So, I was trying out planck units, I divided plank length by planck time, which is supposed to be 1. But it is c in SI units. that was a long row to hoe just to hand wave SI_c to 1 in a whole 'nother unit system. I could have done that in our SI unit system without planck units.
The Math Doesn't Lie: The actual numerical values derived for Planck length and Planck time, when expressed in a consistent system like SI, have a ratio equal to c_SI, not 1. The "Hand Wave" is Still There: After all the complex definitions involving ħ, c, and G to get l_P and t_P, the Planck system still requires the separate convention or "hand wave" of declaring that within this system, the numerical value of SIc will be treated as 1. Redundancy for If all you want is a system where c=1, you absolutely can achieve that much more simply. For example, keep the SI second and define a "light-second" as your unit of length (effectively scaling the meter by c_SI). Done. c=1 in that system. No need for ħ or G. The Planck Complexity: So, yes, going through the whole process of defining l_P and t_P using ħ and G seems like a ridiculously complicated detour if the only goal is to make c=1. It achieves c=1 only because c is declared to be 1 by convention.
In fact planck units would still require constants with value to scale between all the differently scaled units.
In SI units:
4.79924307337e-11 K = 1 Hz = 7.37249732381e-51 kg = 6.62607015e-34 J
In Plank Units:
1.416784E+32 temp = 1/5.391247E-44 Hz = 2.176434E-8 mass = 1.9561E+9 energy
In natural units:
1 K = 1 Hz = 1 kg = 1 J
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