by neufer » Wed Dec 08, 2021 5:38 pm
johnnydeep wrote: ↑Wed Dec 08, 2021 4:12 pm
Late to this interesting discussion, but I was always perplexed by why, if gravitational waves are just "ripples in space-time", they should be limited to propagating at the speed of light. That is, no THING is physically moving through space, so the c speed limit should be irrelevant. I guess it's because a full description of relativity says that no INFORMATION can propagate faster than c, and GWs are conveying information. Then there's the still hypothetical (I think?) existence of gravitons, and if they are indeed found to be the PARTICLE mediators of the gravitational force, I suppose they WOULD be limited by c.
Also, GWs apparently have a wavelength and frequency in inverse proportion to each other. But this APOD also mentions their energy, which is represented by the brightness of the spectra. So, how does the energy relate to the wavelength and frequency? We say light of higher frequency (and shorter wavelength) has higher energy, don't we? Yet neufer's first post above says that larger mass BHs generate lower frequency GW "chirps", but those would also be more energetic, wouldn't they?
Mass-less (spin 2) gravitons have the nominal quantum relationship: E = hν = hc/λ
- where h = 6.626×10−34 Joule⋅seconds/
Total gravitational radiation power corresponds to:
the total number of emitted gravitons per second times their minuscule quantum energies.
The Hulse–Taylor (pulsar plus neutron star) binary are in a pair of 27,900 second period elliptical orbits.
By transforming its kinetic energy into (mostly ~13,950 second [i.e., 27.9 AU] long) gravitational waves
the Hulse–Taylor binary emits
~ (7.35 × 1024 Joules/second)(13,950 seconds) / (6.626×10−34 Joule⋅seconds)
~ 1.55 × 1062 gravitons/second 
https://en.wikipedia.org/wiki/Hulse%E2%80%93Taylor_binary wrote:
<<In the Hulse–Taylor binary the pulsar and its neutron star companion both follow elliptical orbits around their common center of mass. The period of the orbital motion is 7.75 hours, and the two neutron stars are believed to be nearly equal in mass, about 1.4 solar masses. The orbit has decayed since the binary system was initially discovered, in precise agreement with the loss of energy due to gravitational waves described by Albert Einstein's general theory of relativity. The ratio of observed to predicted rate of orbital decay is calculated to be 0.997 ± 0.002.
The total power of the gravitational waves emitted by this system presently is calculated to be 7.35 × 1024 watts. For comparison, this is 1.9% of the power radiated in light by the Sun. The Solar System radiates only about 5,000 watts in gravitational waves, due to the much larger distances and orbit times, particularly between the Sun and Jupiter and the relatively small mass of the planets. With this comparatively large energy loss due to gravitational radiation, the rate of decrease of orbital period is 76.5 microseconds per year, the rate of decrease of semimajor axis is 3.5 meters per year, and the calculated lifetime to final inspiral is 300 million years.>>
Note that even passing interstellar objects (such as our own Oumuamua) lose a tiny amount
of kinetic energy due to gravitational Bremsstrahlung of very low frequency/energy gravitons. [quote=johnnydeep post_id=318905 time=1638979975 user_id=132061]
Late to this interesting discussion, but I was always perplexed by why, if gravitational waves are just "ripples in space-time", they should be limited to propagating at the speed of light. That is, no THING is physically moving through space, so the c speed limit should be irrelevant. I guess it's because a full description of relativity says that no INFORMATION can propagate faster than c, and GWs are conveying information. Then there's the still hypothetical (I think?) existence of gravitons, and if they are indeed found to be the PARTICLE mediators of the gravitational force, I suppose they WOULD be limited by c.
Also, GWs apparently have a wavelength and frequency in inverse proportion to each other. But this APOD also mentions their energy, which is represented by the brightness of the spectra. So, how does the energy relate to the wavelength and frequency? We say light of higher frequency (and shorter wavelength) has higher energy, don't we? Yet neufer's first post above says that larger mass BHs generate lower frequency GW "chirps", but those would also be more energetic, wouldn't they?[/quote]
Mass-less (spin 2) gravitons have the nominal quantum relationship: E = hν = hc/λ
[list]where h = 6.626×10[sup]−34[/sup] Joule⋅seconds/[/list]
Total gravitational radiation power corresponds to:
[size=125][b][u][color=#0000FF]the total number of emitted gravitons per second[/color][/u][/b][/size] times their minuscule quantum energies.
The Hulse–Taylor (pulsar plus neutron star) binary are in a pair of 27,900 second period elliptical orbits.
By transforming its kinetic energy into (mostly ~13,950 second [i.e., 27.9 AU] long) gravitational waves
the Hulse–Taylor binary emits [b][color=#0000FF]~ (7.35 × 10[sup]24[/sup] Joules/second)(13,950 seconds) / (6.626×10[sup]−34[/sup] Joule⋅seconds)
[c][size=150] ~ 1.55 × 10[sup]62[/sup] gravitons/second[/size] :!: [/c]
[/color][/b]
[quote=https://en.wikipedia.org/wiki/Hulse%E2%80%93Taylor_binary]
[float=left][img3=Orbital decay of PSR B1913+16. The data points indicate the observed change in the epoch of periastron with date while the parabola illustrates the theoretically expected change in epoch according to general relativity.]https://upload.wikimedia.org/wikipedia/commons/0/04/PSR_B1913%2B16_period_shift_graph.svg[/img3][/float]
<<In the Hulse–Taylor binary the pulsar and its neutron star companion both follow elliptical orbits around their common center of mass. The period of the orbital motion is 7.75 hours, and the two neutron stars are believed to be nearly equal in mass, about 1.4 solar masses. The orbit has decayed since the binary system was initially discovered, in precise agreement with the loss of energy due to gravitational waves described by Albert Einstein's general theory of relativity. The ratio of observed to predicted rate of orbital decay is calculated to be 0.997 ± 0.002. [b][u][color=#0000FF]The total power of the gravitational waves emitted by this system presently is calculated to be 7.35 × 10[sup]24[/sup] watts.[/color][/u][/b] For comparison, this is 1.9% of the power radiated in light by the Sun. The Solar System radiates only about 5,000 watts in gravitational waves, due to the much larger distances and orbit times, particularly between the Sun and Jupiter and the relatively small mass of the planets. With this comparatively large energy loss due to gravitational radiation, the rate of decrease of orbital period is 76.5 microseconds per year, the rate of decrease of semimajor axis is 3.5 meters per year, and the calculated lifetime to final inspiral is 300 million years.>>[/quote]
[c][b][color=#0000FF]Note that even passing interstellar objects (such as our own [url=https://en.wikipedia.org/wiki/%CA%BBOumuamua]Oumuamua[/url]) lose a tiny amount
of kinetic energy due to gravitational [url=https://en.wikipedia.org/wiki/Bremsstrahlung]Bremsstrahlung[/url] of very low frequency/energy gravitons.[/color][/b][/c]