The Stark effect is measured under an electric field, not in a constant potential.
What is the effect on the hydrogen spectrum?
According to our new energy-momentum relation, the electron has an imaginary mass if the potential is > +511 kV, and should behave in a weird way.
A van de Graaff generator can create voltages up to 25 MV.
What about observers inside the static electric field? How do they measure the inertial mass of the electron?
An electron inside a positively charged van de Graaff generator
If positive voltages over +511 kV can be generated, how can we explain that no weird physics appears? Could it be that the geometry of the situation assigns the negative inertial mass to something else than the electron? Or is the inertial mass measured by people inside the shell of the van de Graaff generator different than what people outside measure?
Let us put a man standing inside a van de Graaff generator which has a positive voltage V_b. The voltage can be low, too.
+ + + +
____________
+ | | +
| |
e- ---> \O ----------->
| | |
+ |___/\________| +
+ + + +
x y
<--------------- E
The man lets the electron come in and fills an energy store at x with energy E. Then he moves the electron to y and uses an energy E to push the electron out.
We assume that the man is weightless.
The net result is that a 511 keV electron moved from x to y and an energy E moved the other way.
The inertial mass of the electron from the point of view of the person moving it can be positive, though.
rod
--------------------------W weight
--> lever
|
/|\ supporting
/ | \ structure
/ E \
-/----------\------ box floor
If there is a lever which moves a mass E to the left when the man pushes it to the right, the lever certainly has an inertial reaction but still moves mass to the opposite direction. The lever is attached to the box. What if the man uses a rod which is attached to a weight outside the box, to push on the lever? He does not touch the box at all but uses the rod to win the inertia of the lever. The supporting structure of the lever pushes the box to the right.
The end result is that the weight W has moved to the left, as well as the mass E, and the box has moved to the right. The head of the lever "borrowed" some inertia from the box.
If the electron can borrow inertia from the the electric field of the box, then the electron can behave quite normally also in a potential which is higher than +511 kV.
Let the box have a voltage V_b > 0. We conjecture that the man inside the box will feel that the electron has an inertia of
511 keV + |e V_b|,
that is, we need to add the absolute value of the (negative) potential to the inertial mass of the electron. Also an outside observer will think that the electron has that same inertia.
The conjecture assumes that the forces between the electron, the box, and the fields form a kind of a lever system which moves E.
If there are unknown forces between the electron and the box, then the inertial mass of the electron can be arbitrarily high. The electric field of the box might be very "viscous", such that moving the energy hole caused by the electron would require great force.
We definitely need empirical experiments to determine how the electric field behaves.
Classical solution
Classical electrodynamics claims that there are no forces between the box and the electron because the electric field is zero inside the box. Let us calculate what would happen if the man inside the box would feel that the inertia of the electron is M.
The electron performs a displacement of s m, where s = y - x. The man pushes the box left with his feet to win the inertia M. If there are no forces at all between the electron and the box, then the displacement of the box is -s M.
The displacement of E is -s E. We get an equation
s m - s M - s E = 0
<=>
s M = s m - s E.
The formula is not sensible if E > m.
Another way to calculate things classically is to use the Poynting vector. Let us assume that the positively charged box is surrounded by a negatively charged box, such that its charge exactly cancels the field far from the box. We can then restrict ourselves to calculating the electric field energy inside the box and in its immediate vicinity.
The electric field energy of the electron inside the box is essentially 511 keV, because it is the only field there. When the electron moves from x to y, the Poynting vector describes the field energy flow from the right side of the outside of the box to the left side. Thus, the electron also acts as a kind of lever which moves the energy E from right to left.
We see that the Poynting approach of calculating the field energy gives roughly the same result as our conjecture in the previous section: the inertia is
511 keV + |V|.
The inertia depends very much on the geometry of the setup. In the hydrogen atom, the Poynting approach says that the inertia is almost zero when the electron is in a potential -1.022 MeV close to the proton, because the energy of the combined electric field is close to zero. Here we assume that the whole rest mass of the electron is in its field and the field does not gain more energy when the electron comes close to the proton.
Experimental tests of the inertial mass of the electron under a potential
Let us check what literature says about the inertial mass of an electron under a potential.
https://en.wikipedia.org/wiki/Weber_electrodynamics
Wikipedia says that Maxwell electrodynamics does not conserve particle momentum if there is radiation out. That is reasonable. Wilhelm Weber's 1848 theory is claimed to conserve momentum.
http://www.nrcresearchpress.com/doi/10.1139/p04-046#.W-28t_ZuLb0
Mikhailov (1999) measured the dependency of the electron inertial mass on the potential and confirmed that it changes. But further experimenters have disputed his result.
People are trying to break newtonian mechanics with Weber's theory. Since the classical theory, the Poynting approach, and our thought experiments give conflicting results, more experiments are needed.
No comments:
Post a Comment