If the electric field is a complex "mechanical machine", then the packet of energy in E E' could move without inertia
E + E'
| | |
-------------------------------------- - cylinder
- rod --------- ---> v
-------------------------------------- - cylinder
| | |
The cylinder is uniformly electrically charged and its field is E. The rod is uniformly charged with the same sign (-), and its field is E'.
The field E + E' contains an extra energy density from the overlap:
ε₀ E E'.
How do we know where is that extra energy located?
|
--------- -
--------- +
|
We can use capacitor plates to harvest the energy in the field very quickly, by moving the plates apart.
How quickly? The plates could, in principle, move at a relativistic speed. It is a reasonable assumption that the energy of the field E is stored locally. We know that an electromagnetic wave stores its energy locally – that is further evidence.
It could still be that the extra energy E E' does not add to the inertia of the rod. We can imagine that the field is a complicated mechanical machine which takes "instructions" from the rod, and moves E E' around. The rod does not need to give momentum to E E'. The machine could be lossless and would not lose energy in friction.
We cannot "grab" the packet E E' directly because energy is not coupled to electromagnetism.
Gravity comes to the rescue: it allows grabbing an energy packet
The energy in the packet E E' probably does gravitate. That offers us a method to "grab" the momentum in E E'.
Let us assume that mass-energy (energy divided by c²) in E E' is much more than in the rod and its own field E'.
● M
E + E'
| | | ---> v
We can use gravity to make the energy E E' to "bump into" a mass M. The energy in E E' gives up some of its momentum and kinetic energy to M.
Could the system still conspire in the way that M cannot receive a substantial amount of momentum? It is possible. Then, the mass M has to take part in the conspiracy. That is unlikely.
Conclusions
It is likely that the extra energy in the combined field E + E' does add to the inertia of the charge which produces E'.
This solves the Klein paradox, as we wrote on October 31, 2018.
However, we have to solve the mystery why the electric potential does not affect the spectrum of an atom. Also, we have to analyze how an electron or a positron behaves with a potential energy less than -511 keV.
No comments:
Post a Comment