Talk:Galilean invariance

einstein's elevator vs. einstein's cabin
Google searches for einstein's elevator and einstein's cabin give: All three results for einstein's cabin refer to the scientist's own residence, not his thought experiments.
 * 1) Results 1 - 100 of about 442 for "einstein's elevator".
 * 2) Results 1 - 3 of 3 for "einstein's cabin".

This article says Einstein's elevator is used in Einstein and Infeld (1938), which I have somewhere. The article would benefit from any references in which einstein's cabin is used in a thought experiment.

As there appears to be a low-level edit war over this matter, here are two questions:
 * 1) What did Einstein say?
 * 2) Why can't there be two examples, contrasting the inertial and accelerated scenarios?

The article currently reads: "In special relativity, one considers Einstein's cabins, cabins that fall freely in a gravitational field." Is it really necessary to consider so many cabins? I find one cabin charming, but a whole rain of them frightening. :-)


 * --Jtir 16:38, 23 September 2006 (UTC)


 * (transfered from User talk:Mct mht)
 * thanks for the heads up. both "cabin" and "elevator" can be found in the literature. they convey the same idea. no objections from me if you strongly prefer elevatorvand wanna put it back. Mct mht 19:12, 23 September 2006 (UTC)


 * I like cabin in this example, because the cabin is in free fall. An elevator has a cable that can be used to accelerate it, so it provides a somewhat different example. Do you have a particular source, such as textbook, that uses cabin.  I would like to add some references to this article and a title and author is all I would need. If you like, you can put it here and I will do the edit. --Jtir 19:43, 23 September 2006 (UTC)


 * Relevant guidance WP:SET, WP:NOR, and WP:NPOV.
 * —DIV (128.250.80.15 (talk) 03:19, 3 October 2008 (UTC))

"In special relativity ... in a gravitational field."
As an amateur, I'm not 100% positive, but special relatively pretty much avoids the subject of gravity, while general relativity extends special relativity to deal with gravity. IMHO, that sentence should be revised to start: "In general relativity..."

Rhkramer (talk) 14:35, 2 March 2011 (UTC)

examples of inertial frames in the lead paragraph
The lead paragraph reads very nicely until the last sentence: The fact that the earth on which we stand orbits around the sun at approximately 18 km/s offers a somewhat more dramatic example [of an inertial frame].

The Earth has a gravitational field, is subject to earthquakes, and is orbited by a moon, so it is not an example of an inertial frame.

Examples of nearly inertial frames in a gravitational field are the Vomit Comet and the International Space Station. As the article notes later, microgravity is still present in those frames.


 * --Jtir 18:58, 23 September 2006 (UTC)
 * The Earth also rotates. The ship example is triply qualified by assuming the ship moves "... at constant speed, without rocking, on a smooth sea...". Perhaps something similar could be done for the Earth example.--Jtir 17:36, 24 September 2006 (UTC)
 * I'm not sure how relavent this is, since i'm having trouble understanding Newtonian Relativity, the earth does rotate around the sun, as does the International Space Station around the earth, meaning that they are accelerating, as acceleration is not only speed but the direction of motion as well. So, take that into consideration, whoever understands this better than i.--The Sporadic Update 19:08, 28 September 2006 (UTC)


 * Indeed. The Earth also follows a (nearly) circular orbit. It has a constant speed of 18 km/s, but is continuously accelerating to follow a curved path; it is an example of a decidedly non-inertial frame.  TenOfAllTrades(talk) 19:27, 3 October 2006 (UTC)
 * I think that what may have been meant originally is that the orbital acceleration is effectively "cancelled" by the gravitational field of the Sun. The same thing may be said about satellites in Earth orbit. The article needs to help sort this out. --Jtir 19:50, 3 October 2006 (UTC)

Tidal forces example
The example used to show the locality of some frames of reference says:

"In general, the convergence of gravitational fields in the universe dictates the scale at which one might consider such (local) inertial frames. For example, a spaceship falling into a black hole or neutron star would be subjected to tidal forces so strong that it would be crushed. In comparison, however, such forces might only be uncomfortable for the astronauts inside (compressing their joints, making it difficult to extend their limbs in any direction perpendicular to the gravity field of the star). Reducing the scale further, it might have almost no effects at all on a mouse. This illustrates the idea that all freely falling frames are locally inertial (acceleration and gravity-free) if the scale is chosen correctly."

I don't think that this describes tidal forces at all well. Objects in freefall, as described, are stretched: not crushed. I'll give it a few days, and if there's no objection, I'll reword the paragraph quoted above, and reference the spaghettification article. Andy Ross 08:48, 14 June 2007 (UTC)


 * In a sufficiently large freefalling lab, objects will be stretched in the direction of the centre of attraction, but crushed in directions perpendicular to that. See for instance Taylor and Wheeler's Exploring Black Holes - Introduction to General Relativity, Chapter 2:
 * "Consider, for example, the plight of an experimental astrophysicist freely falling feet first toward a black hole. As the trip proceeds, various parts of the astrophysicist’s body experience different gravitational accelerations. His feet are accelerated toward the center more than his head, which is farther away from the center. The difference between the two accelerations (the tidal acceleration) pulls his head and feet apart, growing ever more intense as he approaches the center of the black hole. The astrophysicist’s body, which cannot withstand such extreme tidal accelerations, suffers drastic stretching between head and foot as the radial distance drops to zero.
 * But that is not all. Simultaneous with this head-to-foot stretching, the radial attraction toward the center funnels the astrophysicist’s body into regions of space with ever-decreasing circumferential dimension. Tidal gravitational accelerations compress the astrophysicist on all sides as they stretch him from head to foot. The astrophysicist, as the distance from the center approaches zero, is crushed in width and radically extended in length. Both lethal effects are natural magnifications of the relative motions of test particles released from rest at opposite ends of free-float frames near Earth (Chapter 1, Section 8)."
 * DVdm 11:00, 14 June 2007 (UTC)


 * Ah yeah, I read that paragraph completely wrongly. We might as well delete this section from the talk page, as it's resolved. Andy Ross 14:44, 14 June 2007 (UTC)
 * Adding a link to spaghettification is a good idea — I only learned of the term by reading this discussion. BTW, a talk page is normally archived only when it gets too long. --Jtir 15:13, 14 June 2007 (UTC)


 * ... and no need to remove this section from the talk page. Cheers! DVdm 15:16, 14 June 2007 (UTC)

Torpid matter
According to Evans and Starrs*, Galilean invariance will not hold for certain configurations of matter. — DIV (128.250.204.118 03:17, 18 June 2007 (UTC))

* {“Emergence of a stress transmission length-scale in transient gels”; Journal of Physics: Condensed Matter;  Institute of Physics;  18 March 2002;  14 (10): pp. 2507–2529.}

What exactly is the section "Formulation" claiming to show ?
The section of the article called "Formulation" shows that acceleration (presumably) as a scalar is invariant under a Galilean change of coordinates. If this proves Newton's laws hold, it would be useful to explain why. If we express acceleration as vector and change coordinates, the scalars of the vector do change. So is the invariance of acceleration as a vector (direction and magnitude) the significant fact?

Given any mathematical expression in scalar coordinates, one can create a new expression by doing a coordinate transformation. Elementary physics texts often state what physical laws apply in some standard coordinate system and then assert that they remain valid under a change of coordinates. This approach is not using anything about "invariance" to establish physics. Presumably, the point of Galilean invariance is select expressions that describe physical laws and reject others. The article needs more explanation of what criteria are used. For example, how does the invariance of 'a' select the law F = Ma and reject the law F = Ma^2 ? Or is Galilean invariance inadequate to completely determine physical laws?

Tashiro (talk) 18:00, 16 August 2009 (UTC)


 * All quantities in the formulation section are vectors, or, to be more precise, coordinate triplets. This is expressed by the phrase "A physical event in S will have position coordinates r = (x, y, z) and time t". DVdm (talk) 13:00, 17 August 2009 (UTC)


 * On this topic we have invariant (physics) which is more general. For physical science refer to Galilean equivalence; the current article here is more in the direction of invariant (mathematics) where there is a view of mathematical structures that express the intuition of Galileo's relativity. As for the "Formulation", I would prefer a phrasing admitting the title absolute space and time of the supporting article.Rgdboer (talk) 21:26, 18 August 2009 (UTC)

Why is this turning into an article about relativity?
I don't understand why this article about Galilean invariance is turning into a page more about relativity than anything else. I suggest we link to relativity as much as needed, and keep the article neat and clean. —Preceding unsigned comment added by 95.34.181.62 (talk) 13:42, 15 May 2010 (UTC)

Agreed. The article is called "Galilean invariance". It's not called "a history of ideas about invariance". It's difficult to see why it should be much longer than a paragraph. 10:42, 28 August 2010 (UTC) —Preceding unsigned comment added by 91.84.95.81 (talk)

I disagree. It is very helpful in understanding Einstein's theories (special and general relativity) to understand that there was a relativity before Einstein--Galilean relativity. Rhkramer (talk) 14:35, 2 March 2011 (UTC)

Invariance of acceleration and Galilean invariance
How does the invariance of acceleration under Galilean transformations (together with the invariance of mass) imply Galilean invariance? For this implication to be valid, you would need to show that the full law of motion (Newtons II law, F = ma) is invariant under Galilean transformations (at least for isolated systems). That a' = a is not a physical principle but an elementary mathematical fact, that will also hold in special relativity (under a formal Galilean transformation). The reason, why Galilean invariance is only an approximate symmetry of nature, is that F' != F when electromagnetic interactions (of moving charges) are considered. --Hardi27 (talk) 22:00, 2 September 2012 (UTC)

Not so
Galileo, like Newton, made remarks about absolute motion or being absolutely stationary. — Preceding unsigned comment added by 92.27.109.117 (talk) 08:29, 28 March 2014‎ (UTC)

Wrong
One of these days, I'll stumble on a Wikipedia article written by someone who actually is proficient in English; one of these days."The fact that the Earth orbits around the sun at approximately 30 km/s offers a somewhat more dramatic example, and it is technically an inertial reference frame." The fact offers? Perhaps 'provides' would be better. The "fact" is not an inertial frame (the "it" here has changed the subject, sigh). At ANY one instant, the Earth is accelerating that is: |d²xi/dt²| is almost never zero (for i=1,2,3). It is in 'free fall', but free fall is not the same as non-accelerating.173.189.74.162 (talk) 22:15, 11 April 2015 (UTC)


 * I've the  which incorrectly asserted that the rotating reference frame was inertial.  I leave improvement of the English to you. -- ToE 12:17, 3 May 2015 (UTC)

Galilean Relativity and Objective Truth
The first sentence of the article is quite wrong. Rather, Galilean relativity states that "all motion is relative". This is entirely different to the concept of the 'invariance of law'. The latter, as found in Einstein relativity theories, leads to logical paradoxes. If Galileo's principle seems to do so it is only because of his mix-up with tidal motion. Galilean relativity was soon also mixed up with Newton's absolute space, which latter essentially denies that "all motion is relative". Hence the compromise position taken in the article where Galilean relativity is mongrelized into the 'invariance of law.' —Preceding unsigned comment added by 220.235.60.51 (talk) 02:11, 16 October 2008 (UTC)

This page purports to explain both invariance and relativity, but only the second principle, Galilean 'invariance' is covered from a Newtonian perspective. Yet invariance is fundamentally incoherent without an understanding of Galilean 'relativity'.

Galilean relativity is exemplified by a sleeping man who is both not moving in his bed and is, at the same time, moving around the Earth and moving around the Sun at different velocities. If this single example is true, then Galilean relativity which says that all things are both moving AND not moving at the same time is necessarily implied. This is a fundamental philosophical insight that underlies all modern science.

Galilean invariance is a related inner Galilean/Newtonian principle of physics. It says that the laws of physics are invariant in each of the above three and all other Galilean/Newtonian inertial frames. However, without an infinite number of potential points of view, or origins for potential frames of reference, this scientific invariance would be meaningless.

BlueMist (talk) 14:03, 5 April 2016 (UTC)


 * I think perhaps no one understands the points that you wish to make. Perhaps you could elaborate.  In particular, what do you mean by inner principle of physics and how you see Galilean invariance differing from Galilean relativity.  Constant314 (talk) 15:45, 8 April 2016 (UTC)


 * I wouldn't say "no one", but having researched this topic for years, I agree with you that this quite simple and absolutely incontrovertible principle turns out to be very difficult to accept, even to understand, even for highly intelligent and educated people. The reason for this turns out not to be the principle, but the rigidity of our psychological habits.


 * We live in our personal immediate material world, the one we can touch, taste, and smell, and this world is relative to us, the 'I' each of us is. We are the origin of our unique 'frame of reference', so that 'I am here, now' at all times in all places as long as I live.


 * contrast this to "Galilean relativity" I described above. In the Galilean scientific world, which is different from my world, or my 'I', everything is relative to some arbitrary frame of reference, rather than to my 'I'. That arbitrary frame is set, for practical purposes, such as conceptual or calculational simplicity, to be anywhere, and at any time, in the universe.


 * Now, let's switch from the philosopher's perspective to the physicist's. The physicist accepts without question and without further thought the principles of the physical universe. A principle is different than a hypothesis or a law in this respect. Philosophical principles are unquestionable to a physicist. Once he does question one of the philosophical principles of physics, then he has stepped outside physics, back up to philosophy.


 * "Galilean invariance" is not a principle needed by the philosopher. I don't even think it can possibly be derived from the broader concept of "Galilean relativity". "Galilean invariance" is a practical principle of physics so that physics, as a universal science with universal laws, can do its job. Just as Euclidean space was needed by Newton for his work.


 * Well, I'll assume that this piece of philosophy of science is even harder to understand than the simple "Galilean relativity" I started with.


 * In any case, if you search the internet for "Galilean relativity", most physics notes will immediately talk about "invariance" because that is their practical need. But not all. There are some few physicists out there who do understand the relativity of Galileo's ship thought experiments.  BlueMist (talk) 19:50, 8 April 2016 (UTC)

Bad grammar
Under the heading "Formulation", the second sentence has singulars and a plural which do not agree with one another. This also appears later. — Preceding unsigned comment added by 95.226.0.105 (talk • contribs) 07:07, 29 May 2017 (UTC)


 * Please sign all your talk page messages with four tildes ( ~ ) — See Help:Using talk pages. Thanks.
 * ✅ see . Thanks! - DVdm (talk) 07:48, 29 May 2017 (UTC)

Newton's vs Einstein's Principal of Relativity
The article says an essential difference between Newton's and Einstein's versions of Relativity is that, in Newton's version, relative motion is embedded in absolute space while in Einstein's version it is not. This only happened because Newton admitted the necessity for absolute space to explain centrifugal force in rotational motion - a problem totally ignored by Einstein in his Special Theory (although Poincare did not ignore it). Otherwise Newton's statement of the Principle of Relativity for mechanical motion in Principia (see Corollary V) is essentially the same as Einstein's. JFB80 (talk) 15:18, 11 April 2018 (UTC) JFB80 (talk) 12:13, 17 April 2018 (UTC)

Earlier references
I see here that in 1615 the moving ship idea is already used by Foscarini. Making the 1632 reference late even if it has the right author. "His final argument was a rebuttal of an analogy that Foscarini had made between a moving Earth and a ship on which the passengers perceive themselves as apparently stationary and the receding shore as apparently moving." (Galileo affair) Elegast (talk) 08:06, 10 July 2019 (UTC) Upon control, I see other authors are mentioned in Galileo's ship: "Jean Buridan,[1] Nicolas Oresme,[2] Nicolaus Cusanus,[3] Clavius[4] and Giordano Bruno.[5]"

it
Hi, Frequently a clause or sentence containing the pronoun it is easier to read without it. Here are some examples.

> "compressing their joints, making it difficult to extend their limbs in any direction perpendicular to the gravity field of the star" versus compressing their joints, making extension of their limbs in any direction perpendicular to the gravity field of the star difficult"

> "It is not possible to have a consistent Galilean transformation that transforms both the magnetic and electric fields." versus No consistent Galilean transformation can transform both the magnetic and electric fields.

> "Due to Newton's law of reciprocal actions there is a reaction force; it does work depending on the inertial frame of reference in an opposite way." versus Due to Newton's law of reciprocal actions there is a reaction force which does work, depending on the inertial frame of reference in an opposite way.

Regards, ... PeterEasthope (talk) 21:41, 16 March 2023 (UTC)


 * Go ahead, thus, as if it were, make it so. That is, otherwisely, to say it differently, to boldly edit copy as required to succinctify the textual payload of the article as necessity, for all intents and purposes, absent the naysay of others, for erudite progress.  Cheers.  . Constant314 (talk) 22:28, 16 March 2023 (UTC)