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Casi.Voy equation 
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#1
Jan1112, 04:58 AM

P: n/a

In Summer 2010 I was travelling through southern Poland and Slovakia.
In the attic of some old house, I found a pile of papers filled with notes and dated 1945. They are hardly readable  the Author used almost only abbreviations in Latin, Cyrillic and Hebrew alphabets. There is a signature: "Casi.Voy" (with cyrillic). There are a few equations, and this was the only one I was able to fully decypher: 1/(4πε_0 ) e^2/r^2 =G (((2cℏG^(1))^1/2 )/(4/3 π (√(2.5))^3 ))^2/r^2 would anyone try to interpret it? 


#2
Jan1112, 10:34 AM

P: 7

Well I'm not a Phd or anything but it looks like its got too many arbitrary constants in it to be anything earthshattering. Just my 2 cents though Im still an undergrad physics major.



#3
Jan1112, 02:35 PM

P: 165

Maybe I am wrong, but it looks similar to coulomb's law http://en.wikipedia.org/wiki/Coulomb%27s_law



#4
Jan1212, 02:05 AM

Admin
P: 23,369

Casi.Voy equation
1. The way you formatted the equation it is completely unreadable, please try to use LaTeX (as described here).
2. There are not many arbitrary constants in the equation  G, c, e, [itex]\hbar[/itex], [itex]\epsilon_0[/itex] and [itex]\pi[/itex] have a rather obvious meaning. Only 2.5 looks strange (and apparently is a part of a formula for sphere volume). 


#5
Jan1212, 06:00 PM

PF Gold
P: 1,153

Here is an attempt to TeXify the equation:
[tex] \frac{1}{4 \pi \varepsilon_0 } \frac{e^2}{r^2} = G\frac{\left(\frac{\sqrt{\frac{2 c \hbar}{G}}} {\frac{4}{3}\pi (2.5)^{\frac{3}{2}}} \right)^2 } {r^2} [/tex] 


#6
Jan1312, 02:34 AM

Admin
P: 23,369

r^{2} cancels out.
I can't read pdf version, I get some error message. 


#7
Jan1312, 04:45 AM

P: n/a

Here's the correct version as in the original. Thanks for TeXifying jhae2.718!
[tex]\frac{1}{4 \pi \epsilon_0} \frac{e^2}{r^2} = G \frac{ (\frac{\sqrt{2 c \hbar G^{1}}} {\frac{4}{3} \pi (\sqrt{2.5})^3 })^2}{r^2}[/tex] The meaning of left hand side is quite obvious as BishopUser noted  it's Coulomb's interaction between two electrons. The right hand side is rather strange  it seems a bit like gravitational interaction between masses of some kind. 


#8
Jan1312, 05:09 AM

Admin
P: 23,369

At least looks like units are consistent.
Note that r^{2} and G cancel out. 


#9
Jan1312, 09:02 PM

HW Helper
PF Gold
P: 1,924

The [itex] \sqrt{2 c \hbar G^{1}} [/itex] has units of mass, as expected. But mass of what? Notice there are no variables in the term. Everything is a constant. And the term contains both the gravitational constant and Planck's constant? weird. The [itex] \frac{4}{3} \pi \left(\sqrt{2.5} \right)^3 [/itex] seems to be a ratio of volumes of some kind  Like the ratio of the volume of a sphere of radius [itex] r [/itex] per volume of a cube with a length of [itex] \frac{r}{\sqrt{2.5}} [/itex]. Or instead of a cube, maybe the 2.5 has something to do with the shape of some sort of pyramid or something  something with flat faces so things like pi don't come in. Or perhaps, the [itex] \frac{4}{3} \pi \left(\sqrt{2.5} \right)^3 [/itex] might be a ratio of densities, such as the density of some shape with straight faces per density of a sphere containing the same mass. I can only speculate. 


#10
Jan2212, 01:52 PM

P: n/a

The form of this equation suggests, that author was thinking about connections between electromagnetism (or at least electrostatics) and gravitation. As long as I understand, we don't have any "standard and official" theory combining those kinds of interactions, but we have a number of more or less interesting (or even crazy) attempts to create such  many of them "homemade".
I find this particular equation so interesting, not only because I found it written among old, notes of unknown origin, but because it connects electromagnetism with gravitation in a quantitative manner (gives a "mass equivalent" of a unit charge). I really wonder if there's something to it. 


#11
Jan2212, 03:04 PM

Mentor
P: 16,163

Mulkay, it sounds like you are trying to convince us that they're is something to it.
There is not. First, this is just numerology  attempting to relate different numbers together. There is no "something" yet for there to be "to it". That would require some sort of explanation as to why these numbers are related. Second, the person who wrote this doesn't know the most elementary physics, or they would have noticed that many of the terms they wrote down cancelled. Finally, when you complete the path of cancellations, and replace the ε and c with μ (which has the numeric value of 4π x 10), you will be left with an hbar, and a pile of algebra involving numbers. I can always take a single number and represent it as a pile of algebra. Sorry. 


#12
Aug1912, 09:26 PM

P: 77

Hi.
Term [itex]\sqrt{\hbar c /G}[/itex] is Planck mass: http://en.wikipedia.org/wiki/Planck_mass Author related Planck mass to electrostatic Coulomb force. Planck mass is the mass of micro black hole: it evaporates, then gravitationally condenses back to micro black hole, then it Hawkingevaporates again and so on. But wait, isn't it elementary particle, being so small? It can't blow apart, can it? Yes it can. How? At Planck length usual notions of continuous spacetime make no longer any sense. Spacetime becomes grained. Particles become black holes falling in and out of singularity. It's definitely some new physics there at Planck scale. So author knew something about Planck mass. The meaning of term [itex]4 \pi {\sqrt{2.5}}^3 /3[/itex] is beyond me: it is obviously of a form of a volume of sphere, as already noticed earlier. So the author was young Hawking is our only possible conclusion, I guess, or at least Hawking's previous incarnation :D Cheers. 


#13
Aug2012, 01:16 AM

P: 77

Hi.
How come the number of MUKAY's posts reported below his nick in his last post a bit above says: 0? Cheers. 


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