*Post by Luigi Fortunati*Phillip Helbigundress to reply mercoled=EC 11/01/2023 alle ore 09:32:14

*Post by Phillip Helbig (undress to reply)**Post by Luigi Fortunati*Why bother the distant universe if rotation (like any other

acceleration) are "absolute"?

Matter is made up of atoms with a nucleus inside.

If we rotate the matter (ie the atoms) the nuclei that "float" inside

them "push" outwards and generate centrifugal force opposed by the

centripetal force of the molecular bonds.

The presence of these two opposing internal forces of matter is

confirmed by the internal tension of the rotating bodies.

Yes. No-one debates the fact that accelerations are absolute. The

question is WHY that is the case. Imagine an empty universe with one

object in it, say a merry-go-round. Should it be possible to tell if it

is rotating, as it would be under normal conditions? If so, with

respect to what is it rotating? There is nothing else in the Universe.

There is a contradiction in what you write.

First you say that accelerations are absolute and then you ask "with

respect to what is it rotating?".

It is an empirical fact that they are absolute. But the very word

"rotation" implies that it is rotating with respect to something. But

what?

*Post by Luigi Fortunati*If they are absolute, they cannot depend on the reference!

Another way of looking at it is that they provide an absolute reference,

absolute space, a Newtonian idea which some think Einstein did away

with.

A more modern interpretation of the Newtonian space-time framework is

that there is not an absolute space and time but that there exists a

class of inertial frames, in each of which Newton's 1st Law holds true.

Further the assumption is that any inertial observer describes space as

a 3D affine Euclidean manifold, and time is just an independent

parameter parametrizing a causal order.

Then special relativity has been discovered out of the necessity to also

make electromagnetism consistent with the special principle of

relativity and the observation that there's no preferred inertial frame

(something like an "ether rest frame"). The result is that instead of

the Galilei-Newtonian fiber-bundle structure one get's a 4D affine

Lorentzian manifold as the spacetime model with the Poincare group as

symmetry group. Since Newton's first postulate still holds there's still

the class of global inertial frames.

General relativity then can be understood as the idea that Poincare

symmetry is made a local symmetry, i.e., there exists only local

inertial frames, and rotations or other proper accelerations are always

relative to the local inertial frame.

*Post by Luigi Fortunati*I say that the "real" rotations (those where centripetal and

centrifugal forces are manifested) are absolute and the "apparent"

rotations (those where neither centripetal nor centrifugal forces are

manifested) are relative.

I am sitting on a chair. If I can feel it pushing on me, then I am

really being accelerated, as opposed to someone thinking I am because of

some strange coordinates. (Ignoring for the moment that I also feel it

pushing on me at rest in a gravitational field.)

*Post by Luigi Fortunati*In an empty universe there could be only real rotations, those where

the question "with respect to what is it rotating?" it has no reason to

exist, being absolute and not relative.

Right. But do such real rotations imply some sort of absolute space?

It's a hard question. Einstein spent years thinking about it.

*Post by Luigi Fortunati**Post by Phillip Helbig (undress to reply)*Some would claim that there would be no way to tell in such a case, i.e.

no inertia.

I did not get this.

That is a claim some people make. If one thinks that what determines a

real acceleration is acceleration relative to some average of mass in

the Universe, then it makes sense for inertia to be proportional to such

mass.

I don't think that GR in any way has something to do with this "Machian

ideas", because it's a theory, which is strictly local, i.e.,

interactions are described by a local field theory, and thus

accelerations of (test) bodies relative to a local inertial frame are

due to interactions of the body with a field (e.g., the electromagnetic

field, acting on an electrically charged test particle). The

gravitational interaction is usually reinterpreted as "geometrized",

i.e., a free test particle moves on geodesics in curved spacetime, and

relative to a local inertial frame there's no force, and only "tidal

forces" on extended bodies are the "true gravitational forces".

*Post by Luigi Fortunati*Do you think that in a completely empty universe there would be no

centripetal and centrifugal forces?

I don't know.

--

Hendrik van Hees

Goethe University (Institute for Theoretical Physics)

D-60438 Frankfurt am Main

http://itp.uni-frankfurt.de/~hees/