From: starmaker@ix.netcom.com
On Wed, 4 Feb 2026 20:24:22 +0100, Thomas 'PointedEars' Lahn
wrote:
>Paul B. Andersen wrote:
>> Den 04.02.2026 01:06, skrev Thomas 'PointedEars' Lahn:
>>> Paul B. Andersen wrote:
>>>> Den 03.02.2026 16:14, skrev Thomas 'PointedEars' Lahn:
>>>>> Paul B. Andersen wrote:
>>>>>> Den 03.02.2026 10:07, skrev Maciej Wo?niak:
>>>>>>> Anyway, for any context motion is absolute.
>>>>>> Speed is relative, acceleration is absolute.
>>>>> Wrong.
>>>>
>>>> Acceleration is absolute in Newtonian mechanics.
>>>
>>> That is not so. If two reference frames are non-inertial (in the Newtonian
>>> sense), then it is possible that one is not accelerating relative to the
other.
>>
>> It was Maciej Wo?niak who used the word "absolute".
>>
>> In this context, "absolute" means "not relative".
>
>Of course. We do not have a difference of definition.
>
>> Speed is relative because the speed of an object depend
>> on in which _inertial_ frame of reference it is measured.
>> > In Newtonian mechanics the acceleration dv(t)/dt of an object
>> will be the same independent of in which _inertial_ frame of
>> reference the speed v(t) is measured.
>
>One does not have to {use|be in} an inertial frame of reference for one's
>measurements.
>
>> Acceleration is not relative, it is absolute.
>
>Nonsense does not make sense by repetition.
>
>>> That is precisely the case (approximately), when a falling observer is
>>> observing a nearby falling object and we assume approximatively that the
>>> gravitational field is uniform. Then that object would be observed by thta
>>> observer to be at rest even though it would be accelerating for an inertial
>>> observer.
>>
>> You are in free-fall. An apple is right above your head,
>> and will stay there.
>
>That is why it is NOT accelerated in *that* frame of reference, which is
>exactly my point.
>
>> (If you are falling towards the Earth, the distance between your
>> head and the apple will increase very slowly. We ignore it.)
>>
>> You will know that since you are in free-fall your and the apple's
>> proper acceleration is exactly zero. (no air resistance)
>
>According to the Einstein equivalence principle it is not possible to
>distinguish, without external reference, free fall in a uniform
>gravitational field from a state of rest not under the influence of
>gravitation, or motion in an accelerated reference frame not under
>the influence of gravitation from motion in a frame at rest under
>the influence of uniform gravitation.
>
>So it is not correct to say "acceleration is absolute".
1. The equivalence holds only locally, and "uniform gravitational
field" is an idealization that doesn't exist in reality
The principle never claims perfect, global indistinguishability only
approximate equivalence in a sufficiently small region of space and
time (small enough that tidal effects become negligible compared to
measurement precision).
In any real gravitational field (Earth, Sun, black hole, etc.),
spacetime has curvature ? the Riemann tensor is nonzero ? tidal forces
exist. Two objects in free fall a meter apart will experience slightly
different gravitational accelerations ? they drift toward or away from
each other. No amount of coordinate transformation in a rocket with
constant proper acceleration can reproduce those relative tidal
accelerations.
An accelerometer measures proper acceleration (the thing you actually
feel), which is zero in free fall but nonzero when standing on the
ground or in a constantly accelerating rocket. But a sufficiently
sensitive array of test masses, or even a very precise gravimeter,
gyroscope array, or laser interferometer spread over
meters-to-kilometers, will immediately reveal whether curvature (tidal
gravity) is present. The equivalence breaks as soon as you allow
experiments larger than "infinitesimal".
So the phrase "uniform gravitational field" is a theoretical fiction
useful for motivating the principle, but not something nature ever
provides. Once you drop the uniformity assumption, the clean
equivalence disappears.
2. "Acceleration is not absolute" is only true in a very restricted,
coordinate-dependent sense proper acceleration is absolute
In special relativity (and in flat spacetime regions), proper
acceleration (what an accelerometer reads, the magnitude of the
4-acceleration vector) is Lorentz invariant all inertial observers
agree on its value for a given worldline. You cannot transform it
away.
In general relativity, the same proper acceleration remains an
invariant scalar along a worldline. Standing on Earth, your proper
acceleration is ~9.8 m/sē upward (provided by the normal force from
the ground). In free fall, it is zero. In a rocket accelerating at 1 g
in empty space, it is also ~9.8 m/sē. These are absolute,
coordinate-independent facts.
What the equivalence principle actually eliminates is the absolute
nature of being at rest in a gravitational field versus accelerating
in flat space. But it does not make all notions of acceleration
relative in the same way velocity is. The feeling of weight, the
reading on an accelerometer, the proper acceleration these remain
absolute markers distinguishing non-inertial motion from inertial
(geodesic) motion.
Einstein himself wrote in 1916 that the assumption of exact
equivalence makes it impossible to speak of the absolute acceleration
of the system of reference but later formulations (and modern GR
textbooks) emphasize that this applies to coordinate acceleration or
global concepts of "at rest", not to proper acceleration.
3. The principle is local ? global descriptions differ dramatically
You can locally mimic gravity with acceleration only in small enough
patches. Globally:
A rocket with constant proper acceleration follows a hyperbola in
Minkowski space its worldlines never form closed causal structures.
Real gravitational fields (Schwarzschild, Kerr, FLRW, etc.) allow
closed timelike curves in some cases, event horizons, singularities,
frame-dragging, gravitational waves, cosmological expansion none of
which can be reproduced by any globally accelerating coordinate system
in flat spacetime.
Trying to cover the entire exterior of a black hole (or the whole
universe) with accelerated frames fails badly. The global causal
structure reveals the difference immediately.
4. Quantum mechanics and the equivalence principle create tension
(modern objection)
In quantum field theory on curved spacetime, or in attempts at quantum
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