- #1
Kolahal Bhattacharya
- 133
- 1
I have some difficulty in understanding linear superposition's domain of validity and reading Jackson's 1st chapter.I found the following lines but to confess it out, could not grasp the whole meaning...Please help.
"The Maxwell equations in vacuum are linear in the fields E and B.This linearity is exploited so often, for example,...,that it is taken for granted.There are of course, circumstances where nonlinear effects occur-..."
"What evidence do we have to support the idea of linear superposition?At the macroscopic level, all sorts of experiments test linear superposition at the level of 0.1% accuracy-...At the macroscopic and even at the atomic level, linear superposition is remarkably valid."
"It is in the subatomic domain that departures from linear superpossition is legitimately sought.As charged particles approach each other very closely, electric field stengths become enormous.If we think of a chargd particle as a localized disstribution of charge, we see that its electromagnetic energy grows larger an larger as the charge is localized more and more.It is natural,to avoid infinite self-energies of point particles,to speculate that some sort of saturation occurs,that field strengths have some upper bound.such classical non-linear theories have been studied in the past...(Born-Infld equation)...It suffices to illustrate the general idea.Fields are obviously modified at short diastances;all electromagnetic energies are finite.But for such theories suffer from arbitrariness in the the manner of how non-linearity occrs and also from from grave problems with a trnsition to quantum theory.Furthermore, there is no evidence of this classical non-linearity...(the next part contains examples that quantum theory correctly predicts using linear superposition)."
So, where we are?Once he says at subatomic level linearity does not hold good; after that he says quantum mechanics correctly predicts many things using linear superpostion at the subatomic level.I think what he says is true...But, I am going wrong somewhere...Please help.
"The Maxwell equations in vacuum are linear in the fields E and B.This linearity is exploited so often, for example,...,that it is taken for granted.There are of course, circumstances where nonlinear effects occur-..."
"What evidence do we have to support the idea of linear superposition?At the macroscopic level, all sorts of experiments test linear superposition at the level of 0.1% accuracy-...At the macroscopic and even at the atomic level, linear superposition is remarkably valid."
"It is in the subatomic domain that departures from linear superpossition is legitimately sought.As charged particles approach each other very closely, electric field stengths become enormous.If we think of a chargd particle as a localized disstribution of charge, we see that its electromagnetic energy grows larger an larger as the charge is localized more and more.It is natural,to avoid infinite self-energies of point particles,to speculate that some sort of saturation occurs,that field strengths have some upper bound.such classical non-linear theories have been studied in the past...(Born-Infld equation)...It suffices to illustrate the general idea.Fields are obviously modified at short diastances;all electromagnetic energies are finite.But for such theories suffer from arbitrariness in the the manner of how non-linearity occrs and also from from grave problems with a trnsition to quantum theory.Furthermore, there is no evidence of this classical non-linearity...(the next part contains examples that quantum theory correctly predicts using linear superposition)."
So, where we are?Once he says at subatomic level linearity does not hold good; after that he says quantum mechanics correctly predicts many things using linear superpostion at the subatomic level.I think what he says is true...But, I am going wrong somewhere...Please help.