Uncovering the Mystery of Centrifugal Forces: Hafele and Keating Experiment

[matheinste]

Hello all.

From Laurent – Introduction to Spacetime. Referring to the Hafele and Keating experiment.

---Let us neglect gravitation and picture the Earth as a merry-go-round all alone in empty space. The rim of the merry-go-round corresponds to the equator. Let us further assume that two space ships are flying along the rim in opposite directios with such a speed that they circle once relative to the merry-go-round while it rotates one turn. This has the effect that centrifugal forces are felt on board one of the ships but not on board the other one.-----

Why! Obviously some fundamental law or principle is involved.

Matheinste.

 

[Doc Al]

Imagine the motion of each ship as seen by an inertial observer watching the Earth rotate. The one going in the same direction as the spinning Earth clearly undergoes circular motion (and feels a centrifugal force), but the one going against the Earth's rotation is really just sitting there with respect to the inertial frame.

 

[matheinste]

Hello Doc Al.

As simple as that. Thanks.

Matheinste.

 

[Al68]

Hello all.

From Laurent – Introduction to Spacetime. Referring to the Hafele and Keating experiment.

---Let us neglect gravitation and picture the Earth as a merry-go-round all alone in empty space. The rim of the merry-go-round corresponds to the equator. Let us further assume that two space ships are flying along the rim in opposite directios with such a speed that they circle once relative to the merry-go-round while it rotates one turn. This has the effect that centrifugal forces are felt on board one of the ships but not on board the other one.-----

Why! Obviously some fundamental law or principle is involved.

Matheinste.

The principle of inertia. Einstein addressed a similar problem in this paper: http://hem.bredband.net/b153434/Works/Einstein.htm

As a local system, there is no cause to be found for the centrifugal forces. Einstein called this an "inherent epistemological defect" in classical physics, and in SR. And he points out that the cause must lie outside the system, ie distant masses as the cause of inertia.

I've asked questions about this on this board, but no one seemed interested in it.

Al

 

[Pippo]

Imagine the motion of each ship as seen by an inertial observer watching the Earth rotate. The one going in the same direction as the spinning Earth clearly undergoes circular motion (and feels a centrifugal force), but the one going against the Earth's rotation is really just sitting there with respect to the inertial frame.

I don't suppose he is sitting, he has the same absolute speed with respect the inertial frame as the other, and his speed with respect to the surface of the Earth could be the double as the other one.

 

[Doc Al]

I don't suppose he is sitting, he has the same absolute speed with respect the inertial frame as the other, and his speed with respect to the surface of the Earth could be the double as the other one.

The speeds are defined in the original quote. They each circle once with respect to the Earth in the time it takes the Earth to rotate once. So with respect to the inertial frame, one will have speed 2ωR, the other 0.

 

[Pippo]

The speeds are defined in the original quote. They each circle once with respect to the Earth in the time it takes the Earth to rotate once. So with respect to the inertial frame, one will have speed 2ωR, the other 0.

Perhaps I am still missing something, but what happen if the Earth stops rotating ?

 

[Doc Al]

Perhaps I am still missing something, but what happen if the Earth stops rotating ?

If the ships maintain their speed with respect to the Earth's surface and the Earth stops rotating, then the ships will have the same speed ωR but in opposite directions. Of course this in an entirely different situation than that described by Laurent.

 

[Naty1]

How does neglecting gravity affect the selection of an inertial frame here?

 

[LURCH]

With gravity, either ship would be in an inertial frame (assuming they are at the right altitude for geosynchronous robit; around 22,365 mi). Without it, of course, neither is.