Do our inertial frames rotate with the Milky Way?

[Vincentius]

In a 1925 paper, Erwin Schrödinger mentions that "our inertial systems are free of rotation precisely with respect to our stellar system", instead of being "anchored...in much more distant stellar masses". Is this really the case?

If so, this suggests that the total gravitational potential here is mainly due to the Milky Way, and much less due to all other galaxies. Can anyone provide a reference on this subject?

thanks

 

[Drakkith]

What does the gravitational potential have in common with rotation free inertial frames?

 

[ibysaiyan]

What does the gravitational potential have in common with rotation free inertial frames?

Hm.. aren't they different things altogether. I mean if one were to be in a gravitational potential then their frame of reference is being accelerated while a reference frame which doesn't rotate is simply inertial but both are subject to time dilation.

Am I right ?

 

[D H]

Hm.. aren't they different things altogether. I mean if one were to be in a gravitational potential then their frame of reference is being accelerated while a reference frame which doesn't rotate is simply inertial but both are subject to time dilation.

Am I right ?

Huh?Let's start with a frame of reference that is obviously rotating: A frame rotating with the Earth. From the perspective of this frame, Neptune's apparent velocity is over the speed of light; that of the nearest star is several thousand times the speed of light. There's nothing wrong with those apparent superluminal velocities. Relativity doesn't disallow them. How could it? It is exactly what we apparently see.

One can do physics from the perspective of a rotating frame of reference. You just have to deal with the fictitious forces that arise. The key reason for using a non-rotating frame of reference is that these fictitious forces vanish.

As far as the stars being used to define our best guess at a non-rotating frame, astronomers don't do that any more. Astronomers switched from using stars to using extra-galactic sources as the basis for defining astronomical reference frames starting in the early 1990s. This switch has been completed. Quasars are now used as the defining objects for the best guess as to what constitutes a non-rotating frame of reference.

 

[Vincentius]

What does the gravitational potential have in common with rotation free inertial frames?

Well, if the potential here is dominated by the Milky Way, then everything around here is frame-dragged with the rotation of the Milky Way. The common view is that the more distant stellar systems make the biggest contribution to the potential here (they outnumber the less distant stellar systems via r², while the potential falls off by 1/r)

Is there support of Schrödinger's statement on the Milky Way?

 

[D H]

It's an 87 year old paper, for crying out loud. Looking back is a very good idea from the perspective of history and philosophy of science. Looking back that far is a bad idea from the perspective of understanding science.

This is particularly true for what was at that time a brand new science. At the time the article was published, the formalization of the concept of a frame of reference was only 40 years old, and the development of General relativity was less than a decade old. Schrödinger had no idea of the size of the Milky Way, let alone the universe (no one did in 1925).

One thing that has not yet been accomplished in those ensuing 87 years is to make relativity compatible with Mach's principle. There are aspects of GR that definitely do not follow Mach's principle. Rotating frames is one of them.BTW, the title of the paper is The possibility of fulfillment of the relativity requirement in classical mechanics. I haven't been able to find where it was published, but I did find a partial google books extract here: http://books.google.com/books?hl=en&lr=&id=fKgQ9YpAcwMC&oi=fnd&pg=PA147#v=onepage&q&f=false.

 

[Joe Quellen]

Bear in mind that the Newtonian gravitational potential falls off as 1/r, whereas the mass of a thin shell of matter at a distance r goes up as r^2. So in this model the most distant mass distribution has the greatest contribution to the total Newtonian potential.

When Schrödinger published the paper he was not aware of the full size and age of the observable universe. He thought the galaxy would have a much greater effect. Some of this is covered in the discussion about the paper when it was reprinted in the book Mach's Principle: From Newton's Bucket to Quantum Gravity.

By the way, it is possible to calculate frame dragging from the galaxy using General Relativity. It's a classic example of the Lense-Thirring effect.