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Electron/Proton mass ratio

  1. Aug 19, 2010 #1
    So I read somewhere about some equation that might explain the Electron/Proton mass ratio, but it was off by several percentage points and the equation seemed complicated.
    Unfortunately I forget where I originally read this.
    Anyway, I was not particularly impressed, so I wrote a C program to try billions of relatively simple equations and look for ones whose solutions come closest to the Electron/Proton mass ratio.
    Obviously many of the more complicated ones had the right answer within machine or measured accuracy, but some did "silly" operations that I could nto see in physics such as taking a sine of sine. One surprisingly simple equations came reasonably close. It is off by less than a tenth of percent so it is obviously wrong, none the less I found it interesting. Essentially the program was looking for a coincidence and that is probably all it found, but here is the equation:

    Let x = electron/proton mass ratio

    sqrt(x) ~= sqrt(PI/3) - 1

    Could be written as:
    sqrt(PI/3) = sqrt(1) + sqrt(x)

    The equation is similar to that of a circle, but with square roots instead of squares.
    PI/3 is obviously very common being the angle of equilateral triangles. Sqrt(PI) is important in probability and statistics regarding the Beta function.

    Anyway, I am not a Physicist having taken just 2 physics courses in college, but figured I would throw what is probably just a coincidence out there to see if it meant anything to anyone else.
  2. jcsd
  3. Aug 19, 2010 #2


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  4. Aug 20, 2010 #3
  5. Aug 20, 2010 #4

    Vanadium 50

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    As pointed out, it's numerology. It's also wrong - the difference between your formula and the true value is 100,000 larger than the uncertainty on the true value.

    To be honest, I am surprised with billions of trials, you didn't do better.
  6. Aug 20, 2010 #5
    I had a professor in college who told us that the true blue value of the fine structure was exactly 1/137 (based on numerology?), and the disparity on the measured value (~1/137.02) was experimental error. Six years later, he won the Nobel prize in experimental physics. I guess anyone can have dubious theories once in a while.

    Bob S
  7. Aug 20, 2010 #6
    There were plenty of equations that were within machine/measured accuracy, but they were far more complex and did silly operations. As you say the error of .08% is far more than the measured error so it is clearly not the correct equation.

    Essentially I scored answers by their accuracy, their simplicity and whether the equations did things that make sense in terms of units. Square of Square Root and Square Roots of Squares make sense. Sin of arctan makes sense. Stuff like Sin of Cos or Ln of Ln make less sense.

    This one equation was an outlier, in that every equation more accurate was either far more complicated or did more "silly" operations.

    These is numerology and is likely nothing more than noting 22/7 is close to pie, but I figured I would throw it out there in case some physicist saw the equation and recognized it from some other theory.
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