Talk:Galilean transformation

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i fixed the mispelling ( cooordinate > coordinate)uhuh uhuh... at the last edit.

later mr. uhuh uhuh man

coool

Could somebody please explain briefly what all this means, without having to know any math? Because if it's "common sense", I suppose one could explain it for those of us who failed high school algebra.

See Two New Sciences for Galileo's experiments, where he figured out a quantity that remained unchanged during all the experiments. In this article, that unchanged quantity was the rate of change of velocity u.

[edit] Invariance

I have a serious question. Can anyone work out for me how Maxwell's equations (differential forms, of course) are not Galilean invariant, but are Lorentz invariant? I attempted the problem before but couldn't see anything conclusive in the math. Every book I've run across says "it's easy to show...." ub3rm4th 19:49, 30 Dec 2004 (UTC)

The fact that all electromagnetic waves propagate at the speed of light is enough to show they're not Galilean covariant. As for Lorentz covariance, see Faraday tensor. Phys 17:23, 18 Jan 2005 (UTC)
in the language of differential forms, Maxwell's equations are dF=0 and *d*F=j. The first is invariant under all diffeomorphisms of spacetime. The second is only invariant under transformations which preserve the metric. Lorentz transformations preserve the metric but Galilean transformations do not. Just check what happens to the Hodge star in a Galilean boosted frame. -Lethe | Talk 17:07, Apr 24, 2005 (UTC)
Actually, the latter is invariant under all conformal transformations. Phys 01:08, 13 November 2005 (UTC)
Maybe any transformations which preserve the volume form as well? I forget, but it sounds plausible... -Lethe | Talk 01:21, 13 November 2005 (UTC)
The "macroscopic" Maxwell equations (div D = rho, curl H - dD/dt = J, div B = 0, curl E + dB/dt = 0) have an invariance group containing GL(4) (as well as a superset of the conformal group), since they can be expressed in the language of differential forms. Their invariance, therefore, is independent of the distinction between Galilean versus Poincare (versus Euclidean, even!)
The distinction arises from the constitutive laws. The Lorentz relations (D = epsilon_0 E, B = mu_0 H) are Lorentz invariant. That's directly tied to the duality operation F -> *F, which both requires a metric to be defined, and effectively defines a metric. When the Maxwell field is regarded also as a special case of a gauge field, the duality also involves the metric associated with the gauge group. Here, the role of the gauge group metric and its dual is played respectively by (epsilon_0 c) and (mu_0 c).
In contrast, the older Maxwell relations, which are equivalent to (D = epsilon_0 (E + G x B), B = mu_0 (H - G x D)), would be Galilean covariant, with G transforming as G -> G + v under a boost by velocity v. Maxwell's G was removed by the time of Lorentz once its non-observation became apparent. This is why you see a gap in Maxwell's alphabet soup A, B, C, D, E, F, H, I, J.
The invariance of the macroscopic equations is a "superset" of the conformal group because it also includes a residue of the complexion transformation: D -> D + kB, H -> H - kE, E -> E, B -> B. Consequently, it's best to distinguish the field (D,H) from the dual *F. The fields that come out of the Heisenberg-Euler Lagrangian in effective field theory, for instance, embody a transformation by a non-zero k, as well as having a variable epsilon.

[edit] This article is terribly written

The English in this article is terrible - example:

"From the point of view of group theory, Einstein's special theory of relativity the Lorentz transformation group events, it is essentially a particle do uniform motion of the Lorentz transformation group - This is the core of Einstein's special theory of relativity all."

I'm not an expert in this field so don't feel comfortable editing it, but that sentence is embarrassing.

What is worse: the article contains absolute nonsense. JocK (talk) 21:31, 4 January 2008 (UTC)
Have made a start with a thorough clean-up. JocK (talk) 21:57, 4 January 2008 (UTC)

[edit] Do we have t' = t when v = 0?

Let me arrange two inertial systems first. One with observer Mr. A holding his clock A at the origin point O of the stationary system S and the other one with observer Mr. B holding his clock B at the origin point O’ of the moving system S’ and x axes is on the same line of x’ axes while system S’ is moving at a constant speed v toward the positive direction of x axes. The y axes is parallel to the y’ axes and so does z axes to z’ axes. Clocks A and B are identical and set to 0 when O’ = O.

1. Postulate

The main purpose of Galilean Transformation, GT, is to study the result of measurements for location and time when an event is measured by Mr. A and Mr. B. The time formula t' = t is a postulate when GT started.

2. Believed

However, if we let v = 0, then the time formulas in Lorentz Transformation, LT, and Special Theory of Relativity, STR, all become t’ = t. Even scientists cannot let LT and STR coexist, most of them believe that one of LT and STR must be correct. Since both LT and STR indicate if v = 0 then t' = t it is fair to say that most scientists believe in that "If v = 0, then GT is correct." But how do we prove that if v = 0 then t’ = t?

3. Investigation

Let me describe an experiment just finished this morning for your reference. The system S’ stopped when Mr. B was about 900 meters away from Mr. A this morning and Mr. B threw an orange into the air then caught it 2 seconds later. Mr. B could use his clock B to record the beginning and ending time of that event. At that time, how did Mr. A measure the t’ for that same event? Do we have t’ = t for that event? My answer is no.

4. t' = t is not correct

Since that event was 900 meters away from Mr. A when it started, we know that the picture of the moment the orange was leaving Mr. B’s hand would take some time to arrive Mr. A’s eyes. (900 meters) / (300000000 (meters/second)) = 3000 nanoseconds. That means if Mr. B recorded the beginning of that event as 5 minutes according to the clock B then Mr. A would record the beginning of that same event as 5 minutes and 3000 nanoseconds according to the clock A. If we assume that both clocks are able to read nanoseconds then we already proved that t’ = t is not true when v = 0.

5. Nanosecond Formula

To an observer at point o, an event starts ta at point a is recorded as it is started t’a = ta+(ao/c) so that t’a is always later than ta by the difference of the time that photons spend in traveling the distance ao from point a to point o. If the event ends tb at point b, then the time period of that event tab = tb-ta is recorded as t’ab = t’b-t’a = (tb-ta)+((bo-ao)/c). The formula t’ab = tab+((bo-ao)/c) is the nanosecond formula.

John C. Huang (talk) 02:29, 19 May 2008 (UTC)

An "experiment just finished this morning" belongs in the realm of Original Research. Wikipedia does not deal with Original Research.
I have reverted your most recent edits to the pages talk:Time and talk:Lorentz transformation and left another warning on your talk page. How many times and in how many way do we have to explain this to you? DVdm (talk) 14:45, 19 May 2008 (UTC)