# Inertial and non inertial frames

stevendaryl
Staff Emeritus
Yeah, sure, I wonder why Einstein even thought of the necessity to use a curved spacetime to describe all physics.
Are you kidding, now?

I said that in FLAT spacetime, you can describe physics using inertial Cartesian coordinates. I didn't say that all spacetimes were flat.

stevendaryl
Staff Emeritus
In other words the reason we can describe "accelerated motion" locally in flat spacetime with inertial coordinates is the Equivalence principle, this is what is implied when in the wikipedia page it is claimed that the implicit knowledge about GR is used.

Oh my gosh! No, that's not true at all. The equivalence principle allows us to use SR locally to describe motion in a gravitational field. In the absence of gravity, you don't need the equivalence principle to describe accelerated motion.

There are too many confusions in what you're saying to address all of them, but you are misunderstanding the point of the equivalence principle and why it was important to Einstein in the development of General Relativity. If you understand Special Relativity, then you don't need the equivalence principle in order to describe physics in a curvilinear or accelerated coordinate system. You just need calculus: take the description in terms of inertial Cartesian coordinates, and perform a coordinate transformation to get a description in terms of noninertial coordinates.

What you will find if you do that is that when described using noninertial coordinates, there are location-dependent effects, such as: a clock at the rear of an accelerating rocket runs slower than a clock at the front of an accelerating rocket. You don't need the equivalence principle to deduce this effect: it follows from pure Special Relativity, plus calculus. (You do need something called the "clock hypothesis", which is that the rate of a clock doesn't depend on its acceleration but only on its instantaneous velocity: http://en.wikipedia.org/wiki/Clock_hypothesis)

What the equivalence principle allows you to do is to solve problems involving clocks in a gravitational field by transforming to an equivalent problem involving accelerating clocks, which can be solved using SR. The importance is that you reduce a new problem (the behavior of clocks in a gravitational field) to a solved problem (the behavior of accelerating clocks in SR).

D H
Staff Emeritus