swansont

Because the value of the function depends on whether y>x or not If the functional value had depended on a hard value for y, you would integrate to that limit.

That's not actually strictly true, because the earth is itself in motion (it rotates) and is thus not an inertial frame of reference. In the Hafele-Keating experiment (though these were subsonic aircraft, I believe), the westbound clocks sped up. That's because they were moving slower relative to an inertial observer.

No, I don't think anyone is going to do your homework for you. You give it a shot, and show your work, and you'll get some help. deep already gave you two equations that apply to many of your problems. For #3 you need N=rFsin(theta) whenre N is the torque, r is the moment arm, F is force, and theta is the angle between the force and the moment arm.

In a GPS satellite there is a gravitational term as well as a kinetic term in the timing correction. Does that answer your question?

The energy that generated that heat comes from somewhere else - you have to form the bubble first. Absent a fusion (or chemical) reaction this is a net energy sink, not a source.

Respect is earned. I was attempting to discuss actual science, but apparently you don't want to go there - as you've pointed out a few times, you attempted to stop me from arguing those points. Oh well.

No, what I'm saying is that the length of time something lasts does not necessarily have to do with relativity. You asked where your logic failed, and I pointed out an instance. No need to get snippy about it.

I think a large number of physicists would disagree with that, given the success of QM.

I don't think you could do this with a gas. You need long-range order and lots of interactions, which basically means you need a solid in a lattice. Piezoelectric devices expand when you apply a voltage (or generate a voltage under pressure/compression). Solids can have different behavioral characteristics along different axes, but the randomness of a gas probably precludes this effect. The only possibility I can think of would be if you could polarized your sample and maintain that. Then there's a slight possiblity that there could be expansion along one axis due to an electric or magnetic field. But I've only heard of this type of thing happening in solids - not liquids or gases.

"lasting longer" does not mean the time passed more slowly

It's possible to assert anything you please. But in science, assertions mean nothing without data to back them up. Absent that, you're just blowing smoke. You should have heeded your own advice and not gone there, for the smoke is thick. What scientists have notices is that observation changes the properties of the state of a particle (Heisenberg Uncertainty Principle). This does not equate to consciousness or spirit interaction. Detection can be done by an inanimate object, and I don't think you want to argue that a chip of silicon has sentience or a spirit.

Nothing happens to the clock. What is different is the measurement of the clock.

I used to. I know what they are, but haven't done any rotation calculations in a long time.

Again, though, that's the phosphor you are seeing.

No, I meant longitude. It's the "finish line" that the sun has to cross to measure solar noon in my example. The sun moves east-west, so the line it crosses has to be north-south. Think of the circle of longitude, and make its radius larger. That circle is now the celestial meridian. All the celestial sphere is, is a mapping of earth coordinates onto a larger sphere.

If all you want to do is test GR with gravitational potential changes then we do this already, continually, with GPS clocks. All you have to do to test the mass effect is convince someone to put an atomic clock under the ground, in a controlled environment. I imagine some people do this already but they aren't the types to come out and admit that they have the equipment buried (or more importantly, where it is buried).

I'm not sure what effect that would have. It may give you a band structure, so that the fluorescence would have a wider spectrum, if they were involved in the optical transitions. But that's just speculation.

Mostly Hollywood, I would guess. Also possibly the green phosphor used to detect charged radiation.

It's going to depend on the strength of the coupling. It may be that there are no transitions in the visible, or that they are not strongly coupled. In those cases you wouldn't get fluorescence. I'm not sure what you mean by conjugation.

Yes.