• 8 Posts
  • 38 Comments
Joined 4 months ago
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Cake day: July 13th, 2024

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  • even light can stop following null geodesics because the curvature can be too big compared to the wavelength

    Very interesting! How do you study something like this? Is it classical E&M in a curved space time, or do you need to do QED in curved space time?

    Also, are there phenomena where this effect is significant? I’m assuming something like lensing is already captured very well by treating light as point particles?


  • So if I have a spherically symmetric object in GR I can write the Schwarzschild metric that does not depend on the radial mass distribution. But once I add a second spherically symmetric object, the metric now depends on the mass distribution of both objects?

    Your point about linearity is that if GR was linear, I could’ve instead add two Schwarzschild metrics together to get a new metric that depends only on each object’s position and total mass?

    Anyway, assuming we are in a situation with only one source, will the shell theorem still work in GR? Say I put a infinitely light spherical shell close to a black hole. Would it follow the same trajectory as a point particle?







  • You said the two objects accelerate at the same rate, but then in the PS you said the feather gets accelerated faster. What do you mean?

    Are you saying the feather gets pulled on more because the mass of earth minus feather is greater than the mass of earth minus ball? You would be right. If you lift the feather, measure how long it takes to fall, then lift the ball and measure, you should get the same number. This meme was assuming you either let them fall side by side, or measure them separately but each time conjure the object out of thin air.


  • Re your first point: I was imagining doing the two experiments separately. But even if you do them at the same time, as long as you don’t put the two objects right on top of each other, the earth’s acceleration would still be slanted toward the ball, making the ball hit the ground very very slightly sooner.

    Re your second point: The object would be accelerating in the direction of earth. The 9.81m/s/s is with respect to an inertial reference frame (say the center of mass frame). The earth is also accelerating in the direction of the object at some acceleration with respect to the inertial reference frame.








  • If your bowling ball is twice as massive, the force between it and earth will be twice as strong. But the ball’s mass will also be twice as large, so the ball’s acceleration will remain the same. This is why g=9.81m/s^2 is the same for every object on earth.

    But the earth’s acceleration would not remain the same. The force doubles, but the mass of earth remains constant, so the acceleration of earth doubles.