Planck Charge

[gre]

Has the value of the elementary charge of a particle decreased over time? I'm curious why 'e' is lower than the Planck charge value and if the Planck charge value ever shows up ever in nature.

 

Thanks,

Greg

[insane_alien]

the planck charge is nothing special its just a unit of charge that is based on some fundemental physical constants.

 

there is no evidence of it changing over time.

[swansont]

Since the Planck charge is a non-integral multiple of the fundamental charge, no, it never shows up in nature.

[ajb]

Which opens a question as to why charge is quantised. The best argument I have come across is that of Dirac.

[gre]

ajb, What is Dirac's argument?

[ajb]

It requires some geometry (principle bundles, connections, Chern classes etc.) to understand it clearly, but the Wiki article on magnetic monopoles is a good place to start.

 

It requires the existence of a magnetic monopole. The outcome of this is that the product of the magnetic and electric charge must be an integer (units [math]\hbar = 1[/math]).

 

It turns out that the existence of just one magnetic monopole would imply that electric charge is quantised.

 

I'm not sure how much to say here, you need to know a little about gauge transformations and geometry to proceed much further with this. It is outlined in a report I wrote a couple of years ago.

[Martin]

I'm curious why 'e' is lower than the Planck charge value and if the Planck charge value ever shows up ever in nature.

 

Has anyone ever seen a presentation of the Planck units in which the Planck charge is defined to be precisely equal to the elementary charge e?

 

This would mean that the coulomb force constant would be derived (rather than being a unit itself.)

 

Using the fine structure constant, alpha, approximately 1/137, the coulomb force constant would be

[math]\alpha \hbar c/ e^2[/math]

 

It would also mean that the Planck charge value does show up in nature (all the time! )

 

I think it's optional. You have a choice when you set up Planck units.

 

Wikipedia is not always the best source.

http://en.wikipedia.org/wiki/Planck_units

The authors there are pushing the version of Planck units with the coulomb force constant used as unit.

But I've seen different versions.

Edited March 24, 2009 by Martin

[gre]

"e" does seem like an oddball. And coulombs (1/(4*pi*Electric_Constant)) seems to convert elementary charge (e) to Planck charges, anyway.