Why does the bend in space time not affect the gyroscope?

[San K]

The bend in space-time due to Earth's gravity was measured by a gyroscope.

A bend in space-time causes even light to bend, how does a gyroscope escape this?

The angular momentum being discussed in a gyroscope, is this the same as the one we call "spin" in the entangled photons/electrons?

 

[WannabeNewton]

I don't see what you mean. When you send a gyroscope around a loop such as around the Earth to measure space - time curvature the gyroscope will start and a point, travel the loop, and return to its original point but it will not come back at the same orientation. The difference in its return is proportional to the area of the loop as well as the Riemann Curvature Tensor (and maybe something else that I am forgetting) and this will tell you about the geometry of space - time around say the Earth. Also, I think this is more of a GR question than a QM question?

 

[Naty1]

A bend in space-time causes even light to bend, how does a gyroscope escape this?

Nothing "escapes gravity".

See "Geodetic precession and frame-dragging" here:
http://en.wikipedia.org/wiki/General_relativity#Orbital_effects_and_the_relativity_of_direction

See my closing paragraph below.

The angular momentum being discussed in a gyroscope, is this the same as the one we call "spin" in the entangled photons/electrons?

vaguly perhaps. Wikipedia describes it this way:

Spin is a type of angular momentum, where angular momentum is defined in the modern way (as the "generator of rotations", see Noether's theorem).[1][2] This modern definition of angular momentum is not the same as the historical classical mechanics definition, L = r × p. (The historical definition, which does not include spin, is more specifically called "orbital angular momentum".)

As the name suggests, spin was originally conceived as the rotation of a particle around some axis. This picture is correct in so far as spins obey the same mathematical laws as do quantized angular momenta. On the other hand, spins have some peculiar properties that distinguish them from orbital angular momenta:

Spin quantum numbers may take on half-integer values;
Although the direction of its spin can be changed, an elementary particle cannot be made to spin faster or slower.
The spin of a charged particle is associated with a magnetic dipole moment with a g-factor differing from 1. This could only occur classically if the particle's internal charge were distributed differently than its mass.

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


I'd be interested to hear from an expert on how angular momentum is encapsulated in Einstein's tensor based field equations for gravity. Since the field equations capture the energy momentum effects of matter curving spacetime, a simplistic view MIGHT suggest that the extra momentum [energy] of a spinning gyroscope MIGHT make it more subject to gravitational influences rather than less. But how that meshes with frame dragging I have no idea.

 

[bcrowell]

The bend in space-time due to Earth's gravity was measured by a gyroscope.

A bend in space-time causes even light to bend, how does a gyroscope escape this?

Could you clarify what you mean? First you say that spacetime curvature is detectable with gyroscopes (which is correct, it was done by Gravity Probe B). Then you ask how a gyroscope escapes being affected. It sounds like you're asserting X and then asking why X is false. X isn't false, it's true!

 

[San K]

I don't see what you mean. When you send a gyroscope around a loop such as around the Earth to measure space - time curvature the gyroscope will start and a point, travel the loop, and return to its original point but it will not come back at the same orientation. The difference in its return is proportional to the area of the loop as well as the Riemann Curvature Tensor (and maybe something else that I am forgetting) and this will tell you about the geometry of space - time around say the Earth. Also, I think this is more of a GR question than a QM question?

Thanks, you answered my question. Namely the gyroscope is in operation/spinning, all the time, ...while traveling the "loop/route".

 

[Cleonis]

The bend in space-time due to Earth's gravity was measured by a gyroscope.

A bend in space-time causes even light to bend, how does a gyroscope escape this?

Thanks, you answered my question. Namely the gyroscope is in operation/spinning, all the time, ...while traveling the "loop/route".

I have a hunch now what the intention of your original question was.

For comparison:
It is always asserted that even the most accurate length measuring device cannot measure an instance of relativistic length contraction because the measuring device will always be Lorentz contracted itself.

Perhaps your thinking was that detection of spacetime bending is possible only with a device that itself remains unaffected by spacetime bending.


Well, sure enough it's not possible to detect spacetime bending with just a spot measurement. You can't measure it locally. You need a big spatial loop.

For example, in geometrically straight space the ratio of circle radius and circle circumference is 2*pi
If we would be able to measure the Earth's radius and circumference sufficiently accurate we would find a deviation from euclidean result. The distortion of space by the Earth's gravitation makes the ratio deviate slightly from 2*pi.


Gravity Probe B in its orbit, that's also a case of closing a loop. According to GR the gravity probe B gyroscopes would accumulate relativistic effects loop after loop. It's that accumulation that made the Gravity Probe B experiment a viable project.

(Actually there were other non-relativistic things going on with the gyroscope rotors that, some not anticipated, that all had to be subtracted from the raw sensor readings in order to bring out the relativistic effects. The relativistic effects were almost drowned out.)

 

[San K]

I have a hunch now what the intention of your original question was.

For comparison:
It is always asserted that even the most accurate length measuring device cannot measure an instance of relativistic length contraction because the measuring device will always be Lorentz contracted itself.

Perhaps your thinking was that detection of spacetime bending is possible only with a device that itself remains unaffected by spacetime bending.


Well, sure enough it's not possible to detect spacetime bending with just a spot measurement. You can't measure it locally. You need a big spatial loop.

For example, in geometrically straight space the ratio of circle radius and circle circumference is 2*pi
If we would be able to measure the Earth's radius and circumference sufficiently accurate we would find a deviation from euclidean result. The distortion of space by the Earth's gravitation makes the ratio deviate slightly from 2*pi.


Gravity Probe B in its orbit, that's also a case of closing a loop. According to GR the gravity probe B gyroscopes would accumulate relativistic effects loop after loop. It's that accumulation that made the Gravity Probe B experiment a viable project.

(Actually there were other non-relativistic things going on with the gyroscope rotors that, some not anticipated, that all had to be subtracted from the raw sensor readings in order to bring out the relativistic effects. The relativistic effects were almost drowned out.)

You guessed it right Cleonis and I like your description.

can you provide some examples of the non-relativistic things that had to be subtracted out? ...just curious

 

[Cleonis]

can you provide some examples of the non-relativistic things that had to be subtracted out? ...just curious

I came across an article from 2008 detailing the problems encountered in analysing the data of the
http://spectrum.ieee.org/aerospace/space-flight/the-gravity-probe-b-bailout/0" mission

The Gravity probe B mission had two objectives:
- Corroboration of the geodetic effect
- Corroboration of frame dragging.

The second is far more demanding than the first, because it's a much smaller effect.

I gather from that article that in 2008 NASA pretty much pulled the plug for the data-mining efforts to show that frame dragging had occurred. The geodetic effect was far less of an achievement; it had already been confirmed with other means (but not as directly as in the Gravity probe B setup)
So to stop funding the data-mining short for the frame-dragging effect is a significant decision.

Only this year, 2011, has the data analysis team announced final results are ready.What was anticipated, and planned for, was a classical phenomenon called polhode motion. The polhode motion was expected to repeat very consistently. Anything that repeats very consistently can be subtracted in a relatively straightforward manner. However, the polhode motion decayed over the duration of the mission, making it much more challenging to model.

It has become a challenging data-mining effort. Other effects are far bigger, to subtract them they have to be modeled to a very high precision.
The criticism is that with such extensive data-mining there is opportunity for "massaging" the data.

In a corroboration effort it's tempting to discard preliminary results that are unfavorable, and go with decisions that yield the desired corroboration. There are always judgement calls. It becomes very difficult to see whether the judgement calls are biased. That casts doubt on the final resultsSources of specific information:

A PDF about http://einstein.stanford.edu/highlights/GyroPolhodeMotion.pdf"

A webpage, written by a member of the data analysis team, about http://einstein.stanford.edu/highlights/hl_polhode_story.html"