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I was wondering if it is possible to compute e.g. bohr radii for a metric system whose correspondence to real units is unknown and only the speed of light is known.

Let's say the only thing I know is that lightwaves travel x spaceunits in t timeunits, therefore defining the speed of light. The obvious problem is that I lack correspondance to real units such as meters for space and seconds for time.

So the question is: Is it possible to compute e.g. the bohr radius of an electron in groundstate in the hydrogen in units of x (or alternatively ct, lightspeed time) from just this defined lightspeed ? I've read that sometimes physisists set c=1 and hbar=1, but I don't get how to convert the dependent constants appropriately. Would this help solve my problem at all ? And if so how would this be done exactly ?

Thanks and cheers.

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# De Broglie wavelength computable by just fixing speed of light ?

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