A dimensionless number is a number which does
not depend on what system of units you use,
whether you refer to cm or inches or any other units you like, a dimensionless number will
always be the same. An example of a dimensionless
number, provided by nature, is the ratio of
the mass of the proton to the mass of the
electron. It does not matter whether you measure
your mass in pounds or grams you always get
the same ratio. There is another dimensionless
number which connects Planck's constant and
the electronic charge. You get a number which
is about 137, quite independent of your units.
Now when a dimensionless number like that
turns up a physicist thinks there must be
some reason for it, why it should be just 137 and
not 256 or something quite different. At present
one cannot set up a satisfactory reason for
it. Still people believe that with future
developments, a reason will be found.
Now there is another dimensionless number
which is of importance. If you have an electron
and a proton the electric force between them
is inversely proportional to the square of
the distance. The gravitational force is also
inversely proportional to the square of the
distance. The ratio of those 2 forces does
not depend on the distance. That ratio gives
you a dimensionless number. That number is
extremely large, about 10^39. Of course this
does not depend on which units you are using.
It is a number that is provided by nature
and we should expect that theory would someday
provide a reason for this number. How could
possibly hope to get an explanation for such
a large number? Well you might connect it
with another large number: the age of the
universe.
The universe has an age because one observes
that the spiral nebulae (galaxies), the most
distant objects in the sky, are all receding
from us with a velocity proportional to their
distance and that means at a certain time
in the past they were all extremely close
to each other. The universe started quite small,
perhaps as a mathematical point, and there
was a big explosion and these objects were
shot out and the ones that were shot out fastest
are the ones which are furthest away from
us. That explains the relationship, Hubble's
relationship, that the velocity of recession
is proportional to the distance and from the
connection between the velocity of recession
and the distance we get the age when this
universe started off. It's called the Big
Bang Hypothesis; there's a definite age when
the big bang occurred and most recent observations
give it to be about 18 billion years ago. Now you
might use some atomic unit of time instead
of years, years is quite artificial depending
on our solar system. Take an atomic unit of
time, express the age of the universe in this
atomic unit you again get a number about 10^39. Roughly the same as the previous
number. Now you might say this is a remarkable
coincidence but its rather hard to believe
that. One feels that there must be some connection
between these very large numbers a connection
which we cannot explain at present but one
which we will be able to explain in the future
when we have a better knowledge both of atomic
theory and of cosmology. Let us assume that
both of these numbers are connected. Then
one of these numbers is not a constant. The
age of the universe of course gets bigger
and bigger as the universe gets older, so
the other number must also be increasing in
the same proportion.
That means that the electric force, compared
with the gravitational force, is not a constant
is not but is increasing proportionally to
the age of the universe. The most convenient
way of thinking of that is to use atomic units
which make the electric force constant and
then, referring to these atomic units, the
gravitational force will be decreasing. The
gravitational constant, usually denoted by
G, when expressed in atomic units is thus
not a constant anymore but is increasing inversely
proportional to the age of the universe. One
would like to check this result by observation
but the effect is very small. However, one
can hope that observations will be made in
the next few years and it would be possible
to check whether G is really varying or not. If
it is varying then we have the problem of
fitting in this varying G with our previous
ideas of relativity. The ordinary Einstein
theory demands that G should be a constant.
We have to modify it in a certain way, we
don't want to abandon it altogether because
it is so successful. I have proposed a way
of modifying it which (Edward Milne) refers
to 40 years ago but he used different arguments
from mine, his equations are in some respects
similar to mine, in other respects there are
differences ,so that this theory of mine is
essentially a different theory from Milne's
although based on some ideas which were first
introduced by Milne and one should give Milne
the credit for having the insight of thinking
that perhaps the gravitational constant is
not really constant at all. Nobody else had
questioned that previously.
The amount of particles, elementary particles
protons and neutrons, in the universe is about
10^78; the square of the age of the universe
and this seems again, once you say that this
is not a coincidence, that there is some reason
behind it. Therefore the number of particles
in the universe will be increasing proportionally
to the square of the age of the universe,
so that new matter must be continually created.
There was previously a theory of continuous
creation of matter, called the Steady State
Cosmology, but this theory of mine is different
from the Steady State Cosmology, because the
Steady State Cosmology demands that G shall
be a constant; everything has to be steady
and in particular G has to keep a steady value.
Now I want to have G varying and I also want
to have continuous creation, it's possible
to combine those two ideas and I have worked
out some equations and models of the universe
incorporating them. Because there would be
a maximum size, this maximum size, expressed
in atomic units, would give you a large number
which does not vary with the time. Now I want
all large numbers to be connected with the
age of the universe so that they will all
increase as the universe gets older and if
your model gives you a large number, on the
order of 10^39, which is constant, you must
rule out that theory. It must go on expanding
forever and it can't turn around and contract
like many people believe.
