572 



NA TURE 



[October 28, 1922 



Letters to the Editor. 



! The Editor does not hold himself responsible tor 

 opinions expressed by his correspondents. Neither 

 can he undertake to return, or to correspond with 

 the writers of, rejected manuscripts intended for 

 this or any other part of Nature. No notice is 

 taken of anonymous communications.'] 



Relativity and Physical Reality. 



In a review by Prof. H. Wildon Carr entitled 

 " The New Way of Thinking Physical Reality," 

 which appeared 'in Nature of October 7, p. 471, 

 the writer (speaking of a work by Prof. Leon Brun- 

 schvicg) says regarding physical reality : " Accord- 

 ing to Einstein, we cannot say, speaking absolutely, 

 that there is any picture even for God." 



It seems to follow from this that not even the 

 Almighty himself could understand the theory of 

 relativitv. If this be so I cannot help thinking 

 that the fault lies with the theory of relativity and 

 not with the Almighty. 



The writer then proceeds to say : " The picture 

 is only known as a function of the frame. That is, 

 the things measured are only known through the 

 measurings, and the measurings are bound up with 

 the things they serve to measure." 



This seems" to imply that measurement is the 

 fundamental thing to be considered in space-time 

 theory, and with this I am not in agreement. 



In my book, " A Theory of Time and Space," 

 published in 1914, I showed that the ideas of measure- 

 ment could be built up from the ideas of before and 

 after, which were regarded as absolute and not 

 dependent on any particular individual. 



In my smaller book, " The Absolute Relations of 

 Time and Space," I gave an abbreviated account of 

 this work and added an appendix showing how the 

 various complicated geometries which are treated 

 of in Einstein's generalised relativity could be obtained 

 by means of a modified measure of interval. 



"However, most relativists have been too busily 

 engaged in praising Einstein to spare the time to go 

 into my work. 



One result of this has been that, by taking the idea 

 of measurement as the fundamental thing, a very 

 large number, if not the majority, of relativists have 

 fallen into the very serious error of asserting that 

 the length of what they call a " world-line " is a 

 minimum between any two points of it. In my 

 " Theory of Time and Space " I showed (p. 360) 

 that this is not correct. 



Finding that a number of writers were making 

 this mistake, I wrote a letter which appeared in 

 Nature (February 5, 1920, p. 599) in which I invited 

 attention to this matter and pointed out that in 

 what I called " inertia lines " the length, so far from 

 being a minimum, was actually a maximum in the 

 mathematical sense ; while, in what I called " separa- 

 tion lines " the length was neither a maximum nor 

 a minimum. 



In this letter I gave actual numerical examples to 

 illustrate these points. I invited attention to the 

 matter again in my " Absolute Relations of Time 

 and Space " (p. 71), published in 1920. 



In spite of these efforts of mine, I again find this 

 blunder cropping up in works published this year. 

 Now it seems to me that it is a very important point 

 since, in ordinary geometry, there is no such thing 

 as a " longest " line joining two points. 



The idea would, 1 think, be apt to cause bewilder- 

 ment in the mind of a person meeting it for the first 

 time, unless it were properly presented to him. 



NO. 2765, VOL. I IOJ 



The idea of a " straight line " which was neither a 

 maximum nor a minimum would, I fancy, cause even 

 greater bewilderment, and he would wish to know 

 how such lines were to be defined. 



In Einstein's generalised relativity, the element of 

 interval is taken as a starting-point, although the 

 idea of an interval in the minds of many writers is 

 so obscure that they ascribe a minimum property to 

 it which it does not possess. 



Although I have tried so often to impress on 

 relativists that the ordinary method of treating space- 

 time theory is unsatisfactory, I propose to make one 

 more attempt to show that the measurement of 

 intervals is not the simple thing that is so often 

 supposed. 



Let us consider the simple time-space theory in 

 which the length of an element ds of what I call a 

 " separation line " is given by the formula : 

 ds 2 =dx 2 +dy 2 + ds*-dt*. 



Let O be the origin of co-ordinates and let P be 

 any point on the axis of x, at a distance I from O, 

 measured, say, in the positive direction. 



Let F(x) be any arbitrary differentiable function 

 of x which is continuous and single valued, and 

 which is equal to zero for x =0 and for x =1. 



Now consider the space-time curve the equations 

 of which are : 



y =U=F(x), 

 z =0. 



It is evident that this curve passes through O and P. 



But now we have 



dy =dt, 

 dz =0, 

 and so ds* -dx*. 



Thus we have ds =dx, and so the length measured 

 along the space-time curve from O to P is equal to 

 the length from O to P measured directly along the 

 axis of x. That is, it is equal to /. 



Thus a space-time curve the equations of which 

 contain an arbitrary function can have the same 

 length between two points as the direct length 

 measured between those points. 



Alfred A. Robb. 



October 11, 1922. 



The Miraculous Draught of Fishes— an Explanation. 



We have in the Gospel according to Saint John, in 

 his twenty-first and last chapter, an account of the 

 miraculous draught of fishes in the lake of Galilee for 

 which modern research into the habits of the Galilean 

 fishes offers a perfectly reasonable explanation. The 

 account is as follows : 



" Simon Peter saith unto them [certain of the 

 disciples], I go a fishing. They say unto him. We 

 also go with thee. They went forth, and entered into 

 a ship immediately ; and that night they caught 

 nothing. But when the morning was now come, Jesus 

 stood on the shore. . . . Then Jesus saith unto them, 

 Children, have ye any meat ? They answered him, 

 No. And he said unto them, Cast the net on the right 

 side of the ship, and ye shall find. They cast there- 

 fore, and now they were not able to draw it for the 

 multitude of fishes." 



Simon Peter then girded his fisherman's garment 

 around him and leaped overboard. But the other 

 disciples brought their boat to shore dragging the net 

 full of fishes with them. Further on we read : 

 " Simon Peter went up, and drew the net to land full 

 of great fishes, an hundred and fifty and three : and 

 for all there were so many, yet was not the net broken." 



The explanation of this is to be found in a study of 

 the habits of the fishes living in the lake of Tiberius or 



