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First you said the year, now you're saying the day. These are unrelated lengths of time.
Oops my bad. This is a rotational thing, not an orbital thing, so I most definitely mean day, not year. Although, there will surely be a similar mechanism between the earth and sun, and in the case where the earth is becoming tidally locked to the sun, where the earth's rotation slows relative to the sun, the earth would also drift relative to the sun, so this would change the orbit. But if we're ignoring the sun, and just looking at the earth-moon system, then the length of the year is unchanged.
What we're looking at here is gravitational friction. The tidal bulge of a non-tidally locked body will migrate around the body, and this causes internal friction. We see this on the earth with the tides being slightly behind the the moon, because it takes time for the tidal effect to take place. There is resistance. This friction causes heat dissipation, and that energy is coming from the earth-moon system. The oceans aren't the only things affected by tidal forces... everything is. That friction exists in everything on the planet, it's just much more obvious when we look at massive bodies of water.
It's not at all clear to me that the universe contracting would require a decrease in entropy. Stuff collapses and gets hot all the time.
It seems very clear to me. Sure stuff collapses and gets hotter all the time. We know entropy can decrease in isolated systems, so long as the total entropy of the universe remains constant or increases. This isn't a problem. But if EVRYTHING is collapsing, this is a very different scenario. Entropy is decreasing. If we assume the universe was a singularity before the big bang, this singularity is literally the lowest entropy possible in the universe. If this is the ultimate fate of the universe, then the total entropy of the universe must decrease to get there.
If we can say with 100% certainty that entropy cannot decrease, then that's the same as saying that the universe cannot collapse into a singularity. At least, that's how I interpret it.
If the moon were slowing down, it would be drifting toward the Earth.
Again, I'm talking rotational velocity here, not orbital. The moon's rotational velocity has slowed down to the point of stopping, relative to earth.
If we, as humans, extract the tidal energy, the bulge is not moved, but it is diminished.
The bulge is slowed, which is the same as moved. If you stand in front of a train and get hit by it, you will very slightly slow the train down as it hits you. That's pretty much the same as causing the train to move. That's more obvious if we imagine two people running into each other... both will stop. Is this not relative motion? Is this not "movement"?
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