The Master said, “(9) The special relativistic effect in #4 exactly cancels the general relativistic effect in #8. In other words, people at the pole and at the equator age at the same rate.”
Exactly? The two are governed by different equations. It would be a vast coincidence if this were so. And, in fact, given that the earth’s rotation is slowing (microscopically) if the offset had been “exact” in 2013, it would not be so today.
The two effects do counteract each other…but not exactly.
It’s not a coincidence though - it’s a consequence of the Equivalence principle, regardless of the rate of rotation. As Powers says below, elevation does matter, but everyone at sea level ages at the same rate, regardless of how you calculate the answer.
It is exact (provided everyone involved is at sea level), and it’s not a coincidence. Both points are at the same effective gravitational potential, and so both have the same time dilation.
Also, it’s not quite accurate to say that the general relativistic effect cancels out the special relativistic effect. Rather, the total GR effect includes the SR effect, so just looking at the GR effect gives you everything.
Ah! Gotcha; I overlooked that, as the rate of rotation slows, the earth “springs back” in shape slightly toward the spherical. Okay; my bad. Hats off to the Master.
Also fair enough; one is a proper subset of the other.
This triggered a weird thought.
If there was nothing in the universe, but one rotating body. Would it rotate forever? Ignore why it started rotating. There is no external drag or other forces to slow it. Is there any other reason it would slow and eventually stop?
Then a further thought.
Same body. Alone in the universe. But it is moving. For the sake of argument it’s axis of rotation is perpendicular to it’s direction of movement. Seems to me, it would slow and eventually stop rotating. Due to one side moving faster in it’s direction than the other side. So being more massive than the other side rotating away from the bodies direction.
So even though it is the only thing in the universe. Seems you could tell that it was moving. With no other reference. And velocities that are not balanced seem to create a drag force due to relativity. So maybe the body would slow in rotation and it’s straight line velocity.
Of course, this could all be old basic ideas. But I like when they pop into my head as an amateur.
There are two effects (that I can think of) that could slow a rotating object in an otherwise empty-ish universe. First, there’s gravitational radiation - but that will be very weak indeed, since a cylindrically symmetrical object won’t radiate gravitational waves, so only the tiny variations of the object from complete symmetry would radiate. Second, there’s interaction with the cosmic background radiation, another tiny effect.
What about that gravity anomaly near San Marcos, Texas? It’s about 30 miles from the capital and could explain a lot of the going ons in the Lone Star State.
The things that people call gravity anomalies usually aren’t. What people usually call gravity anomalies are just places where, for some reason, the typical visual cues for things like hills are misleading (for instance, “vertical” trees might actually be tilted one way due to the prevailing winds). In the case in the link, a house has been deliberately constructed to make the cues misleading. Water still flows downhill in such places, just as you’d expect: In fact, “the direction that water flows” is a pretty good definition for what “downhill” means.
There is such a thing as genuine “gravity anomalies”, but they’re due to concentrations of more or less dense material than normal, and they’re usually not noticeable as such to humans: Down is still down. It’s not in the same direction that “down” would be if it were not for the density variations, but since you don’t have any way of seeing “what down would be”, it doesn’t matter.
Neither side is more massive than the other, at least not in any sense that’s relevant for any effect. The notion that mass changes with speed is a very long-standing misconception about relativity, that resulted from an ill-advised attempt to beat the equations into submission, when being politer to them would have yielded much simpler results.
True. But there is the effect that it requires a slight increase in energy input to increase speed as speed increases. Negligible at low speed. But there. One side of the body is moving slower relative to the path of travel, then comes round and increases speed relative to the path. Seems some energy loss would be involved.
I have seen this thought touched on by other threads in the past. I did special relativity in high school many years ago. Not sure I got much further in college. So I learned it the old way. Can you link to a (fairly) simple site that explicates the difference in thinking or perhaps suggest a few keywords that I can google up?
