Clifford Pickover |
In a post I published in this blog over three years ago, I talked about the fine structure constant and some of its physical peculiarities. In this post I am going to talk about some of its mathematical peculiarities. I have taken them from a book I have mentioned on other occasions: A Passion for Mathematics, by Clifford A. Pickover.
As we know, the
most exact value of this constant is this:
α = 1/137.035999206
Pickover points out that Eric W. Weisstein, in his World of Physics website, offers two mathematical approximations incredibly close to this value:
α–1 ≈ 44 π – cos–1(e–1) = 137.03600
. . .
α–1 ≈ 96(e1/2
+ 21/3)1/3 =
137.03599 . . .
Arthur Eddington |
Physicist Arthur
Eddington, who we have talked about often in
this blog, was fascinated by the fine structure constant. Apart from
stating that its value should be exactly equal to 1/137 (although the most
exact measurements show that it is not), he also maintained that this value is
related to the number of electrons in the universe (another statement that many
physicists do not accept).
Another curious
formula, proposed by a Russian mathematician, relates (approximately) the value
of the fine structure constant to the number
π and the
golden number ϕ, according to the following formula:
As could be
expected, this constant has also been associated to the pyramid of Cheops and
the megalithic monuments of Stonehenge.
Richard Feynman |
Richard Feynman
wrote this about the fine structure constant:
[The value of the fine structure
constant] has been a mystery ever since it was discovered more than fifty years
ago, and all good theoretical physicists put this number up on their wall and
worry about it. Immediately you would like to know where this number for a
coupling comes from: is it related to pi or perhaps to the base of natural
logarithms? Nobody knows. It’s one of the greatest damn mysteries of physics: a
magic number that comes to us with no understanding by man. You might say the
‘hand of God’ wrote that number, and ‘we don’t know how He pushed His pencil.’
We know what kind of a dance to do experimentally to measure this number very
accurately, but we don’t know what kind of dance to do on the computer to make
this number come out, without putting it in secretly!” (Richard Feynman, QED,
1988).
Thematic Thread on Particle Physics: Previous Next
Manuel Alfonseca
Have a happy vacation. See you by mid-August.
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