6 Bateman, TJic Physicixl Aspect of Time. 



In order that Galileo's method of comparing times at 

 different points of space may be suitable for a sober 

 world, it seems necessary to suppose that a body cannot 

 move with a velocity greater than that of light, and it 

 may be of interest to remark that this view is supported 

 by modern electrical theories. 



Now let us suppose that a second system of observers, 

 B , B.-,,...B,,, find that their observations are in agreement, 

 and so can regard themselves as a standard system. It 

 may happen that according to their measurements the 

 first system of observers /} ^, A,,,... A,, are in motion, and 

 then it is easy to see that the specifications of position 

 and time as made by the J's and the ^'s will not agree. 



iiiLcrnally by a given sphere associated will) A, or if \vemake/„=0 il is clear 

 that there is only one sphere of the series which passes through a given point 

 in space, provided the radii of the spheres associated with £ are all positive ; 

 the equivalent supposition in the other case is that /^ > /., 



If B is moving with a velocity greater than that of light, two of the 

 spheres associated with it may intersect, and so two of them may be touched 

 internally by the same sphere belonging to A, and then B is able to see more 

 than one picture of the same event. See Figs. 2 and 3. 



Fz^. 2. F/^. 3. 



Again, if .4 is moving with a velocity less than that of ligiit the spheres 

 associated with A lie within one another or surround one anotlier in succession, 

 and it is clear that there is only one sphere of the series which touches 

 internally a given sphere associated with B. Hence B cannot see two 

 different states of A at the same time. If A is moving with a velocity 

 greater than that of light two of its spheres may intersect, and then it is quite 

 possible for B to see two or more different positions of ^ at a given time. 



If B and A are moving with \elocities less than that of light, and v\ e 



