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emc2cracker
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I have recently come up with an idea about trying to build an apparatus to run some gravitational wave experiments. Now I am still a novice so I wrote Professor Scott Hughes about my idea, he provided me with the mathematical equations that basically show the experiment is impossible. I will share with everyone what I have to work with because I want to figure out a work around or maybe I can build this to study methods of transfering momentum or energy. Here is what I am studying courtesy of professor Hughes:
Mr. Vogeler:
To get any interesting GW power, the spheres would have to move at a
significant fraction of the speed of light.
To set an upper limit, I'll take the spheres to be 2 meters in
diameter (a bit larger than your 5 feet). I'll take them to be
filled with mercury (denser than gallium; I'm not suggesting you
actually do this, just doing the calculation to prove the
principle). Mercury has a density of a bit less than 14 grams per
cubic centimeter, so the spheres would each have a mass of about
M = (4/3) pi (14 grams/cm^3)(100 cm)^3 = 59,000,000 gm
(At each step I've rounded up slightly, so my calculation will be an
overestimate.) If I have two "stars" of mass M orbiting one another
with their centers separated by a distance R and orbiting with a
period T, then the power generated by gravitational waves is given by
P = (8/5) (G/c^5) M^2 R^4 (2 pi/T)^6
(As you'll see in a minute, the factor of G/c^5 --- where G is the
gravitational constant, and c is the speed of light --- really kills
us. This is why all GW experiments are based on astrophysical
sources, where we can get masses that are stellar or larger.)
For your experiment, M = 5.9 x 10^7 grams. The center to center
separation R is 200 cm (well, 5 feet --- but I'm rounding up a bit to
get an overestimate). The period is
1/(2000 rpm) = 0.005 minutes = 0.03 seconds
The numerical factor G/c^5 is 2.76 x 10^(-60) sec^3/(gm cm^2). Let's
put all of this together:
P = [8/5][2.76 x 10^(-60) sec^3/(gm cm^2)][5.9 x 10^7 gm]^2 [200 cm]^4
[2 pi/(0.03 sec)]^6
= [2.76 x 10^(-60)][7.52 x 10^(38)] gm cm^2/sec^3
= 2.08 x 10^(-21) erg/sec
Converting to Watts (1 Watt = 10^7 erg/sec), your proposed apparatus
would generate a gravitational wave power of about 2 x 10^(-28)
Watts. If we imagine that you can make the rotational frequency go
arbitrarily high, it would be useful to see how this results scales
with that frequency:
P = 2.08 x 10^(-28) Watts (f/2000 rpm)^6.
Doing a little bit of algebra, we see that if want this to get up to
1 Watt, we need to dial the frequency up to about 82,000,000
revolutions per minute. At this speed, the spheres would be moving
at a speed of about 1,400,000 meters per second --- about 0.5% of the
speed of light. (Of course, at this speed, the material out of which
the spheres are made would not be able to hold together. This is why
astrophysical gravitational wave sources are objects like neutron
stars and black holes --- their enormous self gravity is what allows
them to hold together while they whirl about one another at speeds
which are an appreciable fraction of the speed of light.)
I'm afraid there's no way to overcome the fundamental limits set by
that factor of G/c^5 --- you just need enormous masses and enormous
speeds. Anything you can make on Earth will not do the trick.
Please note I'm going to be away from my email for the holidays and
am unlikely to answer any followup questions on a short timescale.
Scott Hughes
Now I am not satisfied lol. It seems to me we should be able to come up with a way to pull something off.
First are there any better alternatives than using mercury, materials that would hold together. What about super-fluids it seems to me a super-fluid might be able to be rotated magnetically thus reducing stress on the machine.. maybe it would hold together at these extreme forces. I wish I paid attention during chemistry!
Secondly what would be the minimum detectable output power as opposed to hitting 1 watt, I have no idea what kind of equipment would be used to detect this and what its sensitivity could be tuned to.
Now even if there is absolutely no way around lowering the speed enough and still making it work. What about using the apparatus to study methods of inducing a gravitational wave without the wave itself. It would seem to me the amount of energy needed to set the wave off would be large and easily detectable.. possibly at far lower velocities. So do you believe I could at least use my apparatus to study methods of transferring potential energy into magnetic energy?
Mr. Vogeler:
To get any interesting GW power, the spheres would have to move at a
significant fraction of the speed of light.
To set an upper limit, I'll take the spheres to be 2 meters in
diameter (a bit larger than your 5 feet). I'll take them to be
filled with mercury (denser than gallium; I'm not suggesting you
actually do this, just doing the calculation to prove the
principle). Mercury has a density of a bit less than 14 grams per
cubic centimeter, so the spheres would each have a mass of about
M = (4/3) pi (14 grams/cm^3)(100 cm)^3 = 59,000,000 gm
(At each step I've rounded up slightly, so my calculation will be an
overestimate.) If I have two "stars" of mass M orbiting one another
with their centers separated by a distance R and orbiting with a
period T, then the power generated by gravitational waves is given by
P = (8/5) (G/c^5) M^2 R^4 (2 pi/T)^6
(As you'll see in a minute, the factor of G/c^5 --- where G is the
gravitational constant, and c is the speed of light --- really kills
us. This is why all GW experiments are based on astrophysical
sources, where we can get masses that are stellar or larger.)
For your experiment, M = 5.9 x 10^7 grams. The center to center
separation R is 200 cm (well, 5 feet --- but I'm rounding up a bit to
get an overestimate). The period is
1/(2000 rpm) = 0.005 minutes = 0.03 seconds
The numerical factor G/c^5 is 2.76 x 10^(-60) sec^3/(gm cm^2). Let's
put all of this together:
P = [8/5][2.76 x 10^(-60) sec^3/(gm cm^2)][5.9 x 10^7 gm]^2 [200 cm]^4
[2 pi/(0.03 sec)]^6
= [2.76 x 10^(-60)][7.52 x 10^(38)] gm cm^2/sec^3
= 2.08 x 10^(-21) erg/sec
Converting to Watts (1 Watt = 10^7 erg/sec), your proposed apparatus
would generate a gravitational wave power of about 2 x 10^(-28)
Watts. If we imagine that you can make the rotational frequency go
arbitrarily high, it would be useful to see how this results scales
with that frequency:
P = 2.08 x 10^(-28) Watts (f/2000 rpm)^6.
Doing a little bit of algebra, we see that if want this to get up to
1 Watt, we need to dial the frequency up to about 82,000,000
revolutions per minute. At this speed, the spheres would be moving
at a speed of about 1,400,000 meters per second --- about 0.5% of the
speed of light. (Of course, at this speed, the material out of which
the spheres are made would not be able to hold together. This is why
astrophysical gravitational wave sources are objects like neutron
stars and black holes --- their enormous self gravity is what allows
them to hold together while they whirl about one another at speeds
which are an appreciable fraction of the speed of light.)
I'm afraid there's no way to overcome the fundamental limits set by
that factor of G/c^5 --- you just need enormous masses and enormous
speeds. Anything you can make on Earth will not do the trick.
Please note I'm going to be away from my email for the holidays and
am unlikely to answer any followup questions on a short timescale.
Scott Hughes
Now I am not satisfied lol. It seems to me we should be able to come up with a way to pull something off.
First are there any better alternatives than using mercury, materials that would hold together. What about super-fluids it seems to me a super-fluid might be able to be rotated magnetically thus reducing stress on the machine.. maybe it would hold together at these extreme forces. I wish I paid attention during chemistry!
Secondly what would be the minimum detectable output power as opposed to hitting 1 watt, I have no idea what kind of equipment would be used to detect this and what its sensitivity could be tuned to.
Now even if there is absolutely no way around lowering the speed enough and still making it work. What about using the apparatus to study methods of inducing a gravitational wave without the wave itself. It would seem to me the amount of energy needed to set the wave off would be large and easily detectable.. possibly at far lower velocities. So do you believe I could at least use my apparatus to study methods of transferring potential energy into magnetic energy?