Proposal for measurement of Lens Thirring effect

[stevenstritt]

I don't possesses enough knowledge of GR to know if this proposal is feasible (or even remotely possible) I would welcome any constructive criticism of the following idea for detecting Lens Thirring effect:

Apparatus consists of a dense, massive sphere or disc, rotating at high velocity. Around the circumference is wound many kilometers of optical fiber. A CW laser beam is shot through the fiber and enters an interferometer along with reference beam. As the rotational velocity varies, a moving interference pattern should be detected.

Is this proposal remotely achievable?

 

[bcrowell]

A CW laser beam is shot through the fiber and enters an interferometer along with reference beam.

How is the reference beam different from the other beam? Won't they be equally affected?

 

[stevenstritt]

The reference beam and interferometer would be located at a distance from the massive rotating body.

 

[bcrowell]

I think the Lense-Thirring effect scales like m\omega/r. For a fixed density, this translates into r^2\omega. The factor of r² is about 10¹² times bigger for the Earth than for a laboratory mass.

 

[stevenstritt]

I think the Lense-Thirring effect scales like m\omega/r. For a fixed density, this translates into r^2\omega. The factor of r² is about 10¹² times bigger for the Earth than for a laboratory mass.

Wow- it would definitely be difficult to measure such a small effect in the lab, but just to throw some numbers out there, assume:
tungsten sphere of radius 1.0 m (approx mass 80,000kg rotating at 1000rpm)
100 km of fiber wound closely around the equator (approx 16000 windings)
laser wavelength 1340nm

Start the experiment with the sphere at rest. Turn on laser. Beamsplitter sends one beam through the fiber, other is reference beam. Other end of fiber terminates at interferometer. Adjust interferometer so beams are in phase.
Now turn on the rotating sphere. as it gets up to speed, would we observe a phase shift? BTW wouldn't any frame dragging be cumulative over time? However small the effect, you could conceivably run the experiment indefinitely!

 

[Jonathan Scott]

The effect of rotational frame-dragging is that an object with constant orientation near to a large moving or rotating object experiences internal effects as if it were rotating slightly, and if it instead rotates at the same rate in the opposite direction, it does not experience those effects.

These effects could be locally detected for example by a laser gyro. A constant rate of rotation produces a constant offset in the interference pattern, not a cumulative effect.

The effect is of the form

<br /> \omega_{drag} = k \frac{G m \omega_{mass}}{rc^2}<br />

where k is a constant of order 1 which depends on the configuration of the mass and where the drag is being measured (see MTW equation 21.155). I'm not totally sure what k is for a solid sphere just outside the equator, but from a quick glance at Ciufolini and Wheeler "Gravitation and Inertia" chapter 6 "The gravitomagnetic field" I think it's probably -2/5 (that is, the effect is in the opposite direction to the effect near the poles because it is dominated by the nearby moving surface).

One thing I'm not sure about is the effect of putting the ring gyro around the whole spinning object, as that would effectively require a rotation of the whole of that ring about its center, whereas the Lense-Thirring effect describes a local effect at each point around that ring. However, it might have a similar effect to putting it around the pole of the object, giving an overall rotational effect in the same sense as the object is rotating. This involves a straightforward calculation using the Kerr solution.

So there you have all the information you need to calculate at least an order-of-magnitude answer to whether the result would be detectable.