Proton mass ( split from How many quarks in a proton?)

[SergUpstart]

And I have another question about the proton. The proton mass refers to the electron mass as 6*Pi^5. Why is Pi in the fifth power? Is this an indication that our space has 10 or 11 dimensions? The volume of a ten-dimensional ball (Pi^5)*(R^10)/120

[swansont]

2 hours ago, SergUpstart said:

And I have another question about the proton. The proton mass refers to the electron mass as 6*Pi^5. Why is Pi in the fifth power? Is this an indication that our space has 10 or 11 dimensions? The volume of a ten-dimensional ball (Pi^5)*(R^10)/120

Where does the proton mass "refer to the electron mass" in this way?

[SergUpstart]

12 minutes ago, swansont said:

Where does the proton mass "refer to the electron mass" in this way?

In physics, the proton-to-electron mass ratio, μ or β, is simply the rest mass of the proton (a baryon found in atoms) divided by that of the electron (a lepton found in atoms). Because this is a ratio of like-dimensioned physical quantities, it is a dimensionless quantity, a function of the dimensionless physical constants, and has numerical value independent of the system of units, namely:

μ = m_p/m_e = 1836.15267343(11).^[1]

The number enclosed in parentheses is the measurement uncertainty on the last two digits. The value of μ is known to about 0.1 parts per billion.

It was also noticed that μ ≈ {\displaystyle 6\pi ^{5}.}^[2]

 

^{https://en.wikipedia.org/wiki/Proton-to-electron_mass_ratio}

And the number pi in the fifth power is included in the formula of the volume of a ten-dimensional ball.

 

[swansont]

“it was noticed that”

There doesn’t seem to be a claim that there is an actual connection or physical significance.

 

[MigL]

The two sqiggly lines, one above the other, mean 'approximately'.
That means the numbers are in the same ballpark ( and that ballpark could be large ).
It does not mean that the ratio   6*Pi⁵ was derived in any way other than a noticed coincidence.

[SergUpstart]

38 minutes ago, MigL said:

It does not mean that the ratio   6*Pi⁵ was derived in any way other than a noticed coincidence.

But string theory also states that the dimension of the space of the universe is 10+1. A coincidence????

[swansont]

Absent any actual physics, that’s all one can validly conclude