# Frame Dragging Effect vs Spin Orbit Coupling in GR

• I
• cosmik debris
In summary, the frame-dragging effect is verified by Gravity Probe B as a result of something other than spin-orbit coupling.
cosmik debris
I believe that GR cannot describe exchange of classical intrinsic angular momentum and orbital angular momentum. The exchange of orbital and intrinsic angular momentum requires that the momentum tensor be non-symmetric during the exchange. GR cannot accommodate a non-symmetric momentum tensor because the Ricci tensor is symmetric in Riemannian geometry.

My question, assuming what I said above is true, is the frame-dragging effect verified by Gravity Probe B a result of something other than spin-orbit coupling, because on the surface it looks similar.

Thanks.

cosmik debris said:
I believe that GR cannot describe exchange of classical intrinsic angular momentum and orbital angular momentum.

What do you mean by "classical intrinsic angular momentum"?

cosmik debris said:
The exchange of orbital and intrinsic angular momentum requires that the momentum tensor be non-symmetric during the exchange.

What "momentum tensor" are you talking about?

cosmik debris said:
GR cannot accommodate a non-symmetric momentum tensor because the Ricci tensor is symmetric in Riemannian geometry.
That is not at all what this implies. This means that the theory does not introduce any asymmetry. It is perfectly feasible for the source to introduce asymmetry.

PeterDonis said:
What "momentum tensor" are you talking about?

I think he's talking about the stress-energy tensor. There is a line in Wikipedia saying this:

"In some alternative theories like Einstein–Cartan theory, the stress–energy tensor may not be perfectly symmetric because of a nonzero spin tensor, which geometrically corresponds to a nonzero torsion tensor."

https://en.wikipedia.org/wiki/Stress–energy_tensor

I never understood the details, either why spin can make the stress-energy tensor asymmetric, or why regular GR would have to be modified to account for it.

stevendaryl said:
I see that this has been discussed previously

Post #5 in that thread confirms what I thought, that there is no "gravitational spin-orbit coupling" in GR.

cosmik debris said:
is the frame-dragging effect verified by Gravity Probe B a result of something other than spin-orbit coupling

Yes, since, as above, there is no spin-orbit coupling in GR.

cosmik debris said:
I believe that GR cannot describe exchange of classical intrinsic angular momentum and orbital angular momentum.

If "classical intrinsic angular momentum" just means the spin of some body like the Earth whose internal structure we are not modeling, then this statement would be very surprising, since Newtonian gravity, which is a valid approximation to GR under appropriate conditions, can describe this just fine (for example, the slowing down of the Earth's rotation and the increase in the Moon's orbital radius due to tidal interactions).

stevendaryl said:
I think he's talking about the stress-energy tensor. There is a line in Wikipedia saying this:

"In some alternative theories like Einstein–Cartan theory, the stress–energy tensor may not be perfectly symmetric because of a nonzero spin tensor, which geometrically corresponds to a nonzero torsion tensor."

https://en.wikipedia.org/wiki/Stress–energy_tensor

I never understood the details, either why spin can make the stress-energy tensor asymmetric, or why regular GR would have to be modified to account for it.

Yes, I was thinking about this in relation to Einstein-Cartan theory. I see I will have to do a lot more reading but thanks for all the replies anyway.

Cheers

PeterDonis said:
If "classical intrinsic angular momentum" just means the spin of some body like the Earth whose internal structure we are not modeling, then this statement would be very surprising, since Newtonian gravity, which is a valid approximation to GR under appropriate conditions, can describe this just fine (for example, the slowing down of the Earth's rotation and the increase in the Moon's orbital radius due to tidal interactions).

Yes, that was my confusion, I see that the Earth-Moon system behaves in he way you have described and was trying to understand what this had to do with the non spin-orbit coupling in GR. I see that I was totally off track and need to do a lot more reading. Thanks for your input anyway.

Cheers

## What is the frame dragging effect in general relativity?

The frame dragging effect, also known as the Lense-Thirring effect, is a phenomenon predicted by Einstein's theory of general relativity. It states that the rotation of a massive object, such as a planet or a star, creates a "dragging" of the surrounding spacetime, causing other objects to move along with it.

## How is the frame dragging effect different from spin orbit coupling?

Spin orbit coupling is a quantum mechanical effect that describes the interaction between the spin of a particle and its orbital motion around a central object. This is different from the frame dragging effect, which is a classical effect in general relativity that describes the dragging of spacetime by a rotating massive object.

## Which objects exhibit the frame dragging effect?

The frame dragging effect has been observed in objects such as planets, stars, and even black holes. Any object with a non-zero angular momentum can exhibit this effect, but it becomes more pronounced as the mass and rotation of the object increases.

## How is the frame dragging effect measured?

The frame dragging effect can be measured using various techniques, such as the Gravity Probe B satellite, which used gyroscopes to measure the tiny changes in their orientation caused by the frame dragging effect of Earth. Other methods include observing the orbits of objects around massive rotating objects, such as binary star systems.

## What are the implications of the frame dragging effect in astrophysics?

The frame dragging effect has important implications in astrophysics, as it affects the motion of objects in the vicinity of rotating massive objects. It also plays a role in the formation and evolution of galaxies, as well as the dynamics of accretion disks around black holes. Understanding this effect is crucial for accurately predicting the behavior of objects in our universe.

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