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In Interstellar, wouldn't Miller's planet be fried by blue shifted radiation? The 61,000x time dilation multiplier would make even cosmic background radiation photons into Extreme UV photons.

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The short answer is "Yes". A more qualified answer would be "Yes, except for the operation of other, unknown physical processes." A single hour passing on Miller's planet equates to seven years passing on Earth, implying a relativistic time dilation of about 60,000. As the poster notes, a naive calculation implies that such a huge time-dilation would blue-shift the cosmic background radiation to be lethal.

One can of course perform the analysis more thoroughly. Miller's planet is orbiting a rotating black hole named Gargantua, and so gravitational lensing would produce an effect where the blue-shifted CMB radiation would appear to come from a small region in the planet's sky. Using relativistic ray-tracing software, physicists Opatrný, Richterek, and Bakala found that for the case of Miller's planet the region is "comparable to the angular size of the planet Neptune as seen from Earth". Despite its small size this spot would irradiate the planet with prodigious energy, leading to a surface temperature of about 890 Celsius. So the water waves the astronauts see, and indeed the presence of liquid water, cannot occur.

For those who want to see the calculations in detail, Life Under a Black Sun is published in the American Journal of Physics, or is freely available at the arXiv preprint server.

As far as I can tell, the additional physical processes needed to make Miller's planet cool and habitable are not explained, or even hand-waved, in the film.

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    Except that it's fine and clearly there isn't a radiation risk on the planet since they're actively considering it as a home for humanity.
    – Valorum
    May 23 at 10:34
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    @Valorum Thing is OP seems to be asking about real world situation, so it's off-topic.
    – Mithoron
    May 23 at 18:55
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    The Science of Interstellar mentions that Miller's planet is nearly tidally locked to Gargantua (with some small rocking back and forth to explain the ocean waves). In the case of a tidally locked planet, I wonder if the bright spot in the sky would always illuminate the same side (presumably the side facing 'forward' relative to the planet's direction of motion compared to cosmic background radiation rest frame), so that there'd be a "darker side" that was only illuminated by the accretion disc (which is rotating at high speed too, perhaps fast enough that it isn't so badly blue-shifted).
    – Hypnosifl
    May 24 at 2:19
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According to The Science of Interstellar, the makers certainly gave some thought to the potential for radiation damage to the planets close in to Gargantua. It would appear that Gargantua itself has been 'tuned' by the writers to emit very little radiation.

A typical accretion disk and its jet emit radiation—X-rays, gamma rays, radio waves, and light—radiation so intense that it would fry any human nearby. To avoid frying, Christopher Nolan and Paul Franklin gave Gargantua an exceedingly anemic disk.

Now, “anemic” doesn’t mean anemic by human standards; just by the standards of typical quasars. Instead of being a hundred million degrees like a typical quasar’s disk, Gargantua’s disk is only a few thousand degrees, like the Sun’s surface, so it emits lots of light but little to no X-rays or gamma rays. With gas so cool, the atoms’ thermal motions are too slow to puff the disk up much. The disk is thin and nearly confined to Gargantua’s equatorial plane, with only a little puffing.

It's also possible that the presence of the black hole is (somehow) causing the background radiation in its vicinity to be very much lower.

She nodded. “Murphy’s Law—whatever can happen will happen. Accident is the first building block of evolution—but if you’re orbiting a black hole not enough can happen. It sucks in asteroids and comets, random events that would otherwise reach you. We need to go further afield.”

Interstellar: Official Novelisation

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    And yes, I'm aware that that's not how these things work, but this is a film where "love" is considered to be one of the fundamental forces, so let's not quibble about cosmic microwaves.
    – Valorum
    May 23 at 10:54
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    It's fine that the accretion disk is faint, but what about the CMBR? That is not so easily escaped. May 23 at 11:05
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    @ClaraDiazSanchez - The black hole is somehow fixing that, I expect. Note that it's not a real black hole, but instead the creation of superpowered humans from a million years into the future. What's sweeping away some microwaves and photons if you can make a black hole from spare parts?
    – Valorum
    May 23 at 11:20
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    The problem is the "somehow". Unless it is stated somewhere what the process is, I don't think we can do better than saying "unknown forces" - whether it's the Power of Love, or magical engineering. May 23 at 11:37
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    The problem is that relative blueshift/redshift would cause Miller's planet to be vastly hotter then the other planets. May 23 at 16:36

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