# What is an inertial frame of reference related to?

Why does one particular 'frame of reference' have fictitious forces (like inertia) whilst another one doesn't.

I understand the basics, but more interested in 'why' space seems to have magically chosen specific frame to be the 'non inertial frame'.

Could space be more absolute than we think it is?

Has any research been done in this problem, which is at odds with a truly relativistic space (although I'm not saying relativity is wrong)

Thank you.

## Answers and Replies

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WannabeNewton
Nature doesn't "magically" choose the inertial and non-inertial frames or the inertial and non-inertial trajectories; such things are determined entirely by the space-time geometry i.e. by gravity.

stevendaryl
Staff Emeritus
Spacetime has properties--its geometry. The geometry of spacetime gives no preference to specific locations or times or directions or reference frames. But it does determine certain things:

(1) The invariant interval between two close-by events.
(2) Which spatial lines are "straight".
(3) Which spacetime paths are inertial.

In the usual treatment of Special Relativity and General Relativity, all of these features are derived from a geometric field called the metric tensor. The metric tensor doesn't determine a preferred state of rest, and it doesn't determine a preferred direction in space, but it does determine which paths are inertial and which lines are "straight".

In the geometric view of spacetime, a path being inertial is exactly analogous to a line being straight.

Dale
Mentor
I understand the basics, but more interested in 'why' space seems to have magically chosen specific frame to be the 'non inertial frame'.
There is nothing magical about it. The reference frame is a matter of choice. If you choose a curved reference frame then you get non-zero Christoffel symbols.

As an analogy, if you have a blank piece of paper, no coordinates, you still have straight lines and curved lines. If you then base your coordinates off the curved lines you would have "coordinate acceleration" of straight lines.

Do you think it is magical that both straight and curved lines exist? Do you think it is magical that they can be distinguished from each other?