Everyone can be a physicist for one day! So I was just playing around a bit with planck units, and put all the important units in a little table, figuring how I could convert one into the other.

If you take a planck mass (m), which is sqrt( red. planck constant (h) * speed of light (c) / Gravitational Constant (G) ): sqrt( h*c / G ), you can go to a planck momentum by multiplying by c, and to planck energy by again multiplying by c.

mass = m (= sqrt( h * c / G ))
momentum (M) = mc (= sqrt( h * c^3 / G ))
energy (E) = mcc = mc^2 (= sqrt( h * c^5 / G ))

We could also invert all of these equations by dividing reduced planck constant by the equation.

h/E = h / mc^2 = time (= sqrt( h * G / c^5 ))
h/M = h / mc = length (= sqrt( h * G / c^3 ))
h/m = h / m = ??? (= sqrt( h * G / c ))

This looks rather puzzling, but to me it's like Russian: look at it and it doesn't make sense, read it out loud and it starts to sound somewhat like English.

Mass seems to be defined as the amount of energy per square lightspeed (m = E/c^2) in the universe.

Momentum is the energy per lightspeed (M = E/c)

Energy is energy (E = E).

Time is energy, but inverted with the reduced planck constant.
T = h/E. How many energy fits in a planck unit? This is apparently the value of time. Or if time is equal to 1 (we advance in time by 1 frame, no more or less), then there's x energy in one planck unit (seems the more sensible way to me).

Length is momentum inverted by h. L = h/M. If we multiply time by the lightspeed, we end up with length. S = v * t, or length = c * t. If you do the maths with time as h/sqrt(h*G/c^5), or "plancks per energy" (as derived from the planck mass equation), you end up with the planck-length equation, in terms of "plancks per momentum".

We could multiply with the light speed one more time, ending up with h/sqrt(h*G/c), "plancks per mass". But this equation has no name as far as I can find. Does the inverted mass have a physical meaning?

I drew a picture:


Inbetween are also alot of planck units, such as power, and force, and density, and volume, but they do not form the basic structure as I see it, they are just by-products.

Let me know what you think!

I was just playing around a bit with planck units, and put all the important units in a little table

this is an important topic in Physics
We use: meters, newtons,seconds ect but all of them are conventional units

Are there universal units which can make sense also to an alien civilization ?
Natural units, in other words
The Plank unit as well as the light speed maybe some of them
All other units should be derived from the universal units
thus they would be assigned a physical meaning
This is just of course a theoratical solution since you can expect huge and very small numbers
Honestly I dont know whether scientists came to some conclusion
I read some letter exchanges between Einstein and a lady on this subject but I did not delve into this topic

It took me a bit to realize that you're using "M" for momentum - I keep thinking of a mass when I see capital "M"s

But what you've done is pretty cool and noteworthy, actually. For instance, consider this:
We currently have two basic "pillars of physics". We have the Standard Model (related to Quantum field theory), which describes particle interactions and, basically, everything apart from gravity (since gravity is too weak to be of concern there). Then, we have General Relativity, which describes how gravity shapes and curves spacetime.
But here's the thing - they can't both be right. It is well-known that GR is a classical theory that cannot be quantified in the same way that, say, electrodynamics can.
In fact, what happens is that infinities appear that we can't get rid of (Note: Infinities appear also in the Standard model, but they can be taken care of and "absorbed", in a process that's known as renormalization). Usually, that means that GR is only an approximation, and valid only to a certain energy scale.
And where does that happen? It happens if we consider masses larger than the Planck-mass, or times shorter than the Planck-Time, etc.

So there's a real physical meaning to those.



What Alberto says is also true - it's incredibly interesting to think about this. There is this one super-fundamental quantity - the speed of light - so it does make sense to set it to "1". Planck's constant is similary "fundamental", so often it is also set to 1.
If we do that, which is very often done in physics, then an inverse mass is nothing but a length (the Planck-length), or even a time (remember that c=1 implies that metres and seconds are "the same kind of unit") (the planck time).

[[Edit: While I know this kind of defeats the point, what I am saying with the above is that while the numerical value of the units is interesting because it gives us real "barriers" where we expect physics to behave differently, from a fundamental, qualitative standpoint, length and time (for instance) can be looked upon as something fundamentally similar - the difference between Planck time and Planck length is just a constant - a fundamental constant, yes, but still - it's just a number.]]

Does that answer your question? I hope I wasn't too technical.



Also, I'm really glad Hilbert's Hotel is more active again

This picture is misleading. The middle line is wrong (p/p*hbar=hbar is not a length).

Also, hbar has the dimensions of an "action" (German: Wirkung).

I found the letters,they are quoted in the book
" The constants of nature from alpha to Omega " by John Barrow

The lady. mrs Ilse Roshental Schneider refers to the Max Plank's proposal of universal units , namely :

The gravitational constant : G
The light speed : c
The Max Plank constant : h

All other units can be derived from these 3 units
for example :

Time t = (Gh/c^5)^1/2 = 1.38 * 10^-43 sec

According to Plank , these are , so to speak, the foundation of the universe but Einstein disagrees
Einstein thinks that even these ones are somehow arbitrary units
The true "bricks" of the universe, the ones which even God could not change, must be dimensionless number same as the constants of math such as thenatural numbers or Pi or "e"
They must be , in other words, a ratio between omogenuo dimensional units
Einstein however admits that he his not be able to prove his claim