4 Where Does the Wave Equation Come From?
37
the quantum theory and the General Theory of Relativity. We do not want to do this
here. In Chap. 15, we will however compare the observations made on the material
crystal lattice and some very old arguments for a discrete background of our physical
spacetime.
Where does the wave equation come from? Up to now, we have shown the following. When an elastic rod is divided up into equal parts, the masses of the parts oscillate
according to the wave equation exactly the way single elastic coupled masses oscillate according to the Newtonian equations, as long as we maintain condition (36)
whilst dividing the rod into sufficient many parts. Is it possible to deduce the wave
equation directly from Newtonian mechanics? This question will be answered in the
next chapter as follows: The wave equation can be completely understood from the
postulates of Newton’s point mechanics. We will generally show how Newtonian
mechanics can in fact imply a continuum such that a mechanical continuum can be
described with arbitrary accuracy using point mechanics.
Notice, independent of that, it is a well-known fact that the wave equation for electromagnetic phenomena derives from Maxwell’s field theory.
37
the quantum theory and the General Theory of Relativity. We do not want to do this
here. In Chap. 15, we will however compare the observations made on the material
crystal lattice and some very old arguments for a discrete background of our physical
spacetime.
Where does the wave equation come from? Up to now, we have shown the following. When an elastic rod is divided up into equal parts, the masses of the parts oscillate
according to the wave equation exactly the way single elastic coupled masses oscillate according to the Newtonian equations, as long as we maintain condition (36)
whilst dividing the rod into sufficient many parts. Is it possible to deduce the wave
equation directly from Newtonian mechanics? This question will be answered in the
next chapter as follows: The wave equation can be completely understood from the
postulates of Newton’s point mechanics. We will generally show how Newtonian
mechanics can in fact imply a continuum such that a mechanical continuum can be
described with arbitrary accuracy using point mechanics.
Notice, independent of that, it is a well-known fact that the wave equation for electromagnetic phenomena derives from Maxwell’s field theory.