# What is the reference frame the earth rotates relative to?

1. Dec 5, 2011

### klaatu2

Please excuse my ignorance - I am a biologist by training - but this is one of those questions that just keeps bothering me and I can't find the answer with Google/Wikipedia.

Take as our example the ocean currents on the earth caused by the Coriolis Effect of the earth turning. When I read up on this accounts quickly jump into the maths of mapping between two reference frames. We talk about sitting in a rotating box and being able to tell it is rotating using a Foucault Pendulum etc.

But how does the earth know that it is rotating relative to the universe and not the universe rotating relative to it? If the universe were spinning around the earth our ocean currents would stop.

Two clear questions:

If spin is always relative to two frames of reference how do the frames of reference decide which one is stationery and which one is spinning?

If spin is not always relative is there some absolute frame of reference against which all mechanical spin is ultimately measured?

Many thanks for your thoughts on this.

2. Dec 5, 2011

### D H

Staff Emeritus
This is a deep question, one to which physicists don't quite have the answer to yet.

To Newton, the answer to this question was clearly "yes". Newton thought motion was absolute. Newton used a spinning bucket of water as an argument for absolute space. One can tell whether or not a frame is rotating with respect to inertial by looking at the surface of a bucket of water. The surface won't be flat if the water in the bucket is spinning.

This troubled various physicists over the years. Mach's principle, named after Ernest Mach, says that the local behavior is somehow dictated by the mass of the universe as a whole. Einstein tried to incorporate Mach's principle into general relativity. However, general relativity is not fully Machian. A bit of a concept of absolute space remains in general relativity.

Imagine a universe that comprised but one liquid planet. Mach's principle would say that there is no way to tell if the planet is rotating. General relativity says that an equatorial bulge would form if the planet is rotating. Whether such a universe could exist, and whether general relativity would describe such a universe: Who knows? There is no way to know.

Getting back to our universe, general relativity, like Newtonian mechanics, has some concept of absolute space. Acceleration and rotation are locally absolute in general relativity. Reference frames are only local in general relativity. Compare to Newtonian mechanics, where the concept of absolute space is global. Reference frames in Newtonian mechanics have infinite extent.

3. Dec 5, 2011

Thanks DH.

4. Dec 5, 2011

### klaatu2

Moderator note: This is in response to a now-deleted post.
I am leaving this post intact because that deleted post caused confusion that needs to be cleared up.

I am not sure I follow you.

I think you are saying we live in a euclidian universe and so there is a single frame of reference that spin is measured against. i.e. the ocean currents are caused by the earth spinning relative to the invisible 3D, euclidian graph paper we live in.

Is that right?

Last edited by a moderator: Dec 5, 2011
5. Dec 5, 2011

### Bill_K

No it isn't.

What DH said is that in general relativity there is an absolute local definition of rotation. It has nothing to do with the universe being Euclidean (which it isn't). And you don't have to look at the stars at all, you can sit in a closed room and define a nonrotating frame very simply using just local experiments.

Here's what to do: send light pulses out along three perpendicular directions, your x, y and z axes. Put mirrors in the way so the light pulses reflect off the mirrors and come back at you. The directions that you see them come back are the same as the original x, y and z directions. You have just built a photon gyroscope, and as long as the light beams keep reflecting back at you, (x, y, z) constitute a local nonrotating reference frame.