I Hafele-Keating Exp: Balancing SR Effects in Plane Ref Frame

[PeroK]

So the transformation would make the "gravity" component higher?

The transformation would transform the spacetime metric AND the worldlines of all the clocks. I don't think it's helpful to think of the gravity component when looking at general coordinate transformations. I said early that the mathematics of GR was complex and flexible. Complexity is the price you pay for flexibility. You can choose any coordinates you like (flexible), but you have a compelxity in terms of how to explain what's happening.

In addition, you are potentially going down the wrong road altogether here by insisting on a physical understanding of the changes, when in fact nothing physical is changing. It's the same experiment with the same result whatever frame of reference you use to analyse it.

Especially when it comes to GR this is the wrong way to think about things.

 

[name123]

Thanks to everyone that answered, I think I roughly get it now, even though I'm ignorant of the complexities. Thanks all for your patience.

 

[vanhees71]

With General Relativity, there is no such thing as what is "really" happening. All three descriptions are on equal footing. We "just" (as if this is an easy thing) have to express the "metric" so that the laws of physics work correctly in the chosen coordinate system.

If the laws of physics work, the frame is as real as it needs to be.

I'd rather say, in GR what's "really happening" is described by coordinate independent, i.e., generally invariant, quantities.

 

[PeterDonis]

I was thinking of time dilation "caused" by something accelerating vs something not undergoing proper acceleration.

You are misleading yourself by focusing on acceleration. See below.

the clock on Earth would be accelerating at the same speed as a plane at constant altitude in the experiment, and so there would be no relative time dilation.

Yes, there would, because the plane is at a higher altitude than the clock on Earth, and the different in altitudes means a difference in potential, which does cause time dilation. As I posted multiple times earlier in the thread, that time dilation is the "GR time dilation" that appears in the analysis of the Hafele-Keating experiment.

 

[PeterDonis]

the explanation for the hurricanes requires the Earth to be spinning in a certain direction.

Not in any absolute sense. The "spinning in a certain direction" is relative to a local "non-spinning" frame in which the center of the Earth is at rest, where "non-spinning" is defined by Fermi-Walker transport of the spatial basis vectors along the worldline of the center of the Earth (think of a set of imaginary gyroscopes located at the center of the Earth and defining three mutually perpendicular directions in space). If you choose a different frame, the "spinning" of the Earth will be different, but so will a lot of other coordinate-dependent things that all change in concert to keep all of the physical invariants, like the presence of a hurricane, the same.