• 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.,

    https://physlab.org/wp-content/uploads/2016/03/primer_smartphones.pdf

    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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