Talk:Frame of reference/Archive 1

"Frame of reference" not only used in physics
The term "frame of reference is not only used in physics. Need to include something about how the sense of the phrase" frame of reference" is used by the everyday person. 124.171.169.155 (talk) 12:38, 5 December 2008 (UTC)

A reference frame is a "box of rocks"?.....I deleted this....but it's still a mess. rsl

Ugh. Reads as a snobbish essay, not an encyclopedia entry. I don't even know where to start with fixing this one... -- Jake 06:21, 26 Sep 2003 (UTC)
 * I suggest ignoring it completely and rewriting it from scratch, not letting it hang around our necks like a dead albatross. It doesn't say anywhere that edits have to be incremental. If someone who knows physics would just boldly replace this with something less inscrutable? I don't see incremental edits ever salvaging this. In particular, the procedural flavour has to go. As a reader I don't care about "constructing" a frame of reference, I just want to know what it is. I don't expect a guided tour of a car factory when I ask what a car is, after all. JRM 16:54, 2004 Dec 3 (UTC)

I (different I) got a few sentences in, noticed that it was suggested that a moving car has to be accelerating, and stopped reading.

rewrite finished
I did the major rewrite, (I wasn't signed in that's why it just has my ip). I mentioned on the needs attention page some things that I think still need to be done. For instance the equations look horrible because I don't know latex. Also I think the application of reference frames in special relativity should get more attention. I don't remember a lot of the conventions, and won't have time to look them up until the semester is over. I don't know if it's exactly what we wanted, but at least it's not an essay anymore, and might help someone if they came here looking for how to work some problem. Let me know what you think! :) Starfoxy

The railroad car analogy is well-known for an example as an inertial frame of reference, since the train attempts to operate at a constant speed; hence the railroad car (the frame) is not accelerated. Is that what the requesters were looking for when they asked for a rewrite? That is a single sentence. Ancheta Wis 02:20, 3 Jan 2005 (UTC)

I added some more information on measurements in accelerating reference frames and tweaked the formatting to hopefully make it a bit easier to read. I think I also addressed the point above about a constant-velocity frame being inertial, and I think the LaTeX looks a little better, although experts are of course welcome to come in and fix it :-). I'm not too sure I like the organization, but I couldn't think of a way to fix it, so I left it as is. Steven Luo 05:39, 9 Jan 2005 (UTC)

I revised the paragraph about the dependency of observations on the frame of reference and added a link to the principle of relativity.StuTheSheep 16:33, Mar 1, 2005 (UTC)

I think the story about 'Alfred and Betsy' is very unlike encyclopedic style. I think there is no need for an article on 'frame of reference', I think a dictionary-style description is sufficient.

Frame of reference caution is equally important in newtonian dynamics and in special relativity. But the transformations of special relativity are counterintuitive, so in special relativity it is harder to switch mentally from the perspective of one frame of reference to the perspective of another frame. --Cleon Teunissen 17:49, 2 Mar 2005 (UTC)

i have trouble figuring this out: i really dont know what the frames of refrence is and what would it be in this sentence: The sun is over the horizon??

Clarified an ambiguity in my previous revision. StuTheSheep 05:49, Mar 3, 2005 (UTC)

from pages needing attention

 * Frame of reference - what we have now is inscrutable and probably unsalvageable by incremental edits. Could a student of physics do this anew, and do it right? JRM 16:56, 2004 Dec 3 (UTC)
 * I rewrote the article, but it's still not good. My latex skills are sorely lacking so the equations look bad, and I didn't cover special reletivity very well because it's been awhile, and I don't remember much about the conventions. If anyone could help wikify it, and help me make the equations look better then that'd be great. Starfoxy 12/9/04

The formula for the coriolis force does not describe a transformation
The current article contains a principal flaw. In the current article the following formula is called a transformation:
 * $$\vec F'_\mathrm{coriolis} = -2m\vec\omega \times \vec v'$$

This is incorrect. The formula contains the term $$ \vec\omega $$. $$ \vec\omega $$ is the rotation of the system with respect to an inertial frame of reference. That is, the rotation of the system with respect to a non-rotating frame. Whether a system is rotating or not can be measured in several ways.

In the transformations of special relativity there is symmetry, neither frame that is involved in the transformation is considered "the non-moving frame". In special relativity there is no concept of "the non-moving frame". Any relative velocity can be inserted in the transformation; in the transformed situation the laws of motion once again hold good.

The formula for the coriolis force involves a non-rotating frame and a rotating frame. So it is not a transformation, analogous to the transformations of special relativity. The formula for the coriolis force is an algorithm. The algorithm creates for each rotating frame a "law of motion" that is valid in that frame only. If a system is rotating with an angular velocity of 1 rad per second, then the special, additional "law of motion" for the co-rotating reference frame of that system is the formula for the coriolis force with that particular rotation rate inserted.

General relativity is magnificent, and it certainly is correct, as is shown by the fact that GPS technology takes several consequences of general relativity into account in order to achieve its level of accuracy. Contrary to what many people assume, general relativity does not extend the type of relativity of special relativity to accelerated motion. (Einstein did aim for that, initially, hence the name.) --Cleon Teunissen 21:28, 2 Mar 2005 (UTC)

Perhaps the most remarkable facet of general relativity was Einstein's ability to rectify the error in the longitude of perihelion of Mercury, which was found to be 43 arc seconds per century. With 415 orbits of Mercury per hundred years, 360 degrees per orbit, 60 arc minutes per degree and 60 arc seconds per arc minute, that enormous error is 43 parts in 537840000, or 0.0000079949427338985571917298824929347%. Magnificent work for someone working with a 3 significant figure sliderule and book of log tables. Of course tis was carried out about 100 years ago, and the initial observation of Mercury took place a century before that, so the telescopes 200 years ago were a miracle of optical precision, unequalled today even by HST. Der alte Hexenmeister 17:39, 9 July 2006 (UTC)

PSSC Physics Educational Film Series
There also exists an excellent educational film by the Physical Science Study Committee in the 1950s titled Frames of Reference which explains the problem of the bias of personal perspective in studying problems in physics. (e.g. The earth appears to be stationary; the sun appears to move around the earth. The earth appears to be flat.  Time appears to pass in fixed intervals, rather than relative to the fixed transmission of light.)

Example image
Not to insult the person who made the image for the Example section, but is there something more professional-looking that someone can make to replace it? Super Jedi Droid 04:01, 12 November 2006 (UTC)

Edit to first paragraph and Overview
I decided to edit the first paragraph to remove any reference to an inertial reference frame being one which does not rotate nor accelerate. These terms are relative and therefore meaningless. It is much better to say that Newton's first law is valid in inertial reference frames. I also decided that the overview was in need of a complete re-write and so I decided to dedicate some time to this effect. I hope that my changes are a considerable improvement but I do not pretend that they are in any way complete. This article needs some serious looking over by a professional in this field, which I am not. I hope that we might some day soon reach an article which holds some worth. 130.88.186.123 09:24, 3 May 2007 (UTC)

I'm not going to touch the overveiw, this article's a mess, but i do have to point out that Newton's first law can be applied to non-inertial referecnce frames. A inertial reference frame is moving at a constant velocity. Objects on the Earth are not in an inertial frame due to the constant acceleration of gravity. However for basic physics the car traveling at thirty m/s or whatever is assumed to be inertial as the motion is perpendicular to the acceleration. All Newtonian mathematics can be applied to frames whose motion is perpendicular to the aceleration and less than .1c SilverDream 02:44, 8 June 2007 (UTC)

Propose deletion of references to Minkowski space etc.
These sentences are not very illuminating and should be left to See also links:
 * Inertia is very much real, of course, but unlike force it never accelerates an object. In General Relativity, fictitious forces due to acceleration are indistinguishable from gravity in the small (local region); even in the large, the two kinds of force can be distinguished only in special cases, such as static reference frames or reference frames asymptotic (at large distances) to Minkowskian, or at least static ones.

I propose their deletion. Brews ohare (talk) 23:50, 21 July 2008 (UTC)


 * I agree. Paolo.dL (talk) 08:49, 22 July 2008 (UTC)

Difference between reference frame and coordinate system
The difference is not explained. I use the two expressions as "synonyms". Physicists tend to use the expression "reference frame", rather than "coordinate system", probably because Newton used the first rather than the second. In physics, you always need a coordinate system to define any quantity. This coordinate system can be inertial or not inertial... Paolo.dL 13:02, 24 August 2007 (UTC)


 * This viewpoint is not general. The term reference frame most often refers to inertial or non-inertial frames, while coordinate system is exactly that, that is, one of Cartesian, curvilinear, cylindrical etc. Brews ohare (talk) 16:55, 21 July 2008 (UTC)

In my opinion, a coordinate system is a frame of reference. Another possibility is that a frame of reference is a slightly more generic concept. Namely, we have these two options:
 * 1) a reference frame is a coordinate system, i.e. a set of axes at the origin of which an observer sits and observes the world, with an associated "method" (Cartesian, polar, etc.) to convert vectors in numbers.
 * 2) a reference frame is a set of axes at the origin of which an observer sits and observes the world, without an associated "method" to convert vectors in numbers (i.e. a specific coordinate system using the same axes).
 * The conversion of vectors to numbers refers to coordinate system; the state of motion of the observer is a separate matter and refers to an observational frame of reference. Observational frame of reference is about the need for fictitious forces, coordinate system is not. Brews ohare (talk) 16:55, 21 July 2008 (UTC)

In the second case, for any frame of reference there are several possible kinds of equivalent coordinate systems (polar, cartesian, etc.) which use exactly the same set of axes. However, in both cases, as soon as we define a coordinate system or a vector space basis, we also define a reference frame. Paolo.dL (talk) 13:51, 21 July 2008 (UTC)


 * Hi Paolo: "Reference frame" may be used sloppily as a synonym for "coordinate system", but "inertial frame" and "non-inertial frame" can not. Often the term "frame of reference" is used to refer to these last two as well (but this usage varies), so I'd say "reference frame" is more general than "coordinate system" and, considering this lack of definiteness, probably too vague a choice of term for a lot of technical discussion. Therefore, I've used the term observational frame of reference to refer to inertial and non-inertial frames. Brews ohare (talk) 14:06, 21 July 2008 (UTC)


 * Your point is confused. Inertial or non-inertial are just adjectives which refer to the motion of the axes. So, they can be used to qualify both reference frames and coordinate systems, although "inertial reference frame" is much more frequent than "inertial coordinate system" (for historical reasons, I guess). I wrote a detailed explanation for you. Paolo.dL (talk) 08:32, 22 July 2008 (UTC)

Previous discussion
NOTE: This text was copied from Talk:Centrifugal force. Paolo.dL (talk) 10:41, 22 July 2008 (UTC)

Paolo: Coordinate systems and frames of reference are independent: I can choose to describe a planetary orbit in elliptical coordinates or Cartesian, for example. They both can be referred to the fixed stars (inertial) or they could be fixed to the Sun (approximately inertial), or they could be fixed to the Moon (a wild choice and very non-inertial). More seriously, consider a wire fixed in space. The use of arc length to describe position on the wire in the inertial frame leaves the frame inertial. If now arc length is mapped to time, the frame is still inertial. Brews ohare (talk) 14:11, 16 July 2008 (UTC)


 * Your comment does not make sense to me. Do we agree that, if you choose a Cartesian coordinate system which rotates together with the moon, this is a non-inertial coordinate system and represents a non-inertial frame of reference? This frame of reference can be also represented by a polar coordinate system, or whatever, but chosing a coordinate system means chosing a reference frame. Do you agree? Paolo.dL (talk) 14:44, 16 July 2008 (UTC)

No, we do not agree. There are two separate issues: My impression is that you would not care to imagine an observer on the Earth using a coordinate system centered on the Moon to describe a satellite orbiting the Moon. But that is feasible, and the Earth observer then will include effects due to the Moon orbiting the Earth that are omitted by a Moon observer using the same coordinate system to describe the satellite circling the Moon. Approximating the Earth as a frame more nearly an inertial frame than the Moon, the Moon observer will need to add fictitious forces. Brews ohare (talk) 14:59, 16 July 2008 (UTC)
 * 1) What is our frame of reference? Are we at rest relative to the fixed stars or relative to the Moon, for example.
 * 2) How do we wish to describe what we see? Is it simplest to use arc length, circular coordinates, or what ever. Should the coordinates relate to the path or relate to our origin?

Detailed explanation of my point, with references
As far as I know, Reisnick & Holliday, Physics Volume I (Mechanics), 3rd edition, is one of the most successfull university textbooks in USA. The authors never use the expression "coordinate system". They only use "reference frame", and it is easy to deduce that they use it as a synonym of "Cartesian (orthogonal) coordinate system". For instance, when they introduce the concept of vector, they explain that a vector can be "resolved into scalar components" with respect to the axes of a reference frame. As you know, scalar components means coordinates. They also explain Cartesian notation without calling it Cartesian notation (vectors represented as linear combination of versors), and define the three versors (without calling them versors or basis vectors) as unit vectors codirectional with the three axes of the reference frame.

Wikipedia defines a Frame of reference as a "set of axes...". This implies the existance of an origin, typically defined as the intersection of these axes (although it is possible to choose a set of orthogonal or non-orthogonal axes which do not intersect, as far as I know reference frames are never built with such non-interesecting axes).

But what is the reason why we need a reference frame? It is needed (I agree with Wikipedia) to define (linear and angular) position, velocity, and accelerations of points (such as the center of mass of objects). Additionally, it is also used to define angular kinematics of rigid bodies (i.e. the linear kinematics of a set of directed axes attached to rigid bodies; see rigid body). Moreover, it is also needed to define other vectorial mechanical quantities such as force, moment of force, linear and angular momentum, etc.. However, to define these quantities you need a method to transform vectors into numbers, and this method is provided by one of the many equivalent coordinate systems.

Thus, in my opinion a reference frame is just a coordinate system. However, I guess there might be, for some authors, a slight difference between the two concepts (although this distinction seems useless to me). A reference frame might be defined as a set of directed axes not endowed with a method to tranform vectors from pure geometrical entities into numbers. If you sit in the reference frame origin and move (or rest) togheter with these axes, you can see the position of points, you can tell if they are close or far, above or below, anterior or posterior, etc., but you still cannot measure exactly these positions. However, with these axes you are able to build several kinds of Coordinate systems (Cartesian, polar, etc.), with which you can measure position.

Thus, for some authors there might be several (reciprocally equivalent) coordinate systems for each reference frame. But only one reference frame for each Coordinate system. Namely, as soon as you change the position or velocity or acceleration of the origin, or the orientation or angular velocity or angular acceleration of the axes, you change the reference frame. Paolo.dL (talk) 08:49, 22 July 2008 (UTC)
 * Unfortunately, there is every reason to believe that "reference frame" is used sloppily by many authors to refer to both "coordinate system" and to "observational frames of reference". Reisnick & Holliday are not alone. However, there are two different ideas here, as pointed out very carefully and thoroughly cited. The vagueness of "reference frame" therefore requires some terminology that makes the necessary distinction. I have used "observational frame of reference" as one way to make this distinction. Brews ohare (talk) 10:22, 22 July 2008 (UTC)


 * No, I guess Reisnick and Holliday just don't care about what you call "observational frames of reference" (is there a non-observational one?). I guess RF has only one meaning for them: it is a synonym of CS, and this definition of the concept is not less reasonable than other definitions. Paolo.dL (talk) 23:43, 22 July 2008 (UTC)

Edits by Brews ohare
Brews's massive edits seem to be based on an absurd concept summarized in these sentences: Moreover, I do not like the use of the word "observational" (is there a non-observational reference frame?). This is original and inappropriate terminology.
 * "A change in coordinate system does not change an observer's state of motion". It certainly does, if the new coordinate system moves relative to the first one!
 * "Coordinate systems and observational reference frames are independent". This is just a biased point of view. For instance, two coordinate systems that rotate relative to each other, correspond to two totally different reference frames.

Brews's edits reflect his own questionable opinion on the topic under discussion in this section. Moreover, his new section about Coordinate systems is the least focused and less readable text I have ever read on Wikipedia. This topic is still under discussion, and still nobody else had a chance to post his opinion on this talk page. The topic has been also discussed on Talk:Centrifugal force. Therefore, I propose to remove Brews's edits. Paolo.dL (talk) 10:15, 22 July 2008 (UTC)


 * The section on Coordinate systems is only an outline of the concept, and adequate links and citations are provided to flesh it out for the interested reader. A section like this is needed in the article to make clear what a coordinate system is, as that is one of the meanings of "reference frame" mentioned in the Intro. Brews ohare (talk) 10:27, 22 July 2008 (UTC)


 * However, your version makes it unclear. Better nothing than that. Paolo.dL (talk) 00:30, 23 July 2008 (UTC)


 * All the edits by Brews_ohare are thoroughly documented by citations, and therefore are supported by Wiki policies. Their summary deletion is therefore inadvisable. Brews ohare (talk) 10:17, 22 July 2008 (UTC)

My opinion is also supported by a very reliable source. Your edits are a biased personal interpretation of the reported citations. Paolo.dL (talk) 10:22, 22 July 2008 (UTC)


 * I have not contradicted your source, merely made an important distinction that is very well documented. If you believe the citations I have made are misread, I'd suggest you try interpreting them differently than I have. Brews ohare (talk) 10:29, 22 July 2008 (UTC)

My interpretation is compatible with your references. Actually, I referred to that "distinction", much before your edits, in my 16 July 2008 posting (see above). I have already criticized your biased interpretation (see beginning of this subsection), and my interpretation of the literature is given above (There was an editing conflict when I saved the last version of my previous comment. Possibly, you did not read what I copied above from Talk:Centrifugal force). Paolo.dL (talk) 10:41, 22 July 2008 (UTC)


 * The quotation below appears to me to say a distinction has to be introduced. You seem to say the contrary: that such a distinction is unimportant.


 * Just how do you agree with this quotation, please? The underlying issue is that coordinate systems are a mathematical tool, while observational frames of reference are a physical concept. Brews ohare (talk) 14:52, 22 July 2008 (UTC)

I partly agree with Cornille, but who cares if I or you agree? I already explained that different reciprocally equivalent CSs exist for any given set of axes. I agree with Cornille that you are free to choose any of these CSs. I am aware that two different interpretations of the concept of RF exist in the literature. It does not matter what of them I (or you) prefer. I did not write that I "agree with this quotation". I wrote "my interpretation is compatible with your references". My interpretation is that CSs and RFs are not independent. This is and has always been my main point (since when I posted my first comment on this topic, dated 16 July 2008; see above): "chosing a coordinate system means chosing a reference frame". You wrote the opposite (see absurd sentences copied at the beginning of this subsection). Paolo.dL (talk) 00:30, 23 July 2008 (UTC)


 * If you disagree with this quotation, in what sense is this "compatible with" my references? Brews ohare (talk) 02:20, 23 July 2008 (UTC)

I prefer the definition given by other authors. That does not mean that I want your references out of the article. Nor that I want to express in the article my personal preference. On the contrary, you actually did it. Here's your sentence, that I just removed: "Unfortunately, the term "frame of reference" is used loosely to refer to both coordinate system and observational frame of reference, tending to blur the important distinction between them." (this is not NPOV with respect to the whole literature; it adopts the opinion of a part of the authors).

How many times do I have to repeat to you that I am not fighting against your references, but against your own sentences? Can you please confirm that you know what are the sentences I am taking about? They are written right on top of this subsection. Paolo.dL (talk) 22:13, 23 July 2008 (UTC)


 * Our "debate" really seems to amount to a narrow specific issue: how one separates one procedure: the change from one state of motion to another state of motion; from the different procedure: the change of one coordinate system to another coordinate system while in the same state of motion. Do you have a way to express this distinction that you would endorse? My feeling is that you require a coordinate system to be related to a specific state of motion, but such a restriction is not necessary. You are thinking about a subset of coordinate systems that are attached to particular states of motion. I could imagine a family of observational frames, all with origins that have the same state of motion, but all different in choice for three-space coordinate system: cylindrical, Cartesian etc. Their origins all have the same state of motion. On the other hand, I can imagine a family of origins each with a different state of motion, but all with the same Cartesian axes for three-space. Is there any problem with this? Brews ohare (talk) 02:46, 23 July 2008 (UTC)

Ok, now you started interacting. For the first time I have the feeling that you have read my previous comments. Thank you. Paolo.dL (talk) 22:13, 23 July 2008 (UTC)

How can you imagine "a family of origins each with a different state of motion, but all with the same Cartesian axes"? How can an origin move away from the intersection of those axes? I hope you meant something different from what you wrote. Paolo.dL (talk) 00:09, 25 July 2008 (UTC)

Alternative description of the distinction between RF and CS
As you asked, I will herein adopt your favourite definition(s), according to which RF and CS are not synonyms. In the next paragraphs I will describe this distinction. Let me know if you agree. I have numbered the paragraphs, so you can refer to each of them more easily. Paolo.dL (talk) 23:58, 24 July 2008 (UTC)


 * Paolo: I'll intersperse my comments. Brews ohare (talk) 14:32, 25 July 2008 (UTC)

Step 1
The measure of a vectorial quantity is a mathematical language, as you correctly call it, to represent that quantity with a sequence of numbers (called coordinates). It is impossible to obtain these numbers without a CS, and these numbers mean nothing if you don't refer them to a CS. Thus, a CS provides a method to encode and decode that language. Paolo.dL 23:58, 24 July 2008 (UTC)
 * Maybe I agree; I am not sure to what extent one needs a coordinate system to carry out vector analysis. Brews ohare (talk) 14:32, 25 July 2008 (UTC)
 * What do you mean? Measuring vectors and vector analysis are two different things. I won't discuss vector analysis here. Paolo.dL (talk) 19:48, 25 July 2008 (UTC)

Step 2
A RF is a rigid set of points or a rigid set of (typically, but not necessarily, orthogonal) axes, which are not enough to take a measure (e.g. express a vector as a sequence of coordinates), because this definition of RF does not include a method (Cartesian, polar, etc.) to take vectorial measures. Paolo.dL 23:58, 24 July 2008 (UTC)
 * The "rigid set of points" seems to agree with the authors of the first quotation. I'd leave out the "or a rigid set of axes" part. Brews ohare (talk) 14:32, 25 July 2008 (UTC)

Step 3
I guess that for many authors the definition of this RF includes an origin and an orientation, otherwise where do you put the "observer" who observes the universe from that RF? Or, how could you use "observer", and "RF" as synonyms? However, the RF has no method to measure motion (otherwise it would coincide with a CF). Thus, the observer can observe but cannot measure. (BTW, this is quite sadistic!) Paolo.dL 23:58, 24 July 2008 (UTC)


 * If this is a statistcal observation, I'd agree about "many" authors. Brews ohare (talk) 14:34, 25 July 2008 (UTC)

I have no statistical data. Let's say "some" authors, ok? Now I need to understand exactly what you wrote above (see step 2). Notice that in this step (step 3) I am not describing the "most restrictive" definition (RF = CF), but an intermediate one (a bit schizoid and sadistic), in which you define origin and axes (i.e. orientation), but do not define a method (Cartesian, polar) to use these axes for measuring purposes. Notice that, in my opinion, "observer" means someone who can measure (i.e. a CS). Not a tourist enjoying the landscape. So, this "intermediate definition" makes little sense to me, because the observer cannot observe. So, I am just trying to explore the possibility that authors exist who adopt this sadistic intermediate definition. Please, explicitly answer to this question: I will explain my rationale: if they do, that's good, because it means that nobody adopts the sadistic definition; if some of them do not agree, this implies that they adopt the sadistic definition. Do you see what I mean? Paolo.dL (talk) 20:23, 25 July 2008 (UTC)
 * Let's consider the authors who believe that "observer" and "FR" are synonyms; in your opinion, do they all agree that RF coincide with CF?
 * The observer has the capability to set up a coordinate system, but has freedom to choose among many possibilities. Brews ohare (talk) 22:57, 25 July 2008 (UTC)

Step 4
However, perhaps for some other authors this frame might be just a rigid set of points, with no origin and no directed axes (and no labeled points, from which you can define directed axes). In this case, when you define the RF you do not decide where you put the observer and how to orient him/her. That is: Let's call this the "least restrictive" definition of RF. I don't know if there's someone who adopts it, but I do know that many disagree: those who use "observer" and RF as synonyms. Jean Salençon, Stephen Lyle do not say, in your quotation, if the position of the observer, who is said to "move with the RF", is specified by the definition of the RF or by the definition of the CS. A question for you: as far as you know, is there any author who adopts the least restrictive definition of RD? Paolo.dL 23:58, 24 July 2008 (UTC)
 * you don't know what points are close to or distant from the observer (indetermined magnitude of position vector)
 * you don't know what points are above or below or in front or behind or to the left or to the right of the observer (undetermined direction of position vector).
 * It seems to me to be very close to the quotations; maybe an Origin is given, but that is all. Brews ohare (talk) 14:32, 25 July 2008 (UTC)
 * I noticed that you just inserted (revision as of 17:52, 25 July 2008) a new and clear quotation by Graham Nerlich that coincides exactly with the "least restrictive" definition that I described in this step (because it says that the class of CSs attached to a RF may have infinite origins and orientations). So, now we agree on this as well. Good. Paolo.dL (talk) 20:40, 25 July 2008 (UTC)

Step 5
Since physics is a quantitative science, we need a measure. For that, we need to attach to the RF a CF. This CF will move together with the RF (it will even share its axes, if you define the RF as a set of axes which intersect with each other). Paolo.dL 23:58, 24 July 2008 (UTC)
 * You may eventually need a CS, but it does not have to be part of defining a RF. However, often it is made that way. My main goal is to leave open the choice of CS, not to deny that you need one to finish the job. Brews ohare (talk) 14:32, 25 July 2008 (UTC)
 * Agreed. That is consistent with what I wrote. Paolo.dL (talk) 21:27, 25 July 2008 (UTC)

Step 6
I am sure we agree at least on this: there are several reciprocally equivalent CFs (Cartesian, spherical, cylindrical, elliptical, parabolic, etc.) that are compatible with a given RF. Paolo.dL 23:58, 24 July 2008 (UTC)
 * Yes, that is exactly the point. Brews ohare (talk) 14:32, 25 July 2008 (UTC)

Step 7
If the definition of the RF specifies the position of an observer (or the RF is the observer), then the origin and orientation of the CF is already defined. Otherwise, I guess you are free to put the coordinate axes wherever you like, provided that they "move with the RF" (and their intersection will be the origin, where the observer will "sit"). Paolo.dL 23:58, 24 July 2008 (UTC)
 * I don't follow you on this; it seems to contradict the previous. Brews ohare (talk) 14:32, 25 July 2008 (UTC)

Step 8
Thus, a CF attached to a given RF shares its motion relative to other parts of the universe. Paolo.dL 23:58, 24 July 2008 (UTC)
 * That seems to be so. Brews ohare (talk) 14:32, 25 July 2008 (UTC)

Step 9
If it did not "move with the RF", the CF would not be suited for measuring the motion of the universe as observed by the observer. It would measure a different motion.

Thus, the RF, the CF, and the observer "move together". Paolo.dL 23:58, 24 July 2008 (UTC)


 * Agreed. Brews ohare (talk) 14:32, 25 July 2008 (UTC)

Step 10
I conclude that a CF used by an observer to measure motion is something more and nothing less than a RF. The definition of a RF is the first step of the definition of such a CF. That is, the definition of such a CS includes the definition of the respective RF. Paolo.dL 23:58, 24 July 2008 (UTC)


 * Well not exactly. The RF once chosen leaves open just what choice for CF you want to make. Once the CF is chosen, it does share the state of motion of the RF. However, they are not one and the same, or there would be only one choice to make (the RF) not two: the RF and the CF. Brews ohare (talk) 14:32, 25 July 2008 (UTC)


 * "Not exactly"? And where did I write or imply that they are "one and the same"? Have you read what I wrote? "...is something more and nothing less" means "...is a proper superset", i.e. "...does not coincide with"! Paolo.dL (talk) 22:28, 25 July 2008 (UTC)


 * Are we quibbling here, or is there a substantial implication? There are two choices: first the state of motion, and second the choice of coordinate system in that state of motion. I think we agreed about this already. Brews ohare (talk) 22:59, 25 July 2008 (UTC)


 * Don't ask me. You are the only one who knows the answer. I want to know why you wrote "Well, not exactly". When you write this at the beginning of a sentence, it means that there's something about which you don't agree... So, maybe you (not we), are quibbling. I don't know. Please explain. I cannot see your point. Paolo.dL (talk) 09:58, 26 July 2008 (UTC)

Step 10 - continuing discussion
Paolo: The article states my view on this: The coordinate system is a mathematical concept. It is therefore an idealized concept that can be attached or related to reality by a physicist, but has no necessary connection to motion or any other aspect of reality. A reference frame is a physical concept inseparable from the idea of a state of motion. Thus, a CF is not "nothing less" than a RF; it lives in a different world. Is it "something more" than an RF? Well you could say something like that, because as a tool, it is not limited to any particular application. However, the "nothing less, something more" terminology does nothing for my understanding. It is an unhelpful description. Brews ohare (talk) 13:23, 26 July 2008 (UTC)

How you define a CS in physics
Brews, I see. This is an important topic. I partly agree with you. A CS is a mathematical concept. But without a CS you cannot measure. And physics is a quantitative science. So, in physics, and particularly in mechanics, a CS must have a "state of motion". You already agreed about this, in step 9. This is the reason why I wrote step 9 before step 10.

So, when you ask a physicist to define a CS, he must define the axes using some set of physical points which belong to some RF (for instance, three corners of a laboratory). This is typically done this way:
 * you use three non colinear points to define a plane (e.g., a Cartesian plane)
 * you use two of these points to define a directed axis on that plane, and you assign a label to this axis; let this label be z
 * you set the origin O on that axis, for instance at the first point.
 * you use z and the third point to define a semiplane, on which you define a directed semiaxis, perpendicular to z, and starting from O.
 * you assign a signed label to that semiaxis; let this be +y or -y; this sets name and direction of the second axis, y.
 * you define a third axis, x, as an axis passing through O whose direction is specified, based on the orientation of z and y, by the right-hand rule, or left-hand rule, depending on the handedness of the CS you wish to build.

If you have previously defined another CS, attached to another RF (for instance, the ideal Galilean frame), then you can use position vectors and vector algebra (e.g. vector sum, cross product, and Euclidean norm), to compute the versors of the second CS, and the position of its origin (similarly, in linear algebra, you start from a standard basis to define other vector space bases).

More complex methods to define a CS exist, but they all use a rigid set of points (or lines or planes, but these objects are all made of points). And in physics these points are not arbitrary and idealized mathematical entities. They must be embedded in the space-time continuum. They must exist in the universe. They must belong to some RF. So they are also characterized by a state of motion, relative to any other rigid object (i.e. RF) in the space-time continuum.

In sum, in physics a CS is a mathematical tool to measure physical quantities. Without this tool, physics would not exist; vectorial quantities could not be defined; Newton's laws could not have been experimentally validated. This kind of mathematics is part of physics. High mathematics (abstract algebra) uses vector spaces and bases, rather than RFs and CSs. Does this help you? Can you see that what I maintain is consistent with step 9, about which you fully agreed? (there's another important point on which we disagree; we'll discuss it later, if you don't mind) Paolo.dL (talk) 20:51, 30 July 2008 (UTC)


 * Well, Paolo, I am glad there is some agreement. And I agree that ultimately the physicist wants to describe and measure real things. So he has to set up some CS. However, "Step 9" merely says that once selected to become an addition to an RF, the CS moves with the RF. So a selected CS moves, but a CS itself is an abstract notion with no necessary motion. Brews ohare (talk) 17:19, 1 August 2008 (UTC)


 * In mathematics, you don't even need to specify measurement units. That is essential, however, in physics. Paolo.dL (talk) 21:30, 16 August 2008 (UTC)

A matter of choice
The observer in the RF has lots of choices for CS, and it is this choice that is emphasized by separating the two ideas of RF and CS. It doesn't usually result in the optimal situation if you fix upon one choice at the outset before looking at the problem you really have to describe. You may need to travel, so maybe you need a car, but it doesn't have to be a BMW. You may need a CS, but it doesn't have to be the standard four axes. You have to set up a lab, but it doesn't have to measure space and time directly. (In practice, in fact, the metrology is very indirectly related to space and time, even when one is interested only in setting up the MKS units.)

I believe this emphasis on flexibility of choice is behind the various quotations in the article that support separation of the ideas of RF and CS. On this list of citations are: Brews ohare (talk) 17:36, 1 August 2008 (UTC)
 * 1) John D Norton: General covariance and the foundations of general relativity;
 * 1) John D Norton: General covariance and the foundations of general relativity;
 * 1) John D Norton: General covariance and the foundations of general relativity;
 * 1) John D Norton: General covariance and the foundations of general relativity;
 * 1) John D Norton: General covariance and the foundations of general relativity;


 * Thank you for this list of references. I will read them all before editing. Paolo.dL (talk) 21:30, 16 August 2008 (UTC)

Beyond 3+1 space coordinate systems
If one has a much different axe to grind, something even more unusual might be appropriate, which could involve a CS in a sense more general than a spacetime 4-space coordinate system. At the simplest level, one may wish to choose a subspace of a four-space coordinate system to match the problem, for example, an arc-length description based on a trajectory, or an oblate spheroid to describe motions on the surface of the Earth. In a system of N particles, one might use a configuration space or phase space of many dimensions. From a different angle, one might choose a modal description based on functions of four-space that match symmetry of the system, like molecular orbitals. As a more complex example, in describing a field, one sets up a Hamiltonian description and quantizes the field. This Hamiltonian uses generalized coordinates, a many-dimensional representation, dependent on spacetime, but not a 4-space coordinate system. Likewise for a robot design based upon description of a kinematic chain, a many-dimensional space is used, related to spacetime but not a 4-space.

In some cases, specification of the 4-space coordinate system may not even be necessary: for example, one may need only to know the symmetry operations that describe the system. In this connection, one might postulate a symmetry, say gauge invariance, and then use predictions based on that assumption to test whether the symmetry exists. A beautiful exposition along these lines are H. Weyl's Space, Time, Matter and The Theory of Groups and Quantum Mechanics. Brews ohare (talk) 17:19, 1 August 2008 (UTC)

Attempt to summarize discussion about step 10
In sum, Please let me know if you agree about this short summary. Paolo.dL (talk) 21:30, 16 August 2008 (UTC)
 * In mathematics, a CS is not necessarily used to measure motion. Hence, it is not necessarily characterized by a state of motion relative to some object or set of points. It does not even imply the selection of measurement units (in physics, when we measure motion, we need to define measurement units for length and time).
 * Some kinds of CS frequently used in physics - namely those used by an observer to measure the motion of objects - must be stationary relative to the observer and the RF. In other words, they must move with the observer and the RF; they are characterized by the state of motion of the observer and the RF (see point 9).
 * Thus, even when you separate the concepts of CS and RF, the definition of such a CS implies the definition of a RF. Namely, such a CS cannot be defined unless a RF is also defined. In other words, you need to choose the RF before choosing such a CS.
 * Hi Paolo: I'd say I am close to agreement here. I am of the view that defining a CS is an option of the observer, but is not demanded of the observer, who may elect to use a coordinate-system-free approach to observation. (For example, the observer might decide to limit observations to explosions or collisions, or to employ only vector analysis.) If the option to select a CS is considered by the observer, there are a variety of possible CS's to choose from. So I do take the view that the observer and their RF comes first. Hope I am not being too cautious here. Brews ohare (talk) 00:01, 18 August 2008 (UTC)

Ok, then I guess you would like to add a fourth point: This does not make sense to me. How can you do without scalar components (i.e. coordinates) if you analyze explosions, collisions or vectors? You can geometrically analyze positions and displacements (i.e. geometrical variables). Vector sum can be done geometrically (but with huge difficulties in 3D). That's all you can do without scalar components. Doing cross and dot products, differentiation and integration without scalar components would be masochistic. If you don't use a CS to obtain scalar components, how can you store the results of your observations? How can you determine velocity and acceleration? how can you determine linear momentum to study explosions and collisions? Also: is this possibility practically relevant? Or just a theoretical possibility without practical applications? In other words, if a CS-free approach is possible, is it also preferable for some practical purpose? Is it also useful?
 * A CS-free approach is possible, in some special circumstances. An observer does not always need to use a CS for observations.

However, your point is perfectly compatible with the three points in my summary. Do we agree at least on those three points? Paolo.dL (talk) 12:43, 18 August 2008 (UTC)


 * I agree with the first two points. Let's see where you are going with point 3. Brews ohare (talk) 14:53, 18 August 2008 (UTC)


 * It is quite difficult to understand you. About point 3, you wrote above that "There are two choices: first the state of motion, and second the choice of coordinate system in that state of motion. I think we agreed about this already" (25 July). So, how can you disagree with point 3? And how can you ignore my questions about point 4, which you introduced yourself? I believe you owe me an explanation. If you are too busy, just wait until you have time for answering properly. Paolo.dL (talk) 22:07, 18 August 2008 (UTC)

Rewrite
A preamble section has been added, and the introductory line extended to include all possibilities. Please take a look and offer comments. Brews ohare (talk) 15:10, 25 July 2008 (UTC)

My comments will come as soon as we finish the above discussion. If you don't mind, we need to build agreement about logic foundations based on which we will be able to effectively discuss the introduction and then the first section. Paolo.dL (talk) 20:08, 25 July 2008 (UTC)

Practical application for Reference frame -- in emergencies
I listened to a newscast which highlighted a practical application for the Reference Frame (what to do when your Reference Frame undergoes severe acceleration or experiences a change of state, especially sinking underwater)

You the observer are in your car, moving fast, when you go off the road into a canal, say. You will not be able to open your doors until the water pressure equalizes inside and outside (the car or airplane has completely filled with water). Assuming you have the presence of mind to detect this, you can then open the door.

But first you need to re-orient yourself with the Reference Frame (the car's interior). So the experts recommend that you keep yourself buckled in until you can figure out where you are in the car (upside down, etc.). You might do this by holding on to the steering wheel or holding on the the car door handle until you can get the door to work, or until you can break open the window (there are tools for doing this; corners are the weak points, so stress a corner first, in order to start the shattering process). Car door and window switches are designed to work even underwater for a short time, according to the newscast I heard today.

If you lose your frame of reference you may waste valuable time simply trying to orient yourself within the frame of reference, which may have tumbled, gone underwater, set aflame, etc. You can save your life by opening a window in a drowning car as soon as possible, but first you have to know where the window is.

The same idea applies for airplanes: orient yourself for the exit, within 5 rows for maximum survivability. --Ancheta Wis (talk) 01:46, 16 January 2009 (UTC)

In Psychology
Frame of reference is not only a concept in physics. Another definition is “A set of standards, beliefs, or assumptions governing perceptual or logical evaluation or social behaviour” (Oxford English Dictionary, 2005b). The application of this definition applies strongly to psychology and describing intuitive thinking. This warrants inclusion in the article, perhaps even its own separate article. Mamyles (talk) 05:53, 9 May 2010 (UTC)

A Reference Frame is not a coordinate system
I regard this article as misleading and inaccurate. I believe it propagates a sloppy way of thinking about reference frames and coordinate systems which ultimately leads to confusion about the message of general relativity. Whereas a coordinate system is R^n, and is essentially a mathematical object which can be discussed without reference to matter, the word "frame" refers to matter. A reference frame refers specifically to the matter (and perhaps also the methodology) from which a coordinate system may be defined. E.g. the "frame of the fixed stars", the "Earth-centered, Earth-fixed (ECEF) frame", Earth-centered inertial frame, International Celestial Reference Frame. In fact it is not even essential to define coordinates from a reference frame, as is illustrated by the above entry which refers to a car's interior as a reference frame.

d’Inverno defines a reference frame as a clock, a ruler, and coordinate axes, whereas Rindler describes a reference frame as a “conventional standard” and discusses the attachment of a frame to definite matter, such as the Earth or the fixed stars, while Misner, Thorne and Wheeler define proper reference frame as a Minkowski coordinate system with a given clock at the origin. In each case, reference matter is an essential part of the definition.

Although I agree that many treatments are somewhat sloppy and do not make this distinction clear, I think it would be more helpful if the Wikipedia article were to stick firmly to the strict notion that a reference frame refers to reference matter. RQG (talk) 07:01, 29 May 2011 (UTC)