172 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1949 
of the first observer, although the relation of time and distance is 
such that they both observe the same laws of physics. LHinstein 
formulated his relativity on the philosophy that it is simply impos- 
sible to tell which observer is ‘‘at rest.’”? Complicated as it sounds, 
this scheme has been developed to form a logically complete theory 
in terms of mathematical transformations. Milne extended the 
established principles of relativity in his “cosmological principle,”’ 
which is, in effect, an assumption that the view of the whole universe 
from one spiral nebula must be the same as the view from any other. 
Moreover, he has redefined distance measurements in terms of the 
travel time of light signals, as in radar ranging, thus reducing both 
time and distance measurements to readings of clocks, in principle. 
¢ e e ‘ ¢ . ’ ¢ eo e ¢ e oe 
° e e e e o e ¢ 7 e a e e 
e o . . ¢ e e a e ¢ eo ¢ e 
e ‘ ¢ ¢ o ° e ’ ° eo eo e ¢ 
Us 
o e e ° 2 , e ¢ ‘ eo 6 oe eo 
Figure 4.—Milne’s picture of the universe. If all measurements are made in 
atomic time, on Milne’s theory, the universe started expanding from a point 
3 billion atomic years ago. As we see it now the spiral nebulae shown in the 
left diagram are all moving away from us and (if we could see far enough) 
would be much more numerous near the “edge.”” At this edge the velocity of 
recession is equal to the velocity of light, so we can never hope to see the edge 
itself. On the other hand, if clock time is used for all our measurements, the 
universe is static and the spiral nebulae, as shown on the right above, are 
uniformly distributed on to infinity. The more distant nebulae are redder be- 
cause we see them as they were many years ago with “‘slow” atoms. The 
“edge’’ of this picture comes when this reddening gets so extreme that galaxies 
are no longer visible. 
Milne then raises the disturbing question: How are we sure that 
our clocks are reading constant intervals of time? In fact, the slow- 
ing down of the earth’s rotation (which is normally our ‘master 
clock’’) has been measured as one-thousandth of a second per century 
by comparison with the planets, and we have no philosophically 
sound assurance that the planets keep “‘perfect time.” 
The cosmological principle leads mathematically to two kinds of 
time, one of which is speeding up relative to the other. Milne has 
shown that pendulum clocks, the earth, and the planets keep ‘‘dy- 
