SOLVED: the acceleration of a test mass depends on accelerations of disk parts

We were perplexed about the difference of frame dragging in our August 10, 2023 and August 29, 2023 calculations.

The key to the solution is this section in the August 10 post:

"Eliminating the accelerated motion of dm by letting the ball parts "fly loose""

If we let the disk parts fly loose, so that there is no acceleration in their paths, then the parts on the left of the disk really start a collective movement toward the test mass, and our argument on August 10 that the left parts are "approaching" the test mass faster, is true.

But in a rotating disk, the collective field of the left side of the disk is time-independent. The collective field is not approaching the test mass faster on the left than on the right.

Is the term "dm' approaches faster" correct?

                         <--- v

                        ----------

                   /                 \

                  |                    |   mass loop   

                   ------------------

                         v --->

                             •  m observer

            

Our observation makes the term "dm' is approaching faster" suspect in the August 10 calculation. The collective field of the left side of disk does not approach at all: it is time-independent. The term also appears in the August 29, 2023 calculation of the metric around a rotating disk.

The term might be correct because it does not requite acceleration of mass close to the observer m. On August 7, 2023 we studied the field of a closed loop of moving mass.

                    cylinder

           ==============  ---> v

                         • m observer

Also, the term appears when we treated a moving cylinder on August 28, 2023. There is no acceleration of the mass in the cylinder. Our calculation on August 28 agrees with the calculation on August 14 about frame dragging.

Does a metric in general relativity "understand" what happens when the source of gravity is accelerated?

          neutron star

                                                rope   ---> F force

                     ● --------------------------

                      • 

            m test mass

Suppose that we have a test mass close to a very heavy neutron star. We start to accelerate the neutron star by pulling on a rope. The test mass accelerates with the neutron star. The acceleration of the star directly affects the acceleration of the test mass. Thus, it is not just the linear movement of other masses which matters when we calculate the acceleration of a test mass.

It is not clear if a metric in general relativity truly "understands" what happens if the mass generating the metric perturbation is being accelerated. We have to find out if that is the case.

Rotating disk: the magnetic field versus the gravitomagnetic field

The metric calculated in our previous blog post claims that a rotating disk does not have a gravitomagnetic effect at all. That is implausible. We believe that the Coulomb force and the newtonian gravity force are analogous. Since a rotating disk of charge does have a magnetic field, so should a rotating mass.

This suggests that general relativity does compute gravitomagnetic effects wrong.

Conclusions

We found a possible reason why radial corrections disappear when we calculate the metric around a rotating disk. The end result is that the rotating disk does not have a gravitomagnetic field at all.

We do not think that the result correctly reflects what happens in nature. In the next post we will compare magnetism and gravitomagnetism in detail.