Table 2: Schematic summary of the views of Galileo added to Table 1
Einstein’s railway carriage
Einstein deepened Galileo’s insights. He discusses Galileo’s principle of relativity, which he calls “the fundamental law of the mechanics of [Galileo] Galilei-Newton” at the very beginning of his short popular primer, Relativity (first written in 1916 and still in print). He poses two questions:
“I stand at the window of a railway carriage which is travelling uniformly, and drop a stone on the embankment, without throwing it. Then, disregarding the influence of the air resistance, I see the stone descend in a straight line. A pedestrian who observes the misdeed from the footpath notices that the stone falls in a parabolic curve. I now ask: Do the ‘positions’ traversed by the stone lie ‘in reality’ on a straight line or on a parabola? Moreover, what is meant here by motion ‘in space’?”
Einstein, Relativity, p9
Einstein reminds us that Galileo and Newton (in respect of his first law of motion) have shown that in reality both views are equally valid. Both views, furthermore, are objective descriptions of reality; neither are merely subjective impressions. Despite what Woods maintains, the subjective thoughts or impressions of individuals do not come into it.
Woods argues: “Einstein regretted his earlier subjective idealism, or ‘operationalism’, which demanded the presence of an observer to determine natural processes.” (p167) Einstein never demanded the presence of an observer to determine natural processes. It is a “complete misinterpretation of Einstein’s ideas” as Woods himself says slightly earlier (p163), without appearing to understand what he says. Einstein proceeds to re-phrase his own words this way:
“The stone traverses a straight line relative to a system of coordinates rigidly attached to the carriage, but relative to a system of coordinates rigidly attached to the ground (embankment) it describes a parabola.”
What concerns us is the relative positions of the stone, as measured according to two different system of coordinates, or frames of reference, one moving and one stationary – the train and the footpath.
But does one frame of reference offer a correct description, while the other is merely secondary? No, they are both correct. At first, we may be tempted to say that the pedestrian has the correct view or, to put the same
thing another way, that the stone, as measured according to the frame of reference of the earth, is the correct measurement, because the pedestrian is the ‘stationary’ one, standing on the ‘stationary’ earth.
But the earth is not stationary. We must keep in mind that in the few seconds it took for the stone to fall, the earth and the stone have travelled perhaps thirty kilometres or more around the sun. Why take the earth as the correct or absolute reference point? In addition, the sun itself travels round our galaxy, and our galaxy is moving in a complex gravitational dance with our local cluster of galaxies. And all independent clusters of galaxies in the universe are moving away from us at great speed, in proportion to their distance from us.1
Whose space is the correct space? From the point of view of physics each view, each measurement, whether from the railway carriage, the footpath, or the Andromeda galaxy, is equally valid. According to the Newtonian laws of motion which begin with Galileo’s insight (and which Newton acknowledged), the view from Andromeda is just as valid as the view from the train.
According to classical Newtonian physics, we have no trouble at all translating the measurements of one frame of reference into that of another. They have a very simple, physical relationship. Suppose the train is moving at twenty miles an hour relative to the footpath frame of reference. A passenger is walking towards the front of the train at three miles an hour in the railway carriage, or to put it another way, relative to the railway carriage frame of reference, the passenger is moving at three miles an hour. By simple addition, we say that the passenger is moving at twenty-three miles an hour relative to the footpath frame of reference – the speed of the train plus the speed of the passenger in the carriage.
We make this rather obvious point to make clear that no-one, whether Galileo, Newton or Einstein, is suggesting that, because the measurements are, in the common idiom, relative to the observer, these measurements are “subjective” in some way, or that physics has wallowed in subjective idealism ever since Galileo, which is the unintended essence of Woods’ claim.
However, Einstein realised that these calculations fail to take into consideration the speed of light. When we observed the train moving, we did so with the aid of light. But light does not travel instantaneously as our Newtonian calculation above assumed but at a definite speed. Furthermore, light has very unexpected properties. It is only once we have learnt about the strange qualities of light and have taken them into account that we can start to discuss Einstein’s universe. (In order to calculate the real transformation of the speed of the passenger relative to the carriage into his or her speed as measured from the platform, an equation associated with the physicist Hendrik Lorenz must be used, which takes the strange properties of light into account: the Lorenz transformation.)