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I have never found it comfortable to imagine gravity as a rubber sheet with a weight on it, where Earth's gravity is making the 'model' work by pulling the weig

I have never found it comfortable to imagine gravity as a rubber sheet with a weight on it, where Earth's gravity is making the 'model' work by pulling the weight and stretching the sheet. Trying to turn that into a 3D Sun with a planet orbiting it when there is no 'down' separate to the system, trying to imagine gravitational lensing when there is no way to imagine a NASCAR style banked corner in a stretched void, trying to imagine why a black hole can be so dense that light cannot get away. Imagine a rubber sheet and light as a toy car climbing up the well, it's easy to imagine the well becoming so steep that the car wheels cannot grip it, or the car motor cannot lift the weight of the car. Try imagining light heading directly 'out' from a black hole, space is compressed so much that ... what? Light loses its grip on spacetime? Spacetime is not just stretched but is being pulled inwards like a conveyor belt at 3e8 meters/second so light is at an effective standstill? (yet all frames of reference see light moving away from them at the speed of light). It doesn't fit a rubber sheet for anything, really, even the basic planet orbiting the gravity well has no easy imagining in 3D. It's somehow ... Earth taking the path of least action? a straight line in curved spacetime?

ncmncm 5y ago
It was never a productive metaphor, in any way, but it let people with no mathematics feel like they had a sense of things. If you want to reason correctly, it is a trap.
raattgift 5y ago
The rubber sheet runs into problems when you try to introduce high inclination orbits, or non-inspiralling (or at least very very slowly inspiralling) nearly circular orbits. It also doesn't do well when the mass-to-mass ratios of the objects on the sheet are small. It also doesn't do well when you want the masses to spin. (How many of the large bodies in our solar system have nearly zero spin angular momentum? And the difference between perihelion and aphelion for Venus and Neptune are small, and there doesn't seem to be any danger of them inspiralling sunwards in the next several thousand of their respective solar orbits.)

ncmncm 5y ago

It was never a productive metaphor, in any way, but it let people with no mathematics feel like they had a sense of things. If you want to reason correctly, it is a trap.

raattgift 5y ago

The rubber sheet runs into problems when you try to introduce high inclination orbits, or non-inspiralling (or at least very very slowly inspiralling) nearly circular orbits. It also doesn't do well when the mass-to-mass ratios of the objects on the sheet are small. It also doesn't do well when you want the masses to spin. (How many of the large bodies in our solar system have nearly zero spin angular momentum? And the difference between perihelion and aphelion for Venus and Neptune are small, and there doesn't seem to be any danger of them inspiralling sunwards in the next several thousand of their respective solar orbits.)