3 ms·

I still disagree: the problem is not the number of dimensions, the problem is that the physics is wrong. If one flips the rubbersheet, the geodesics are the sa

by baghira 11y ago

I still disagree: the problem is not the number of dimensions, the problem is that the physics is wrong. If one flips the rubbersheet, the geodesics are the same, but clearly now the model doesn't match our intuition. Indeed the objects are attracted by the mass because of the Earth's gravitational potential, not because of the rubbersheet curvature. The balls are following the variation in height of the sheet (in a sense a first order variation) not the curvature of it (the second order variation). The model is bending the wrong component (space, instead of time), and with the wrong sign (the geodesics are repelled by the mass). As pointed out by Ron Maimon in this answer: http://physics.stackexchange.com/questions/1019/common-false-beliefs-in-physics/13569#13569 http://physics.stackexchange.com/questions/1019/common-false... a much better explanation can be offered introducing proper time and the effect of gravity on it.

danielvf 11y ago
"It is just as easy to explain things correctly, in terms of time slowing down near a massive object, and world-lines trying to maximize their proper time with given fixed endpoints" Could you explain it to me this way?
- baghira 11y ago
  A decent explanation is here: http://www.physicspages.com/2013/03/30/geodesics-paths-of-longest-proper-time/ http://www.physicspages.com/2013/03/30/geodesics-paths-of-lo... (I haven't checked all the calculations though). A similar explanation is shown in Feynman's lectures:http://www.feynmanlectures.caltech.edu/II_42.html http://www.feynmanlectures.caltech.edu/II_42.html
  - nmeofthestate 11y ago
    ...We can now write out the Lagrangian differential equations... Finally, an explanation of gravity in layman's terms.
    - baghira 11y ago
      You are right, of course (although I'd argue that the term layman is poorly defined, on HN I'd expect a significant fraction of readers to know what a differential equation is). Still, there is the kernel of the correct explanation which could probably be presented to the larger public, starting with the well known explanation for refraction in terms of minimal paths (the lifeguard trying to save a drowning man), passing to the fact that in special relativity the trajectory of the free particle maximizes the proper time, and ending up with the gravitational case.

by baghira 11y ago

danielvf 11y ago

"It is just as easy to explain things correctly, in terms of time slowing down near a massive object, and world-lines trying to maximize their proper time with given fixed endpoints" Could you explain it to me this way?

baghira 11y ago
A decent explanation is here: http://www.physicspages.com/2013/03/30/geodesics-paths-of-longest-proper-time/ http://www.physicspages.com/2013/03/30/geodesics-paths-of-lo... (I haven't checked all the calculations though). A similar explanation is shown in Feynman's lectures:http://www.feynmanlectures.caltech.edu/II_42.html http://www.feynmanlectures.caltech.edu/II_42.html
- nmeofthestate 11y ago
  ...We can now write out the Lagrangian differential equations... Finally, an explanation of gravity in layman's terms.
  - baghira 11y ago
    You are right, of course (although I'd argue that the term layman is poorly defined, on HN I'd expect a significant fraction of readers to know what a differential equation is). Still, there is the kernel of the correct explanation which could probably be presented to the larger public, starting with the well known explanation for refraction in terms of minimal paths (the lifeguard trying to save a drowning man), passing to the fact that in special relativity the trajectory of the free particle maximizes the proper time, and ending up with the gravitational case.