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.Both are half full of water.I notice that steamis being emitted continuously from the one pan, but not from the other.I am surprised at this, evenif I have never seen either a gas range or a pan before.But if I now notice a luminous something ofbluish colour under the first pan but not under the other, I cease to be astonished, even if I havenever before seen a gas flame.For I can only say that this bluish something will cause theemission of the steam, or at least possibly it may do so.If, however, I notice the bluish something inneither case, and if I observe that the one continuously emits steam whilst the other does not, thenI shall remain astonished and dissatisfied until I have discovered some circumstance to which I canattribute the different behaviour of the two pans.Analogously, I seek in vain for a real something in classical mechanics (or in the special theory ofrelativity) to which I can attribute the different behaviour of bodies considered with respect to thereference systems K and K1.1) Newton saw this objection and attempted to invalidate it, but withoutsuccess.But E.Mach recognsed it most clearly of all, and because of this objection he claimed thatmechanics must be placed on a new basis.It can only be got rid of by means of a physics which isconformable to the general principle of relativity, since the equations of such a theory hold for everybody of reference, whatever may be its state of motion.Next: A Few Inferences from the General Principle of Relativity45 Relativity: The Special and General TheoryFootnotes1)The objection is of importance more especially when the state of motion of the reference-body isof such a nature that it does not require any external agency for its maintenance, e.g.in the casewhen the reference-body is rotating uniformly.Relativity: The Special and General Theory46 Relativity: The Special and General TheoryAlbert Einstein: RelativityPart II: The General Theory of RelativityA Few Inferences from the General Principle of RelativityThe considerations of Section 20 show that the general principle of relativity puts us in a position toderive properties of the gravitational field in a purely theoretical manner.Let us suppose, forinstance, that we know the space-time " course " for any natural process whatsoever, as regardsthe manner in which it takes place in the Galileian domain relative to a Galileian body of referenceK.By means of purely theoretical operations (i.e.simply by calculation) we are then able to findhow this known natural process appears, as seen from a reference-body K1 which is acceleratedrelatively to K.But since a gravitational field exists with respect to this new body of reference K1,our consideration also teaches us how the gravitational field influences the process studied.For example, we Wayrn that a body which is in a state of uniform rectilinear motion with respect toK (in accordance with the law of Galilei) is executing an accelerated and in general curvilinearmotion with respect to the accelerated reference-body K1 (chest).This acceleration or curvaturecorresponds to the influence on the moving body of the gravitational field prevailing relatively toK.It is known that a gravitational field influences the movement of bodies in this way, so that ourconsideration supplies us with nothing essentially new.However, we obtain a new result of fundamental importance when we carry out the analogousconsideration for a ray of light.With respect to the Galileian reference-body K, such a ray of light istransmitted rectilinearly with the velocity c.It can easily be shown that the path of the same ray oflight is no longer a straight line when we consider it with reference to the accelerated chest(reference-body K1).From this we conclude, that, in general, rays of light are propagatedcurvilinearly in gravitational fields.In two respects this result is of great importance.In the first place, it can be compared with the reality.Although a detailed examination of thequestion shows that the curvature of light rays required by the genernal theory of relativity is onlyexceedingly small for the gravitational fields at our disposal in practice, its estimated magnitude forlight rays passing the sun at grazing incidence is nevertheless 1.7 seconds of arc.This ought tomanifest itself in the following way.As seen from the earth, certain fixed stars appear to be in theneighbourhood of the sun, and are thus capable of observation during a total eclipse of the sun.Atsuch times, these stars ought to appear to be displaced outwards from the sun by an amountindicated above, as compared with their apparent position in the sky when the sun is situated atanother part of the heavens.The examination of the correctness or otherwise of this deduction is aproblem of the greatest importance, the early solution of which is to be expected of astronomers.1)In the second place our result shows that, according to the general theory of relativity, the law ofthe constancy of the velocity of light in vacuo, which constitutes one of the two fundamentalassumptions in the special theory of relativity and to which we have already frequently referred,cannot claim any unlimited validity.A curvature of rays of light can only take place when thevelocity of propagation of light varies with position.Now we might think that as a consequence ofthis, the special theory of relativity and with it the whole theory of relativity would be laid in the dust.But in reality this is not the case.We can only conclude that the special theory of relativity cannotclaim an unlinlited domain of validity ; its results hold only so long as we are able to disregard theinfluences of gravitational fields on the phenomena (e.g.of light).47 Relativity: The Special and General TheorySince it has often been contended by opponents of the theory of relativity that the special theory ofrelativity is overthrown by the general theory of relativity, it is perhaps advisable to make the factsof the case clearer by means of an appropriate comparison.Before the development ofelectrodynamics the laws of electrostatics were looked upon as the laws of electricity.At thepresent time we know that electric fields can be derived correctly from electrostatic considerationsonly for the case, which is never strictly realised, in which the electrical masses are quite at restrelatively to each other, and to the co-ordinate system.Should we be justified in saying that for thisreason electrostatics is overthrown by the field-equations of Maxwell in electrodynamics ? Not inthe least.Electrostatics is contained in electrodynamics as a limiting case ; the laws of the latterlead directly to those of the former for the case in which the fields are invariable with regard to time.No fairer destiny could be allotted to any physical theory, than that it should of itself point out theway to the introduction of a more comprehensive theory, in which it lives on as a limiting case
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