- #1

- 485

- 11

## Main Question or Discussion Point

It is said many times, from the days of Einstein, Minkowski and Poincaré, that Classic or Newtonian Mechanics are not consistent with motion at relativistic speeds, that a new relativistic mechanics is needed, viz.

Albert Einstein: … the apparent incompatibility of the law of propagation of light with the principle of relativity […] has been derived by means of a consideration which borrowed two unjustifiable hypotheses from classical mechanics; these are as follows: 1

Henri Poincaré: From all these results, if they were to be confirmed, would issue a wholly new mechanics which would be characterized above all by this fact, that there could be no velocity greater than that of light, any more than a temperature below that of absolute zero. For an observer, participating himself in a motion of translation of which he has no suspicion, no apparent velocity could surpass that of light, and this would be a contradiction, unless one recalls the fact that this observer does not use the same sort of timepiece as that used by a stationary observer, but rather a watch giving the “local time.[..] Perhaps, too, we shall have to construct an entirely new mechanics that we only succeed in catching a glimpse of, where, inertia increasing with the velocity, the velocity of light would become an impassable limit.3

But just what are the differences? Is there a description?

1 Albert Einstein (1879–1955). Relativity: The Special and General Theory. 1920.

XI The Lorentz Transformation.

2 Raum und Zeit(1909), Jahresberichte der Deutschen Mathematiker-Vereinigung, 1-14, B.G. Teubner

A Lecture delivered before the Naturforscher Versammlung (Congress of Natural Philosophers) at Cologne — (21st September, 1908).

3 Poincaré, Henri (1904/6), "The Principles of Mathematical Physics",

Albert Einstein: … the apparent incompatibility of the law of propagation of light with the principle of relativity […] has been derived by means of a consideration which borrowed two unjustifiable hypotheses from classical mechanics; these are as follows: 1

- The time-interval (time) between two events is independent of the condition of motion of the body of reference.
- The space-interval (distance) between two points of a rigid body is independent of the condition of motion of the body of reference.

Henri Poincaré: From all these results, if they were to be confirmed, would issue a wholly new mechanics which would be characterized above all by this fact, that there could be no velocity greater than that of light, any more than a temperature below that of absolute zero. For an observer, participating himself in a motion of translation of which he has no suspicion, no apparent velocity could surpass that of light, and this would be a contradiction, unless one recalls the fact that this observer does not use the same sort of timepiece as that used by a stationary observer, but rather a watch giving the “local time.[..] Perhaps, too, we shall have to construct an entirely new mechanics that we only succeed in catching a glimpse of, where, inertia increasing with the velocity, the velocity of light would become an impassable limit.3

But just what are the differences? Is there a description?

1 Albert Einstein (1879–1955). Relativity: The Special and General Theory. 1920.

XI The Lorentz Transformation.

2 Raum und Zeit(1909), Jahresberichte der Deutschen Mathematiker-Vereinigung, 1-14, B.G. Teubner

A Lecture delivered before the Naturforscher Versammlung (Congress of Natural Philosophers) at Cologne — (21st September, 1908).

3 Poincaré, Henri (1904/6), "The Principles of Mathematical Physics",

*Congress of arts and science, universal exposition, St. Louis, 1904***1**, Boston and New York: Houghton, Mifflin and Company, pp. 604–622