## The 'New Planck Units'

Discussions on classical and modern physics, quantum mechanics, particle physics, thermodynamics, general and special relativity, etc.

### The 'New Planck Units'

Marshall and I proposed the following set of 'natural units' and symbols for our Forum.

The starting premise is that $\bar{h}$, $c$ and $\bar{F}$ are good natural units, meaningful proportions that are built into nature. This is like the garden gate through which one enters.

$c$ is the limiting speed

$\bar{h}$ is the inherent limit on exactness

$\bar{F}$ is the force expressing the stiffness of geometry. It governs how geometry interacts with matter, because the GR equation basically says:

curvature = $\Large \rho / \bar{F}$, where $\rho$ is matter density.

Curvature is a reciprocal area ("per sq. foot") quantity, and if you multiply force by curvature you get quantities such as pressure and density, describing the concentration of matter. The GR equation's $\bar{F}$ tells, among other things, the concentration of matter that would be needed to produce a given curvature in the geometry---it hitches up the two things. These three: $\bar{h}$, $c$, $\bar{F}$, are woven into existence at a basic level, so we take them as natural units.

Moving on, we show the path to the other natural units, and each one should be Google-calculable so we can get the automatic metric equivalent whenever we want. Simply paste the right-most part of each equation into Google, press enter or search, and you should get an answer in normal metric units.

Force: $\bar{F}=c^4/(8\pi G)$ = c^4/(8pi G)

Area: $\bar{A} = \hbar c/\bar{F} = \hbar / {c^3 \over 8\pi G}$ = hbar*8pi G/c^3

Length: $\bar{L} = \sqrt{\hbar c/\bar{F}}$ = (hbar*8pi G/c^3)^.5

Time: $\bar{T} = \sqrt{\hbar /c \bar{F}}$ = (hbar*8pi G/c^5)^.5

Energy: $\bar{E} = \sqrt{\hbar c \bar{F}}$ = (hbar*c^5/(8pi G))^.5

Momentum: $\bar{P} = \sqrt{\hbar \bar{F}/c}$ = (hbar*c^3/(8pi G))^.5

Mass: $\bar{M} = \sqrt{\hbar \bar{F}/c^3}$ = (hbar*c/(8pi G))^.5

If you bookmark this page, you can easily refer to it anytime in the future.
Last edited by BurtJordaan on September 14th, 2014, 2:48 pm, edited 2 times in total.
Reason: Minor improvement

BurtJordaan
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### Re: The 'New Planck Units'

Hi Burt
It seems that your definition of force is the inverse of the Einstein gravitational constant.
This may be a good thing.
The Einstein constant may be represented as ratios of force.
Your force definition is 8pi times smaller than Plank force.
This may also be a good thing.
The constant 8pi may be shown to be a ratio of thermal forces, including Plank temperature and Hawking temperature.
Regards
Rich
Last edited by RichardKingstone on April 8th, 2016, 6:36 pm, edited 1 time in total.
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### Re: The 'New Planck Units'

BurtJordaan,

I'm definitely procrastinating on my work by being silly here, but...
BurtJordaan » September 14th, 2014, 11:59 am wrote:Moving on, we show the path to the other natural units, and each one should be Google-calculable so we can get the automatic metric equivalent whenever we want. Simply paste the right-most part of each equation into Google, press enter or search, and you should get an answer in normal metric units.
I thought that this point about using Google to evaluate the expressions was really neat.

I thought it could be fun to include links for Google and WolframAlpha as a convenience. And maybe toss in the $\TeX$ in code tags? For example,
BurtJordaan » September 14th, 2014, 11:59 am wrote:Force: $\bar{F}=c^4/(8\pi G)$ = c^4/(8pi G)

could be tabulated as
Proposed format wrote:Force:
Natural ChemE
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### Re: The 'New Planck Units'

Hi again Burt
If you are interested I shall be happy to post a definition of the thermal force ratio.
regards
rich
RichardKingstone
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### Re: The 'New Planck Units'

Hello Burt again

Curvature is represented by the Ricci Scalar (R) in the EFE.
This scalar is a projection of the Ricci tensor.
It may be reduced to a ratio of volumes.
It may further be reduced to a ratio of areas.
If so, then;

curvature = R = A1/A2

If A1 is unit area, then R will reduce to your definition of curvature.

Regards; Rich
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