Galilean invariance has been listed as a level5 vital article in Science, Physics. If you can improve it, please do. This article has been rated as StartClass. 
WikiProject Physics  (Rated Startclass, Highimportance)  


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.
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 lowlevel edit war over this matter, here are two questions:
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. :)
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)
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.
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 gravityfree) 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)
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 lengthscale in transient gels"; Journal of Physics: Condensed Matter; Institute of Physics; 18 March 2002; 14 (10): pp. 25072529.}
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)
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 EinsteinGalilean relativity. Rhkramer (talk) 14:35, 2 March 2011 (UTC)
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)
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)
One of these days, I'll stumble on a popflock.com resource 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: d²x_{i}/dt² is almost never zero (for i=1,2,3). It is in 'free fall', but free fall is not the same as nonaccelerating.173.189.74.162 (talk) 22:15, 11 April 2015 (UTC)
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 mixup 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)
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 o contribs) 07:07, 29 May 2017 (UTC)
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)
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]"