# I Non-arbitrary frame of reference for acceleration?

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1. Nov 25, 2015

The reason we can choose a frame of reference arbitrarily is that a physical system is not dependent on an absolute position, orientation or time.
According to Noether's Theorem, the invariance of a system under a change of position is equivalent to the momentum conservation law.
In the same way, invariance under a change in orientation is the angular momentum conservation law, and time invariance is the law of
conservation of energy.
In Newtonian Mechanics, momentum conservation is expressed as the action-reaction law; If for every force (change of momentum) there's an equal and opposite
reaction force, momentum is conserved.
For fictitious forces however, like the force that acts when the frame of reference itself is accelerating, there's no corresponding
reaction force; Hence there seems to be no conservation law in that case.
Does this not point in the direction of a non-arbitrary frame of reference for acceleration?
I've looked around on google, but I've always heard that this is an unsolved mystery in physics.

Any ideas?

2. Nov 25, 2015

### Staff: Mentor

This is not an unsolved mystery. There is not a single non arbitrary frame, but rather a whole class of them. They are called inertial frames. They are discussed frequently.

3. Nov 25, 2015

You always end up with some kind of 'master' frame of reference that must contain all other frames of reference otherwise you can't express the acceleration
of a reference frame. And within a non-master reference frame, the acceleration of it acts as a fictitious force.
And if you include all of the fictitious forces, including the ones for rotation and accelerated rotation, your laws of physics always look the same
in all reference frames. I believe you can then call your laws generally invariant, even though that term is usually reserved for GR.
But it always requires a Master Frame!
I'm curious whether or not this Master Frame is also required in SR and GR; My gut tells me yes, but ...

4. Nov 25, 2015

### Staff: Mentor

No, you don't. You end up with a set of 'master' frames called inertial frames. You can express the acceleration of a non inertial frame with respect to any of them completely equivalently.

Furthermore, inertial frames do not "contain" non inertial frames. They are simply physically distinguishable from non inertial frames. I.E. the distinction is not arbitrary.