[alancalverd (OP)]

Here's a thought experiment.

Imagine two small test masses suspended on a torsion wire, inside an evacuated tube - the classic "G meter". Now instead of two large masses, have a wheel carrying several large "driving" masses around the circumference,  separated by a distance equal to the diameter of a driving mass.

If you spin the wheel around the G meter,the torsion wire will twist under the gravitational drag force.  Spin the wheel faster and it will deflect further...until the time taken for gravity to transfer from the wheel to the test mass equals the transit time of one driving mass, at which point the torsion wire won't twist any further.

Enough theoretical physics. Would any experimental physicists and engineers out there care to put some numbers to the project?
   

[jeffreyH]

Interesting idea. For more than one reason. How would you dampen vibrations?

[evan_au]

The test masses have an oscillation period of several seconds: the torsion wire has small restoring force, and the test masses are relatively large. So you always have to measure the midpoint of the oscillations.

If the speed of gravity=c (as current theories suppose), won't the driver masses have to be traveling near the speed of light to cancel out?

I assume that the "gravitational drag force" is not referring to "gravitational frame dragging", which is a relativistic effect found near rapidly spinning black holes?

[alancalverd (OP)]

Correct - it's the force that makes tides.

If the wheel rotates continuously, the long period of the torsion balance will simply integrate the gravitational pulses into a continuous tidal force.

[jeffreyH]

The gravitational constant can be approximated using 1/(50c). This factor of 50 must be important in determining the speed of gravity otherwise it would not relate to the gravitational constant so well. How could this be used in such an experiment?

[alancalverd (OP)]

Hmm. My waist measurement in inches can be very closely approximated as 4n/7 where n is my age in years, but I wouldn't suggest it as a means of measuring either! However if we can determine v_G with sufficient accuracy, the constant may well turn out to have interesting properties.

[evan_au]

the long period of the torsion balance will simply integrate the gravitational pulses into a continuous tidal force

When the nearest driver mass is a bit ahead of the test mass, it will provide a torque in (say) the clockwise direction.
When the nearest driver mass is a bit behind the test mass, it will provide a torque in the anticlockwise direction.
As I understand the description, the long period of the torsion balance average out these two effects, resulting in zero overall torque?

I don't see how a torsion balance with no torsion can measure the speed of gravity?

[alancalverd (OP)]

That's why we rotate the driver masses to drag the torsion  balance forwards. At some speed, it will "strobe" and there will be no increase in torque with further increases in rotational speed.

[jeffreyH]

When I say approximate, if we rearrange to 1/(Gc) the answer is 49.99. I'd say that is interesting.

[alancalverd (OP)]

G = 6.67384 × 10^-11 m³ kg^-1 s^-2

c = 2.99792458 x 10⁸ m s^-1

∴ Gc = 2.01 X 10^-2m⁴ kg^-1 s^-3

This is far from the dimensionless number you quote, and if you use the fps system you get an entirely different figure before the decimal point.

[jeffreyH]

G = 6.67384 × 10^-11 m³ kg^-1 s^-2

c = 2.99792458 x 10⁸ m s^-1

∴ Gc = 2.01 X 10^-2m⁴ kg^-1 s^-3

This is far from the dimensionless number you quote, and if you use the fps system you get an entirely different figure before the decimal point.

You haven't taken the reciprocal of Gc. Yes the units are screwed.

[alancalverd (OP)]

You can calculate the reciprocal if you like, but it still won't be dimensionless, so the number has no associated magic.

[jeffreyH]

You can calculate the reciprocal if you like, but it still won't be dimensionless, so the number has no associated magic.

I don't believe that the Gravitational constant is a circular function of the Planck values only. A direct relationship with the speed of light would answer a lot of questions. I haven't found it yet but that isn't going to stop me from trying.

[jeffreyH]

This circularity can be shown by the equation G = 2*pi*lP^2*c^3/h where h balances the units necessary. However the Planck length lP itself relies upon G. This is not a very good situation to be in if we require a quantum theory of gravity.

[alancalverd (OP)]

Radiation dose is measured in joules per kilogram, which has the same dimensions (L²T^-2)as c² but it has absolutely nothing to do with the velocity of anything, nor with the latent heat of fusion which has the same dimensions.

So I wouldn't consider dimensional analysis to be a necessary starting point for determining the speed of gravity, which will be in meters per second, whatever the number turns out to be.

[jeffreyH]

Radiation dose is measured in joules per kilogram, which has the same dimensions (L²T^-2)as c² but it has absolutely nothing to do with the velocity of anything, nor with the latent heat of fusion which has the same dimensions.

So I wouldn't consider dimensional analysis to be a necessary starting point for determining the speed of gravity, which will be in meters per second, whatever the number turns out to be.

I take that point on board. It may turn out though that, like the variations in the experimental measurements of G, any experimental measurement of the speed of gravity may itself be inaccurate. This would be a likely effect of density variations in the earth over time. These would not need to be significant changes to skew results.

[alancalverd (OP)]

The idea that the speed of propagation of gravity could be anything other than the speed of light is intriguing, especially if it turned out to be dependent on the local gravitational field, which is why a laboratory measurement, however inaccurate, would be fascinating at least, and mindboggling if it turned out to be variable.

[jeffreyH]

The idea that the speed of propagation of gravity could be anything other than the speed of light is intriguing, especially if it turned out to be dependent on the local gravitational field, which is why a laboratory measurement, however inaccurate, would be fascinating at least, and mindboggling if it turned out to be variable.

It is worthwhile pursuing. Have you considered other experimental options?