Proposal for measurement of Lens Thirring effect

In summary, the proposed apparatus would consist of a massive rotating body, surrounded by a dense fiber-optic cable, in order to detect a small effect due to the Lense-Thirring Effect. The effect is small, but it would be difficult to measure in the lab.
  • #1
stevenstritt
13
0
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?
 
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  • #2
stevenstritt said:
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?
 
  • #3
The reference beam and interferometer would be located at a distance from the massive rotating body.
 
  • #4
I think the Lense-Thirring effect scales like [itex]m\omega/r[/itex]. For a fixed density, this translates into [itex]r^2\omega[/itex]. The factor of r2 is about 1012 times bigger for the Earth than for a laboratory mass.
 
  • #5
bcrowell said:
I think the Lense-Thirring effect scales like [itex]m\omega/r[/itex]. For a fixed density, this translates into [itex]r^2\omega[/itex]. 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!
 
  • #6
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

[tex]
\omega_{drag} = k \frac{G m \omega_{mass}}{rc^2}
[/tex]

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.
 

1. What is the Lens-Thirring effect?

The Lens-Thirring effect, also known as frame-dragging, is a phenomenon in general relativity where rotating masses can "drag" the fabric of spacetime along with them. This effect was first predicted by Austrian physicists Josef Lense and Hans Thirring in 1918.

2. How does the Lens-Thirring effect impact our daily lives?

The Lens-Thirring effect is a very small effect that is typically only observed in extreme conditions, such as near massive rotating objects like black holes. Therefore, it does not have a significant impact on our daily lives.

3. What is the proposed method for measuring the Lens-Thirring effect?

The proposed method involves using a satellite in a polar orbit around the Earth and measuring the precession of its orbit due to the Earth's rotation. By measuring the precession rate, the Lens-Thirring effect can be calculated.

4. Has the Lens-Thirring effect been observed before?

Yes, the Lens-Thirring effect has been observed before using a satellite called Gravity Probe B. This satellite measured the precession of gyroscopes in orbit around the Earth and confirmed the existence of the effect.

5. What are the potential implications of measuring the Lens-Thirring effect?

Measuring the Lens-Thirring effect can provide a better understanding of the nature of gravity and how it affects the fabric of spacetime. It could also potentially lead to new developments in space navigation and satellite technology.

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