UPDATE May 3, 2023: Our blog post today shows that the pendulum clocks must have the same inertia regardless of the arrangement.
----
UPDATE March 31, 2023: For an electric field, case 1 below cannot be true. We have to assume that case 2 is true, or some similar hypothesis.
----
UPDATE March 29, 2023: our argument about the atomic clock assumes that the (microwave) oscillator of the clock did not move before we started it. We have to check the technical details to determine if that is the case.
----
If our claim is true, then we would expect a radial pulsing movement of a sphere X to have less inertia than a linear movement of the sphere X. If the sphere just expands and contracts, its field outside the sphere stays constant. There is less field energy moving around => less inertia in the movement.
Also, if we nudge X swiftly, the inertia of X is less because the far field has no time to react.
However, we are not sure if this is the right way to explain extra inertia. Laplace calculated that the Moon would quickly fall to Earth if newtonian gravity would have retardation equivalent to the speed of light. Maybe the inertia arises from a process which is "infinitely fast"?
An atomic clock on Earth; a field must affect an object with no delay
The rate of the clock depends on the elevation of the clock from the sea level. It is the interaction with Earth which slows down the clock. The oscillating process in a cesium atomic clock does some 9 billion cycles per second. Light only travels 3 centimeters during one cycle. Most of the gravity field of Earth only learns about the oscillation milliseconds later.
If the extra inertia would depend on energy oscillating back and forth in the gravity field of Earth, then the clock would run faster for the first milliseconds. There are no reports of such a strange behavior of an atomic clock.
We have two possible explanations:
1. the extra inertia is a "package" carried by the object X itself, or
2. there is a strange mechanism which makes X immediately aware of the inertia properties of the gravity field of Earth, so that X can act as if the field would respond immediately to its movement.
Our problem is equivalent to the corresponding problem of explaining the potential of a field through the concept of field energy. The object X feels the pull of the field instantly. However, if we try to explain the pull by the integral of the combined field energy over the entire space, the integral changes slower: it is limited by the speed of light.
We know that the force of a field affects an object instantly. There is no time for the field energy to be updated in remote locations. If we want to use the field energy explanation, we have to assume a magical, infinitely fast process which updates the field.
This question may be related to the long-standing problem of momentum and energy conservation in an interaction: how do the two objects know to move in a way which conserves momentum and energy for the whole system. Retardation definitely happens in the case of a dynamic field, if not in the case of a static field. How does nature handle retardation?
Does a pulsing sphere really have smaller inertia than the sphere in a linear motion?
If in the preceding section, case 1 is true, then each part of the sphere carries its own package of extra inertia, and the inertia is exactly the same in a pulsing motion as in a linear motion.
But case 2 suggests that the inertia less in a pulsing motion than in a linear motion.
Which alternative is right?
Empirical test for inertia of gravity: circularly arranged pendulums
We wrote about this experiment in our January 28, 2022 blog post.
Let us have several extremely accurate pendulum clocks. Let us put them into a circular arrangement around some point x.
|
---- x ----
| pendulum oscillation
Let the pendulums swing synchronously around x. The far field of the system does not change much in the plane of the pendulum movement. If the energy flow in the field affects the inertia (case 2 above), then the inertia should be less than for a standalone pendulum.
Let us calculate how much the Milky Way would affect the inertia. The escape velocity v is 500 km/s, which corresponds to a potential of
V = 1/2 v² ~ 1.4 * 10⁻⁶ c².
Thus, the effect might be of the order one millionth.
It should be easily measurable with the best pendulum clocks.
The Poynting vector is NOT suitable for calculating the energy flow in a static electric field
This is the infamous, unsolved 4/3 problem of physics.
^ Poynting vector
/
● -----> charge
v
Let us move a spherical charge along a vector v. It acquires a magnetic field which circles around v. The Poynting vector claims that the field energy does not move directly along v, but circles around the charge.
There is more momentum in the flow of the field energy than one would expect from a simple translational motion of the charge.
It looks like the Poynting vector does not calculate the energy flow correctly in this case of a static electric field. Maybe it works for dynamic fields?
The field of each charge is private?
Suppose that we have an electrically charged ring rotating in the plane of the ring
O charged ring
->
rotation
The electric field of the ring at some distance is constant. Since the charges move, there is also a magnetic field.
If the electric field would be the only important thing, we could imagine that no magnetic field is present since the electric field does not change.
This suggests that we must treat the field of each elementary charge individually. For example, the sum of their fields may be zero, but that is not equivalent to being in empty space with no fields. We wrote about this in our blog on January 28, 2022.
A pulsing charged sphere probably has the same inertia as the sphere in a linear motion
If we treat the field of each elementary charge individually, that field definitely moves when the sphere expands. Thus, we cannot claim that there is no change in the field outside the sphere.
This suggests that the inertia of a pulsing sphere is the same as in a linear motion, after all.
Conclusions
The concept of a private field of each elementary charge might be the key to understanding the inertia in an interaction.
We predict that the experiment above with pendulum clocks will confirm this for gravity. Clocks should run at the same rate regardless of their configuration.
This also means that a collapsing spherical shell has the same inertia as an individual falling particle. Our claims on March 4 and March 19, 2023 about a very fast collapse of a shell were false.
Generally, the idea of a private field de-emphasizes the importance of the field concept. We could say that it is the interaction between particles which matters, and the (sum) field is not fundamental. The 4/3 problem is a manifestation that the field concept is troubled.
We still need to study this more. If the field is created by polarization of a material, maybe in that case the field of a charge is not private?
Also, how does the gravity of a test mass and pressure add to the inertia of the test mass? Is the inertia a "package" on the test mass, or is it subject to the speed of light like in case 2 above?
No comments:
Post a Comment