Re: Equivalence principle

On 11/06/2024 09:05, Luigi Fortunati wrote:

Hendrik van Hees il 10/06/2024 14:10:37 ha scritto:

Or to put it simpler. In a local inertial reference frame, realized by a point-like non-rotating body in free fall, you observe (e.g., by using pointlike test particles) only the "true gravitational forces", i.e., the tidal forces.
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If you sit on the surface of a planet, you are not in free fall, because there are (electromagnetic) forces keeping you there.
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That's why the accelerometer of your smart phone at rest on Earth shows an acceleration of 9.81 m/s^2, because it measures accelerations relative to a local inertial frame of reference! See, e.g.,

 
Your reasoning is based on two preconceptions.

These are preconceptions well tested with high precision for centuries.
Physics is an empirical science, and theories are built based on precise
quantitative observations of nature.

 
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.
According to GR there are NO GLOBAL inertial frames as there are in
Newtonian mechanics and special-relativistic physics. Pointlike test
particles move on geodesics of spacetime, determined by the
energy-momentum-stress distributions due to the presence of other
bodies, if there are no other forces than gravity, i.e., they are not
accelerated. Geodesics here refer of course to spacetime not to
trajectories in "position space" of some arbitrary observer. E.g., the
motion of the planets around the Sun are such geodesics in spacetime for
an observer resting far away from the Sun (whose spacetime is locally
approximately described by special-relativistic, flat Minkowski
spacetime) the spatial trajectories are of course very close to Kepler
ellipses.

 
Luigi Fortunati

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