My name is Cleon Teunissen, I'm from the Netherlands.

I have contributed to the Wikipedia article on the Principle of Equivalence and to the article on The Structure of Scientific Revolutions. I have written the current articles on Centrifugal force and Fictitious force

Physics, reference frame issues

Inertial reference frames

Historically, the first to use the concept of inertial frame of reference was Galileo Galilei. Galilei argued that all frames of reference that move with respect to each other along a straight line and with constant velocity are fundamentally indistinguishable. Galilei presented the thought experiment of travelling by boat, the boat is moving at a constant speed in a straight line on water without wave action, and he argued that if you are in a cabin without windows, you have no way of establishing your speed. There is no phenomenon in dynamics that will indicate one frame of reference as "the one frame that isn't moving".

In newtonian dynamics, Galilean relativity is one of the basic assumptions. In newtonian dynamics space is assumed to be Euclidian, and in Euclidian space transforming between inertial frames of reference is straightforward and trivial: just addition of the vectors of the velocities.

Symmetry

A word that is quite suitable to express this property of inertial frames of reference is 'symmetry'. Alle inertial frames of reference are perfectly symmetrical with respect to each other. Physicists have a very strong intuition that this type of symmetry simply must be a property of Nature, and as far as known, it is.

Newton argued that this Galilean relativity does not extend to rotation. He argued that you can fill a vessel with a fluid, and if the surface of the fluid stays flat, it is not rotating. If the surface deviates from flatness, it is rotating. In newtonian dynamics, transforming between non-inertial frames of reference is trivial too, you just add the acceleration vectors. (You will need to represent the acceleration vectors as functions of time.)

The Maxwell equations

In the nineteenth century, something unexpected happened. The Maxwell equations of electrostatic and magnetic fields were introduced, and if you assume that the Maxwell equations are correct, and you assume that space is Euclidian, than you must deduce that measuring absolute velocity is possible.

Reluctantly, physicist resigned themselves to the conclusion that Galilean Relativity was not a property of Nature after all. Then, in 1905, Einstein showed that it is possible, by assuming that the Lorentz transformations are the fundamental transformations between inertial frames of reference, that it is possible to have both the Maxwell equations, and full symmetry of all inertial frames of reference.

A complete set of transformations

In Newtonian dynamics, transformation between two reference frames that are not inertial with respect to each other is performed by linear addition of the vectors. If you can represent the acceleration vector mathematically, you can express the transformation of the acceleration as a function of time and/or spatial coordinates.

In newtonian dynamics, if you are sufficiently mathematically able, you can transform between all reference frames. According to newtonian dynamics, the transformations between inertial frames of reference represent a fundamental property of Nature. The other transformations are seen als calculation decvices, not representing a property of Nature

In order to have a fully equipped toolbox, Einsteinian Relativity had to be extended to also provide transformations involving a non-inertial reference frame. In the following years, Einstein pursued two goals, assuming correctly the two goals were profoundly related. Einstein sought to formulate general transformations, and he sought to formulate a law of gravity in which the mediator of gravitational influence would propagate through space-time at lightspeed. (Newton had shown mathematically that with an inverse-square law of gravitation there is conservation of angular momentum only if gravity propagates at infinite speed. Newton argued that only a dynamics with conservation of angular momentum has scientific crediblility.)

In 1915, the two goals were reached in the formulation of General Relativity. Now there was a full set of transformations, just as in newtonian dynamics. According to general relativity, when an observer is accelerating all of space-time appears distorted to the observer, with gravity, local space-time is distorted.

How John Wheeler introduces General Relativity

In his book on gravity, John Archibald Wheeler describes the following thought-demonstration.

Go to an fairly sperical asteroid that doesn't rotate, and drill a corridor that links two antipodal points. Position a space capsule at one end of the corridor, and then release the capsule. From that moment on, the capsule will oscillate between the endpoints of the corridor.

The newtonian interpretation is that a force is pulling the capsule towards the center of the asteroid. At the point of zero gravity the capsule reaches its largest velocity in the course of the oscillation. According to newtonian dynamics, the oscillation is a harmonic oscillation.

According relativistic dynamics, the capsule is in free fall everywhere in the corridor. According to relativistic physics the physics inside the local space-time of the capsule is indistinguishable from zero-curvature space-time. The capsule is accelerating with respect to a more global volume of space-time, but inside the capsule it is fundamentally impossible to measure this (unless there is equipment onboard that is sufficiently sensitive to measure the gradient in the space-time curvature. Then it can be deduced that since there is a gradient, there must be curvature.)

At non-relativistic speeds, general relativity predicts the same oscillation as newtonian dynamics does. The oscillation in the corridor is the geodesic of that capsule, given the initial point of release. If the capsule is not released at surface altitude, but from a point further into the corridor, then the capsule will oscillate along the geodesic that corresponds to that initial condition. Both according to newtonian dynamics and relativistic dynamics at non-relativistic speeds, the oscillation period will be the same for all release-altitudes.

Usually, the concept of geodesic is introduced in connection with planetary orbits. The orbit of an object in the curved space-time around a gravitating body is a geodesic. Free fall in the vacuum of space towards the center of an asteroid is a geodesic too. A geodesic is not necessarily a curved trajectory, it can be a straight line. The curvature of space-time then manifests itself as being accelerated with respect to global space-time.