### Re: Is it possible to generate and receive an gravitational field variation ?

Date: Wed Feb 20 18:11:25 2002
Posted By: Benjamin Monreal, Grad student, Physics, MIT
Area of science: Astronomy
ID: 1012754004.As
Message:

Hello Daniel,

All of the effects and processes you describe are - from a strictly physical standpoint - possible. A gold nucleus does generate a gravitational field. A moving gold nucleus does generate a changing field, which can exert a gravitational force on objects very far away. So, you ask, "could such a system be used as a transponder?"

Unfortunately, I think that you have designed the weakest transponder imaginable. :) Some numbers to illustrate: The gravitational acceleration caused by any mass M, a distance R away, is 6x10^-11 * M/R^2 meters per second per second. 6x10^-11 ... that's 0.006 billionths of a m/s/s, caused by a 1 kg mass 1 meter away. (Note that I'm using the American "billion", which is 10^9, or 1000000000) If you want to use a single gold nucleus, that's 3x10^-25 kilograms ... causing 0.3 billionths of a billionth of a millionth of a m/s/s of acceleration. That is an unimaginably small acceleration. So if you put two gold atoms 1 meter apart and wanted them to fall together gravitationally, it would take on the order of 10^18 years, or a billion times longer than the lifetime of the Universe.

It's amazing how weak gravity is. It's really one of the big mysteries of modern physics - why did nature choose to make this one force so ridiculously feeble? With some examples (from the "fun factoids" school of science education) you can perhaps get a sense of how feeble it is:

• First, heck, notice that humans can stand up at the surface of the Earth. Despite the fact that there are 10^48 atoms pulling you downwards (via gravity) and only about 10^18 pushing you upwards (via, say, the electromagnetic forces between your feet and the floor), we're still able to stand, run, jump ....
• The LIGO project, a pair of huge gravitational-wave detectors under construction in Louisiana and Washington, has a projected cost of about US\$500,000,000. It is designed to detect accelerations of something like 10^-13 m/s/s ... a few thousand billion billion times stronger than the signal you are proposing. Read about it at ligo.caltech.edu.
• In the early 20th century, Albert Einstein realized that his theory of gravitation allowed the production of gravitational waves. One of his famous Gedanken experiments ("Thought experiments") was to imagine the biggest gravitational-wave source possible: hardly a single gold nucleus, he imagined a massive steel rod (30 m long and let's say 10 m thick) spinning as fast as possible without tearing apart (about 30 revolutions per second if I recall correctly). You could call this a "gravitational antenna" and ask how much power it outputs - the answer is around 10^-27 watts. That's a billionth of a billionth of a billionth of a watt. So the entire gravitational wave output of this huge contraption is sufficient, say, to heat up one atom by a millionth of a degree per second. Remember, that's the power that has to be detected by your "receiver".
• I should point out, also, that simply moving something back and forth does not necessarily generate gravitational radiation. This is due to the Conservation of Momentum, or (equivalently) to Newton's 3rd law, "every action has an equal and opposite reaction". Imagine astronaut Dan Bursch on his current spacewalk outside of the ISS. Let's say Dan weighs 70 kg. He wants to send a gravitational signal, so he picks up his wrench (1 kg) and waves it back and forth. However, due to Newton's law, every time he moves the wrench to the right, he himself moves to the left. He moves the wrench 70 cm to the left, he himself moves 1 cm right. Thus, to an observer far away, the mass of the astronaut+wrench system never moves. If Dan and his wrench are exerting a gravitational force on someone far away, that force will not change when he moves the wrench from his right hand to his left hand, since it's still 71 kilograms of mass centered at the same place.

The shape of the 71 kilograms can change - at one moment it might consist of 71 kilos all in one place, at another moment it might be 70 kilos (Dan) on one side and 1 kilo (the wrench) a meter to the side. This results in something called "quadrupole radiation" which is characteristically feeble compared to "dipole radiation" (which is what most E&M antennas send out).

Of course the same thing applies to the Earth (6x10^24 kg) and your single nucleus (3x10^-25 kg) moving back and forth.

• And that's just to illustrate the extreme difficulty of detecting any gravitational waves. Once you detect them, though, you have to figure out where they are coming from. How do you propose to distinguish the "nucleus transducer" gravitational acceleration, from the acceleration and motion of every other mass in the Universe? If you somehow did build a detector that could sense the motion of a single nucleus, it would be swamped by the gravity of, say, a falling speck of dust. A vibrating violin string ten miles away. A compact car exiting a parking lot in Timbuktu. Two neutron stars orbiting each other in the Andromeda Galaxy. In principle you can tune to a specific frequency, but given one "signalling" nucleus amongst 10^50 "background" nuclei, you do not have much of a chance. It's true that a gravitational-wave signal cannot be blocked, but it can easily be obscured by any other moving material in the area. You say you "just filter out the random noise", but that is easier said than done if the noise is 10^50 times stronger than the signal.
Perhaps your mistake was looking at density rather than mass. The gravitational force between two objects, when they are reasonably far apart, depends only on the mass, not on the density. Nuclei may be dense, but on human scales, they're still extremely light, and thus are very poor sources of gravitational waves.

Good question, hope this answer has been interesting. Gravitational physics is a neat topic, and a great challenge to both experimenters and theorists. If you want to learn more, the LIGO webpage linked above makes good reading, as does Brian Greene's book "The Elegant Universe".

-Ben Monreal

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