Talk:Inertial frame of reference

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Problem with this definition in GR
In Misner, Thorne and Wheeler, the "inertial frame" is what the authors call a "free float frame." It's any reference frame in which Newton's laws of motion hold good, and things are weightless. Fair enough. The introduction to this article puts it a little more technically: In general relativity, in any region small enough for the curvature of spacetime to be negligible one can find a set of inertial frames that approximately describe that region. So what then are we to do with the special case of the reference frame occupied by an object in an inertial trajectory, as (for example) a body falling in a vacuum in a gravitational field? Must we say that a body on an inertial path occupies a physically accelerated reference frame that is NOT an "inertial frame"? What a pity. If free fall motion is inertial motion, why is a free-fall reference frame not an inertial reference frame? S B Harris 23:19, 27 June 2012 (UTC)
 * Well for one, because if there is curvature, it is impossible to define "the" reference frame of a freely falling observer. That is, there is canonical way of extending the tangent space along the trajectory of the observer to a frame of reference in his vicinity. It help you to know, that a constant gravitational field has zero curvature.TR 14:11, 25 October 2012 (UTC)

Definition of inertial frame of reference
The definition presented in the beginning is not the usual one. It talks about space and time being homogeneous and isotropic. This is a very advanced concept, and the article does not explain what does it mean for space and time to be homogeneous and isotropic. It is too technical for most readers to understand.

I suggest we adopt the usual definition: "a frame of reference in which the laws of physics take their simplest form". I read the part from Landau Lifshitz where the homogeneous isotropic definition comes from. Before saying that, it says "a frame of reference in which the laws of mechanics take their simplest form".

Italo Tasso (talk) 20:11, 12 November 2012 (UTC)


 * I just spent a while searching for a nice definition (and checked here for discussion as well). I like wikipedia's presentation here.  I think appealing just to "simplest form" isn't as straight forward.  Does that mean only the rest frame of an object is an inertial frame?  The physics can be described "simpler" in such a frame.  Or what about when electrodynamics is written in tensor form, the equations are more compact and the relations more obvious, so is that a "simpler" form?  But that "form" holds in 'any' coordinate system. So is everything an inertial coordinate system?  I think the current definition is as precise as we can get, with the follow up helping give the essence in a less technical manner.  GravyKnives (talk) 11:20, 6 December 2013 (UTC)


 * I just looked up the Landau Lifshitz reference. Inertial frame isn't actually uttered until stating "a frame of reference can always be chosen in which space is homogeneous and isotropic and time is homogeneous. This is called an inertial frame." (emphasis in original) The book then uses these properties to help deduce some physical laws in inertial frames. This would not be possible with suggested "simpler form" definition which is much less precise. GravyKnives (talk) 11:28, 6 December 2013 (UTC)


 * I find the definition a bit confusing too and it is over technical for most readers. It comes from a book that is using it to introduce a discussion of Lagrangians.


 * Why not start the article a simple "dictionary style" definition, paraphrase or quote of a definition such as "A frame of reference in which bodies move in straight lines with constant speeds unless acted upon by external forces, i.e. a frame of reference in which free bodies are not accelerated. Newton's laws of motion are valid in an inertial system but not in a system that is itself accelerated with respect to such a frame.." . Then go on to say that's a Newtonian frame of reference and talk about generalization to relativity theory?


 * Also, when it says "space is homogeeous and istotropic" - the reader might assume that means that matter is distributed in space in a homegeneous and istotropic way which is not a requirement of an intertial frame, and in General Relativity theory then you can only choose such a frame locally - in a universe like ours with matter in it, there is no frame of reference according to which space in general is homogeneous or isotropic - even on the largest scales our universe seems to not quite be either homogeneous or isotropic which, if it's true that matter does warp space time, means that space-time is neither homogeneous or isotropic either.


 * Basically - it is a reasonable way to introduce intertial frames in a book that is about to describe lagrangian theory - but it's not the best way to introduce it in a general article like this, IMHO. Robert Walker (talk) 14:52, 5 June 2017 (UTC)

Merger proposal
Some time ago I proposed merging Inertial space with this article, and no discussion resulted (the original tag is still on Inertial space, but the one on this page was removed). I'd like to reopen the discussion, and this time I'll act fairly quickly if there are no objections. I haven't ever seen a formal definition of "inertial space", but informally it tends to be used for inertial frames of reference when it doesn't matter which frame you choose. It's useful terminology, but not really a distinct concept. Merging it would enhance this article because it would add a discussion of the measurement of acceleration and applications to inertial guidance systems. RockMagnetist (talk) 00:06, 30 March 2013 (UTC)


 * "Inertial space", who ordered that? By all means, go ahead and merge it into here. - DVdm (talk) 09:48, 30 March 2013 (UTC)


 * I have finally done the merger. It was rather difficult to decide how exactly to do it, since much of the source material was unreferenced. I ended up dividing Separating non-inertial from inertial reference frames into Theory and Applications and writing an entirely new description of inertial navigation in the latter. I also copied a paragraph on some work by Schwarzschild into Theory. I don't really know if this work was influential enough to include on this page. Maybe someone else can figure that out. RockMagnetist (talk) 19:07, 26 October 2013 (UTC)

Free-fall equivalence with inertial frames: Newton, or Einstein?
From this article:


 * So much for fictitious forces due to rotation. However, for linear acceleration, Newton expressed the idea of undetectability of straight-line accelerations held in common:
 * If bodies, any how moved among themselves, are urged in the direction of parallel lines by equal accelerative forces, they will continue to move among themselves, after the same manner as if they had been urged by no such forces.
 * —Isaac Newton: Principia Corollary VI, p. 89, in Andrew Motte translation
 * This principle generalizes the notion of an inertial frame. For example, an observer confined in a free-falling lift will assert that he himself is a valid inertial frame, even if he is accelerating under gravity, so long as he has no knowledge about anything outside the lift. So, strictly speaking, inertial frame is a relative concept. With this in mind, we can define inertial frames collectively as a set of frames which are stationary or moving at constant velocity with respect to each other, so that a single inertial frame is defined as an element of this set.
 * —Isaac Newton: Principia Corollary VI, p. 89, in Andrew Motte translation
 * This principle generalizes the notion of an inertial frame. For example, an observer confined in a free-falling lift will assert that he himself is a valid inertial frame, even if he is accelerating under gravity, so long as he has no knowledge about anything outside the lift. So, strictly speaking, inertial frame is a relative concept. With this in mind, we can define inertial frames collectively as a set of frames which are stationary or moving at constant velocity with respect to each other, so that a single inertial frame is defined as an element of this set.
 * This principle generalizes the notion of an inertial frame. For example, an observer confined in a free-falling lift will assert that he himself is a valid inertial frame, even if he is accelerating under gravity, so long as he has no knowledge about anything outside the lift. So, strictly speaking, inertial frame is a relative concept. With this in mind, we can define inertial frames collectively as a set of frames which are stationary or moving at constant velocity with respect to each other, so that a single inertial frame is defined as an element of this set.

This strongly suggests that Newton described free-fall as inertial motion. However, the Equivalence principle article states that this was an Einstein thing:


 * That is, being at rest on the surface of the Earth is equivalent to being inside a spaceship (far from any sources of gravity) that is being accelerated by its engines. From this principle, Einstein deduced that free-fall is actually inertial motion. Objects in free-fall do not really accelerate.

The article on Force also says it was Einstein:


 * The concept of inertia can be further generalized to explain the tendency of objects to continue in many different forms of constant motion, even those that are not strictly constant velocity. The rotational inertia of planet Earth is what fixes the constancy of the length of a day and the length of a year. Albert Einstein extended the principle of inertia further when he explained that reference frames subject to constant acceleration, such as those free-falling toward a gravitating object, were physically equivalent to inertial reference frames. This is why, for example, astronauts experience weightlessness when in free-fall orbit around the Earth, and why Newton's Laws of Motion are more easily discernible in such environments. If an astronaut places an object with mass in mid-air next to himself, it will remain stationary with respect to the astronaut due to its inertia. This is the same thing that would occur if the astronaut and the object were in intergalactic space with no net force of gravity acting on their shared reference frame. This principle of equivalence was one of the foundational underpinnings for the development of the general theory of relativity.

Is the ascription to Newton in this article a mistake? — Preceding unsigned comment added by 50.133.145.226 (talk) 17:46, 11 October 2013 (UTC)

Removal of handedness of coordinate systems
There was an offhand comment in the article which I removed, about the handedness of coordinate systems. Since this matters only for electromagnetism and quantum physics, and the article does not deal with those topics, I think it's preferable to ignore it. Alternatively this could be expanded later in the article, but not in the lead. Bright☀ 18:18, 5 June 2017 (UTC)

Enertial systems
There is no experiment observers can perform to distinguish whether an acceleration arises because of a gravitational force or because their reference frame is accelerating. — Douglas C. Giancoli, Physics for Scientists and Engineers with Modern Physics, p. 155.

Seems a little strange. Firstly gravitational fields are not homogeneous so this must be a infinitesimal situation. The field is detectable as being divergent inside the box that is accelerating. But any geodesic like an orbit around a heavy body surely is a fall in a gravitational field, and also easily detectable not to be inertial. — Preceding unsigned comment added by Burningbrand (talk • contribs)


 * It is explained in the last paragraph of the section Inertial frame of reference: However, the general theory reduces to the special theory over sufficiently small regions of spacetime, where curvature effects become less important and the earlier inertial frame arguments can come back into play. Consequently, modern special relativity is now sometimes described as only a "local theory".
 * - DVdm (talk) 10:45, 15 June 2017 (UTC)
 * Obviously in large enough regions it's easy enough to observe whether the acceleration is due to gravitation or otherwise because of the reasons you stated, but in principle they're equivalent, and their effects are equivalent. Perhaps the quote needs to be expanded to reflect this. Bright☀ 15:38, 15 June 2017 (UTC)

(Problematic?) Mention of Universal Inertial Space
The article currently states, in relation to observations of binary star angular momentum, that:

1) "the angular momentum of all celestial bodies is angular momentum with respect to a universal inertial space."

It also states that :

2) "This phenomenon of geodesic deviation means that inertial frames of reference do not exist globally as they do in Newtonian mechanics and special relativity."

So, do the two sentences contradict each other? At the very least, they seem to be potentially misleading. (1) states makes reference to a, presumably existent, 'universal inertial space' (one would think that this implies a fixed spatial co-ordinate system for the observable universe). (2) states that no Global inertial frame of reference exists (presumably referring to space time).

It might be that the two sentences are somehow logically compatible (when the whole of spacetime is taken into account), but it's not eminently clear to me how. Any explanation of whether the two assertions contradict one another would be appreciated.

ASavantDude (talk) 23:29, 11 January 2018 (UTC)
 * Yes this needs to be fixed, thanks for pointing it out. There is no universal inertial space. There is an apparent universal inertial frame with respect to the very distant stars, I think one of the article's references already mentions this. Bright☀ 12:37, 13 January 2018 (UTC)
 * Yup, the article makes a brief mention of Mach's principle. I think the entire paragraph about double-star systems is superfluous at the moment, but I kept it in because it could be made relevant if the article is expanded. Bright☀ 13:00, 13 January 2018 (UTC)

Article written like a textbook, not a summary
The article is good and useful and well-sourced, but it's written like a textbook. This is not appropriate according to Wikipedia's policies and guidelines. I will eventually overhaul it (unless someone does it before me) and this is a sort of heads-up for page-watchers (who may not have noticed the tag being put up two months ago) so they're not taken by surprise when much of the article's style and order changes. Bright☀ 09:26, 10 March 2018 (UTC)

Netwon's First Law alone does not define an Inertial Coordinate System
At the time of writing this, the first sentence of the article was: "An inertial frame of reference in classical physics and special relativity is a frame of reference in which a body with zero net force acting upon it is not accelerating; that is, such a body is at rest or is moving at a constant speed in a straight line." This is trying to invert Newton's first law and make it a definition of an inertial frame. But this is a necessary but not sufficient property. It is particularly ironic that it mentions special relativity, because if this was the definition of an inertial frame in special relativity, then ANY linear transformation from an inertial frame would satisfy the definition and SR would be falsified. I am changing the first sentence to make it clear that is a property of an inertial frame, not a definition. BunkerQ (talk) 04:54, 15 June 2019 (UTC)

Actually, what is the goal of the section before the introduction? It sounds very stilted, as it's practically a sequence of references and statements jammed together almost like a computer generated summary. Compare that to the first paragraph in the Introduction section which states things in much simpler and fluid language. It even restates the Landau definition without it sounding "advanced" (because the concept really isn't, its just the words Landau uses which makes it sound that way). Anytime I see on wikipedia a series of sentences all marked with references it usually sounds stilted. I feel like the beginning of the article sounds that way because people are trying to jam a definition immediately at the start before even discussing the concepts we need for the definition to make sense. BunkerQ (talk) 05:41, 15 June 2019 (UTC)
 * Yes, these different summaries of inertial frames (Newtonian, analitycal) were jammed together. They give a quick, if somewhat obtuse, overview of the topic. Bright☀ 15:27, 15 June 2019 (UTC)

mischaracterising GR/SR (local) inertial reference frames
this article fails to clarify SR/GR does not use inertial reference frames, where the non-inertial page clearly states they are not inertial from a global perspective.
 * it is my belief this lack of clarity is a symptom of a larger issue. i believe that all "pseudo-Riemmanian" topics should be categorised under mathematical physics and not differential geometry.

the fact is, from the context of, say, the Hasse–Minkowski theorem or theory of the Riemann surface (arguably both of them if you actually know real math), SR does not use inertial reference frames.

they are only seen as inertial when looked at 'locally', but as i said to the biased User:AndyTheGrump: the Riemann surface clearly accounts for a case where global and local behaviour may appear different.
 * the difference in the appearance (topological properties) does not (in any way) change the algebraic properties.
 * this is in stark contrast to the cherished theory whose shortcomings editors clearly ignore.

the global-local principle is very important.

it is hard to have this discussion without discussing the lorentz transform and "pseudo-Riemmanian" geometry, as the frame of reference is a philosophical concept with large consequences on the foundations of a methodology.

so i ask: how is the "pseudo-Riemannian" case, which relaxes the positive definiteness requirement to semi-definiteness, a 'generalisation'? this implies non-full rank and has clear implications on the mathematical properties.
 * it's only a generalisation if the relaxation results in the same properties, but this is obviously not the case.

my field has probably has led the way in showing the usefulness of the PSD relaxation (machine learning) for multiple settings, but in no way do we call it a generalisation. in fact i recall being taught it was a compromise to find stable solutions.
 * it's very handy in the situation where we have one 'zero' eigenvalue (unit eigenvector) that is a solution to an equation (it is not uncommon), but otherwise the assumption of full rank is absolutely necessary for many reasons.

the lorentz transform does not even satisfy the mathematical definition of a transformation. at least editors have enough decency to preference the article with 'In physics'.
 * yet this transform is absolutely the entire key to SR/GR. why does "pseudo-Riemannian" get to hide under the guise of mathematics, while the other (rightfully) is classified under physics?
 * at best, these topics should be considered mathematical physics. they are not differential geometry. maybe it's what physicists call differential geometry, but that doesn't mean it's real differential geometry.

do physicists even appreciate how many mathematicians REVERE Riemmanian Geometry to the point where they avoid writing about it, even though they would love to?

it's hallowed ground. you guys just take it and abuse it. it's time you're held to account. and yes, this is something that is worth fighting over.

198.53.108.48 (talk) 18:06, 14 June 2021 (UTC)
 * Your statement is far from neutral, and at over 3,500 bytes (from the tag to the next timestamp) it is also far from brief. This is much too long for  to handle, and so it is not being shown correctly at Requests for comment/Maths, science, and technology. The RfC may also not be publicised through WP:FRS until a shorter statement is provided. -- Red rose64 &#x1f339; (talk) 21:05, 14 June 2021 (UTC)
 * i have no favourite in the Crank Competition, so i beg to differ about bias. nonetheless you are correct i am incapable of forming proper RfCs (and noticed by User:Volteer1). i thought the RfC just requires a good topic sentence and then the rest is what you're soliciting comments on. how can we fix this? can you help me fix this? i thought my edited version shortened the topic sentence sufficiently. — Preceding unsigned comment added by 198.53.108.48 (talk) 19:26, 15 June 2021 (UTC)
 * Did you read WP:RFCST, or WP:RFCBRIEF? What's with the Depeche Mode stuff, anyway? The whole thing looks like a bunch of random remarks. A good RfC gets straight to the point, see WP:WRFC. -- Red rose64 &#x1f339; (talk) 21:28, 15 June 2021 (UTC)

i will read it and maybe try to fix it.

regarding my statements: they're not really random. it's just that introducing philosophy to mathematics (here, frames of reference are philosophical) introduces additional elements.
 * you can't escape discussion of a transformation when you talk about frames of reference. often the original frame of reference is where you perform the mathematics, and the output can be looked at as a 'new frame of reference'.
 * look at the super-crank diagram on Lorentz transformation. it makes me laugh every time i see it.
 * it's so far from geometrically or mathematically rigorous, but is probably the best intuitive description we have.
 * but i digress.
 * the point of mentioning the Lorentz transformation is that it is responsible for the transformation involving the (allegedly inertial) frames of reference.

to show how meaningless the term 'locally inertial' really is, all we need to do is take a global view:
 * imagine we have some global frame of reference that comprises of more than one 'locally inertial' frame(s) of reference.
 * any of these frames will become non-inertial once they are 'viewed' from another frame (i.e. outside of itself).

the important property an inertial frame of reference is the constant velocity assumption (in my view). it's pretty obvious none of these local frames are moving at constant velocity with respect to each other.
 * rather, each 'locally inertial' frame will have a constant velocity *inside* of it, which may be different from another frame's 'constant velocity'.
 * i guess they try to excuse this with the concept of time dilation, a physical concept with no mathematically robust theory or justification, which is fine.
 * i prefer to avoid dealing with that kind of stuff. in fact, i originally did. i hate having to look at this stuff but i was left no choice.
 * either you have a concept that hundred(s) of people spent decade(s) establishing through multiple hundred publications, little by little, piece [proof] by piece [proof], or you don't.
 * someone has to eventually use them, right? ;)


 * look at this baby, it's straight-up Crank Hall of Fame stuff.
 * i mean, it's not "wrong". it's just not mathematical diagram, and thus becomes 100% crank from my view.

in closing: what's with the depeche mode reference? well, that's my view on this entire subject and i think it's shared by many mathematicians.
 * riemannian geometry is sacred. the constituting proofs and properties are viewed as beautiful by many. i think the statement 'one of the greatest mathematicians of all time' really sums it up.
 * the idea of using riemannian geometry to describe physical phenomena, which should require deference to no more than a few mathematical objects or structure, is considered walking on hallowed ground.
 * you are "putting it in words, writing it down" which is what the physicists attempted to do when contriving pseudo-Riemannian geometry.
 * but they fail to properly respect the (resulting) hallowed ground they walk on. this is best exemplified by calling a weaker property (positive semidefiniteness) a generalisation.

that diagram man. wow — Preceding unsigned comment added by 198.53.108.48 (talk) 19:48, 16 June 2021 (UTC)
 * Adding a further series of random comments does not help in any way. You need to either abide by WP:RFCBRIEF, or remove the tag. -- Red rose64 &#x1f339; (talk) 15:55, 17 June 2021 (UTC)

i mean no disrespect, but are you trained in any relevant topic to the area? my intention behind this question is not to denigrate your (potentially) lack of familiarity with the area, but the comments aren't random.
 * but for someone without any relevant training on the field, they could be seen as random. i don't think anyone wants to argue with me.
 * those who are able to engage don't seem too eager. i know they're reading this.

i hope what they will be learning in the next little bit is to not commit to an academic field out of hero worship.
 * i don't know any mathematician that said 'i am in mathematics because  is the bomb, and i want to continue his legacy'.
 * usually what i'll hear they enjoyed learning about a concept (obscure as it may be, that's how it goes when you do the mathematics properly) and wanted to contribute.

a cult of personality has existed in physics for the last 100 years, which has greatly inflated its head count.
 * it is truly a post-einstein phenomenon. it's not his fault.

but damn, people: if you're in a field because of a person without fully grasping what they did (no one does, that's the truth), you're not in it for the right reasons.
 * feynman at least had the courage to say no one understood QM and he was right, but it's not the same challenge as GR/SR (imo).

the challenge for QM is more general: interfacing rigorous mathematics with an equally-rigorous observation.
 * usually someone who understands the former is incapable of the latter, and vice-versa. you really need to have a good set of eyes.

but i digress. open invitation for any GR/SR worshipper to get SMOK'T

lulz. c'man, potential reader, it'll be just like those famous debates you probably spend so much time imagining.
 * i want to be put in my place with your usage of a canonical 'thought experiment' that'll shut me up!
 * thought experiments in a field purported to focus on reality, eh? go figure. 198.53.108.48 (talk) 18:42, 17 June 2021 (UTC)

I have removed the RfC tag: whatever this is, it's not an RfC. --JBL (talk) 19:35, 17 June 2021 (UTC)

Article Restructure for Encyclopedic Tone/Style
The current state of the article has been flagged by wikipedia for the lack of an encyclopedic tone. I will be working on this article for the next few weeks to meet these standards. My focus will be to make bold and frequent edits to support an encyclopedic tone and offer suggestions for wording that is too technical. BMarie 212 (talk) 18:12, 20 February 2024 (UTC)


 * I suggest that the "delete" key will be very valuable in your effort. Johnjbarton (talk) 18:32, 20 February 2024 (UTC)
 * I agree that the article is too technical. I recomend to delete or severely edit anything coming from as it is considered one of the most technical books to learn mechanics from and mostly reserved for PhD in theoretical physics. Jafloch (talk) 05:34, 25 February 2024 (UTC)
 * There are only two used of Landau and Lifshitz and neither one is complex. Johnjbarton (talk) 16:03, 25 February 2024 (UTC)