Talk:Galilean invariance

einstein's elevator vs. einstein's cabin

Google searches for einstein's elevator and einstein's cabin give:

1. Results 1 - 100 of about 442 for "einstein's elevator".
2. Results 1 - 3 of 3 for "einstein's cabin".

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 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.}

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)

The above comment is correct. This article is importantly wrong.

Galilean relativity is the philosophically and scientifically revolutionary discovery that all motion is relative, as demonstrated in the Ship thought experiment. Invariance is a more-or-less equivalent reformulation of Galilean relativity. BlueMist (talk) 16:05, 18 February 2014 (UTC)

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.