Re: Equivalence principle

The misconception is on your side, not Einstein's ;-).

An inertial frame of reference is operationally defined by Newton's Lex
II: A body moves uniformly (or stays at rest) if it does not interact
with anything.

The mathematical version of the equivalence principle in GR is that
spacetime is described by a torsion-free pseudo-Riemannian (Lorentzian)
manifold. An inertial frame can only be local, i.e., you can choose at
any given spacetime point a Galilean local reference frame. Physically
such a frame is realized by a point-like body in free fall, i.e., by a
body on which only gravitational forces are acting and (non-rotating,
i.e., Fermi-Walker transported) tetrads along its world line.

True gravitational fields always show up in terms of tidal forces, and
any extended test body is thus not force-free. To which extent you can
neglect these forces depends on the extension of this test body. It's
only "force-free" as long as its extensions is smaller than the
curvature radius of space time at the reference point of your
free-falling non-rotating reference frame.

On 13/06/2024 10:29, Luigi Fortunati wrote:

Hendrik van Hees il 11/06/2024 10:46:14 ha scritto:

The first is that the accelerometer measures accelerations (and instead
it only measures forces) and the second is that free fall is an inertial
reference system despite its very evident mutual acceleration towards
the other body (also) in free fall.

I don't know, what's evident in your misconception. By definition bodies
which move without any interactions except the gravitational interaction
are by definition in free fall, and according to the equivalence
principle such bodies define a LOCAL (!!!!) inertial reference frame.

 
The inertial reference frame is one where no forces act.
 
In free fall, tidal forces act and, therefore, you and Einstein are
wrong when you say that free fall is an inertial reference (whether
local or non-local).
 
Luigi Fortunati

--
Hendrik van Hees
Goethe University (Institute for Theoretical Physics)
D-60438 Frankfurt am Main
http://itp.uni-frankfurt.de/~hees/