Not Exactly the latest paper but interesting commentary on the Galilean transform

Mathis wrote:       A Galilean transform is Galilean (instead of Lorentzian) because in the time of Galileo light was thought to have an infinite speed. If light has an infinite speed, then the rocket will see everything at exactly the same time as the object itself. There can be no transform due to velocity. Therefore a Galilean transform with a velocity variable in it is a contradiction in terms. It is impossible.

      The equation x' = x - vt has also been called Newton's Principle of Relativity. But it is not that either. Neither Newton nor Galileo could have had any possible use for a transform caused by velocity, since constant velocity was not believed to make any difference in measurement, no matter how great the velocity was. A transform between coordinate systems was made necessary by distance only; velocity was not a factor.

I have shown that x' = x - vt cannot be true if the x variables stand for points, since a velocity cannot have anything to do with transforming a point on one graph to a point on another graph when these graphs are Galilean. But the equation also cannot be thought of as Δx' = Δx - vΔt, since an observer in a Galilean system cannot possibly find any length contraction. In all Galilean systems with constant velocities, Δx' = Δx.

You can see that what the authors mean by t = t' is really Δt = Δt' . We are being given a period equivalence. Time is going at the same rate in both coordinate systems. If this is true, then the analogous transform for distance between the same two systems should also be in terms of delta variables. That is, Δx = Δx' . The points in the two systems may be different, if we have different origins. But distances are the same. We can make the points equal, too, just by making the origins equal. Then the rocket and the object are in the same system and we don't even need a transform at all. This is the way that Galileo or Newton or anyone before Maxwell would really have solved. Put both objects in the same graph and do direct subtractions of points. Then you can see that action is truly invariant, since it becomes a tautology.

      The authors ask if the Galilean transform is incorrect. The Galilean transform
x' = x - vt is incorrect. But we can provide Galilean transforms that are correct and that provide invariance. They are:
Δt = Δt'
Δx = Δx'
Δy = Δy'
Δz = Δz'
x' = (x - a) is also true and provides invariance, if and only if the x variables are understood to be points measured at the same time.
      Of course, this means that
S' = ½ m (Δx')2/(Δt') = ½ m (Δx)2/(Δt) = S



This paper was sent to the American Journal of Physics in early 2005. In July I received this reply from the editors:

The author brings up an interesting point: Did Galileo (or Newton, "or even a young Maxwell") make use of what we call the Galilean transformation? The author says "the transform actually used by scientists before relativity is x' = (x - a) or some simple variation of that." Here the symbol "a" stands for a distance under the assumption of simultaneity. There are no references in this paper, so we are given no evidence for these historical statements. He continues, saying that time cannot enter this equation and therefore neither can velocity, "since a velocity cannot have anything to do with transforming a point on one graph to a point on another graph when these graphs are Cartesian or when the spaces are Galilean." The entire paper concerns points in space.

We are talking here about a description of motion, and motion is described by EVENTS marking the sequential locations of, say, a particle in spacetime, most simply x and t. Events also dominate quantum physics and general relativity. Events are the nails on which physics hangs. The equation x' = x - a, where "a" is a distance and time is simultaneous has no possible chance of describing motion. I cannot word-search this pdf document, but have not found a single use of the word EVENT in this present manuscript.

This paper is disqualified for publication in AJP because the formalism the author proposes has no chance of describing motion. If the author wishes to convince us that the Galilean transformation would have been foreign to Galileo, Newton, and possibly even the young Maxwell, let him make the case with a study of historical context and references. The editors can then decide if this is a useful footnote on the history of physics and appropriate to the AJP.

AMERICAN JOURNAL of PHYSICS
Jan Tobochnik, Editor
Harvey Gould, Associate Editor
Martin Ligare, Assistant Editor
Jennifer Perry, Assistant to the Editor