Why I Like Planck

Any poor soul who has read all of my stuff, probably an imaginary person, or at the most a bot of some kind, will know that I like Planck units.  I’ve even been accused of assigning more importance to Planck units that one should.

To support an upcoming post, I want to explain why I like Planck.

Key to the FUGE model, making up fully half of the initialism, is granular expansion.  The notion is that the universe is granular at a very small scale.  The question then is precisely what scale most accurately reflects the granularity of the universe.

I prefer the Planck units as natural units for this task, since all but one of the fundamental physical constants resolve to unity when using them.

There is an exception, being the elementary charge, e.  However, it should be noted that the value to which the elementary charge resolves using Planck units is such that α=e², where α is the fine structure constant.  This falls out of the equation α=e²/4πε₀ħc, noting the resolution to unity of the three terms: the reduced Planck constant, ħ; the speed of light, c; and the “raised permittivity”, 4πε₀.  Note also that I consider that q_Pl=4πε₀ħc, because it is more meaningful than the other option (because as a consequence α=e²/ q_Pl²).

Note that α is a dimensionless constant which cannot therefore resolve to unity.  As far as I can tell, the only fundamental physical constant that would change in a universe which had a different value of α would be the elementary charge.

That all said, it is possible that there is another set of natural units that underlie the granularity of the universe.  If so however, each fundamental physical constant when expressed in terms of those natural units would make some sort of sense.  The problem with using an alternative is that the Planck units already make maximal sense of the fundamental physical constants.  Any deviation from them merely adds problems.

There are currently five alternative schemes:

• Stoney units,
• Schrödinger units,
• Atomic units,
• (Atomic) natural units, and
• Strong units

The sixth apparent alternative, “geometrized units”, is really just a subset of any other alternative scheme in which c and G resolve to unity.

The first two, Stoney units and Schrödinger units, are better than the schemes used in atomic physics because in both cases the related energy units are equal to Planck energy.  This might not be immediately apparent for the Schrödinger units, but it must be noted that in that scheme, the speed of light is not 1, but rather 1/α.  These schemes are not suitable for representing the granularity of the universe they both include the fine structure constant α in the definition of dimensional units, which is not dimensional and thus cannot be resolved to unity.  It is introduced via the use of the elementary charge as the basic unit of charge.  The reduction of the natural unit of charge to unity deletes any meaning from the value of α which is, on the other hand, obvious with the Planck scheme (that is, as mentioned above, α=e²/q_Pl²).

The schemes used in atomic physics (atomic units and the unhelpfully named “natural units”) both use the electron mass as a basis and is therefore not suitable for representing the granularity of the universe.  The same applies to strong units used in nuclear physics, which has proton mass as a basis.

If there is a better scheme, I certainly cannot think of one.  If there is any action that takes place in a period of less than one unit of Planck time, I cannot think of one.  If there is any fundamental particle that is shorter than one unit of Planck length or has a wavelength shorter than one unit of Planck length, I cannot think of one.

For that reason, when I think of the shortest possible time or distance, I always think Planck.

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Note that, buried in the next post, is another reason to consider Planck units to be eminently suitable.  It’s just a little difficult to explain.