igor frankensteen, the link doesn’t mention, but that geoid map has a highly exaggerated vertical scale. If they hadn’t exaggerated the scale, it would look to the eye just like a sphere.
This is not correct, and to be honest I cannot follow the train of logic you’re applying to come to this conclusion. One fundamental point is that frames of reference are defined by the observer’s motion in comparison to another frame of reference; in the case of accelerated frames of reference, the subject under greater acceleration (whether due to linear momentum transfer, constant rotation, or being within a gravitational field will be seen to experience the passage of time to be faster relative to an observer in an inertial (unaccelerated) reference frame. (The subject, of course, experience time to pass at the normal boring rate but sees the universe being shrunk in the direction of acceleration.) The time dilation experienced is not a “side-effect” of anything but rather is a fundamental relationship between the qualities we measure as space, time, and acceleration. And (as far as we can tell) it doesn’t matter what the cause of that acceleration is; we experience the same effects regardless.
Stranger
Hard to detect, but it is when he is having a nightmare at the library table. Not really related to their projects but the section tabs will be very clear to anyone who has worked through it at right around the 1:00:00 mark.
Just to take this point, such a description would be incapable of handling anything other than static asymptotically flat spacetimes due to the reliance on certain symmetries and asymptotic symmetries which do not generally hold in general relativity.
However given that the gravitational time dilation is just a function of the g-force felt by a static observer, really showing that objects tend to be attracted to regions where time passes slower as seen by a static observer at infinity is just a matter of showing that a relativistically modified form of Newton’s law of Universal gravitation can be derived in static asymptotically flat spacetimes.
I hate to add this because it is funny, I had to go and look at the movie, and try to find the page that most closely matches the movie. It looks like “18.4. Nearly Newtonian Gravitational Fields” which is on page 445 in my copy.
While this is not for certain due to the angles and image quality; it is funny how apropos it is to this post, if not to the movie.
(Being in track one it could be Mitch’s homework for other classes)
Note that Martin A. Gundersen, a Caltech alumnus and former Dabney Hovse member, was the technical advisor on the film, hence all the “DEI” references. The film is notable for having many accurate science refernces (at least by cinematic standards).
“Would you prepared if gravity reversed itself? The only thing I can’t figure out is how to keep the change in my pockets.”
Stranger
The OP seemed to be musing whether GR time dilation might be driving gravity. I was merely trying to figure out how that possibly could be. It now occurs to me that my error was that time dilation always accompanies a change in the other three dimensions, so my notion about moving faster should be canceled out by the change in space.
YES!! Preach it!! I have been called every version of stupid when making this exact point.
It often comes up in regard to the “vomit comet” aircraft used for training astronauts: The “zero G” experience starts on the upward part of the parabolic flight profile, and continues through the apogee and decent.
It may be apocryphal, but I have heard of errors in early surveys due to mountains (Himalayas I think, but may have been the Andes) deflecting the plumb bobs used as a vertical reference.
Well, you can define “vertical” to mean “the direction a plumb bob points”. But in that case, the error would be in assuming that all verticals are parallel to each other (or converge at the center of the Earth).
Although the GR aspects of the question are inexplicably ignored by the Master (but His ways are unknowable), he speaks, briefly:
What if you fell into a tube through the earth?
Addressed at length in:
Falling t[h]rough the center of the earth?
If I fell to the center of the Earth
How long to travel the Earth’s diameter? [by going through the center]
Man, am I feeling the bibliographic itch today.
Aside from the fact that both questions involve gravity, I can see no connection whatsoever between that question and the one the OP is asking, nor with any other question in this thread.
Center of the earth? Sphere?
OK, normal to center of Earth.
Gimme a break, that took 15 minutes.