Talk:Special Relativity/Principle of Relativity

Inertial reference frames
''An inertial reference frame is a collection of objects that have no net motion relative to each other. It is a coordinate system defined by the non-accelerated motion of objects with a common direction and speed.''


 * It always puzzles me what an inertial reference frame is. It is certainly not a collection of objects as the first sentence states. It is indeed meant to be a coordinate system that is not accelerated, and hence is in rest or moves with constant velocity, as one might think. Might think, because how is this observed, how to be measured? The topic of the theory is precise the relativity of movements.Nijdam 20:01, 16 June 2006 (UTC)


 * Two years almost has gone by, and no one has commented on the above remark. The definition is certainly not correct. I will comment it out till it is corrected.Nijdam (talk) 12:05, 2 June 2008 (UTC)

Hi there. These are good points. The definition was very weak. I looked through the web and found tremendous confusion on this issue. Most of the definitions were circular (ie: they assume SR to define an inertial reference frame). The best, non-circular definition that I could find was by Blandford and Thorne and has been included both as a summary sentence and as a full-length quote. Weyl (Space, Time, Matter) also says the same over a couple of pages. Carroll, a prominent cosmologist, gives a similar definition to that of Blandford and Thorne:

"Let us consider coordinates (t, x, y, z) on spacetime, set up in the following way. The spatial coordinates (x, y, z) comprise a standard Cartesian system, constructed for example by welding together rigid rods which meet at right angles. The rods must be moving freely, unaccelerated. The time coordinate is defined by a set of clocks which are not moving with respect to the spatial coordinates. (Since this is a thought experiment, we imagine that the rods are infinitely long and there is one clock at every point in space.) The clocks are synchronized in the following sense: if you travel from one point in space to any other in a straight line at constant speed, the time difference between the clocks at the ends of your journey is the same as if you had made the same trip, at the same speed, in the other direction. The coordinate system thus constructed is an inertial frame." Carroll, S.M. (1997) Lecture Notes on General Relativity. http://xxx.lanl.gov/abs/gr-qc/9712019

I would have used Carroll's definition but for the fact that he does not specify Einstein Synchronisation.

Relativity holds that moving objects are not attached to any inertial frame of reference but their own rest frame(i.e.: the clocks go out of sync relative to other inertial frames of reference etc.).

Incidentally, the current Wikipedia definition: "an inertial frame of reference is one in which the motion of a particle not subject to forces is a straight line." and the oft quoted "an inertial reference frame is a reference frame in which Newton's First Law is valid" are bizarre because a reference frame is a coordinate system, not a physical law. It may well be the case that where clocks remain synchronised and rods remain the same length at all positions Newton's first law of motion applies but in invoking Newton we are assuming Noether's insights and relativity prior to deciding how we can make the measurements on which these theories are based! RobinH (talk) 15:51, 2 June 2008 (UTC)

Introduction
Special relativity (SR) or the 'special theory of relativity' was developed by Albert Einstein and first published in 1905 in the article "On the Electrodynamics of Moving Bodies". It replaced Newtonian notions of space and time and it incorporates Maxwell's theory of electromagnetism. The theory is called "special" because it applies the principle of relativity to the "restricted" or "special" case of inertial reference frames in 'flat' spacetime where the effects of gravity can be ignored. Ten years later, Einstein published his general theory of relativity (general relativity, "GR") which incorporated these effects.

Beginners often believe that special relativity is only about objects that are moving at high velocities. This is a mistake. Special relativity applies at all velocities but at low velocity the predictions of special relativity are almost identical to those of the Newtonian empirical formulae. Special relativity introduces a deeper understanding of why physical events happen.

This book is intended for undergraduates but can be used by anyone with a higher school level of mathematics. It is arranged in two sections, a general description and a mathematical description of the theory. As a "Wikibook" it is not complete and the next edition can be edited by anyone who feels they have spotted a mistake or wishes to add more detail and clarity.

I have a replacement intro at here EvanR 10:12, 17 July 2006 (UTC)

Reference frame and coordinate system
In general relativity it is important to distinguish reference frames (inertial, flat, curved, etc) from coordinate systems (rectangular, polar, Boyer-Lindquist, etc). It might be helpful to add some text defining these two terms, giving examples of how they are different, and explaining why it is important. I understand the difference myself, somewhat, but not enough to write any good text to describe this. Kwan3217 04:39, 8 August 2007 (UTC)

another view
“Einstein extended the principle of relativity by proposing that the laws of physics are the same regardless of the inertial frame of reference.”

I would not call this an extension. It is more of an “interpretation”, however severely incomplete: in addition, laws of physics must refer to relative velocities only, so that predicted observations are the same regardless of the inertial frame chosen to describe an experiment.

Indeed the principle of relativity of movements stipulates that only relative motion has a reality. Therefore the representation of an object as being at rest or in motion results from a pure convention and should have no impact on predicted observations. For the purpose of describing an experiment where objects are in relative motion, one must first adopt a convention about what is fixed and what is in motion, and then apply laws of physics within this framework.

One may decide to change this convention, leading to another description of the experimental pattern. But according to the principle of relativity of movements the same laws of physics shall apply and the same observations will be predicted within the new framework provided all relative velocities are maintained unchanged through the change of convention… Otherwise it would not be true that only relative motion has a reality.

From the above one can clearly see why it is not sufficient to require that the same laws apply: they must refer to relative velocities only.

When swapping from one convention to another, all velocities are affected by adding the same vector v, more precisely the mathematical representation of the velocity of every object is affected by this vector, leaving the relative velocities between objects unchanged. Of course the same system of coordinates can be used for the mathematical representation of both frameworks…

In this context it is correct to state that v marks the difference between both conventions, between both frameworks used for applying laws of physics. However it would not make sense to imagine the “conventions” being in relative motion, or telling that one goes faster than the other, or claiming that one can be at rest.

Should you try and replace the word “convention” by “reference frame”? If it has any bearing to the principle of relativity of movement, a reference frame must relate to the motion of objects, not to their position. A change of convention concerning what is moving and what is at rest (a change of reference frame then), must remain independent from a change of positions, the latter being obtained through a change of the coordinate system, another arbitrary convention according to the principle of relativity of positions in space. Sugdub (talk) 22:19, 17 December 2009 (UTC)

For readers who do not already know what you mean
The current text says: The velocity transformations for the velocities in the three directions in space are, according to Galilean relativity: and then it goes on to list: $$\mathbf{u^'_x = u_x - v}$$

etc. The problem for the beginning reader is that s/he does not know where the "U" factors are coming from. Even though it is easy to argue that the stated form of something is defensible if correctly understood, it would be better to avoid creating a stumbling block for the beginning reader -- especially in regard to something that already has the reputation of being incomprehensible. It only costs the writer a moment to define terms. Failing to do so could discourage a reader for a lifetime. P0M (talk) 02:48, 30 December 2010 (UTC)

Confusion
I've been trying to understand the problem mentioned in the text for nearly an hour. It's not clear from the illustration's text that the coordinates (x,y,z,t) and (x',y',z',t') refer to the event and not the observers. It's also unclear that the two observers are at the exact same point at t=0.


 * Thank you for pointing this out. I have extended the text.  RobinH (discuss • contribs) 18:29, 1 January 2012 (UTC)

Arriving at spacetime equation
"Einstein himself (Einstein 1920) gives one of the clearest descriptions of how the Lorentz Transformation equations are actually describing properties of space and time itself. His general reasoning is given below. If the equations are combined they satisfy the relation:"

It is not clear which are the equations combined to give rise to the Pythagoras' Theorem extension, resulting in arguably the first critical point in the article, the concept of spacetime described by the math. It would be better to indicate exactly which/how the equations are combined.

Jakesee (discuss • contribs) 04:52, 24 February 2015 (UTC)

Reference works cited
I made a small change to add a "References" section heading before the last book cited (Blandford &c.); then realised that several other works cited (e.g. Einstein 1920) didn't appear there, but at the end of the section that cited it. Also remembered reading just now that the Wikibooks MOS talks about having a bibliography (or References) page, not a ref. section. So I undid my change.

Some questions:
 * 1) Would the reader benefit by our gathering these (four or so) book references at the bottom of the current page?
 * 2) Or in a separate section named "References"?
 * 3) Or on another entirely separate page called "Bibliography" or "References"?
 * 4) Or are they better left exactly where they are, each at the end of the citing section?
 * 5) And if we do leave them where they are, should we format them differently from the main text, to make clear they're some kind of footnote to the section (e.g. by indenting them)?

Yahya Abdal-Aziz (discuss • contribs) 12:18, 14 November 2018 (UTC)


 * Answering my own questions …! I've just read Help:Editing (help - editing - References, which says, inter alia:
 * "Footnotes may also be listed at the ends of each section of text by closing the template with the "close" parameter, as shown in the box just above."
 * and refers to the example .  So, (being BOLD) I'm just going to see how well that works. Yahya Abdal-Aziz (discuss • contribs) 12:49, 14 November 2018 (UTC)


 * End-of-section reflists added. Seems to work quite well.  I'd appreciate any feedback on whether you think this is an improvement.  Yahya Abdal-Aziz (discuss • contribs) 13:27, 14 November 2018 (UTC)