Talk:Principle of relativity/Archive 1

Proposal for new article
I'd like to propose a new article. first I copy the current article here, then I replace it with the article I wrote, so you can use the history to compare the content. I appreciate your comments. Cleon Teunissen 16:21, 27 Jan 2005 (UTC)

Galilean relativity
Historically, the first principle of relativity that was formulated was a principle of relativity of magnitude and direction of uniform motion suggested by the observation that there didn't seem to be a phenomenon in dynamics that will allow an observer to establish a zero point of velocity, nor a preferred direction.

Every choice of a zero point of motion, a choice necessary in order to perform a calculation, constitutes a choice of reference frame. All reference frames that move with respect to each other with uniform velocity are called inertial reference frames. The circularity of this definition is inescapable, since there is no preferred inertial reference frame

In Galilean relativity, reference frames are related to each other in a intuitive way: to transform the velocity of an object from one frame to another, the vector representing the velocity of the object is added to the vector representing the velocity difference between the two reference frames. Such a transformation is called a Galilean transformation. The geometry of space is assumed to be Euclidian, and the measurement of time is assumed to be the same for all observers.

Some laws of motion are valid indepent of reference frame. For example: in all inertial reference frames, the common center of mass of a group of particles moves in uniform motion. The independency of reference frame suggests that that law of motion is fundamental, more so than other laws.

Accelerated motion
When accelerated motion is involved, there are phenomena that will allow an observer to establish a zero point, there are phenomena that determine a preferred reference frame. It is possible to measure angular velocity inside a room that is cut off from all information, other than the fact that the room occupies space. Navigational gyroscopes inside a ship can detect the rotation of the earth and the direction of the rotation of the earth, allowing ships to know the geographic North without a magnetic compass. See also the external links of this Gravity probe B, and the Sagnac effect.

A frame with zero acceleration is not a zero point of motion. Rather, the zero point of acceleration is related to all inertial reference frames simultaneously, as if all inertial reference frames are in fact a single all-in-one state.

In performing calculations it is possible to transform from a rotating frame of reference to an inertial frame of reference and vice versa. As with all transformations in Euclidian space the vectors are added, but in the case of a rotating frame of reference the acceleration vector is a function of time and/or spatial coordinates.

Special relativity
Einstein saw, as did his contemporaries, that if one assumes that both the Maxwell equations are valid, and that Galilean transformation is the appropriate transformation, then it should be possible to measure velocity absolutely. Einstein showed that if one assumes that the Lorentz transformations are the appropriate transformations for transforming between inertial reference frames, then that constitutes a principle of relativity that is compatible with the Maxwell equations.

The assumption that the Lorentz transformations are the appropriate transformations has vast implications. The intuitive assumption that time is universal has to be relinquished.

General relativity
Since space is not Euclidian the existing transformations between an inertial reference frame and an accelerating reference frame were clearly not appropriate.

Einstein formulated a new theory, unifying the description of the geometry of space-time and the description of the interaction of mass and the geometry of space-time, achieving two goals at once: a theory of gravity in which the mediator of gravity propagates at lightspeed, and the geometric means to perform in calculation a transformation between any two reference frames, inertial of non-inertial.

Being able to calculate a transformation doesn't in itself imply nature works that way. Before and after the introduction of General relativity, angular velocity was measured with devices that make a local measurement. The background reference frame of these sensors is space-time itself. Currently, mechanical gyroscopes onboard the satellite Gravity probe B are used to measure a rotation of space-time itself, space-time close to Earth that rotates with respect to the universe, due to the rotation of planet Earth nearby. If general relativity is correct then the gyroscopes should, over the course of a year, deviate 42 milliarc-seconds due to frame dragging.

External links:

 * Gravity probe B experiment to measure frame dragging
 * Reflections on Relativity, section 2.7 The Sagnac effect
 * Ring interferometry experiment. University of Canterbury, New Zealand