PDA

View Full Version : Gravitational waves

Ring
2001-Nov-02, 01:44 AM
It has been my understanding that gravitational waves require a time varying quadrupole moment because the gravitational field has a retardation correction for both constant velocity and constant acceleration. This is unlike the electric field which has a correction for only constant velocity and therefore admits dipole radiation.

However the following link (and many others I have found) say that the quadrupole moment is required due to conservation of momentum. This explanation eludes me could someone explain?

"The gravitational waves are generated by accelerated masses as electromagnetic
waves are produced by accelerated charges However, due to momentum
conservation in a closed system, a gravitational dipole is not able to radiate. The first
multi-pole component which produces waves is the quadrupole."

http://www.lal.in2p3.fr/presentation/bibliotheque/publications/2001/web/node4.html

Mr. Wree
2001-Nov-02, 04:14 PM
<<...the gravitational field has a retardation correction for both constant velocity and constant acceleration. This is unlike the electric field which has a correction for only constant velocity and therefore admits dipole radiation....>>

Electric fields arise from both postive or negative charges, the gravitational field arises from only a positive 'charge'.

<font size=-1>[ This Message was edited by: Mr. Wree on 2001-11-02 11:36 ]</font>

Ring
2001-Nov-02, 05:22 PM
Yes, I'm aware of that. A time varying dipole is like a spinning rod with a positive charge on one end and a negative charge on the other.

A time varying quadrupole moment is like the same spinning bar but with like charges on both ends.

However, this doesn't seem to answer the consevation of momentum question.

<font size=-1>[ This Message was edited by: Ring on 2001-11-02 12:23 ]</font>

Mr. Wree
2001-Nov-03, 12:17 AM
Consider a rotating rod with identical charge on both ends and a rotating sphere with identical charge all around the circumference/surface.

Gravitational radiation comes from mass density periodicity (the quadrapole end-over-end rod as opposed to the same rod rotating longitudinally).

A neutron star spinning at relativistic velocity can't radiate very much gravitational energy because it's mass density remains fairly constant over time. Though it may lose angular momentum to surrounding space by magnetic drag on a surrounding gaseous/particulate medium, its mass density remains fairly constant (assuming nuclear strong force is esentially deaf to relativistic velocity centripetal force(s)).

Binary neutron stars radiate gravitational energy as the system's mass density varies over time -- like the rod with same charged ends. The system loses energy by grav radiation, the masses move closer together, mass density increases as does orbital velocity, more energy is radiated at higher frequencies.

<font size=-1>[ This Message was edited by: Mr. Wree on 2001-11-03 06:20 ]</font>

Mr. Wree
2001-Nov-03, 07:59 PM
<<<...the gravitational field has a retardation correction for both constant velocity and constant acceleration...>>

From sci.astro Astrophysics FAQ (http://sciastro.astronomy.net/sci.astro.4.FAQ):

"...For weak fields, though, one can describe the theory in a sort of Newtonian language. In that case, one finds that the "force" in GR is not quite central---it does not point directly towards the source of the gravitational field---and that it depends on velocity as well as position. The net result is that the effect of propagation delay is almost exactly cancelled,..."

And, "...moving at a constant velocity, it exerts a force that points toward its present position, not its retarded position,..."

And, "...Consider two bodies---call them A and B---held in orbit by either electrical or
gravitational attraction. As long as the force on A points directly towards B and vice versa, a stable orbit is possible. If the force on A points instead towards the retarded (propagation-time-delayed)
position of B, on the other hand, the effect is to add a new component of force in the direction of A's motion, causing instability of the orbit. This instability, in turn, leads to a change in the mechanical
angular momentum of the A-B system. But *total* angular momentum is conserved, so this change can only occur if some of the angular momentum of the A-B system is carried away by electromagnetic or gravitational radiation."

"(Technically, the lowest order radiation is dipole radiation, which depends on the acceleration.) So to the extent that A's motion can be approximated as motion at a constant velocity, A cannot lose angular momentum. For the theory to be consistent, there *must* therefore be compensating terms that partially cancel the instability of the orbit caused by retardation. This is exactly what happens; a calculation shows that the force on A points not towards B's retarded position, but towards B's "linearly extrapolated" retarded position. Similarly, in general relativity, a mass moving at a constant acceleration does not radiate (the lowest order radiation is quadrupole), so for consistency, an even more complete cancellation of the effect of retardation must occur. This is exactly what one finds when one solves the equations of motion in general relativity."

<font size=-1>[ This Message was edited by: Mr. Wree on 2001-11-03 15:00 ]</font>

DStahl
2001-Nov-04, 01:11 AM
Nice post, Mr. Wree. I hadn't heard that explained except in a kind of cursory way. Thanks.

Wiley
2001-Nov-05, 06:56 PM
On 2001-11-01 20:44, Ring wrote:

"The gravitational waves are generated by accelerated masses as electromagnetic
waves are produced by accelerated charges However, due to momentum
conservation in a closed system, a gravitational dipole is not able to radiate. The first
multi-pole component which produces waves is the quadrupole."

I would like to add a little side note: A common misconception is that a charge moving at a constant velocity does not radiate electromagnetic energy. This is not quite true.

A charge moving with a constant velocity can radiate, if they velocity is greater than that of light in the medium. This is known as Cherenkov radiation. Andy Sommerfeld in 1905 showed how a charge moving faster than c radiates energy, but since Al's paper, On the electrodynamics of moving bodies, was released a few months earlier, Andy's work was largely irrelevant. Until 1934 when Pavel Cherenkov used Andy's work to explain a faint bluish light which occurs when water is exposed to gamma rays.

The most common example of Cherenkov radiation is the bluish glow of water cooling radioactive rods (from nuclear power plants). However a better astronomy example is the white flashes of light seen by Apollo astronauts. Cosmic rays interacting with the eye's vitreous humour can also cause Cherenkov radiation. (see Fazio, Jelley, and Charman, "Generation of Cherenkov light flashes by cosmic radiation within the eyes of the Apollo astranauts", Nature, Nov. 12, 1971.)

Mr. Wree
2001-Nov-05, 11:37 PM
Actually, Cherenkov radiation (http://zebu.uoregon.edu/~js/glossary/cerenkov_radiation.html) occures only during the deceleration phase of transitioning between mediums, thus an acceleration. /phpBB/images/smiles/icon_wink.gif

Mr. Wree
2001-Nov-05, 11:42 PM
I meant "transitioning between media, since everyone knows that transitioning between mediums remains a pointless exercise in futility.

/phpBB/images/smiles/icon_biggrin.gif

2001-Nov-06, 11:39 AM
On 2001-11-01 20:44, Ring wrote:
It has been my understanding that gravitational waves require a time varying quadrupole moment because the gravitational field has a retardation correction for both constant velocity and constant acceleration. This is unlike the electric field which has a correction for only constant velocity and therefore admits dipole radiation.

However the following link (and many others I have found) say that the quadrupole moment is required due to conservation of momentum. This explanation eludes me could someone explain?
5:16 A.M. HUb' November 6, 2001 [97209]
No I cannot, nor did i try the link today
Listen? the line below will be added later
Later = 5:21 A.M.
omy Bulletin Board - View Topic (p1 of 15)
y Bulletin Board - View Topic (p15 of 15
http://www.lal.in2p3.fr/presentation/bibliotheque/publications/2001/web/node4.html
so there WAS room actually for this 5:22 A.M.

<font size=-1>[ This Message was edited by: HUb' on 2001-11-06 06:44 ]</font>

Wiley
2001-Nov-06, 08:44 PM
On 2001-11-05 18:37, Mr. Wree wrote:
Actually, Cherenkov radiation (http://zebu.uoregon.edu/~js/glossary/cerenkov_radiation.html) occures only during the deceleration phase of transitioning between mediums, thus an acceleration. /phpBB/images/smiles/icon_wink.gif

I think your link is wrong. Frank and Tamm developed the theory behind Cherenkov radiation assuming a point charge moving with a uniform velocity. If you're willing to take trip to the local university library, here's the references: M. Frank and I. Tamm, "Coherent visible radiation of fast electrons passsing through matter", Dokl. Akad. Nauk SSSR, vol. 14, pp. 109-114, 1937 and I. Tamm, "Radiation emitted by uniformly moving electrons," Journal of Physics, Academy of Sciences USSR, vol. 1., pp 439-54, 1939. /phpBB/images/smiles/icon_razz.gif

Although Cherenkov radiation is a classical phenomenon, quantum mechanics allows transitioning through mediums. This is known as Chopra tunneling. /phpBB/images/smiles/icon_smile.gif

<font size=-1>[ This Message was edited by: Wiley on 2001-11-06 16:05 ]</font>

Mr. Wree
2001-Nov-06, 11:32 PM
Perhaps we both can be right, and wrong. /phpBB/images/smiles/icon_wink.gif

Cherenkov radiation is emitted whenever charged particles pass through matter with a velocity exceeding the velocity of light in the medium.

The charged particles polarize the molecules, which then turn back rapidly to their ground state, emitting prompt radiation. (http://rkb.home.cern.ch/rkb/PH14pp/node26.html)

And you wrote, "Frank and Tamm developed the theory behind Cherenkov radiation assuming (my bolding) a point charge moving with a uniform velocity.

Now, I can imagine that for an interval of time a charged particle can move though a matter medium at a constant velocity, but I can't imagine that the entire path of a charged particle through a matter medium will be at constant velocity (unaccelerated).

So, I will concede that Cherenkov radiation can occur as a charged particle moves at uniform >c velocity through a matter medium on its way to decelerated < c velocity.

I trust you will concede that, although you stated "A charge moving with a constant velocity can radiate, if they velocity is greater than that of light in the medium" that it is actually the electrons of the excited medium that radiate and not the charged particle moving at constant velocity.

/phpBB/images/smiles/icon_wink.gif

<font size=-1>[ This Message was edited by: Mr. Wree on 2001-11-06 18:35 ]</font>

Wiley
2001-Nov-07, 07:44 PM
On 2001-11-06 18:32, Mr. Wree wrote:
Perhaps we both can be right, and wrong. /phpBB/images/smiles/icon_wink.gif

Cherenkov radiation is emitted whenever charged particles pass through matter with a velocity exceeding the velocity of light in the medium.

The charged particles polarize the molecules, which then turn back rapidly to their ground state, emitting prompt radiation. (http://rkb.home.cern.ch/rkb/PH14pp/node26.html)

And you wrote, "Frank and Tamm developed the theory behind Cherenkov radiation assuming (my bolding) a point charge moving with a uniform velocity.

Now, I can imagine that for an interval of time a charged particle can move though a matter medium at a constant velocity, but I can't imagine that the entire path of a charged particle through a matter medium will be at constant velocity (unaccelerated).

So, I will concede that Cherenkov radiation can occur as a charged particle moves at uniform >c velocity through a matter medium on its way to decelerated < c velocity.

I trust you will concede that, although you stated "A charge moving with a constant velocity can radiate, if they velocity is greater than that of light in the medium" that it is actually the electrons of the excited medium that radiate and not the charged particle moving at constant velocity.

/phpBB/images/smiles/icon_wink.gif

<font size=-1>[ This Message was edited by: Mr. Wree on 2001-11-06 18:35 ]</font>

Having done the derivation of Cherenkov radiation from Maxwell's equations, I can aver that according to classical electromagnetics the radiation is caused by the fast moving charge, not the electrons of the medium. Note the phrase "according to classical electromagnetics".

The web site you linked says "The charged particles polarize the molecules, which then turn back rapidly to their ground state, emitting prompt radiation." Classical EM theory does not account for the different energy states of atoms and molecules. This is quantum mechanics; EM theory only can only account for change in the dipole moment.

So this brings up another point. How does a general charge radiate in a medium? And how does it differ from radiation in a vacuum? There is very little difference in the (classical) derivation of the radiation from a slow (not necessarily uniformly) moving charge (v < c/n) and a fast moving charge (v > c/n, n is the index of refraction). In other words, classically radiation is a consequence of the motion of the particle. If the web site is correct, any radiation is also a consequence of motion and medium.

I don't know how quantum theory say light propagates through a medium, let alone a relativistic particle. I suspect the answer lies here.

<font size=-1>[ This Message was edited by: Wiley on 2001-11-07 14:45 ]</font>

Mr. Wree
2001-Nov-08, 12:54 AM
<<...the radiation is caused by the fast moving charge, not the electrons of the medium...>>

I'll admit my mistake of thinking only in terms of electrons interchanging radiating photons with media electrons as they pass one another.

I must also admit to being unable to visualize ionized nuclei radiating electromagnetically. (I'm a spatial conceptualist.) Are they (fast moving (+) charges) robbing media nulcei of photon-emitting electrons as they go by?

So I am left with wondering how many photons can be emitted by a decelerating electron without regard photons contributed by media electrons.

I know I can no longer do the requisite math.

Help.