JohnMS
Jan14-09, 06:00 AM
Since a few years, some physics teachers are advised to say "momentum
flow" instead of "force". This helps students to focus on what is
really happening whenever a "force" acts. Ok, let me follow this
advice and apply it to a specific case: relativity. The first thing
needed is to make a 4-vector out of it, so that I get "energy-
momentum flow" - in old terms: "power-force"- four vector. Ok, that is
standard stuff. Then comes the crackpottery: there are people (better
unnamed) claiming that this four vector has an uppermost value: c^4/G
(force) or c^5/G (power).
Some time ago I used to call this the ultimate crackpottery.
Then I started reading textbooks. In Kenyon's General Relativity, it
is said that gravitational wave emission is limited by c^5/G. A
similar statement appears in Ohanian and Ruffini. In fact, similar
limits appear in most books that discuss the matter, because the
formulas for power emission do not allow to go above c^5/G! The
expression c^5/G is indeed a power, it has units of Watts. Astronomer
call power "luminosity". Known starts are much less bright.
Guys, is c^5/G really the uppermost value for power/luminosity from
gravitational radiation?
That is a simple question, and it must have a simple answer. Of
course, a maximum power for gravity waves is not a maximum power for
all types of energy, so the crackpottery remains.
(But s..t: c^5/G is also the luminosity/power of a black hole just
before evaporation, when it is of Planck length size, thus when it is
brightest. And that includes all types of energy.) I must admit: I am
getting nervous about this.
John
flow" instead of "force". This helps students to focus on what is
really happening whenever a "force" acts. Ok, let me follow this
advice and apply it to a specific case: relativity. The first thing
needed is to make a 4-vector out of it, so that I get "energy-
momentum flow" - in old terms: "power-force"- four vector. Ok, that is
standard stuff. Then comes the crackpottery: there are people (better
unnamed) claiming that this four vector has an uppermost value: c^4/G
(force) or c^5/G (power).
Some time ago I used to call this the ultimate crackpottery.
Then I started reading textbooks. In Kenyon's General Relativity, it
is said that gravitational wave emission is limited by c^5/G. A
similar statement appears in Ohanian and Ruffini. In fact, similar
limits appear in most books that discuss the matter, because the
formulas for power emission do not allow to go above c^5/G! The
expression c^5/G is indeed a power, it has units of Watts. Astronomer
call power "luminosity". Known starts are much less bright.
Guys, is c^5/G really the uppermost value for power/luminosity from
gravitational radiation?
That is a simple question, and it must have a simple answer. Of
course, a maximum power for gravity waves is not a maximum power for
all types of energy, so the crackpottery remains.
(But s..t: c^5/G is also the luminosity/power of a black hole just
before evaporation, when it is of Planck length size, thus when it is
brightest. And that includes all types of energy.) I must admit: I am
getting nervous about this.
John