial surface in a
> small region S. He shows that the change propagates no faster than
> the speed of light in the sense that the future geometry does not
> change outside the causal future -- essentially the forward light
> cone -- of the region S.
Do you claim that this applies to finite changes? I am only aware of
> Low assumes a globally hyperbolic spacetime, so the past and future
> are completely determined by data on a Cauchy surface. He chooses
> an initial surface, and (arbitrary) initial data that he propagates
> both forward and backward in time to get the full spacetime. He then
> asks what happens if he changes the data on the initial surface in a
> small region S. He shows that the change propagates no faster than
> the speed of light in the sense that the future geometry does not
> change outside the causal future -- essentially the forward light
> cone -- of the region S.
proofs that infinitesimal changes propagate within their forward light
cone. They change the metric and therefore also the lightcones. In
second order they propagate in a changed forward lightcone which, to
all what I know, is not necessarily contained in the original
lightcone.
--
Superstition brings bad luck
www.itp.uni-hannover.de/~dragon
Tom Roberts
May 8, 2012, 8:14:00 AM5/8/12
to
On 5/5/12 5/5/12 11:38 AM, Norbert Dragon wrote:
the Cauchy surface.
> I am only aware of
> proofs that infinitesimal changes propagate within their forward light
> cone.
So add this to your awareness:
R. Low, "Speed Limits in General Relativity", Class.Quant.Grav.
16 (1999) 543-549, http://arxiv.org/abs/gr-qc/9812067.
> They change the metric and therefore also the lightcones.
Low's approach does not directly consider lightcones, but rather the
Cauchy developments of the region S and its compliment. The key
condition is that the region containing the modified initial data is a
submanifold of the Cauchy surface; the region outside the Cauchy
development of that submanifold is isometric to the same region in the
manifold with unmodified Cauchy surface.
Understanding his argument and notation probably requires
familiarity with Hawking and Ellis, _The_large_scale_structure_
_of_space-time_.
Tom Roberts
> * carlip...@physics.ucdavis.edu writes:
>> Low assumes a globally hyperbolic spacetime, so the past and future
>> are completely determined by data on a Cauchy surface. He chooses
>> an initial surface, and (arbitrary) initial data that he propagates
>> both forward and backward in time to get the full spacetime. He then
>> asks what happens if he changes the data on the initial surface in a
>> small region S. He shows that the change propagates no faster than
>> the speed of light in the sense that the future geometry does not
>> change outside the causal future -- essentially the forward light
>> cone -- of the region S.
>
>> Low assumes a globally hyperbolic spacetime, so the past and future
>> are completely determined by data on a Cauchy surface. He chooses
>> an initial surface, and (arbitrary) initial data that he propagates
>> both forward and backward in time to get the full spacetime. He then
>> asks what happens if he changes the data on the initial surface in a
>> small region S. He shows that the change propagates no faster than
>> the speed of light in the sense that the future geometry does not
>> change outside the causal future -- essentially the forward light
>> cone -- of the region S.
>
> Do you claim that this applies to finite changes?
Low's argument applies to any finite change within a bounded region of
the Cauchy surface.
> I am only aware of
> proofs that infinitesimal changes propagate within their forward light
> cone.
R. Low, "Speed Limits in General Relativity", Class.Quant.Grav.
16 (1999) 543-549, http://arxiv.org/abs/gr-qc/9812067.
> They change the metric and therefore also the lightcones.
Cauchy developments of the region S and its compliment. The key
condition is that the region containing the modified initial data is a
submanifold of the Cauchy surface; the region outside the Cauchy
development of that submanifold is isometric to the same region in the
manifold with unmodified Cauchy surface.
Understanding his argument and notation probably requires
familiarity with Hawking and Ellis, _The_large_scale_structure_
_of_space-time_.
Tom Roberts
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