## Planck Constant Estimation Using Constant Period Relativistic Symmetric Oscillator

**Authors:** J. Bar-Sagi

The electromagnetic wave quantum-energy depends only on its frequency, not on the emitting
system's radiation power. The proportionality constant between the frequency and the quantumenergy
of the electromagnetic wave, the Planck's constant is in the essence of quantum mechanics.
This constant is known experimentally but till now there was no clue for calculating its value
on a theoretical basis. In the present work a methodology for calculating a lower bound for
Planck's constant is presented, based on simple principles. In order to get a reasonable good
lower bound it is necessary to have a model of a relativistic oscillator whose period is independent
of its energy and which efficiently radiates electromagnetic energy. It is highly desired that
the mathematics involved is simple enough to enable good insight into the results. Such a model
can also be used for other investigations, and therefore, in this work a potential that conserves the
vibration period of symmetric oscillators at relativistic velocities is found and analyzed. The
electrically charged system of constant period is used to calculate a lower bound H_{m} of the
Planck's constant h . The value of H_{m} is smaller than h by a factor very close to √3 . The
explanation of this factor also explains the value of Planck's constant. From this value the fine
structure constant value is calculated and a new interpretation of this constant obtained.

**Comments:** 15 pages

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### Submission history

[v1] 14 Jul 2010

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