Then perhaps you should clarify what you are truly stating as the energy/mass relations also apply to any field as well
Einstein's Mass-Energy is equivalence is applicable in only two special cases.
Clarify this statement as reading your replies your being inconsistent
Yes, the total energy for entire wave would be constant but those values would vary at a set point. A similar example would be a charge flowing through a medium. However, in that case the flow of electrons would contribute to added mass.
All particles are essentially field excitations under boundary binding conditions. ie a quanta in a finite (point-like )region.
Mass and energy is literrally different mathematical treatments to describe the properties of what is commonly referred to as particles.
mass is resistance to inertia change
energy is the ability to perform work.
A field being an abstract device to describe any collection of objects/events
They are fundamentally two properties of the same thing. Much like an object has properties of length/volume (3d object)
Or density/pressure and temperature.
OK I recognize this is far too advanced for most people but lets look at a Spinless particle under QFT treatment.
the state of a system is governed by the Schrodinger equation
where H is the Hamilton for the notation this is the Dirac bra-ket notation which is a convenient vector notation.
so a simple system with no forces acting upon it of a spinless non relativistic particle is
where m is the particles mass and P the momentum operator.
in the position basis the first equation becomes
to generalize this spinless particle above in relativistic motion take
the ..... denoting higher order corrections
with the Hamilton and Schrodinger the above becomes
there I just described a spinless particle in both relativistic and non relativistic treatment. However the last equation requires some limits to avoid infinities. Without going into detail as the above is tricky enough to understand we end up with the Klein_Gordon equation
the point being is the above shows a particle is not some bullet but a field excitation. how we measure that field excitation requires observer treatments described by relativity.
How one measures a field of the above spinless objects are also under observer corrections via the redshift equations regardless of whether you are measuring a vacuum/field/object/particles the observer influence is always a factor.
One can correlate the above to any particle via its spin ie electrons spin 1/2 etc
Edited by Mordred, 22 January 2017 - 08:19 AM.