- #1
chastiell
- 11
- 0
Hi again, probably this seems to be a simply question, but in last days i becomes a really strange one.
We all know that there are many kinds of constants in physics, some of them, are found experimentally with great accuracy in too expensive projects, but no matter how accurate can be measured such constant, they still have uncertainty. So imagine we made an experiment were any constant of this kind is measured , charge electron, charge to mass ratio, Newton gravitatory constant , ...
How to achieve an hypothesis proof on this constants considering that they have uncertainty ?
I has been searching this on Internet, but the nearest answer is given by the comparison of two gaussian variables with the t student distribution using:
t={|\bar{X_1}-\bar{X_2}|\over \sqrt{{\sigma_1^2\over n_1}+{\sigma_1^2\over n_2}}}
where
\sigma_i^2
are the estimators of variance of each variable
but in this form is assumed that the values n_i are known , thing that is not true for the experimental reference values , and this restrict us to always use a mean value, what if we determine this by linear fit, nonlinear fit ?
We all know that there are many kinds of constants in physics, some of them, are found experimentally with great accuracy in too expensive projects, but no matter how accurate can be measured such constant, they still have uncertainty. So imagine we made an experiment were any constant of this kind is measured , charge electron, charge to mass ratio, Newton gravitatory constant , ...
How to achieve an hypothesis proof on this constants considering that they have uncertainty ?
I has been searching this on Internet, but the nearest answer is given by the comparison of two gaussian variables with the t student distribution using:
t={|\bar{X_1}-\bar{X_2}|\over \sqrt{{\sigma_1^2\over n_1}+{\sigma_1^2\over n_2}}}
where
\sigma_i^2
are the estimators of variance of each variable
but in this form is assumed that the values n_i are known , thing that is not true for the experimental reference values , and this restrict us to always use a mean value, what if we determine this by linear fit, nonlinear fit ?