• #### Re: Equivalence principle

From Hendrik van Hees@21:1/5 to Mikko on Mon Jun 10 12:10:37 2024
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.

If you sit on the surface of a planet, you are not in free fall, because
there are (electromagnetic) forces keeping you there.

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.,

On 10/06/2024 13:46, Mikko wrote:
On 2024-06-08 17:40:15 +0000, Luigi Fortunati said:

In the video https://www.youtube.com/watch?v=R3LjJeeae68 at minute 6:56
it states that there is no measurement that can be made to distinguish
whether you’re being accelerated or whether you are sitting still on the >> surface of a planet.

So, I ask: what stops us from measuring the presence (or absence) of
tidal forces? If tidal forces are there, then we are stationary on the
surface of a planet, if they are not there, we are experiencing a
non-gravitational acceleration.

Consider a situation where you are not sitting on a surface of a planet
but acclerated by a real non-gravitational interaction; and this happens
near a planet or a star: you can measure a tidal force (if your instruments are big and sensitive enough).

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

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• From Mikko@21:1/5 to Luigi Fortunati on Mon Jun 10 11:46:37 2024
On 2024-06-08 17:40:15 +0000, Luigi Fortunati said:

In the video https://www.youtube.com/watch?v=R3LjJeeae68 at minute 6:56
it states that there is no measurement that can be made to distinguish whether you’re being accelerated or whether you are sitting still on the surface of a planet.

So, I ask: what stops us from measuring the presence (or absence) of
tidal forces? If tidal forces are there, then we are stationary on the surface of a planet, if they are not there, we are experiencing a non-gravitational acceleration.

Consider a situation where you are not sitting on a surface of a planet
but acclerated by a real non-gravitational interaction; and this happens
near a planet or a star: you can measure a tidal force (if your instruments
are big and sensitive enough).

--
Mikko

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• From Hendrik van Hees@21:1/5 to Luigi Fortunati on Tue Jun 11 08:46:14 2024
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.

If you sit on the surface of a planet, you are not in free fall, because there are (electromagnetic) forces keeping you there.

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/

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• From Hendrik van Hees@21:1/5 to Luigi Fortunati on Thu Jun 13 10:38:48 2024
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/

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