Genady

No. I don't think we do. Even if we could, we would recover a sum of all sounds that hit the object throughout history. That would be just noise.

I don't think we know.

Let's look at it this way. The piston moves down with a constant velocity. Thus, any volume of fluid above it moves down with the same constant velocity. Thus, total force on that unit =0. The force down is its weight. The force up is the pressure difference. Thus, this pressure difference is equal its weight. This is exactly what the "normal" pressure is. Thus, the pressure above the piston is the "normal" pressure.

Yes, you're right. ds2 = dt2 - dx2. (c=1)

They (in the link above) mention but do not emphasize that there is nothing "unique" in visiting mikva. It is a rather mundane and regular thing. E.g., women go there every time after having period.

Yes, here: Event 1: the light hits a point on the Moon. Event 2: the bullet hits the same point on the Moon.

I'll think about the suction, but regarding this: I suggest a mental experiment. What happens if there is vacuum above the piston? When it moves down, the pressure under it gets higher, but the pressure above remains zero. Thus, the overall pressure gets higher.

Here is the diagram. Spatial coordinate is horizontal, temporal is vertical. The light, the ship, and the bullet leave the origin, i.e., the same point in space at the same time. The orange line is the light trajectory, the blue is the ship, and the red is the bullet. (No gravity.)

The points in Minkowski spacetime ARE events. The same point cannot be at a different time or spatial distance, in a given reference frame.

I don't think it will happen. Certainly not the reduced gravitational pull - the latter requires an accelerated fall, but the ball/piston rather moves in the fluid with a constant speed except momentarily at the very beginning. I think, there is a higher pressure under the piston, a normal pressure above it, and a pressure gradient in the gap where the fluid moves up.

Certainly not.

I think I can consider, for simplicity, instead of a sinking ball, a piston with a narrow gap being pushed down. This makes it obvious (to me) that there will be an increased pressure under the piston. Why the pressure above the piston will be lowered?

Got it. Thank you. I looked, by mistake, on the secondary, upside-down rainbow.

Phosphorus is used by life. Life is not used by phosphorus.

This explanation is symmetrical in regard to different colors. Perhaps I miss something. It would explain if the rainbow band were red on the edges and violet in the middle. What makes the violet to appear on the outside edge and the red on the inside edge of the rainbow band?

No prob. Cheers.

I don't think so. If the fluid motion is caused by the paddle wheel, i.e., by a shaft work, it will not cause a decrease in pressure.

Here is how one could measure 30 minutes with the rope.

I don't know if it matters here, but generally mathematical objects can be considered in a variety of perspectives. For example, a complex number can be considered as built of real and imaginary parts or of phase and magnitude.

Sorry, I've tried but failed to understand the analogy. Thus, don't know what to say.

You are right. Very good analysis. +1

Thanks. I knew about FSA and PDA, but not about LBA. Of course, they are weaker than TM. If the expansion of the universe slowed, the observable universe would grow with time. In this case, it's not clear if it were bounded. However, with the accelerated expansion, the observable universe actually shrinks. In this case, it is bounded for certain. I understood the OP question as asking if AI is stronger than TM. It seems that we agree on the answer, no, it is not.

I am sure that the boat will not rise. Because if it rises, its weight is not balanced by the decreased buoyancy, and it goes down. I cannot tell how the internal forces will redistribute to balance each other, but they will. BTW, you might be interested in this discussion, which is somewhat related: https://www.scienceforums.net/topic/128670-buoyant-force/?do=findComment&comment=1227608 Feel free to skip unrelated comments in that thread.

I am reasonably clear about what you mean saying "exist", i.e., the mathematical existence. However, I still don't know what "end" means. For example, number 3 exists. Does it "end"?