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So I saw the movie Interstellar, and it got me thinking. I won't even mention all the plot holes, but I wanted to ask about a planet orbiting a black hole. I always thought you had to travel near the speed of light in order to experience time dilation.

  1. If you pointed a strong telescope at people on the planet's surface, will you see them moving very slowly?
  2. Since photons do not experience time dilation and always move at the same speed, will the surface of that planet and objects appear darker, almost dim and black?
  3. When a photon is absorbed by an atom on the surface and then discharged and reflected back, is the atom's electron orbital speed slower with respect to the speed of light, and absorption also slower with respect to the speed of light?
  4. Would more light hit a radiometer per unit time from the radiometer's perspective, and would it cause it to spin faster or slower (radiometer time, revolutions/s)? Wouldn't there be a build up of 'light pressure' because atoms could not absorb and reflect the photons as quickly?

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    $\begingroup$ Yes, gravitational time dilation exists. $\endgroup$ – ACuriousMind Apr 10 '15 at 22:39
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    $\begingroup$ Gravitonal time dilation is a part of general relativity. Time dilation due to velocity is special relativity. $\endgroup$ – Jimmy360 Apr 10 '15 at 22:43
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    $\begingroup$ Chloe, when one hovers over the up vote button, the hover box content is: "This question shows research effort; it is useful and clear". While your question(s) is well written and clear, there is no research effort shown. However, given the popularity of "Interstellar", I do wonder aloud if this site should have an "Interstellar" 'master question' with links to various related questions and answers. $\endgroup$ – Alfred Centauri Apr 10 '15 at 23:17
  • $\begingroup$ @AlfredCentauri Thanks. I read all the 'related' questions on the sidebar. I could have asked on movies.stackexchange.com, but I wanted a more rigorous answer from a physicist. $\endgroup$ – Chloe Apr 10 '15 at 23:23
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    $\begingroup$ Chloe, you seem to be on the right track. But for question 3 and 4 you will have to specify what you mean by "slower". Do you mean slower as observed in the superpower telescope mentioned in 1, or slower as observed by someone on that planet? A person on that planet would in fact find no observable difference in almost anyway, given the assumption in the movie that it is a supermassive blackhole. $\endgroup$ – Xiaolei Zhu Apr 11 '15 at 3:32
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OK, let's take you questions one by one.

  1. Theoretically, the answer is yes. If you manage to observe the people on the planet from an area not in the vicinity of any significant mass, you would see the people moving much slower, clocks running slower, etc.

  2. Although the speed of light is a constant in a vacuum, the frequency of the light will be different to an outside observer. The entire scene would be redshifted. In essence, the light that you would detect would seem to have less energy than the light that left the planet.

If the planet has a large enough gravitational field, you may find that what you are able to 'see' is actually part of the x-ray or ultraviolet part of the spectrum, which has been redshifted into a frequency that can be perceived by the eye. Since there are far less sources of x-ray and ultraviolet light, you would see a dim, almost black scene.(When I say sources of UV or X ray, I also imply that since no ultraviolet light reaches the planet's surface, there is none reflected. Also, light in the higher part of the spectrum is more easily absorbed than reflected.)

  1. When you say slower with respect to the speed of light, do you mean slower than what it would be for a surface observer. If so, then the answer is yes. Gravity is responsible for time dilation, which would make everything on the planet seem slower to an external observer. As I understand it, the speed of light here is only a reference speed. Correct me if I am wrong.

  2. Since the scene was redshifted, the photons that hit the radiometer (carried by an external observer), would have lower energy and hence, lower momentum. The radiation pressure would be less. At least to my understanding.

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  • $\begingroup$ More wow. I imagine in space, without gravity, an atom would get 1 photon per electron revolution. In the gravity well, an atom would get 2 photons per electron revolution. I was curious what happens with the extra photons - could they be processed? Redshifting takes care of that, since they are less energetic, everything balances out. Such elegance. $\endgroup$ – Chloe Apr 19 '15 at 3:34
  • $\begingroup$ Concerning reflected light: wouldn't in-falling visible light be blue-shifted to higher wavelengths, reflect off various surfaces, and be red-shifted back to visible light on the way out? I'm assuming the light falling on the planet from the universe in general. $\endgroup$ – Asher May 10 '15 at 22:37
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Due to gravitational time dilation, for an observer of the planet, the frequency of electromagnetic radiation would be slower. Visible light emitted from the planet would appear as infrared or micro-waves. The amplitude of the radiation would not change. Since frequency decreases while amplitude remains constant, the radiometer would receive less cumulative energy and would spin slower.

I do not believe there would be any change in the rate at which an atom absorbs a photon. The speed of light is infinitely faster than mass can travel. Objects inside a massive gravity well absorb photons the same way objects in open space do.

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