What Happened to Heisenberg's Constant in Planck Units?

[droog]

I'm very confused. Energy can be expressed as:

h.C/wavelength

So, in Planck units, the energy of the plank mass could be written

h-bar.C/Lp

h-bar is in units of m^2 S ^-1 and C is in m s^-1
In plank units h-bar=Lp^2 Tp^-1 and C=Lp/Tp
So h-bar.c/Lp=Lp^2. T^-1.Lp.T^-1.Lp^-1 = C^2

Giving energy for plank mass = C^2 and mass = 1

Where did Henisenberg’s constant go? How can it be lost by selecting a different form of notation?

 

[Meir Achuz]

Any constant with diumension can be transformed away by using suitable dimensions. For instance, if light years are used for distance and years for time,
c disappears.

 

[droog]

Any constant with diumension can be transformed away by using suitable dimensions. For instance, if light years are used for distance and years for time,
c disappears.

But surely we can't just "transform away" something like Heisenberg Uncertainty. I'm still missing something incredibly simple here.

 

[Meir Achuz]

The HUP comes from Fourier analysis where \Delta k \Delta x>1/2.
It is only when you want to talk in terms of momentum rather than k that hbar
enters.