The use of a principle of relativity in the description of Nature indicates a sensible wish to represent physical phenomena independently of the position and motion of observers. Specifying I sets of observers for whom the laws of physics appear the same amounts to determining sets of equivalent reference frames.
Galileo had already noticed that there was an equivalence between the observations of two experimenters, one shut in the hold of a ship, stationary with respect to the land - for instance docked in a port - and another on board a ship which was travelling away from the port in a straight line at constant velocity. If each of the experimenters dropped a ball from metre above the floor of the hold, the results were identical: a vertical fall lasting 0.45 second. *
Galileo had inferred from this that the ship moving away fromI the port had a circular motion (due to the Earth being round) and influenced by the ancient idea of circular perfection, he had therefore deduced that the circular motion represented the ‘natural state of bodies, which was indistinguishable from rest. Descartes discovered that it was in fact the motion of uniform translation, that is, in an infinite straight line at a constant velocity (with neither
acceleration nor deceleration), which was indistinguishable from rest. In modem times, we have all sat on a train in a station watching a neighbouring train pull slowly away, and had the impression that our own train was pulling out in the opposite direction.
These observations are simple yet profound, because they suggest that in fact there is no difference between rest and uniform translation. Just as rest is a state of inertia, a uniform translation is equivalent to rest and is also inertial.
The Principle of Inertia can be expressed in the following way: a free body, i.e. one not subject to any force, moves with constant velocity.
The Earth itself is an almost ideal inertial reference frame: in its orbit around the Sun, for the usual limited duration of laboratory experiments, it appears in first approximation to be moving in a straight line at a constant velocity of 30 km/s. The Earth’s inertial reference frame is specified by choosing directions pointing towards fixed stars, so as to compensate for the diurnal rotation.
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