The notions you're calling BS seem unrelated to the points that follow.

What frame dependent gravitational effects could anyone possibly deduce from the vague notions I describe?

Well , for one, you all claim that the "upper half" of the wheel has more energy (kinetic, total) than the "lower half". So, since total energy does gravitate, it follows that any moving frame could detect this disparity while the axle frame will obviously not detect anything.

The problem is that no one else was using that interpretation of "halves", which means you're on a different wavelength to everyone else,

That is true, because none of you is willing to accept the idea that the midline separating the two halves is frame dependent.

For example:

Are we all agreed that in the moving frame, the portion of the wheel above the level of the axle has more kinetic energy than the portion of the wheel below the level of the axle?

NO. None of you posted a formal calculation supporting this claim.

Pot, kettle.

You made a specific claim (that in the moving frame, the upper half of the wheel's mass has the same KE as the lower half of the wheel's mass). So far, this claim has been supported only by armwaving.

You are getting personal again. I will post my calculation AFTER you post yours supporting the opposite claim. So far , neither you, nor

**przyk** posted any calculations. You made no attempt,

**przyk** made a sketch that I have shown to contain an invalid parametrization of the length of the halves as a function of the arc length. AFTER you post a complete proof, I will post my rebuttal.

I'm suspicious of that claim. I don't claim it's false, but I'm not prepared to accept it as true, because of my own armwaving reasons.

You said you did the exact integral earlier. Where is it?

Once again, once you or anyone else posts their complete proof, I will immediately post mine.

Yes, that's GR spookiness. Here Be Dragons. I'm completely incapable of calculating whether an event horizon forms in an arbitrary situation like this, or the value of any other frame-dependent effect.

How about you?

Do you have calculations, or just armwaving?

You mean that you still maintain that you can get gravitational effects by moving by the wheel? And your answer is just "GR spookiness"? Let me ask you this, if you move very fast wrt the wheel, will it collapse into a black hole?

That would make the velocity of the rim in the axle frame exceed c.

We know that:

$$\omega R < c$$

$$-R < x_1' < 0$$

$$0 < x_2' < R$$

So given $$R>0$$ and $$\omega > 0$$...

$$0 < \frac{-\omega^2Rx_1'}{c^2} < 1$$

$$0 < \frac{\omega^2Rx_2'}{c^2} < 1$$

Yes, you are right. I get that the spokes are on the same side of the diameter, though my math is different since I have the parametrization of x and you the reverse of yours:

$$x'=R sin (\omega t' +\phi)$$

$$y'=R cos (\omega t' +\phi)$$

leading to the exact equation of the spokes given early in the thread:

$$y-R=\gamma (x-Vt) ctan[\omega \gamma (t-Vx/c^2)+\phi_i ]$$

t=0 results into:

$$y-R=\gamma x ctan (\phi_i-\omega \gamma Vx/c^2 )$$

$$x'=\gamma x$$

Therefore:

$$y-R=x' ctan (\phi_i-\omega V x'/c^2)$$

So, for:

$$\phi_1=0$$

$$y_1-R=x'_1 ctan (-\omega V x'_1/c^2)<0$$

$$\phi_2=\pi$$

$$y_2-R=x'_2 ctan (\pi-\omega V x'_1/c^2)<0$$

which leaves us with the paradox of having the spokes bunched up on one half of the wheel. To make matters even worse, the spokes bunch up "above" the fence of height R in your parametrization of the circle and bunch "under" the fence of height R in my different parametrization of the circle.