Slowing down of clocks
Let us make a mechanical clock whose parts possess an electric charge. If we put the clock close to a large electric charge Q, then the parts have more inertia => the clock ticks slower.
All charged objects have more inertia close to Q. Everything with charged objects happens slower. As if time itself would have slowed down.
Since all material objects possess a gravity charge, in general relativity one is led to think that time, as an abstract entity, really has slowed down in a gravity field. In this blog we do not believe that time itself slows down. We want to use the straight Minkowski time.
Can we cancel the extra inertia of a gravity field with electric repulsion?
Question. A test mass m in the gravity field of a mass M acquires as the extra inertia the work W which the gravity of M did when we lowered m close to M. Suppose that we cancel the attraction of gravity by putting electric charges of the same sign to m and M. Does this cancel the extra inertia in m?
If the answer to the Question is yes, that is strong evidence for our claim that time itself does not slow down in a gravity field. A mechanical clock slows down for two reasons:
1. its parts have greater inertia in a gravity field;
2. the energy to drive the clock did work when we lowered the energy down in the gravity field: there is less energy to drive the clock.
We might be able to cancel 1 with electric repulsion. Can we do something to cancel 2? Ship the energy to drive the clock as an electrically charged particle? But we cannot annihilate a charged particle without having the opposite charge.
Stretching of the radial metric
If a charge q moves radially relative to Q, then energy is shipped to q over the distance between q and Q. The inertia of q is larger in a radial movement than in a horizontal (tangential) movement. As a result of this, charges tend to move slower in the radial direction. It is as if the radial metric would have stretched. The charge Q makes radial distances to appear longer.
Frame dragging
If a test charge q goes closer to Q, and Q is moving, then q is dragged to move along Q, because q gains more inertia in the field of Q.
To prevent q from following Q, we have to apply a force. The "inertial frame" is dragged to move along Q.
Precession of the perihelion of Mercury
Let us have a test charge q in an eccentric orbit around a charge Q. When q comes close to Q, it acquires more inertia. It takes q a surprisingly long time to pass Q, and Q has more time to give an impulse to q. This larger impulse makes q to turn more. The elliptic orbit of q precesses around Q to the same direction as q orbits Q.
Bending of light close to the Sun
Since the photon possesses a charge in gravity, its path is bent when it passes close to the Sun.
The analogue is a particle q which has an electric charge and moves almost at the speed of light. When q passes close to Q, the path of q is bent because of the electric Coulomb force. Also, q acquires extra inertia in the field of Q, and moves slower, just like a photon moves slower close to the Sun. The slowdown bends the path of q toward Q.
Gravitational waves and the undulating metric
If we move a test charge inside an electromagnetic wave, the test charge has some extra inertia since energy is shipped around. This creates similar effects to the ones in a gravitational wave.
Gravity of pressure
Let us have a test charge q bouncing back and forth in a long box. The box has "pressure" in it. We lower the box toward a large charge Q, in such a way that q bounces radially relative to Q.
box
----
| | ^
| | |
| • | q bounces
| | |
| | v
----
|
|
v
● Q
There is some frame dragging. The "natural inertial frame" for q is somewhat "attached" to Q. The test charge q sees that the bottom of the box is moving downward in this natural inertial frame. When q bounces from the bottom, q loses some momentum in the natural inertial frame. It is like pressure doing work in a box whose volume is growing. Where does this work go? It might go to pulling Q closer to q. That is, "pressure" in the box would attract Q.
We have to think about this in more detail. Frame dragging and the natural inertial frame need clarification.
Conclusions
Electromagnetism contains analogues for all peculiar phenomena of general relativity. This is strong evidence for our claim that gravity is an ordinary, newtonian force, and that gravity does not affect the underlying metric of spacetime in any way. The underlying metric is the Minkowski metric.
A quantum theory of gravity should be quite similar to the quantum theory of electromagnetism. In electromagnetism, the phenomena with the "metric" are side effects of the electromagnetic field. The same holds for gravity: the apparent metric of spacetime is just a side effect of a very ordinary newtonian force field.
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