Re: [math-fun] graviton-like cellular automaton
So, does a two-body system radiate away energy as gravity waves? Even if it's made of two point particles so no tidal forces? If so a simulation of a tiny (ie tractable) system with powerful gravity (to overcome the smallness) might dissipate its energy quickly.
From: Steve Witham <sw@tiac.net> To: math-fun@mailman.xmission.com Sent: Mon, July 5, 2010 7:00:07 PM Subject: Re: [math-fun] graviton-like cellular automaton So, does a two-body system radiate away energy as gravity waves? Even if it's made of two point particles so no tidal forces? If so a simulation of a tiny (ie tractable) system with powerful gravity (to overcome the smallness) might dissipate its energy quickly. _______________________________________________ This is totally correct, with one tiny exception. In order to have gravity waves, these waves need to have a finite velocity, so the simulation must be in the context of general relativity. The point particles are then black holes. Two black holes with a separation a few times their Schwartzchild radii will distort each other, and that could be attributed to tidal forces. As the black holes approach each other, their orbital period decreases. The gravitational luminosity is proportional to the square of the third time derivative of the quadrupole moment, i.e. to (M R^2 / T^3)^2. It ends with a burst of power at the merger point that is limited by radiation damping to about 10^52 watts. There is much more, all very interesting, in Misner, Thorn, and Wheeler, "Gravitation", chapter 36. -- Gene
Date: Mon, 5 Jul 2010 20:47:44 -0700 (PDT) From: Eugene Salamin <gene_salamin@yahoo.com>
From: Steve Witham <sw@tiac.net> To: math-fun@mailman.xmission.com
So, does a two-body system radiate away energy as gravity waves? Even if it's made of two point particles so no tidal forces?
If so a simulation of a tiny (ie tractable) system with powerful gravity (to overcome the smallness) might dissipate its energy quickly.
This is totally correct, with one tiny exception. In order to have gravity waves, these waves need to have a finite velocity, so the simulation must be in the context of general relativity. The point particles are then black holes. Two black holes with a separation a few times their Schwartzchild radii will distort each other, and that could be attributed to tidal forces. As the black holes approach each other, their orbital period decreases. The gravitational luminosity is proportional to the square of the third time derivative of the quadrupole moment, i.e. to (M R^2 / T^3)^2. It ends with a burst of power at the merger point that is limited by radiation damping to about 10^52 watts. There is much more, all very interesting, in Misner, Thorn, and Wheeler, "Gravitation", chapter 36.
Hulse and Taylor received the physics Nobel in 1993 for observing this effect in the binary pulsar 1913+16: http://nobelprize.org/nobel_prizes/physics/laureates/1993/press.html (Googling "binary pulsar gravity waves" will find many references.) This is a neutron star binary, where both partners are (a) very stable in pulse period and (b) facing the right way to observe their pulsing from earth. So using the pulsars as clocks and measuring the Doppler effect, one can measure the orbital period to very high precision. The rate of decay of the orbit is very nicely explained by radiating away gravitaitonal radiation. The dimensions of the system are large enough to rule out energy dissipation by tidal forces and so on. It's indirect observation, and there could of course be some whacky tidal thing going on that nobody understands -- but for now, it sure looks (quantitatively!) like radiating away energy by gravity waves. -- Steve Rowley <sgr@alum.mit.edu> http://alum.mit.edu/www/sgr/ Skype: sgr000 It is very dark & after 2000. If you continue, you are likely to be eaten by a bleen.
participants (3)
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Eugene Salamin -
Steve Rowley -
Steve Witham