34 RELATIVITY 



sheet would not balance. In accounting for the rest of 

 space there is left only 3 feet between the crown of his 

 head and the soles of his boots. His balance-sheet 

 length is therefore "written down" to 3 feet. 



The writing-down of lengths for balance-sheet pur- 

 poses is the FitzGerald contraction. The shortening of 

 the moving rod is true, but it is not really true. It is not 

 a statement about reality (the absolute) but it is a true 

 statement about appearances in our frame of reference.* 

 An object has different lengths in the different space- 

 frames, and any 6-foot man will have a length 3 feet in 

 some frame or other. The statement that the length of 

 the rapid traveller is 3 feet is true, but it does not indicate 

 any special peculiarity about the man; it only indicates 

 that our adopted frame is the one in which his length is 

 3 feet. If it hadn't been ours, it would have been some- 

 one else's. 



Perhaps you will think we ought to alter our method 

 of keeping the accounts of space so as to make them 

 directly represent the realities. That would be going to 

 a lot of trouble to provide for what are after all rather 

 rare transactions. But as a matter of fact we have 

 managed to meet your desire. Thanks to Minkowski 

 a way of keeping accounts has been found which 

 exhibits realities (absolute things) and balances. There 

 has been no great rush to adopt it for ordinary purposes 

 because it is a four-dimensional balance-sheet. 



Let us take a last glance back before we plunge into 



*The proper-length (p. 25) is unaltered; but the relative length is 

 shortened. We have already seen that the word "length" as currently- 

 used refers to relative length, and in confirming the statement that the 

 moving rod changes its length we are, of course, assuming that the word 

 is used with its current meaning. 



