Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Uncertainty as √N — why?

  1. Jul 25, 2012 #1


    User Avatar

    My physics teacher told me once about Arthur Eddington's famous observation that the ratio of scaling factors of the electromagnetic and gravitational forces was the same order as the uncertainty of N where N is the number of particles in the universe. From then on, I wondered what "uncertainty" could possibly mean. He couldn't really explain it to me, or I didn't understand it (or both).

    I can see that for "random" or acausal (stochastic) phenomena, the "absolute" uncertainty in a measurement is equal to the square root of that quantity of measurements. What is that about? I think I understand square roots and squaring just fine, and am looking for a little help in explanation.
  2. jcsd
  3. Jul 25, 2012 #2


    User Avatar
    2017 Award

    Staff: Mentor

    In example of radioactive decay, you can calculate the probability for each number of decays within one second, it follows a poisson distribution. And you can evaluate the standard deviation - it is sqrt(N).

    Many phenomena which involve counting have an uncertainty of sqrt(N).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook