The Forgotten Mystery of Inertia

[SkyHiker]

The Forgotten Mystery of Inertia

[Juno16]

Good read Henk!

Thanks!

[helicon]

Nice article and thanks for the share!

[Lady Fraktor]

Very interesting.

[SkyHiker]

Einstein may have provided the answer himself by discovering what was later named the Lense-Thirring effect - frame dragging inside a hollow shell. If the hollow shell represents the universe, a gyro will align with the rotation of the shell. Lense-Thirring uses the Einstein Field Equations. People are still on the fence as to whether LT proves Mach. It involves unproven equality of some constants but also more clarity about how Mach's principle (inspired by Mach but coined by Einstein) should be defined. This muddled the waters.

A Gravity Probe B was launched to detect the Lense Thirring effect by detecting gyro spin changes caused by Earth. Earth itself barely provides enough gravity to prove this. GPB found the LT effect within an error margin of 15%. Misner, Thorne and Wheeler claim in their book "Gravitation" that LT explains (their definition of) Mach, thereby explaining inertia. It is more fluffy talk than a solid proof though, IMHO.

Other approaches use a weak field approximation to the EFE described similarly to electromagnetism named Gravito-ElectroMagnetism. It simplifies the EFE tremendously and allows the use of known results in electromagnetism. Sciama's paper "On the origin of inertia" is an example of that. In that paper he derives inertia based on the mass of the entire visible universe. The gravitational constant then becomes a function of the mass in the visible universe. It is not fully valid because of the inherent GEM approximation, to be fixed in a follow-on paper that took a long time.

Sciama later reformulated his GEM-based approach using the EFE in "The physical structure of general relativity" that became one of the foundations of ECSK gravity. The focus of that paper shifted to unification theory using a Cartan instead of a Riemannian geometry. As a result of this focus shift the inertia explanation fizzled out, so we can't really say that he proved inertia.

A modern equivalent of Newton's rotating bucket are gyros based on the Sagnac effect like ring laser and fiber optics gyros that have no moving parts. According to Bondi in "The Lense Thirring effect and Mach's principle" these gyros can detect rotation relative to the stars in the universe. I find that pretty amazing. While we have all kinds of vehicles using this idea, we still don't have an explanation of inertia. Isn't it about time, like the paper says. Especially before jumping at conclusions like DM to explain inertia-related problems.

[SkyHiker]

Here are some links about gravito-electromagnetism mostly focused on gravito-magnetism that is seen as the origin of inertia:

An explanation of galactic rotation curves based on gravitomagnetism that does not require dark matter: Factoring_in_gravitomagnetism_could_do_away_with_dark_matter. This page contains a link to the paper in small print at the bottom.

Evidence provided by Gravity Probe B for the Lense-Thirring effect / frame dragging: Gravity Probe B status

Searching for "gravitomagnetic field of the universe" provides many links to support that the origin of inertia (and explains Mach) is in the gravitomagnetic effect of the entire universe. There are many authors and papers based on various approaches. They commonly use the weak field and gravitomagnetic PDE approximation even mixed in with special-relativistic reasoning. I won't provide a link because I don't know their value but these Wikipedia links to frame dragging and gravito-electromagnetism are useful. It would be nice if these results were confirmed in some big way.

[Gmetric]

Really interesting stuff, Henk. I don’t have much time as I’ve got to work but a while back I found some interesting articles on frame dragging and galaxy rotation curves. Just a quick search finds this https://arxiv.org/pdf/2109.00357.pdf
And also nFA posted a thread where the effects had been observed here viewtopic.php?p=57782&hilit=Frame+dragging#p57782

I gotta rush. Be back later.

[John Donne]

Very interesting Henk !
I enjoyed this link very much.
Thank you for posting.

[SkyHiker]

...a while back I found some interesting articles on frame dragging and galaxy to rotation curves. Just a quick search find this https://arxiv.org/pdf/2109.00357.pdf

That article by Toth claims the opposite of the one by Ludwig that I linked based on simple rules of thumb. You may want to look at the original article, if you get a chance let me know what you think.

Toth is a programmer by profession, while Ludwig is an astrophysicist or plasma physicist, judging from his affiliation and publications. He goes into great detail of modeling the problem accurately as a fluid in a disc not just a point mass in a spherical structure. The additional modeling complexity of course has the risk of making more mistakes.

I agree that Ludwig's enticing results are unexpected because the gravitomagnetic component is generally small. It only becomes important near dense masses like black holes and neutron stars, and also when the entire universe is taken into account (Mach). A galaxy is just a speck compared to the universe so how can the gravitomagnetic component explain this. While Toth's back-of-the-envelope estimates are crude, they make sense and show that the effect is off by orders of magnitude. A double-check of Ludwig's results is definitely called for so let's keep our eyes open for more news.

[Gmetric]

Hey Henk, thanks for the response.

I think Toth’s “back-of-the-envelope” calculations are a good approximation of the fact that GEM effects are indeed minor.

It has also been argued that Ludwig appears to have made some errors in his approach to characterising galactic disks, which are full of stars, as zero-pressure dust. Principally, because stars hardly ever collide. The argument is that "pressure" should instead count the number of stars passing through a given cross-sectional area per unit of time. So Ludwig’s paper may not be error-free in its approach.

A further and more robust analysis of this has been completed here https://arxiv.org/pdf/2207.09736.pdf and finds that when modelled for baryonic matter only, both GR and the GEM effects are equivalent to Newtonian. This paper closely agrees with Toth. And to quote from the paper “Therefore, the observed phenomenology of galactic rotation curves at large radii requires Dark Matter in GR exactly as in Newtonian gravity.”

“so let's keep our eyes open for more news.” Couldn’t agree more.

[SkyHiker]

I learned a bit more about GR than when I posted the link. In the end I don't think there is a mystery at all, here is why. We can simplify the gyro or Foucault pendulum to a satellite circling Earth that is rotating relative to the universe. Assuming everything perfectly circular and round etcetera this fits the Kerr metric, which is the 2nd solution to the Einstein field equations discovered 35 years after the much simpler derivation of the Schwarzschild metric. Applying these formulas on the Wikipedia page leads to about 196 arc seconds per year, for the case of the Gravity Probe B satellite example. This is at the North pole to be precise, but that value agrees with other results that were obtained using weak field equations. In other words, the rotation of the orbital plane is negligible relative to the background metric. This background metric is the asymptotic Kerr metric, which is identical to our everyday XYZ/time metric that is determined by the homogeneous and isotropic mass distribution of the universe, modeled by the FRLW metric that comes with it. Therefore, a satellite's orbital plane is fixed relative to the universe (ignoring aforementioned frame dragging effect), and so are those of a Foucault pendulum at the pole, or a gyroscope. Case closed, I think. I emailed the author about this line of thought but haven't heard back yet. The discussion about whether or not inertia depend on the mass distribution of the universe (Mach's principle) goes beyond this but this; that's a much harder question that still keeps the minds busy.