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اهمیت عدد 137 از این نظر مطرح می شود که به صورت زیبایی ثابت های الکترودینامیک را به یکدیگر ربط می دهد. این عدد تعدادی از ثابت های اساسی طبیعت را با یکدیگر ترکیب می کند

و از چپ به راست بار الکترون، سرعت نور، ثابت پلانک تقسیم بر دو پی و ثابت گذردهی خلاء است
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What is the
significance of the number 137 in physics?
The importance of the number 137 is that
it is related to the so-called 'fine-structure constant' of quantum
electrodynamics. This derived quantity is given by combining several
fundamental constants of nature:
where e is
the charge on the electron, c is the speed of light, h-bar is Planck's constant
and the epsilon represents the permittivity of free space. Despite the fact that
each of these constants have their own dimensions, the fine-structure constant
is completely dimensionless!
The importance of the constant is that it measures the strength of the
electromagnetic interaction. It is precisely because the constant is so small
(i.e. 1/137 as opposed to 1/3 or 5 or 100...) that quantum electrodynamics (QED)
works so amazingly well as a quantum theory of electromagnetism. It means that
when we go to calculate simple processes, such as two electrons scattering off
one another through the exchange of photons, we only need to consider the simple
case of one photon exchange -- every additional photon you consider is less
important by a factor of 1/137. This is why theorists have been so successful at
making incredibly accurate predictions using QED. By contrast, the equivalent
'fine-structure' constant for he theory of strong interactions (quantum
chromodynamics or QCD) is just about 1 at laboratory energy scales. This makes
calculating things in QCD much, much more involved.
It is worth noting that the fine-structure 'constant' isn't really a constant.
The effective electric charge of the electron actually varies slightly with
energy so the constant changes a bit depending on the energy scale at which you
perform your experiment. For example, 1/137 is its value when you do an
experiment at very low energies (like Millikan's oil drop experiment) but for
experiments at large particle-accelerator energies its value grows to 1/128.
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