Electrons inside a positively charged sphere
Suppose that we have a positively charged spherical shell, and electrons move inside it.
+ + +
+ +
+ +
+ +
+ +
+ + +
If we have just a single electron, it is carrying its negative potential energy around, and its inertia has grown by the absolute value of the potential energy.
But what if we have a whole cloud of electrons randomly bouncing around?
The electric field of the system does not change much when the electrons bounce. Has the extra inertia gone away?
That does not sound right.
What if we have a little shell of electrons inside the shell of positive charge? The shell keeps expanding and contracting. The outside field of the shell does not change appreciably. Is the inertia of the electrons in the shell still the same as for random electrons bouncing around?
The Poynting vector does not show any energy flow in this case. The logical conclusion is that the electrons in the little shell do not have extra inertia in that kind of a coordinated movement.
If the inertia of the shell turns out to be the same as for random electrons, then the field of each electron has to be "private", so that Nature can track the energy flow separately for each individual electron. That would be surprising.
Implications for gravity and cosmology
There are no reports that the inertia of masses of a shell in a radial movement would be less than the inertia in other kinds of a movement.
Either our reasoning above does not hold for gravity, or the effect of distant masses on the inertia is very small.
The effect should be of the same order of magnitude as other general relativistic effects. On the surface of Earth the effect of Earth's gravity is ~ 10⁻⁹.
The effect of the gravity of the Milky Way is ~ 2 * 10⁻⁶.
The effect of the gravity of the local cluster of galaxies is ~ 10⁻⁵.
The equivalence of the inertial mass and the gravity mass has been measured to an accuracy 10⁻¹⁵. We have to check if the experiments would have noticed a difference in coordinated movements of masses.
Measurements of the gravity constant G keep giving conflicting results
The variation in measurements of G is a whopping ±0.03%, and the uncertainty has not been reduced in the past 80 years.
A possible reason for the discrepancies in the measured values is that the inertia of the torsion balance depends on the way that the masses in it move.
We have to check the design of the balances which researchers have used.
What is the speed of light outside the observable universe?
If the observable universe is embedded in the Minkowski space, and if the matter in the observable universe creates a potential well, then the speed of light in the observable universe is slower than in the surrounding, possibly empty, Minkowski space.
Then the speed of light which we observe would not be the largest possible speed of a signal.
Question. What is the gravity field of an explosion like? If the fringes of the explosion are receding from us faster than the local speed of light, are we in a potential well or not?
Inertia caused by an expanding sphere of electric charges - retardation
+ + +
+ +
+ +
+ e- ● ---> +
+ +
+ + +
Suppose that we move an electron inside a static spherical shell of positive charges. The magnetic field generated by the moving electron will make the Poynting vector non-zero outside the sphere. The Poynting vector describes energy flow in the field. The energy flow explains the extra inertia which the electron feels.
However, the magnetic field of the moving electron does not immediately reach the electric field outside the sphere. There is a delay which is caused by the finite speed of light.
How does Nature know beforehand that there will be energy flow, and the electron should feel extra inertia?
The problem sounds very much like the problem of how Nature makes sure that momentum and energy are conserved in all processes, despite delays caused by the finite speed of light.
In retardation of the electric field, Nature seems to calculate beforehand where a charge will be.
Suppose then that the sphere of positive charges is expanding fast. When the magnetic field of the moving electron reaches outside the sphere, the sphere has expanded greatly. The Poynting vector will generate much less energy flow than for a static sphere. The inertia is equivalent to the case where a static sphere is very large.
In gravity, this means that inside a rapidly expanding explosion cloud the inertia which masses feel is much less than for a similar static cloud. Clocks tick much faster than in a static cloud.
Conversely, inside a rapidly contracting ball of dust, masses feel surprisingly much inertia, and clocks tick surprisingly slowly.
The depth of a potential well can be defined by the redshift of light sent from the well to faraway space. The redshift is determined by how much slower clocks tick inside the well. We see that the potential well inside a rapidly expanding explosion cloud is surprisingly shallow.
Suppose that we have a rapidly moving large charge Q passing a test charge q. The behavior of q is calculated by switching to a frame where Q is static. In that frame we can assume that Q has a static electric field which has a potential function. In the new frame Q may be very far from q when we move q to determine the inertia of q, even though in the old frame Q was close.
Dark energy cancels the inertia that would be caused by the masses in the observable universe?
The inertia caused by the local cluster of galaxies should be ~ 10⁻⁵. The inertia grows by
r³ / r
as we add the effect of the mass within the radius r from us. This is because the total mass grows as r³ and the gravity potential at the edge of the mass declines as 1 / r.
Thus, the masses of the observable universe might contribute 10% more inertia for a test mass in a linear movement.
There certainly is not 10% more inertia in a linear motion than if we construct a small expanding and contracting shell of mass on Earth.
A possible explanation is that dark energy balances the effect of mass and cancels the extra inertia for a linearly moving mass.
A possible alternative solution: the total energy of the explosion is zero. The final state is infinitely redshifted radiation spreading into the Minkowski space. We have to study the zero energy hypothesis of the universe. The extra inertia from the large-scale structure would be zero.
If the total energy of the universe is zero, then large-scale gravity in the universe is zero. The spatial metric is the flat Minkowski metric. Clocks tick at the same rate as in the surrounding Minkowski space.
A zero energy universe would have a constant expansion rate. We have to check if the measurements about the expansion rate are consistent with a constant expansion rate.
No comments:
Post a Comment