Hi Adel,
According to my model, whatever unit of time we use, the value of the Planck time will always be the same (ie: will always follow the same equation including Phi and 8Pi-1). So if we were counting time in Martian days, the value of the Planck unit would be 5.386 x 10xx Martian days. (nothing says that the Planck time has got a fixed value, it is only fixed in relation to the base unit we choose). The same thing with the Planck length, whatever unit of length we choose, it will always have the same value in relation to that unit of length and because the speed of light is the ratio between the Planck Length and the Planck Time, the speed of light will always be the same. The only thing that will change is the scale factor, this scale factor is changing with the age of the Universe, (it does not need to be exact, the precision of our instruments will never allow us to detect a change in a short period). The scale factor of 1020 in my equations is not a fudge, it is the cubic root of the age of the Universe in Planck units (see my model for exact explanation). Basically, by choosing a unit of time and a unit of length, we choose the scale of our reality.(in a certain way, the size of the pixels)
One easy way to check that out would be to change our "meter" unit and our "second" unit and check the size of a proton again, I bet that it will have the same value.
Cheers,
Patrick