, the acceptance of the electromagnetic formula connecting
and
is a slight affair. There is no presumption against it, once granting the conception of diverse time-orders which had not hitherto been thought of.
11.6 But there are certain objections to the acceptance of Einstein's definition of simultaneity, the 'signal-theory' as we will call it. In the first place light signals are very important elements in our lives, but still we cannot but feel that the signal-theory somewhat exaggerates their position. The very meaning of simultaneity is made to depend on them. There are blind people and dark cloudy nights, and neither blind people nor people in the dark are deficient in a sense of simultaneity. They know quite well what it means to bark both their shins at the same instant. In fact the determination of simultaneity in this way is never made, and if it could be made would not be accurate; for we live in air and not in vacuo.
Also there are other physical messages from place to place; there is the transmission of material bodies, the transmission of sound, the transmission of waves and ripples on the surface of water, the transmission of nerve excitation through the body, and innumerable other forms which enter into habitual experience. The transmission of light is only one form among many.
Furthermore local time does not concern one material particle only. The same definition of simultaneity holds throughout the whole space of a consentient set in the Newtonian group. The message theory does not account for the consentience in time-reckoning which characterises a consentient set, nor does it account for the fundamental position of the Newtonian group.
[12. Congruence and Recognition]. 12.1 Again the theory that measurement is essentially coincidence requires severe qualification. For if it were true only coincident things, coincident both in time and space, could be equal, yet measurement can only be of the slightest importance in so far as some other element not coincidence enters into it.
Let us take a simple example. Two footrules are placed together and are found to coincide. Then at the moment of coincidence they are equal in length. But what is the use of that information? We want to use one rule to-morrow in London and the other rule a week hence in Manchester, and to know that the stuffs which they measure are of equal length. Now we know that, provided they are made of certain sorts of material (luckily, materials easy to procure) and treated with certain precautions (luckily, precautions easy to observe), the footrules will not have altered their lengths to any extent which can be detected. But that means a direct judgment of constancy. Without such a judgment in some form or other, measurement becomes trivial.