4 ms·

I think it's a fine way to introduce the notion that mass bends spacetime, and "gravity" is the phenomenon of traveling that curved spacetime. We can show the w

by scott_s 11y ago

I think it's a fine way to introduce the notion that mass bends spacetime, and "gravity" is the phenomenon of traveling that curved spacetime. We can show the warping of a two-dimensional plan by projecting it into the third-dimension, giving an intuition by analogy. I don't know how to actually show warped three-dimensional space, since we can't project into into a fourth-dimension.

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.
Jun8 11y ago
The main problem with this analogy is that the thing it's trying to explain (gravity) is tangled into the analogy (balls bend the sheet because of gravity) so it doesn't provide an independent viewpoint. On first encounter this analogy seems to lead to great enlightenment but a bit of thought reveals that it doesn't really explain anything, even in simplified terms. It's not hard to summarize the basic tenants of GR, here is a very good attempt: http://physics.stackexchange.com/a/3018/852 http://physics.stackexchange.com/a/3018/852. For a layperson I would focus on (1), what a geodesic means (what's the shortest way to travel from NYC to London, etc.). Then I would move to (2) and say that we don't know why that is the case. This would be a nice segue into a discussion about how Physics just describes observed phenomena with equations and the explanations are iterative.

by scott_s 11y ago

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.

Jun8 11y ago

The main problem with this analogy is that the thing it's trying to explain (gravity) is tangled into the analogy (balls bend the sheet because of gravity) so it doesn't provide an independent viewpoint. On first encounter this analogy seems to lead to great enlightenment but a bit of thought reveals that it doesn't really explain anything, even in simplified terms. It's not hard to summarize the basic tenants of GR, here is a very good attempt: http://physics.stackexchange.com/a/3018/852 http://physics.stackexchange.com/a/3018/852. For a layperson I would focus on (1), what a geodesic means (what's the shortest way to travel from NYC to London, etc.). Then I would move to (2) and say that we don't know why that is the case. This would be a nice segue into a discussion about how Physics just describes observed phenomena with equations and the explanations are iterative.