Can you see on Miller's planet?

Question

I have read this question:

Miller's world would be fried by a strong flux of extreme ultraviolet (EUV) radiation. The cosmic microwave background (CMB) would be blueshifted by gravitational time dilation

There are two effects acting on a body in a deep gravity well that increase this radiation:

• Blueshift: Time going 61,000$\times$ slower would increase the observed frequency of the photons by the same amount. The energy of photons is proportionally increased. ($E=hf$)

Wouldn't Miller's planet be fried by blueshifted radiation?

There is a very nice explanation by @profrob, and I must ask a follow-up question because there are two point where I am asking for some more details how specifically gravitational time dilation would cause blueshift:

1. Is there an effect of gravitational time dilation that would increase all photon's frequency just because they (and the observer) are in a deep gravitational field? Can someone please explain that effect and how that works? And is it correct to say that this affects all photons, so not just CMB?

2. All along I thought gravitational time dilation was a effect that is only realizable when compared to another frame, far away from the black hole. If you are on Miller's planet, your clock runs normally for you. It is only when you compare it to another clock, you realize that your clock runs much slower on Miller's planet, relative to the other clock far away from the black hole. Isn't this the same way (because of relativity) with photon's energy? Photon's energy in GR is observer dependent. For an observer on Miller's planet, the photon's would be normal (i.e. visible would still be visible), it is just when you would compare it to another photon far away from the black hole that you would see the energy difference?

Now if you go with the calculations to that question, and all photons are blueshifted just because they are in a strong gravitational field (even for a local observer on Miller), then this means not just CMB, but all photons are blueshifted, including visible light photons (which would be blueshifted to non-visible range), but that means it is impossible to see on this planet.

Question:

1. Can you see on Miller's planet?

Answer 1

I think the answer is yes, but the illumination levels would be similar to a heavily overcast day on Earth.

The CMB is a blackbody continuous spectrum, so even though the peak is blueshifted into the ultraviolet, there are still visible photons hitting the planet.

Indeed, a higher temperature blackbody is more intense at all wavelengths than a cooler blackbody of the same emitting area.

I use italics because the blueshifted CMB comes from a tiny hot spot in the sky with a much smaller angular extent than the Sun for instance.

I ran the numbers using this calculator.

According to my answer to the linked question (and recall, these are numbers from a GR ray-tracing simulation published by others), the radiation incident upon Miller's planet is in the form of blackbody radiation at about 700,000 K from an intensely bright spot on the sky, which bathes (one side of) the planet with 400 kW/m$^2$ of mainly EUV and UV radiation. If you calculate what fraction of this blackbody flux falls in the visible band between 400nm and 700nm, it is only about 2.2 W/m$^2$.

This is several hundred times fainter than direct illumination by direct sunlight. This is similar to the illumination one might experience on a heavily overcast day. Of course the spectrum is very, very different and heavily weighted towards the UV.

Answer 2

You could see perfectly well. If you didn't get fried you could use a lantern to enlight the stuff around you. You could hide in a deep cave to take shelter from the burning CMBR (not sure if that has turned to visible). The visible stars would not be visible anymore. They would have become UV at least. In the cave, just switch on the light, smoke a cigar, and enjoy the daily TV show.

Okay, a little elaboration. Time on the planet runs about 61000 times as slow as the time in the space where the stars shine happily along. This means the radiation they emit (assuming them Sun-like) will have it's black body peak frequency increased by 61000. Look at the Sun's frequency spectrum:

Now the max will shift into the non-visible part. The low frequencies get higher and shift to the visible. But the intensity is much smaller. So the stars will turn very dim.

The light of a flashlight won't be influenced because the light is produced on the planet.

What amazed me was that in the movie there was a fully enlightened Miller. What caused this light? Studio spotlights?

Answer 3

Neglecting any brightness from the low energy part of the blue-shifted CMB (which might be significant, as ProfRob points out), a surface temperature of 890 degrees Celsius corresponds to a red-orange glow which would provide sufficient dim light for vision. Neglecting hot spots and cold spots, it would have a comparable brightness to completely covering the surface of the planet with iPhones with the screens set to a fairly dim setting.

If you were not protected by a reflective suit, you would also spontaneously combust, providing abundant, if short-lived light for anyone in the vicinity.

I'm not sure if approximating the whole planet as an 890 degree blackbody is reasonable - there might be e.g. yellow-hot lava oceans at the equator and polar "ice caps" of black solid rock at the poles.