SPACE, TIME 287 



same as the down-up direction, the right-left is the same as 

 the left-right, and the here- there is the same as the there-here. 

 Spatial lines have no arrows. Directional passage in space 

 is not affected by the character of space. Isotropy in both 

 of these senses is required for measurement. Though it is 

 properly the material object, i.e., the scale, which is presumed 

 to be unchanged by any movement in space, corresponding 

 properties are attributed to space itself. "For example, 

 it is assumed that the interval associated with any two 

 points on a rigid rod (used as a scale) is independent of 

 any motion of the rod; that is, no matter how the rod is 

 moved about as a measuring instrument, the interval re- 

 mains the same. This is a natural assumption; it is difficult 

 to see how measurement could be carried out at all simply 

 without it. Yet we must recognize its postulational nature. 

 As soon as we have transferred it from its status as a postu- 

 late about operations with physical objects to a postulate 

 about 'space,' it becomes equivalent to the assumption of 

 isotropy and homogeneity (or free mobility, as we shall 

 later call it) which are then considered characteristics of 

 physical space." * 



In the directional sense time may or may not be consid- 

 ered isotropic, depending upon the level of abstraction at 

 which it is examined. From the empirical point of view, 

 as will be seen later, time has an obvious arrow; events 

 which are now future become present and then past; time 

 "flows" from the future to the past and not from the past 

 to the future. From the scientific point of view, however, 

 the story may be different. At least if one asks what the 

 symbol t means, as it occurs in physical equations, he may 

 receive a different answer. If one limits himself to the equa- 

 tions of mechanics, "the equations are just as valid for 

 negative values of / as they are for positive values. If the 



1 Reprinted by permission from Foundations of Physics by R. R. Lindsay and 

 H. Margenau, published by John Wiley and Sons, Inc. Professor Carl Eckart 

 has pointed out to the author that this "assumption" of Lindsay and Margenau 

 should be taken either as a definition of "rigidity" or as a definition of "interval." 

 To make it an assumption involves a needless multiplication of undefined terms. 



