What Happened to Heisenberg's Constant in Planck Units?

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Discussion Overview

The discussion centers around the implications of using Planck units on Heisenberg's constant and the Heisenberg Uncertainty Principle (HUP). Participants explore how constants can appear or disappear based on the choice of units and the mathematical frameworks employed, particularly in the context of energy, mass, and dimensions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about the disappearance of Heisenberg's constant when using Planck units, suggesting that energy can be expressed in terms of Planck mass and constants.
  • Another participant argues that any dimensional constant can be transformed away by selecting appropriate dimensions, using the example of light years and years to illustrate this point.
  • A later reply questions the validity of "transforming away" Heisenberg's uncertainty, indicating a belief that the HUP is fundamentally different from other constants.
  • Another participant notes that the HUP arises from Fourier analysis and that Heisenberg's constant only becomes relevant when discussing momentum rather than wave number (k).

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the treatment of Heisenberg's constant and the Heisenberg Uncertainty Principle in the context of dimensional analysis and unit transformations. Some believe constants can be transformed away, while others argue that the HUP cannot be dismissed in the same manner.

Contextual Notes

The discussion highlights the complexity of dimensional analysis and its implications for fundamental constants, but does not resolve the underlying assumptions or definitions that may affect interpretations.

droog
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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?
 
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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.
 
Meir Achuz said:
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.
 
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.
 

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