Device to measure curvature of spacetime.

[yuiop]

While posting a reply in another thread, I had an inspiration for a device to measure spacetime curvature. It is well know that we can measure this curvature by measuring the angles of a large triangle or comparing the circumference of a circle to its radius, but his device may may be simpler or more portable.

The device requires two rulers, one 10 meters long and the other 1 meter long. Reflectors are placed at the ends of each ruler and the other ends are aligned with each other and common signal emitter is placed there. The light path on the short ruler is arranged so that signal bounces to and fro ten times before returning to an interferometer. The light path on the longer ruler does one round trip before being routed to the interferometer. In flat space the signals should return at the same time and there will be no interference detected when tuned and calibrated correctly. Now if the device is placed in a gravitational field or in the pseudo gravitational field of a linearly or rotationally accelerating frame the device will detect curvature as an interference pattern (although it might be argued that it is detecting proper acceleration and is simply acting as a relativistic accelerometer with no moving parts).

A similar device might have the short ruler connected at right angles to the longer ruler. Rotating this device slowly to different orientations in curved space will produce changes in the interference pattern.

Yet another device will simply have identical signal sources placed a fixed distance from each other and detect the difference in redshift between the two sources as an indication of curvature (or acceleration?).

Any thoughts on the workings or the interpretations of the indications?

I am also curious if such devices would detect any curvature when in free fall in a gravitational field, assuming the device is sufficiently rigid to maintain reasonably constant proper length?

 

[waht]

Something like this was already done with Gravity-B probe:

http://www.nasa.gov/mission_pages/gpb/index.html

http://en.wikipedia.org/wiki/Gravity_Probe_B

 

[PAllen]

To measure actual curvature, rather than 'non inertial motion through spacetime', J.L. Synge has a proof in his book on GR that you need a minimum of 5 points. He then defines an idealized 5 point curvature detector. I don't know how easy it is to get this book, but I don't really want to type in the whole discussion. It is fun though - he even carries it out to producing ideal rods, trying to arrange them in a certain way, and the last one minutely fails to fit if there is actual curvature.

 

[1MileCrash]

http://www.ligo-la.caltech.edu/

Ever heard of LIGO? I visited the place a couple of years ago.

LIGO will detect the ripples in space-time by using a device called a laser interferometer, in which the time it takes light to travel between suspended mirrors is measured with high precision using controlled laser light. Two mirrors hang far apart, forming one "arm" of the interferometer, and two more mirrors make a second arm perpendicular to the first. Viewed from above, the two arms form an L shape. Laser light enters the arms through a beam splitter located at the corner of the L, dividing the light between the arms. The light is allowed to bounce between the mirrors repeatedly before it returns to the beam splitter. If the two arms have identical lengths, then interference between the light beams returning to the beam splitter will direct all of the light back toward the laser. But if there is any difference between the lengths of the two arms, some light will travel to where it can be recorded by a photodetector.

The space-time ripples cause the distance measured by a light beam to change as the gravitational wave passes by, and the amount of light falling on the photodetector to vary. The photodetector then produces a signal defining how the light falling on it changes over time. The laser interferometer is like a microphone that converts gravitational waves into electrical signals. Three interferometers of this kind were built for LlGO -- two near Richland, Washington, and the other near Baton Rouge. Louisiana. LlGO requires at least two widely separated detectors, operated in unison, to rule out false signals and confirm that a gravitational wave has passed through the earth.

You seem to be on the same track as they are. Theirs is just, well, bigger.

 

[bcrowell]

I don't think it works in the version where the two rulers lie along the same line, because you can't have curvature in 1+1 dimensions.

The 90-degree version does sound equivalent to LIGO, but LIGO is not a general-purpose curvature sensor, it's a gravitational wave sensor. LIGO can't sense the curvature due to the Earth's field, for example.

[EDIT] Is what you're proposing basically the Kennedy-Thorndike experiment?

 

[yuiop]

I don't think it works in the version where the two rulers lie along the same line, because you can't have curvature in 1+1 dimensions.

Hmmm.. you might be right. I was thinking of the case of comparing the ruler distance to the radar distance along a radial line on the surface of a rotating disc, where the measurements are noticeably different. The same is true on a radial line in a gravitational field and in a accelerating rocket traveling in a straight line in flat space. However, it might be that all the parallel device is measuring is extrinsic curvature due to acceleration that can be transformed away, rather than the intrinsic curvature of a gravitational field. Any thoughts on this, anyone?

The 90-degree version does sound equivalent to LIGO, but LIGO is not a general-purpose curvature sensor, it's a gravitational wave sensor. LIGO can't sense the curvature due to the Earth's field, for example.

I agree. Presumably LIGO would be calibrated to give a null reading the Earth's gravitational field and wait for a gravitational wave to disturb that null reading.

[EDIT] Is what you're proposing basically the Kennedy-Thorndike experiment?

The right angled version is certainly very similar to the K-T experiment, but I think in the K-T case they were looking for something other than curvature. Your comment prompted me to look up that experiment and I noticed some curious statements in the literature.

This Wiki link http://en.wikipedia.org/wiki/Kennedy–Thorndike_experiment mentions "By making one arm of the experiment much shorter than the other, a change in speed of the Earth would cause changes in the travel times of the light rays". Why would they expect the speed of the Earth to change? Do they mean the difference in speed relative to the CMB over periods of months or years as the Earth rotates around the Sun and the Sun rotates around the Galaxy?

In this link http://www.wordiq.com/definition/Kennedy-Thorndike_experiment they mention "By making one arm of the experiment much longer than the other, differences in rotational speed between one end and the other (relative to the Earth) would cause a fringe shift to occur." and " However the Kennedy-Thorndike experiment also ruled out any simple explanations here as well, as the two ends of the experiment had different rotational speeds, and thus should have different length contractions.". Why would there be different rotation speeds between one end of the experiment and the other?

Most references to the K-T experiment suggest that while the MM experiment can be explained by length contraction alone, the K-T experiment requires both length contraction and time dilation to explain it. However, this reference suggests that is a mistaken interpretation: http://www.springerlink.com/content/586l2l2w9321335v/ I am not very familiar with K-T experiment. Anyone care to elaborate?On a different subject. I think I have figured out that the names in bright pink are fully paid up members, but why pink? Sort of jars with the sober muted grey tones of the theme.

 

[bcrowell]

This Wiki link http://en.wikipedia.org/wiki/Kennedy–Thorndike_experiment mentions "By making one arm of the experiment much shorter than the other, a change in speed of the Earth would cause changes in the travel times of the light rays". Why would they expect the speed of the Earth to change? Do they mean the difference in speed relative to the CMB over periods of months or years as the Earth rotates around the Sun and the Sun rotates around the Galaxy?

They didn't know about the CMB then. The hypothesis they were probably testing against was that there was an aether, which would be at rest with respect to the sun.

On a different subject. I think I have figured out that the names in bright pink are fully paid up members, but why pink? Sort of jars with the sober muted grey tones of the theme.

I'm glad I'm not the only one wondering about this :-) Still using a kleenex to wipe the blood away from my eyeballs from that shocking pink.

 

[Buckethead]

On a different subject. I think I have figured out that the names in bright pink are fully paid up members, but why pink? Sort of jars with the sober muted grey tones of the theme.

It shows up as Gold on my monitor. Quite fitting I think.

 

[Buckethead]

The device requires two rulers, one 10 meters long and the other 1 meter long. Reflectors are placed at the ends of each ruler and the other ends are aligned with each other and common signal emitter is placed there. The light path on the short ruler is arranged so that signal bounces to and fro ten times before returning to an interferometer. The light path on the longer ruler does one round trip before being routed to the interferometer. In flat space the signals should return at the same time and there will be no interference detected when tuned and calibrated correctly. Now if the device is placed in a gravitational field or in the pseudo gravitational field of a linearly or rotationally accelerating frame the device will detect curvature as an interference pattern (although it might be argued that it is detecting proper acceleration and is simply acting as a relativistic accelerometer with no moving parts).

Could you explain why the time to travel one rule over the other would change in a linearly accelerating situation if the two rulers are placed in a single line as you describe? (I'm assuming you mean that the rulers are aligned to the direction of acceleration)

 

[yuiop]

Could you explain why the time to travel one rule over the other would change in a linearly accelerating situation if the two rulers are placed in a single line as you describe? (I'm assuming you mean that the rulers are aligned to the direction of acceleration)

Sorry BH, I missed this reply. Yes, I mean aligned to the acceleration. I will try and explain my reasoning, but there are some subtle aspects that I want to check before posting. Hopefully I will be be able to post a clear explanation with worked examples in a few days when I should have more time.

P.S. The shocking pink got changed shortly after Ben and I had our little dig at it

 

[grav-universe]

What you have described sounds like an extended Michelson-Morley experiment along a gravity gradient. http://www.youtube.com/watch?v=7T0d7o8X2-E"