Re: The Elevator in Free Fall

On 12/22/24 2:57 AM, Luigi Fortunati wrote:

Can we define the interior space of the elevator as "local" or is it
too big?

This depends on: a) the curvature of spacetime where the elevator is
located, b) the size of the elevator (including duration), and c) one's
measurement accuracy. For an ordinary-sized elevator near earth falling
for ten seconds, and a measurement accuracy of microns and microseconds
(or larger), its interior can be considered a LOCALLY inertial frame.

If it is shown that there are real forces inside the free-falling
elevator, can we still consider this reference system inertial?

Depends on the details (and the meanings of words). For internal forces
that are small enough to not significantly distort the steel elevator,
it can be considered LOCALLY inertial, as long as it meets the criteria
above.

Are tidal forces real?

This depends on the meanings of words, and is therefore ambiguous and
uninteresting to me.

Do we mean by "freely falling bodies" only those that fall in the very
weak gravitational field of the Earth or also those that fall in any
other gravitational field, such as that of Jupiter or a black hole?

"freely falling" means not subject to any external forces. This is
independent of the size of nearby bodies. Note that an object with size
comparable to curvature cannot be considered freely-falling. (Here
gravity is not a force.)

The size of a locally-inertial frame depends on the criteria of my first
paragraph above. The inside of the elevator above but near Jupiter can
be considered a locally-inertial frame. For a one-solar-mass black hole
just outside its horizon, such an elevator is too big. For a
billion-solar-mass black hole just outside its horizon, it can be
considered a LOCALLY inertial frame. (More massive black holes have
smaller spacetime curvatures at their horizon.)

Tom Roberts