ORIGIN OF THE EARTH—PAGE tzZ3 
namic’”’ or clock time, while vibrating atoms and radioactive decay 
have constant period only in “kinematic”’ or atomic time. There is 
no philosophical reason for choosing one kind as the “correct” time; 
if we used a pendulum clock to time atoms we would find, after a very 
long interval, that the atoms are gradually speeding up in their 
vibration, if we used an atomic clock we would similarly find that the 
planets are slowing down in their orbits. 
If this is correct—and no one has yet proved it otherwise—the 
age of the earth is 3 billion atomic years as determined from radioactive 
decay, but it is many more clock years, since in the past the clock 
year was shorter than the atomic year. (They are equal at present— 
by definition.) 
The coincidence between the age of the earth and the time of reces- 
sion of the spiral nebulae Milne explains as a result of the difference 
in these two kinds of time. Since the light we observe from a spiral 
100 million light-years away left there 100 million years ago, we are 
seeing the atoms there ticking off the units of atomic time in use 100 
million years ago. Compared to our present atoms, these early 
atoms ran slow; as a result, the light they emitted is redder than the 
light emitted now by similar atoms on the earth. 
From this effect and his cosmological principle, Milne calculates 
that in the past infinite number of clock years there were 3 billion 
atomic years. The origin of the earth, and the time when all the 
spirals were close to our galaxy, both of them 3 billion atomic years 
ago, therefore occurred at the beginning of time (since one could hardly 
expect more than infinite time on the clock scale). 
Now for Haldane’s suggestion, which he calls ‘A Quantum Theory 
of the Origin of the Solar System.” It is based, as its name implies, 
on the well-established quantum theory of radiation, and on a mathe- 
matical result of Milne’s theory: that the universe, as measured in 
atomic time, has expanded with the velocity of light, starting from a 
point of zero radius 3 billion atomic years ago. 
Since the universe started from zero radius, Haldane was able to 
pick an early enough instant, just a fraction of a second after the start 
of atomic time, when the whole universe was but a fraction of an inch 
in diameter—much smaller than the wave length of visible light— 
smaller, by far, than the wave length of X-rays or gamma rays. 
(These fractions are too small to write out easily; the first requires 
72 zeros after the decimal point, the second, 62!) ‘The wave lengths 
of radiation in existence in this small universe could scarcely have 
been bigger than the universe itself, Haldane reasoned, therefore the 
only radiation in existence was of these incredibly short wave lengths. 
But the basic principle of the quantum theory is that radiant energy 
comes only in packets, or ‘quanta,’ inversely proportional to the 
wave length in size. So, at this early instant all radiation was in 
