How to create frame of reference?

Question

Is this possible to create a inertial frame of reference in the earth?

How it is possible?

Answer 1

I might have misunderstood your question. If you mean, is there an absolute "motionless"? The answer is No, because all motion is relative.

Inertial reference frames are reference frames that are not accelerating - two inertial reference frames move at a constant velocity with respect to each other. Whilst there is no absolute motion, there is absolute acceleration.

Is it possible to create an inertial reference frame on earth? Yes, an inertial frame is one which is freely falling in a gravitation field, e.g. a falling elevator.

This might seem counter intuitive - surely something falling to the earth is accelerating? - but in General Relatively gravity is geometry, and a freely falling object is moving along its path (geodesic) without forces or acceleration. Contrariwise, if you are standing on the earth, you feel the upwards force of the earth on your feet.

Answer 2

First of all, I think that you should formalise what a reference frame is. Some people say that it is the same thing as the coordinate system, but stated this way, it is something physically senceless. Somewhere I heard the following definition of a reference frame:

A reference frame is an observer with a device that can measure the relative position of other objects with respect to the observer, and the observer and the device are considered to be very small.

In a sence, this is the same as some coordinate system with some specific definition of the time coordinate. The device can be just the eyes of the observer, or some kind of idealized radar.

For a flate space, the observer knows how light propagates, and can build some coordinate system and determine the coordinates of the objects. He can give a sense to the Newton's definition of an interial frame (in our sence, inertial observer) by considering gravity as an external force.

For a curved spacetime, with general metric, the observer does not a priori know the way light propagates, and what he knows is the data returned by his radar. Even if it is possible and the observer is smart enough to restore the general picture -- to build some coordinate system in which he will know all the coordinates of all objects and metric components, I doubt that there is a sensible meaning for the word inertial.

However, we can consider a local situation, that is, the observer cares only about a small area around himself, on the scale where the spacetime can be considered to be nearly flat. Then everything is as we are used to see it, but only locally. Now let us try to define inertiality. Newton says that in such a reference frame, a body should move with constant velocity unless it is subject to an external force. But is gravity an external force? I'd rather say no, because we know that locally it is indistinguishable from an inertial force. So I would say that we should call inertial the frame in which a body to rest should remain in rest, unless it is acted upon by a force of non-gravitational nature. This is a freely falling observer.

Actually, I said all this in order to explain why I want to answer: "just let yourself fall freely in vacuum, being isolated from external non-gravitational forces". That put aside, I think that it is a question of precision, up to some point, and then it becomes a question of definition of the word "inertial".

Answer 3

I can't understand why you ask, whether we can create something which is totally mathematical and not some physical "thing". A reference frame is totally for our convenience to measure the parameters like position, time or orientation of some object relative to a co-ordinate system we've preferred.

So, No - It's not possible in any known way.

I suggest you to go deeply into Wiki (about 3 levels) on articles on Inertial reference frame, Reference frame, co-ordinate system and also geometry if you want...

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But, we can still consider Earth as an inertial reference frame. Even you can be a reference frame and a physicist can tell how I move in space (-time) relative to you..!