Talk:Inertial frame of reference/Archive 2

Versions of definition
The article intro has been revised several times. I believe the present version has several advantages over one based upon an older Newtonian version:
 * 1) It is consistent with special relativity
 * 2) It very adequately describes the Newtonian version, which is a special case.
 * 3) It is historically more up to date and more consistent with today's usage
 * 4) It fits in with the rest of the article much better than a Newtonian version. In particular, the modern view (as expressed in the quote from Arnol'd) is related to the absence of fictitious forces as the best criterion.

In any event the focus should be upon transformation properties and families of frames, not upon the Newtonian view of "free motion" that runs into some difficulties concerning how to insure an experimental situation where the only forces present are real, and are adequately accounted for. These issues are discussed in the article. Brews ohare (talk) 21:35, 19 August 2008 (UTC)
 * I don't have any problem with that, but:
 * the first sentence should make the context clear, i.e., begin with "In physics, an inertial frame of reference is";
 * "Inertial frames of reference share the same and simplest Laws of Physics ." (The  tag has been deprecated for years; why should we indeed use oblique Times Roman? also, neither laws nor physics are proper nouns, bur apart that...) physical laws are the same no matter what; God/nature/call_it_whatever_you_like doesn't give a damn about which coordinate system you use; it's the (mathematical) form of physical laws which is simplest in inertial frames;
 * "As a result of this requirement": what requirement? that the laws of physics be the same? (The same as what?) It seems somewhat vague to me...
 * "no fictitious forces occur in inertial frames; that is, no forces occur that can be made simply to vanish by changing frames"; is that supposed to be a definition of inertial force? I can make a non-fictitious force vanish by choosing a suitably perverse reference frame; for example I can make the electrical force on an electron in an electric field of 1 eV/m vanish by using a reference frame accelerating at 1 m/s2. So that isn't a definition good enough. If, instead, you define a fictitious force as a force which is due to a non-inertial reference frame, defining an inertial frame as one without fictitious forces is a circular definition. Or you can define a fictitious force as one which isn't due to an interation with something else, and toghether with F = ma you obtain that this is equivalent to saying that in an inertial frame a body which isn't interacted upon doesn't accelerate, which is the very definition you object to.
 * But I'm trying a compromise solution. -- A r m y 1 9 8 7 ! ! 23:45, 19 August 2008 (UTC)
 * (Note that, with the definition in the current version, "inertial" does or does not mean "free-falling" depending on whether fundamental interactions do or do not include gravitation; this is consistent with general relativity and the Standard Model.) -- A r m y 1 9 8 7 ! ! 00:09, 20 August 2008 (UTC)
 * I'd suggest dropping the following two sentences, which seem to be covered very well later in the article, and are something of a grab-bag of disjointed thoughts:
 * In non-inertial frames of reference, the form of physical laws is complicated by the appearance of fictitious forces, that is forces which are not due to fundamental interactions, but merely reflect the acceleration of the reference frame. In inertial frames, Newton's law of inertia holds, stating that a body which does not interact with other bodies does not accelerate.
 * What do you think? Brews ohare (talk) 01:28, 20 August 2008 (UTC)
 * Yes, now that I read them again they're awkward, but I think that a minimum of "historical" perspective should be kept in the lead, as the reader might otherwise be puzzled on why they are called "inertial", or fail to recognize a concept they already knew... But yes, for now I'm removing them, until someone comes up with a better way to express that. -- A r m y 1 9 8 7 ! ! 10:51, 20 August 2008 (UTC)
 * As for the "which seem to be covered very well later in the article" issue, the lead section ideally should summarize the whole article, so that a reader can have a general idea of a subject by just reading the lead: see WP:LEAD. So there is nothing wrong in introducing in the lead concepts which are discussed more in depth later in the article. -- A r m y 1 9 8 7 ! ! 11:01, 20 August 2008 (UTC)
 * I find the opening paragraph rather non-definitive. It needs to state precisely what an IRF is i.e. "a set of axis whose directions do not change and whose origin is not accelerating". The opening sentence itself uses the phrase 'inertial frame of reference' to describe an inertial frame of reference. Green0eggs (talk) 23:13, 30 March 2009 (UTC)

I agree with Green0eggs. The intro is not very good at introducing. Move the bulk of it down below. Reading this I have no idea what IFR means. 209.90.238.118 (talk) 00:55, 1 May 2009 (UTC)

Consider the basic definition of this article: "an inertial frame of reference is a member of the subset of reference frames with the property that every physical law takes the same form in each such frame" -Let A:R^4->R^4 -any automorphism of R^4 -Let "A-frame of reference" is any frame of reference A*X where X -any "inertial frame of reference" -Then, evidently "every physical law takes the same form in each such frame" (in each A-frame) So, this definition of IFR isn't correct...

Consider the "Newton's definition": "An inertial frame of reference is one in which the motion of a particle not subject to forces is in a straight line at constant speed." -It's evidently that the set of such FR is closed relatively any linear transformations! -So, this definition of IFR isn't correct also..

IMHO, The right definition of IFR sounds so: - The space-time is supplied with some family of frames of reference called "inertial frames of reference". This family of FR is minimally-closed (inreducible-closed) relatively Lorenz's (Poincare's) transformations.

In other words, the definition of IFR can't be "operational", it must be "axiomatic" Pavel Suvorov (talk) 10:04, 11 November 2009 (UTC)

Quotations
Why so many quotes in this page??? They should be moved to wikiquote or wikiversity .In the present form,the article can't convey the physical idea of inertial frames to a begginer --sruthy (talk) 09:42, 26 October 2008 (UTC)
 * This is ridiculously out of hand. 67.158.4.171 (talk) 06:57, 1 December 2008 (UTC)
 * I'm going to have to agree here. I came to this page to find a relatively simple definition, and I can't even read the article because I'm blown away by a lot of quotations. Moreover, the intro doesn't even have a laymens' terms definition. Wizard191 (talk) 03:36, 9 December 2008 (UTC)

The introduction is now two isolated sentences. I hope it is understandable.

The quotations are an historical result of continued argument on this page that could be settled only by citing the opposing views into oblivion. One could remove them, but history shows that there is a lot of misunderstanding in this area, and people will stick to their guns unless authoritative background gets the point across and makes it clear that the article's view of things is more than off-the-cuff opinion of a few cranks. These quotes are now in a "background" section. Brews ohare (talk) 06:26, 11 December 2008 (UTC)

I can understand that a series of quotations can be off-putting, but I don't think the article is hard to follow if you actually read it. Brews ohare (talk) 06:38, 11 December 2008 (UTC)
 * Thank you for removing the quotes from the intro, however I still have two problems:
 * The introduction is still a little tough to understand for those who don't have a background in physics.
 * Why can't some of these quotations be moved to the footnotes? This is common practice. You can still back up your POV/text, but then you don't have to clutter the article with disconcerting quotations every paragraph, which, IMO, does impact readability.
 * As far as the technical template goes, I feel that the whole article is geared towards physicists with PhD's. There's nothing wrong with having very technical information on a very technical topic like this, however it also needs to be accessible to non-technical people. I propose that at least a section be created at the beginning of the article to layout the idea in laymen's terms. See general relativity and introduction to general relativity for a great example. Wizard191 (talk) 16:32, 12 December 2008 (UTC)


 * I removed the templates having had no response from you about the revisions. Figured you were either satisfied, or had lost interest.
 * I am at a loss to see what can be clearer than the lead sentence. It does not define a "frame of reference" but does link to the article where this info is found. Beyond that, it points out what inertial frames are, and what more can be said.? Any suggestions?
 * As for the quotes, they all are relevant. They are clear, and they are authoritative. If a reader isn't interested they can skip the section and go on to Newton's frame. Maybe you object to the quote there from Einstein? Brews ohare (talk) 18:26, 12 December 2008 (UTC)


 * I think your latest rev of the intro is the best so far. However, I'm confused by the following two sentences:
 * "In an inertial frame of reference, unlike others, all physical laws have the same form and also have their simplest form. There are many inertial frames, all moving relative to each other at a constant velocity, without relative acceleration."
 * What does "same form" mean in the first sentence? I don't see how the second sentence fits into the rest of the introduction.
 * As for the quotes, I'm not objecting to the content of any of them (to be honest I haven't read but a couple). I'm contesting them on the grounds of readability and layout. If the quotes don't have to be read by the reader, as you stated above, then that means they aren't there to convey anything fundamental, but rather to backup points in the surrounding text. As such, they should be converted into footnotes, because that's what footnotes are for. This allows the reader to analyze the footnotes if he/she wants to, but doesn't impact readability for those who don't need it from the physicists' mouth. Wizard191 (talk) 19:06, 12 December 2008 (UTC)


 * I added two more paragraphs before reading your remarks.


 * Let me take a shot at your comments. The "same form" question is toughie, I'd say. One answer is that in an inertial frame, fictitious forces aren't needed, so the laws are simple, and that remains true on switching to another inertial frame. In contrast, on switching (e.g.) to a rotational frame, suddenly centrifugal and Coriolis forces crop up. The key issue is that it is the transformation between frames that has to be watched: transforming between inertial frames never introduces forces that were not in the original frame. This emphasis on what happens when frames are switched is why the sentence on there being a set of inertial frames is put in there.


 * I'd not say the quotes do not add anything fundamental. I'd say rather that they delve into some deep water that is probably not what the casual reader wants to plunge into. However, I'd also say that the casual reader should not dictate what is in the article. Putting this stuff into footnotes places it in a subsidiary role that I find doesn't do it justice. Brews ohare (talk) 19:25, 12 December 2008 (UTC)
 * We are getting there, but I really thing we need to do something about the "same form" sentence. I understand what you are saying now, but I don't think the phrase "same form" conveys that message readily (when I first read it, I thought you were saying that all of the equations of took on the same algebraic form, which seemed impossible). If we fix that then the sentence after it will probably make more sense.
 * As for the quotes, I see what you are saying about them taking the back seat. Is there anyway that we can change some of them into inline quotes, instead of putting them in quote boxes. Possibly the smaller quotes? Wizard191 (talk) 14:25, 13 December 2008 (UTC)


 * I've done further rewrite and added citations. As far as more on the "simpler" form, I could add a mathematical example showing the transformation leading to Coriolis force, for example, but for an introduction that seems a bit too much detail. Some of the intro citations are simply to show that the notion of simpler form is supported. Maybe that is sufficient for an intro? Brews ohare (talk) 22:25, 13 December 2008 (UTC)
 * The introduction now is more like a summary of the entire article, and sketches material in other articles like fictitious force previously only linked. Is this intro an improvement? Brews ohare (talk) 17:40, 14 December 2008 (UTC)
 * Most definitely the intro is better. I attempted to clarify that one sentence, let me know what you think. Wizard191 (talk) 00:16, 15 December 2008 (UTC)


 * I retained your change, but replaced the general discussion of real vs. fictitious forces with an example. Something concrete, I thought, might get the point across more easily, although it requires either a bit of mathematical background or a willingness to take things on faith. Brews ohare (talk) 16:43, 15 December 2008 (UTC)
 * I like the example, but I don't like all of the equations. Can you just replace the second two equations with text to get your point across? I'm afraid your 3rd equation is going to scare people off. It scared me at first, but after reading the associated text it made sense. Wizard191 (talk) 16:59, 15 December 2008 (UTC)


 * Dropping the equations puts us back where things were without the example. I rearranged things a bit to advise the reader not to get too involved in the math, more or less the way an experienced reader would handle matters on a first reading. Brews ohare (talk) 18:03, 15 December 2008 (UTC)
 * Fair enough. I'll concede that point to you. I've removed the intro temp as the intro is much better now. Thanks for all your hard work! Wizard191 (talk) 18:19, 15 December 2008 (UTC)


 * Thanks for provoking revision; frankly, I thought it was pretty good to start with, but a little pushing convinced me otherwise. Brews ohare (talk) 19:19, 15 December 2008 (UTC)

A flood of micro-edits
Hello Brews ohare,

I noticed the style of editing that you used when editing the inertial frame of reference article. Over the course of a working session there are dozens of micro-edits, often only a minute apart.

Can you please save up your edits over the course of a working session, and then upload them in a single go? Uploading dozens of micro-edits has a disadvantage: the version history becomes cluttered. When I revisit an article I like to go through the version history, to see which editors have made which edits. A cluttered version history makes that very time-consuming. Can you please edit in such a way that the version history remains overseeable and accessible. Cleonis | Talk 09:47, 24 December 2008 (UTC)

The Euler force
Whereas none of the "fictitious forces" arises in the case of Ω = 0, The Euler force also vanishes when dΩ/dt = 0

By convention, the expression 'rotating observer' refers to rotation with uniform angular velocity. If you want to discuss the case of a 'rotating observer' that is also undergoing angular acceleration then you must declare so explicitly.

It should be stated explicitly that the Euler term arises only in the case of angular acceleration of the coordinate system that you are transforming to. Cleonis | Talk 10:51, 24 December 2008 (UTC)

Inertia as the prime organizing principle for dynamics understanding
In the opening section of this article it is claimed:


 * The laws of physics change from frame to frame

I want to examine that claim in the light of the case that is depicted in the animation: the apparent retrograde motion of Mars. Of course, Newtonian dynamics and general relativity describe the nature of gravitational interaction very differently. But they do have that fundamental concept in common: gravitational interaction.



It's interesting, I think, to state explicitly why we prefer the Newtonian point of view over the pre-Newtonian point of view. Compared to the Newtonian point of view the pre-Newtonian view is disjointed and incoherent. Newton assumed universal inertia and the universal law of gravity. By taking inertia as the organizing principle for dynamics understanding a coherent and tight-knit framework of thought is achieved

It is straightforward to compute the motion of Mars relative to the Earth. The computation can be executed in any order you like. You can first compute the motion relative to a Sun-centered coordinate system, and then perform a coordinate transformation on the computed trajectories, or you can perform all of the computation in terms of motion relative to an Earth-centered coordinate system. When performing the computation in an Earth-centered coordinate system you add appropriate acceleration terms to the equations of motion. Both calculation strategies yield the same result; they are equivalent.

Obviously, the laws of motion themselves aren't any different when you are using an Earth-centered coordinate system; all you do is transform. Transforming from one coordinate system to another is a perfectly superficial procedure, it's just as superficial as converting form miles to kilometers, it has no bearing on the physics understanding.

Equivalence class of inertial coordinate systems

The laws of motion are valid for motion relative to any member of the equivalence class of inertial coordinate systems. That is too long an expression, I will use as physics shorthand: the laws of motion are valid in an inertial coordinate system. That is the physics shorthand, the intention is always to refer to the equivalence class.


 * $$\boldsymbol F' = \boldsymbol F - 2 m \boldsymbol\Omega \times \mathbf{v}_{B} - m \boldsymbol\Omega \times (\boldsymbol\Omega \times  \mathbf{x}_B )  - m \frac{d \boldsymbol\Omega}{dt} \times \mathbf{x}_B \, $$

The centrifugal term, the coriolis term and the Euler term all contain Ω, the rotation rate of the non-inertial coordinate system with respect to the inertial coordinate system. The point is: all laws of motion refer to the equivalence class of inertial coordinate systems. There are no exceptions to this rule: all laws of motion refer to the equivalence class of inertial coordinate systems.

Conclusions: - The laws of motion are the same from frame to frame; all that is different from frame to frame is the notation of the laws of motion. - The significance of the equivalence class of inertial coordinates systems lies in the fact that in modern physics (Newtonian physics and relativistic physics) inertia is the prime organizing principle of our dynamics understanding. Cleonis | Talk 12:08, 24 December 2008 (UTC)

=
==============

It´s never clear who moves. Who or what moves and what or who not can not be determined absolutely. Neither can it be proved nor disproved.

91.19.40.170 (talk) 12:25, 1 March 2009 (UTC)

The laws of motion are the same from frame to frame
This statement needs clarification. In an inertial frame Newton's second law has real forces in it that every observer agrees upon whatever frame they are in. In a noninertial frame Newton's second law has extra fictitious forces in it. Just what these extra forces are varies from one noninertial frame to another, depending upon its peculiar acceleration. If we compare these two forms of Newton's second law, one form has "extra" force terms. I'd say it is fair to say that the laws of motion are therefore different in different noninertial frames. However, of course, Newton's law in general terms as force=mass x acceleration is valid in both frames. Brews ohare (talk) 14:33, 6 March 2009 (UTC)


 * I emphasize the following: all laws of motion refer to the equivalence class of inertial frames of reference.


 * 1) When motion is mapped in an inertial coordinate system then the laws of motion as they are notated refer directly to the equivalence class of inertial coordinate systems.
 * 2) When motion is mapped in a non-inertial coordinate system, such as a rotating coordinate system, then the extra terms (centrifugal term, Coriolis term, Euler term), each refer to the equivalence class of inertial coordinate systems.


 * A) The term that represents the centrifugal force, &Omega;x&Omega;xr, contains &Omega;, the rotation rate of the non-inertial coordinate sytem with respect to the inertial coordinate system.
 * B) The term that represents the coriolis force, 2m&Omega;v, contains &Omega;, the rotation rate of the non-inertial coordinate system with respect to the inertial coordinate system.
 * C) The term that represents the Euler force, contains d(&Omega;)/dt. Like the other two, the Euler term is determined by the rotation rate of the non-inertial coordinate system with respect to the inertial coordinate system.


 * It is clear what the common factor is: both when mapping motion an inertial coordinate system and when mapping motion in a non-inertial coordinate system the common reference of the equations is the inertial coordinate system. --Cleonis | Talk 19:11, 6 March 2009 (UTC)

Versions of definition 2
I copy and paste from above.
 * I find the opening paragraph rather non-definitive. It needs to state precisely what an IRF is i.e. "a set of axis whose directions do not change and whose origin is not accelerating". The opening sentence itself uses the phrase 'inertial frame of reference' to describe an inertial frame of reference. Green0eggs (talk) 23:13, 30 March 2009 (UTC)

Hi Green0eggs,

you suggest that the criterium given in the opening paragraph is circular reasoning. However, that is not the case. The opening paragraph states that a clear distinction can be made within the set of all frames of reference. On one hand inertial frames of reference and on the other hand non-inertial frames. The criterium is that when motion is mapped in a non-inertial frame additional terms are needed in the equation of motion (often referred to as fictitious forces), in order to make the equations work. When motion is mapped in an inertial frame no such additional terms are needed. (Also, the members of the set of inertial frames of reference are interconnected: none of the members of the set rotates relative to the set of inertial frames, and each member of set is either stationary relative to other members, or has a uniform velocity relative to other members of the set.)

The above demarcation criterium is an operational criterium. Which are the applicable equations of motion? Answer, equations of motion that work are applicable. When motion is mapped in an inertial frame then the properties of inertia are embodied by the coordinate system itself: when motion is mapped in an inertial frame objects will tend to move along straight lines of the very coordinate system.

This operational way of defining the concept of inertial frame of reference is the only way the concept of inertial frame of reference can be defined at all.

Finally, let me point out that the description that you propose is insufficiently defined: "a set of axis whose directions do not change and whose origin is not accelerating" Not accelerating with respect to what? --Cleonis | Talk 21:01, 1 April 2009 (UTC)

What does "same form" mean?
The first paragraph of the current article speaks of an inertial reference frame in the singular and implies that the set of such frames have the property that "each physical law portrays itself in the same form in every inertial frame". I did not see any subsequent clarification of what "same form" means in the article.

The example of a rotating frame being non-inertial in Newtonian mechanics seems to disqualify such frames on the basis that they introduce "ficticious forces". My guess about the mathematical meaning of these remarks is that when we say F = ma should keep the "same form" in inertial frames, we want each individual term of the equation to be invariant when we transform coordinates to the system used by an observer in an inertial frame. But the term "invariant" needs clarification. As a set of 3 coordinates the vector F does not remain invariant in all inertial frames. It remains invariant as a "geometric object". That type of invariance can be defined by declaring what mathematical functions ( e.g. length of the vector) associated with F must remain invariant.

Tashiro (talk) 16:55, 17 August 2009 (UTC)

Yes, you're correct that this language is not very clear. The true statement is that the lagrangian density from which the equations of motion of the theory are derived should be a scalar under Lorentz transformations, which in turn implies that the action itself is completely invariant. Waleswatcher (talk) 15:00, 2 February 2010 (UTC)

First paragraph and SR
The first (and only truly necessary) postulate of special relativity is that the laws of physics are identical in all inertial reference frames. That assumption, together with the laws themselves (for example Maxwell's equations, which fix the speed of light to be c regardless of the velocity of the emitter), is all that is necessary to derive the interesting and bizarre properties of SR. To be a little more precise, it is invariance of physical law under Lorentz transformations that is the key element, but that's both too mathematical and too specific for an introduction to this article. I agree that the way the article is phrased now it _sounds_ empty, but it most certainly is not - SR has many deep and profound consequences.

As for fictitious forces, they should certainly be _mentioned_ and discussed, but their absence does not and cannot _define_ inertial frames. Modern physics is not formulated in terms of Newtonian forces, it's formulated in terms of fundamental particle interactions. Those interactions are Lorentz invariant, i.e. they look the same in all inertial frames of flat Minkowski space, but fictitious forces are not part of that language and hence cannot be used as a definition.

The language as it is now can probably be improved, and I support such changes. But please bear the above in mind, or discuss it here before making major changes again. Waleswatcher (talk) 14:51, 2 February 2010 (UTC)


 * Two quick things, if you say:
 * "The first (and only truly necessary) postulate of special relativity is that the laws of physics are identical in all inertial reference frames"
 * 1) The point is that SR is a scientific theory; it is an experimentally falsifiable theory. We can experimentally check Lorentz invariance.  If you instead DEFINE an inertial frame by the properties that SR needs to be true,  then SR is true by definition .


 * Basically, instead of being able to test for Lorentz invariance, if Lorentz invariance was found to be violated on some energy scale, then according to your definition, SR would still be true (since it is now a tautology) but the things we used to call inertial frames are no longer inertial frames. Do you better understand the problem here?


 * To summarize, SR postulates details about inertial frames. This is separate from the definition of what an inertial frame is.


 * 2) I would disagree with your statement. Take an inertial coordinate system.  Do a parity transformation.  The new coordinate system is still an inertial coordinate system, don't you agree?  However the laws of physics are NOT the same in this inertial coordinate system.  So the way you are defining SR makes it false by experimental evidence.


 * The base problem with your wording of SR is the very problem we are having here. It is difficult to precisely define an inertial coordinate system.  In fact, I've seen more than one physics textbook that explicitly avoid the discussion all together, noting some issues in defining them, and instead note properties of inertial coordinate systems and how they are related.  Also, this is why the modern statement of SR is usually given as: SR requires the physical laws to have Poincare symmetry.  Not only have I heard physicists use this definition directly in discussions, but advanced textbooks (often quantum field theory, etc.) often take this as the definition and starting point for enforcing a theory to be "relativistic".


 * I looked through the history and saw a lot of definitions. Many are close but faulty, and many are well backed by quotes, but if we avoid "fictitious forces" I think the closest could be paraphrased as:
 * An inertial coordinate system is one which describes space and time homogeneously and isotropically.


 * I feel this maintains the essence of what Newton and Galileo expected, and is still correct with modern expectations. The "essence" of what SR adds here then is the amazing realization that there are infinitely many such frames (instead of the one "absolute" inertial frame, as Newton felt there would only be one "frame" in which we'd be at "rest" with respect to "space" .. ie only one frame in which space is described homogeneously and isotropically).


 * I realize from your previous comments that you may agree with these properties, but do not feel they are sufficient to define an inertial frame. Please help discussion move forward by answering the following:  Let's agree, by definition, that there exists some inertial coordinate system (ct,x,y,z) ... please define a new coordinate system (ct',x',y',z') via a coordinate transformation from the unprimed frame which is a counter example to the proposed definition.  ie. space and time are described homogeneously and isotropically, yet it is not an inertial coordinate system.  Only with an explicit example can we understand what your objection is here.


 * 98.222.50.164 (talk) 08:15, 3 February 2010 (UTC)

Wow, I think I learned more about inertial frames by reading the discussion page than the article page. I agree it appears really tough to define a concept precisely that we all seem to intuitively get some concept of. Maybe being more frank in the article would be helpful. For example, note some major properties in the introduction (sort of like introducing, not defining, an apple by describing its properties), then in the very first part of the article be frank that it is difficult to define precisely. Then explain why with various example definitions and how they may subtly miss the point. Such a discussion can teach a lot (as reading the discussion here helped me understand a lot more). The article is already broken into sections of different properties, and the changes to the beginning just seem to keep trying to choose one and make it the defining property. So I think my suggestion would fit well and could help stabalize the article.

I don't feel qualified to edit, and rearrange, this article, but thought I'd give insight from someone who came to the article to learn. Thanks. 130.126.15.40 (talk) 18:20, 3 February 2010 (UTC)

It certainly IS difficult to define precisely and without any circularity. For one thing, according to general relativity there are no truly inertial frames, and there is no distinction between real and fictitious forces. In flat Minkowski space, i.e. with gravity turned off so that GR->SR, inertial frames can be defined as the set of coordinate systems related to the standard flat coodinates by Poincare transformations. In slightly more plain English, they are the set of frames related to standard rectilinear coordinates by rotations, translations, and Lorentz boosts.

But how to define them in the intro to this article? Let me first respond to 98.222.50.164 and then make a suggestion. Yes, of course Lorentz invariance is experimentally testable. A violation of it would indicate that the laws of physics are not invariant under Lorentz transformations. The article says essentially that in the second sentence, where it states " In flat spacetimes, all inertial frames are in a state of constant, uniform motion with respect to one another." So the definition as given in the article is falsifiable - if frames related by constant uniform motion do not exhibit identical laws of physics, the statements in the first two sentences of the article are wrong. There is a problem there in that two NON-inertial frames related by uniform motion do not necessarily have the same laws of physics... but the sentence can perhaps be re-worded to avoid that annoyance.

About homogeneity and isotropy. The article before I edited it said something different than what you say above. It said "This requires space to be described isotropically, and time homogeneously." That doesn't suffice, because it doesn't say space must be described homogeneously (which it needs to be - if you want to define an accelerating frame or a non-isotropic frame to be non-inertial, then spherical coordinates aren't inertial either). The language in your comment above is "an inertial coordinate system is one which describes space and time homogeneously and isotropically". That's a bit better, but it still has a major problem - it doesn't apply to Minkowski space in standard coordinates. Space and time are distinguished in the Minkowski metric, they are not isotropic (inside the lightcone of a point is physically different from outside the lightcone). You could say "describes space homogeneously and isotropically, and time homogeneously, but it's still not quite good enough. For example de Sitter space is spatially homogeneous and isotropic and can be written in coordinates that are homogeneous in time, but it's not inertial.

About parity - that's a bit of a quibble. The article as currently written does not necessarily include parity transformed frames as inertial (because they differ from the starting set by more than just constant motion). Anyway without going into a discussion of the mathematics of the Lorentz group it's going to be hard to explain that very well.

Still... I'm not saying the current language is perfect, far from it. So let me make a suggestion - perhaps we should just say that inertial frames are the set of coordinate systems with metric -dt^2 + dx^2 + ...? We could describe that in English by saying that they are the set of coordinate systems related to each other and to "standard Cartesian coordinates" (or some language like that) by rotations, translations, and constant velocity motions. Then we could add that the laws of physics take the same form in all such coordinates systems (with an exception for improper Lorentz transforms like parity). What do you think? Waleswatcher (talk) 22:47, 3 February 2010 (UTC)


 * One possible approach is to define an inertial frame as one in which Newton's first law holds, i.e. relative to which all free-falling particles move at constant velocity. Of course, you still need to define what a "free-falling particle" is... --  Dr Greg   talk  23:26, 3 February 2010 (UTC)

Hmmm... your point about de Sitter space is pretty good. However there spacetime is not flat, and the coordinate system you are referring to sounds like the flat slicing in which case it IS the local inertial frame about the origin (and a local inertial frame is the best we can do in curved spacetime). So it seems like that definition is headed in the right direction. But yes, I see what you mean, that definition would claim that coordinate system is a global inertial frame, when it "clearly" is not.

I like your metric idea, but I'm not sure how to describe that in plain english well enough for the introduction. If you have an idea how to word it, please do change the current introduction/"definition".

Dr. Greg, I agree Newton's first law is an important property, but unfortunately any linear transformation from an inertial coordinate system will preserve this property. So we can't define an inertial frame as you suggested there. Hopefully Waleswatcher's idea will pan out, because I'm not sure I have any other ideas myself. I've been asking physic students all day, and no one has a good precise definition. It's so simple, yet so hard to define! 98.222.50.164 (talk) 08:46, 4 February 2010 (UTC)

Merge discussion
The page Inertial space appears to be on the same subject as this page, although with a different emphasis. --RockMagnetist (talk) 21:29, 25 September 2010 (UTC)

Still too technical?
I see that the "technical" tag has been around for a couple of years. Does it still apply? I would say yes, as far as the introduction goes. Someone who understands the discussion of rotation probably already knows what a rotating reference frame is. A perfect example of what is needed in the introduction can be seen in Fictitious_forces. Anyone can relate to the feeling of being pushed back in their seat! --RockMagnetist (talk) 18:57, 14 October 2010 (UTC)

Sentence taken out of context
User twice took a statement out of its context:  and. I undid the move twice: and. Looking at the statement following the moved statement ("By contrast, in a non-inertial reference frame...") and at the logical flow, the move cripples the lead by effectively orphaning the sentence. DVdm (talk) 20:42, 14 October 2010 (UTC)


 * Just above this section there is a question: is this article plain and intelligible? So I ask: If a friend of yours asked to you: "What is an inertial frame", would you answer with the first lines of this article ("describe time homogeneously... fictitious forces...same handedness")? Or would you say: it is a frame which does not move, or has a uniform, rectilinear motion with respect to Earth, approximately, and more precisely with respect to stars and all other inertial frames?


 * For as concerns the out of context, the phrase you say is in direct contrast with the one I moved says "by contrast, in a non-inertial reference frame..."; does not say "in a frame that does not move uniformly...". And, in the following, it is simply said the laws depend on the frame, with fictiyious forces, etc. Only after two or three more lines acceleration is referred to. So also the formal reason for letting the phrase to stay there does not sussist. But, if you think the phrase is orphaned, I will adjust it by adding other words.


 * Matters must be told with simplicity in their concreteness, and with a logical line: speaking of fictitious forces before having explained which kind of frames are able to "describe time homogeneously and space homogeneously, isotropically, and in a time independent manner" is not logically consistent. And I have rarely seen a more abstract definition.--GianniG46 (talk) 21:46, 14 October 2010 (UTC)


 * I think the way to have a logical flow is to separate the motion of reference frames from the implications for physical laws. I have rewritten the lead section with this in mind. --RockMagnetist (talk) 23:08, 14 October 2010 (UTC)

I definitely agree that the lead section was to be rewritten. Mine was just a way to amend it a little bit with minimum work and friction. But, why "an acceleration that cannot be detected from within the frame of reference"? This would include an orbiting capsule and in general free-falling bodies, in which there is only a virtually undetectable tidal effect to signal that they are not inertial. Perhaps we should start by the classical definition, with "fixed stars" et cetera, and then refine by discussing relativity and other modern adjustments--GianniG46 (talk) 07:14, 15 October 2010 (UTC)


 * I think you're right about separating the theories. It makes the exposition much more straightforward. I don't think it's necessary to get into "fixed stars", though - just a simple statement about acceleration will do. After all, this is just the lead section, and readers shouldn't be scared away by deep philosophical questions. --RockMagnetist (talk) 14:05, 15 October 2010 (UTC)


 * Ok, but "accelerating" needs the contestual specification of with respect to what. And saying "with respect to one another" needs the specification that in this set of frames the laws of physics are written in the most simple, homogeneous and isotropical way possible. Which is intricate, a bit philosophical, and can be told later. Perhaps a provisional recalling of the good, old "fixed stars", to be refined immediately afterwards, is less "scaring".--GianniG46 (talk) 15:52, 15 October 2010 (UTC)


 * How about referring to proper acceleration - acceleration you can feel? --RockMagnetist (talk) 16:30, 15 October 2010 (UTC)

Lead looks slightly better now. Enjoy the honing :-) DVdm (talk) 15:40, 15 October 2010 (UTC)


 * Thanks, . --RockMagnetist (talk) 18:10, 15 October 2010 (UTC)

I like your most recent change,. I was thinking on similar lines, but I never actually did it. --RockMagnetist (talk) 18:10, 15 October 2010 (UTC)


 * Thanks. I think perhaps some other improvements could be made by explaining in words the relevance of fictitious forces in everyday life. (Just to joke on perhaps: my mother language is not English, but I believed one could use it for qualitative arguments, in the sense of "loosely speaking": I was not pretending to have a precise definition of "most popular example".) --GianniG46 (talk) 08:50, 16 October 2010 (UTC)


 * The problem is, there are already pages on non-inertial frame of reference and fictitious forces. So the main focus of this page should be the subject of the title. --RockMagnetist (talk) 02:36, 18 October 2010 (UTC)

Definition discussion yet again
Reading the talkpage there is already much discussion on preferences. Let me suggest another way to quickly narrow down the possibilities which shouldn't involve prefences: agreeing on what an inertial frame is NOT.

If there exists an inertial frame with coordinates (x,y,z,t), I assume we can agree that the coordinate system (x',y',z',t') is not inertial in the following cases:
 * 1) an accelerating frame: x'=x+t^2,y'=y,z'=z,t'=t
 * 2) a spatial shrinking in one direction, so while space is still homogeneous, it is not isotropic:  x'=ax,y'=y,z'=z,t'=t (Note: as this is a linear transformation, Newton's first law still holds.)
 * 3) space is still homogeneous and isotropic, but now time dependent: x'=a(t)x,y'=a(t)y,z'=a(t)z,t'=t
 * 4) space is homogeneous and time independent, but time is not homogeneous: x'=x,y'=y,z'=z,t'=t^2

So if any proposed definition includes those coordinate systems that are not actually inertial frames, we can quickly eliminate it.

To complement what it should not be, I might as well list what I feel it should be. I think the current definition is nice for three reasons:
 * 1) It holds in the "space-time" approach of special relativity
 * 2) It holds in the "space" + "universal time parameter" approach of Newtonian mechanics
 * 3) It separates the "stage" (spacetime and coordinates labelling it) from the "actors" (the physical fields / particles and whatever laws governing them)

The first two I consider requirements. The third I admit is a preference. The physical laws are separate from a coordinate system as shown by the ability to write them in a coordinate free manner. It seems weird to try to go backwards and describe the coordinate stage with forms of laws that themselves depend on the coordinates. Someone above even tried to argue that we can't define an inertial frame operationally (I'm not sure I'd go that far). Separating them also helps avoid circular definitions and tautologies.

Anyway, let's move forward. Can anyone improve the wording, without changing the meaning of the definition? FlyingBob (talk) 03:01, 13 January 2011 (UTC)


 * Attempt #1: In physics, an inertial frame of reference (also inertial reference frame or inertial frame or Galilean reference frame) is a frame of reference that describes space and time completely uniformly. Simply this means the relation between coordinates can be consistently mapped onto a choice of standard ruler and clock, regardless of location and orientation of the clock or ruler.
 * Is that better? This brings the "actors" a bit on stage, but in I think a fairly harmless way as we can use any choice of ruler of clock. The only worry I have now is that there is a loop hole for clock synchronization.  I fill that is kind of intuitively covered by the vaguish "completely uniformly", but it would be nice to choose a better wording. FlyingBob (talk) 03:25, 13 January 2011 (UTC)

The problem with all these definitions is that one cannot really separate the "stage" (as you put it) from the fields/particles. Here's a simple example. Einstein defined his frame using rays of light (his 1905 paper is very careful and explicit about exactly how he did it). Clocks and rulers are synchronized via light travel times, and it's that procedure that guarantees that the speed of light will be constant and isotropic. Now imagine doing exactly the same thing, but with sound in some air-filled space. It works perfectly (so long as the frame isn't moving faster than the speed of sound relative to the air, that is), and now the speed of sound is constant and isotropic- but the speed of light isn't!

That "sound frame" is not a Lorentz frame, but it does fit the current description in the article. Actually the same goes for Galilean frames - they fit the definition, but they are NOT inertial in the sense that the speed of light is NOT constant or isotropic in them. But I'm really not sure how best to explain this in non-technical language and in a few sentences. To me, it seems that we ought to re-write the intro to separate Lorentz frames from Galilean, and describe Lorentz frames in terms of light (we should say it's a frame in which the speed of light is constant and the same in all directions).Waleswatcher (talk) 18:41, 14 January 2011 (UTC)

What does "describes" describe?
There is a collection of editors who are really fond of the definition "a frame of reference that describes time homogeneously and space homogeneously, isotropically, and in a time independent manner," and keep referring to the talk page. Yet all I find on the talk page is a statement by one anonymous editor that he/she prefers this definition and a lukewarm response from some other editors. I see two problems with this definition: In Mechanics by Landau and Lifshitz, there is a very nice discussion of inertial frames of reference in which they make a very similar statement: "a reference frame can always be chosen in which space is homogeneous and isotropic and time is homogeneous. This is called an inertial frame". But they precede and follow this statement by discussion that makes the physical meaning clear. The very next sentence is "In particular, in such a frame a free body which is at rest at some instance remains always at rest." Can't we agree on a definition that involves motion and action rather than "describes"? RockMagnetist (talk) 03:34, 13 January 2011 (UTC)
 * 1) It is calculated to repel readers who don't already know what an inertial space is.
 * 2) It is practically meaningless (how do you "describe time"?).


 * So maybe you found the reference where the phrasing originally came from. If you want to use simplier language, feel free to suggest something. I tried my best in a suggestion above.  If you can use motion to do it, so be it.  But it better not just be Newton's first law as that isn't enough even in Newtonian mechanics.
 * As for "describe time", it just sounds like a simplified version of "parameterize time" or "label time systematically and numerically" (ie. in a coordinate system)
 * Oh, and I'm the anonymous editter from earlier today. So there's one less person in that collection. Hopefully others will comment. FlyingBob (talk) 04:04, 13 January 2011 (UTC)


 * No doubt the simplest and more concrete definition is saying that in an inertial frame Newton's law must hold, in particular first law. This is what an encyclopedia reader expects. After this one can discuss the more abstract points that, for this to be true, we must have homogeneity, isotropy and so on, and that an inertial frame allows the laws of physics to be expressed in the simplest way possible, and can speak more in depth of Galileo, Newton, and Einstein. This is, for example, the point of view of the interesting article of Stanford Encyclopedia of Philosophy: "The laws of Newtonian dynamics provide a simple definition: ...the motion of a body not subject to forces is always rectilinear and uniform, accelerations ... proportional to ... applied forces ... equal and opposite reactions. ... By inquiring more narrowly into its origins and meaning, however, ...", and continues with an in-depth discussion of related history, physics and philosophy. And, in general, the Newton's laws approach is adopted by most academic articles I have seen.--GianniG46 (talk) 09:28, 13 January 2011 (UTC)


 * I think we definitely should start with frames in which Newton's laws hold good. This can be used to define global inertial reference frames in Galilean and special relativity, and local ones in general relativity. See this, and much more of the same to be found with, (note the numbers of citations), , and . Later we can build towards alternative definitions and explanations in terms of homogeneity, isotropy, and time independency. DVdm (talk) 15:34, 13 January 2011 (UTC)


 * Flying Bob, I overlooked your earlier posts, probably because I was adding to the discussion page at the same time. I think a statement about homogeneous time, etc., is good, but we need to approach it gently. Because of the format of Wikipedia articles, we often feel obliged to pack a complete, general definition into the first sentence. But that approach does not always lead to clarity. Maybe we should use a whole paragraph to define the concept. I think it would be best to start with the purpose of an inertial frame of reference, which is to make the laws of mechanics as simple as possible. Then say something about the law of inertia, and then make a statement about time and space. On the other hand, maybe we should just put a redirect to that Stanford article (Thank you, GianniG46), because I don't see how it could be expressed any better! RockMagnetist (talk) 15:41, 13 January 2011 (UTC)

I might as well mention my worry about trying to define inertial frames with Newton's laws. Let's look for example at the Stanford's suggestion: "The laws of Newtonian dynamics provide a simple definition: an inertial frame is a reference-frame with a time-scale, relative to which the motion of a body not subject to forces is always rectilinear and uniform, accelerations are always proportional to and in the direction of applied forces, and applied forces are always met with equal and opposite reactions." Note their subtle way of trying to say 'no fictitious forces'. This really is the problem with this method. It requires us to agree ahead of time what the laws of physics are, as we are trying to define an inertial frame mainly by how forces act in this frame. This is a bit backwards as usually Newton's second law F = dp/dt(which can be generalized with relativistic momentum to still be true in SR) is used to define forces, and then the "laws of physics" attempt to lay out what forces there are to match observed motions. Even if we ignore this possibly circularity and these philosophical issues, note that magnetism already breaks that definition anyway. It shouldn't be a surprise that electrodynamics, the same thing which ultimately broke Newton's reign, also breaks a definition relying on Newton. Consider two moving charges. The forces felt due to each other's fields are not necessarily equal and opposite at every point in time (as hinted by Griffith's book, if they were, this 'action at a distance' would allow an absolute definition of simultaneity which is clearly not possible). So while it contains some good hints, that definition is wrong.

Thinking about this more, and rereading the talk page for ideas, I like RockMagnetist's comment that "Maybe we should use a whole paragraph to define the concept" and the caution against trying to shove every detail of a general definition into the first sentence when we have a whole article to discuss it. Also a previous editor suggested to possibly "note some major properties in the introduction (sort of like introducing, not defining, an apple by describing its properties), then in the very first part of the article be frank that it is difficult to define precisely. Then explain why with various example definitions and how they may subtly miss the point. Such a discussion can teach a lot (as reading the discussion here helped me understand a lot more). The article is already broken into sections of different properties, and the changes to the beginning just seem to keep trying to choose one and make it the defining property." I wish I had noticed that earlier. To me that really hit home. In the article history the definition has been changed a lot over years, and many times the "flaw" was exactly that: people choosing one property and trying to define it by that property. So maybe we should take the Stanford encyclopedia's approach and give some properties of an inertial frame, but also comment in the beginning that trying to understand this seemingly simple concept in more detail/rigor led to much insight in 20th century physics. Then progressively define it better in the intro section. This will require more editing to make it all fit together, but may be the only way to do it well. Does this sound like a reasonable direction to proceed? FlyingBob (talk) 17:57, 13 January 2011 (UTC)


 * Sounds good to me. Keep in mind that there is some redundancy between this page and various others (Non-inertial frame of reference, fictitious forces). RockMagnetist (talk) 21:51, 13 January 2011 (UTC)

As I said above, I think the correct way to define Lorentz frames is in terms of light propagation. Newton's laws don't really help, since you cannot really distinguish between "fictitious" forces (the kind that arise in non-inertial frames and "applied" forces (especially gravity). In other words, how do you decide in practice what's an "applied force"?  Still, I don't like the way the definition is written now, and I do think a definition in terms of Newton's laws would be preferable to the one that's there now (which is both confusing and vague to the point of being simply incorrect). Waleswatcher (talk) 18:47, 14 January 2011 (UTC)


 * You can distinguish a fictitious force by saying that, in principle, a true force is a force that we can ascribe to one of the force types known by physics, nowadays gravitational, electro-weak, strong.
 * In practice, it is sufficient to find just one body that we can assume to be free from true forces, to define an inertial frame solidal with it. In all frames in rectilinear uniform motion with respect to this one, all forces are to be considered true. --GianniG46 (talk) 00:17, 15 January 2011 (UTC)


 * Your solution to distinguishing them is to just define every "real" force? And the inertial frame is defined in terms of whether we can describe physics without other "fictitious" forces arising?  This is the most extreme version I've ever heard of that I was warning against earlier: instead of taking a coordinate system and then possibly measuring the evolution of a system (and hence the physics) using these coordinates, you are requiring all the physics to be laid out before we can even discuss what an inertial frame is... that I feel is severely inverting the situation.  Newton didn't need to wait until we understood the strong force to use inertial coordinates systems, nor will we need to re-conceptualize inertial frames if we need to add more interactions terms to the standard model later.  We should be able to describe the stage without needing to know so many details about the actors.
 * Regarding your second comment though, if you have an inertially moving body, one could use that to define an origin for your coordinate system. But that is just one spatial point.  One worldline of coordinate labels isn't enough.  How do you use this to give position and time labels to all the other events in spacetime?  It is all those implicit details that you left out which are the heart of the issue here.  It does bring to mind another approach though.  We can ensure space is described uniformly etc. if we use Einstein's thought experiment of building a 3-D grid of standard rulers with clocks at each vertex.  And if clocks were synchronized by slow clock transport, this would give the correct idea for Newton's universal time, and even in Einstein's flat spacetime of SR.  For visual learners this might be an okay way to rephrase our current description of an inertial coordinate system.  But it is probably still confusing sounding, and possibly misleads people by making an analogy to a physical structure that isn't really there or needed.
 * I tried to rewrite the opening paragraph to refer to properties of inertial frames instead of just outright defining it there, and I failed (didn't even bother saving it). I'll try again later.  There's got to be a way we can describe an inertial frame without having to define it immediately, so that we can leave discussing all the details (and even how the concept evolved, as already discussed in the article) to the introduction and main body of the article. FlyingBob (talk) 17:23, 15 January 2011 (UTC)


 * Concerning the first point, a "fictitious" force is just a force that does not fit into the picture physics makes of the "true" forces. This is how physics works: I use what physics presently knows to explain experimental observation, and, if I see phenomena which are not explained, maybe I have to modify the principles. If I knew only gravitational and not-better-specified "contact" forces, and I saw that near a piece of amber the trajectories of objects are not inertial, I could try to attribute this to fictitious forces. If I don't succeed to do so, I am compelled to admit that there is another true force, non-contact and non-gravitational, which I call "electrical". Or, conversely, if I see that the forces I know cannot explain the precession of Mercury or the curvature of light paths, I can change entirely my conception of gravitation and inertia, and speak of geodetics of a curved space, rather than of a gravitational force.
 * For the second point, I meant just that, once I have found one inertial frame, it is easier to distinguish the forces, but (incorrectly) I addressed only the way to distinguish forces which affect the trajectory, neglecting rotations, so forget the second phrase. --GianniG46 (talk) 08:04, 18 January 2011 (UTC)

I'm afraid I disagree - you cannot define fictitious forces as those that cannot be attributed to gravity or other "true" forces, because gravity IS a fictitious force in every sense. That's what Einstein's equivalence principle says, and it's what general relativity is about. In fact for that reason in the real world there are no inertial frames. There are only approximately inertial frames that describe small regions of spacetime.

If we could somehow turn off gravity, the way to construct an inertial frame would be to use the procedure detailed in Einstein's 1905 paper, where you use light rays and synchronized clocks to build a coordinate system. In practice that works pretty well in a human-scale lab on earth, since the curvature due to gravity is small. Waleswatcher (talk) 23:44, 29 January 2011 (UTC)


 * On the contrary, I see that you agree with me in that defining a force to be "true" or not depends on the physic model we are referring to. In classical (and special relativiy) mechanics, gravity is a force, and in a free-falling reference frame we explain the apparent absence of gravity by saying that there is a "fictitous" force, due to acceleration, which exactly balances (apart from tidal forces) the "true" force, gravity. In the same frame, but in general relativity, there are no gravity-related forces, neither the true, nor the fictitious ones. --GianniG46 (talk) 15:44, 31 January 2011 (UTC)

Proposed revision
In the following section I propose the following revisions (in italics):

"Special relativity. Einstein's theory of special relativity, like Newtonian mechanics, assumes the equivalence of all inertial reference frames, but makes an additional assumption, foreign to Newtonian mechanics, namely, that in free space light always is propagated with the speed of light c0, a defined value independent of its direction of propagation and its frequency, and also independent of the state of motion of the emitting body. This second assumption has been verified experimentally (i.e. is no longer an assumption but a confirmed observation--an empirical datum if you will)and leads to counter-intuitive deductions including:

--time dilation (moving clocks tick more slowly) --length contraction (moving objects are shortened in the direction of motion) --relativity of simultaneity (simultaneous events in one reference frame are not simultaneous in almost all frames moving relative to the first).

These deductions are logical consequences of the stated assumptions and empirical data, and are general properties of space-time, only in conjunction with additional (absolutist metaphysical) assumptions about the metaphysical nature of space, time, light-energy etc."

(As Henri Bergson tried to explain to Einstein in their famous Société française de Philosophie debate: Bergson, Ecrits et Paroles, vol. 3, pp. 497; Bergson, ―Discussion avec Einstein, Mélanges Paris: Presses Universitaires de France, 1972. I.e., the success of Special Relativity in no way depends on the truth of the three alleged "logical deductions." The article should not imply that it does.)74.66.14.94 (talk) 08:53, 14 June 2011 (UTC)