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Apologies in advance, as I'm not a physicist, and may use terms incorrectly.

In the movie Interstellar, the planet Miller has a time dilation of one hour to seven Earth years. This has brought up several questions for me:

  1. At what point would someone (outside the gravitational force surrounding Miller) begin experiencing the time dilation?

  2. How long would it take to send data from the surface to said someone in space outside Miller?

  3. Would a one hour audio clip recorded on Miller take seven years to play once transmitted?

Qmechanic
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Glen Solsberry
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2 Answers2

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Re 1., gravity has infinite range, so the effect of gravitational time dilation will just grow weaker, but theoretically not go away entirely.

In the idealized case of a single source of gravity, the time dilation factor is given by

$$ \frac t{t_0} = \sqrt{\frac{1-\frac{r_s}{r}}{1-\frac{r_s}{r_0}}} $$

where the Schwarzschild radius $r_s$ represents the mass of the source, $r_0$ the position of a clock close to the source and $r$ the position of an observer that sees the clock as having slowed down by this factor.

Re 2., transmission times would also increase by the factor above. If you want two-way communication, you also have to take into account the travel time of the signal. While I did the calculation, I'm not sure how interesting that expression would be for you (it's less nice than the term above).

Re 3., depends on your mode of transmission: I imagine you'd have to properly restore any digital signal before it could even be decoded, but once that's done, playback would happen without any slowdown. On the other hand, ignorant person that I am (ie without having looked at how radio actually works), I'd expect a direct playback of an analog radio signal would indeed be slowed by the factor above as well (and possibly otherwise distorted, in particular in case of frequency modulation). Also note that the carrier wave would be shifted towards longer wavelengths.

Christoph
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It was a fictional story. It was not well researched. According to Newtonian physics, it would take about a year to accelerate to the speed of light at 1G. If the movie were more realistic, then once you're that deep in a gravitational potential well, it would probably take many years of apparent time on the ship to accelerate to a spot where the gravitational time dilation factor is only 2. I think neutron degenerate matter has the highest ratio of bulk modulus to density of any material. I think that a neutron star at its tipping point just barely large enough to begin the runaway effect towards collapsing into a black hole doesn't have enough gravitational time dilation at it surface for 23 years to be perceived as 2 hours on the surface.

Timothy
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