Planck units

It has been shown that the Planck charge differs considerably from the elementary one e = 1,6 X 10^{-19} C

q_{P} ~11.7 e

a seemingly poor prediction.

The implications of this result have however been overlooked or misunderstood. Indeed by simply squaring the above equation

q_{P}^2 ~137 e^2

one obtains

alpha _{P} \simeq 137 alpha = 1

Thus at the Planck scale the fine structure constant is one.

The same applies , by equating Planck forces (and potential) proportional to GM^{2} _{P} = h c to the other interactions, also to the other coupling constants.

alpha = alpha_{strong} = alpha_{w} = 1 where the Planck suffix has been omitted (see enclosed figure ).

Thus the statement that "comparing masses and charges is like comparing apples with oranges" is totally contradicted. At a fundamental level (i.e not for the proton mass) they are closely connected.

page4image188

Figure 1. Time and temperature dependence of the different interactions. Not in scale. This shows how from the present very different values, the coupling constants tend to one at the Planck origin of space-time.

Christillin, P. (2023) On the Fine Structure and the Other Coupling Constants at the Planck Scale. Journal of Modern Physics , 14, 666-669. https://doi.org/10.4236/jmp.2023.145037

References

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