We are all obsessed with numbers. And we are obsessed with trying to find patterns in numbers. Even those who are not interested in mathematics are obsessed with desire to find patterns in numbers. We all have favourite or “lucky” numbers. We have all searched for our lucky numbers in our car registration numbers, or our house numbers etc. Is this search for patterns illogical? Perhaps! But remember that all our science and mathematics is based on the desire to find patterns and to create new patterns. That is why the search for beauty and the search for science are the same thing.
In today’s VERITAS we will see how Physicists also indulge in this seemingly illogical quest to find relationships between their favourite numbers. And we will see how this “illogical” quest gives us some deep insights about Nature and her laws.
What are the favourite numbers of Physicists? The constants of nature. The speed of light(denoted by c), the mass of an electron(me), the mass of an nucleon(mn), the charge of an electron(e), Planck’s Constant(h) etc.
But these numbers are not very “natural”. For example the speed of light is measured in metres per second. And metres and seconds are man made creations. We need to express the constants of nature in terms of numbers without involving man made scales.
Lets invent a natural constant of nature. Divide e squared by h(Plank’s constant) and by c and we get a number 1/137. No matter what scale we use to measure h or c or e we will always get 1/137 when we divide e squared by h and c. This number ( we will denote it by a) is called the fine structure constant and it found in several equations of physics( whenever light interacts with particles). The number 137 is so popular with physicists that you can use it to open the codes of their bags or their passwords!
Lets find more: the ratio of mass of an electron and the mass of a nucleon is a natural constant ( 1/1837).
So now we have a set of natural constants: 1/137, 1/1837, 137 and 1837. Note the reciprocal of a natural constant is also a natural constant.
Can we find more? Yes: The electrical force between an electron and a nucleon is proportional to e^2( e squared). The gravitational force between the electron and the nucleon is propotional to G X me X mn. The ratio of these forces is a natural constant: .2 X 10^40. So it is a huge huge number: of the order of 10 raised to the power 40. We can find several more constants whose size is of the order 10^40.
Now Physicists noticed this very strange thing: either the constants are close to unity( 1/1837, 1/137, 137, 1837 etc), or they are close to( ie of the order of ) 10^40. So either the constants are very small or 40 orders of magnitude larger.
So lets group the constants into two parts: C_small and C_large.
The C_small are 10^40 times smaller than C_large. So the natural constants are lumped around these extreme values.
Now a even stanger thing: the size of the universe is about 15 light years across( this is called the hubble length). When we divide this by the size of a nucleon to make it a natural unit we get the number : 5 X 10^40! This is of the same size as C_large. The size of the universe and the ratio of the electrical and gravitational forces is of the same size!!!!
Friends, let me tell you that this is not a small coincidence.
Physicists suspect that there is a deeper relationship between the size of the universe( expressed in terms of nucleon size) and the constants C_large.
But what are we saying!!? We are saying that the size of the universe is related to the ratio of gravitational and electrical forces between the electron and proton!!! Either we are crazy or we have seen a very deep fact in the structure of the universe.
But we also know that the universe is expanding and thus the size of the universe is changing. So what happens to the relationship between the size of the universe and C_large?
Some physicists like Dirac have suggested that the constants of nature change in time so that the equality between the size of the universe and C_large is always maintained.
Some physicists like Dickie have suggested that the constants of nature do not change with time. But then what about the relationship between the size of the universe and C_large?
Dickie suggests that life can exist in a universe only at a time when the size of the universe is approximately of the size of C_large. So a conscious living being will always observe this strange relationship.
This suggestion is closely related to the Anthropic principle ( see VERITAS: The Anthropic Principle, 25 Aug 2004)
How is the universe related to these numbers? We do not know. Our knowledge is so limited. Yet through these numbers sometimes we see the thoughts of God. Maybe there is indeed a purpose in all this. Maybe the size of the universe is indeed related to the forces between electrons.
Maybe this thread that spans the layers of size of the universe is the fabric of the universe. Maybe … Maybe….
From Man or Angel the great Architect
Did wisely to conceal, and not divulge,
His secrets, to be scanned by them who ought
Rather admire. Or, if they list to try
Conjecture, he his fabric of the Heavens
Hath left to their disputes — perhaps to move
His laughter at their quaint opinions wide
Hereafter, when they come to model Heaven
And calculate the stars: how they will wield
The mighty frame: how build, unbuild, contrive
To save appearances; how gird the Sphere
With Centric and Eccentric scribbled o’er,
Cycle and Epicycle, Orb in Orb.
Go, wondrous creature! mount where Science guides:
Go, measure earth, weigh air, and state the tides:
Instruct the planets in what orbs to run,
Correct old time and regulate the Sun;