As far as humans surviving for a while deep underground — how deep would I have to dig?
Even before they thought of it as a god?
If the Sun stopped producing photons at its core, wouldn’t it implode?
Yeah, that’s the problem with the hypothetical. If you assume that all fusion reaction at the sun’s core stops suddenly, but everything else remains the same, such as photons making their way out, there are lots of other things that happen.
Lord Kelvin calculated that the Sun could produce its current output for 30 million years by the conversion of gravitational energy into heat.1
Whoooosh?
You do realize of course, from your own source, that Kelvin’s hypothesis of how the sun generates energy was that the energy of infalling meteors continuously heats it up. Your source even says “Kelvin was wrong”.
I can only assume your post was facetious.
Would it still be producing heat photons? 
If you read it more carefully, that was the first version of his hypothesis:
Later, he adopted Helmholtz’s version of the hypothesis. See Kelvin-Helmholtz mechanism.
Kelvin may have been wrong about the source of the Sun’s power, but Helmholtz and Kelvin were correct about the amount of heat that could be generated from gravitational energy. If fusion ceased in the Sun’s core, it would continue to generate heat from gravitational energy for millions of years.
Oh wow, you were serious.
Then you really need to stop linking to sources that undermine what you say. Your unsourced Wikipedia article states that the 18,000,000 year number was arrived at assuming a uniform density for the sun. That’s an inaccurate assumption. So even if the sun could keep shining, there is much less material to make this happen than is assumed in that hypothesis.
The sun has the size and shape it does because that’s the point at which the outward force from the fusion reactions at the core balance the gravitational attraction of the cooler material farther out.
If the nuclear furnace were to suddenly shut off today, you’d have a cooler shell of gas with nothing to hold it out where it is. The sun would collapse in on itself, and likely cause some kind of cataclysmic event.
Possibly a helium flash, which would cause the sun to expand into a red giant ahead of schedule, baking our planet.
A photon that is “absorbed and then re-temitted at the same wavelength” is identical from the before and after state, save for the vector of its momentum. All photons of identical energy levels, and all other fundamental particles are indistinguishable from their fraternal particles, just like members of Sigma Nu from each other. In the case of energy generated by fusion in the Sun’s core (and similarlly with other stars) the original light emitted is in the powerful gamma range, and is reduced again and again until most of the light emitted by the photosphere is in the visiable and infrared range, with a small portion of the energy remaining to drive the Sun’s gas dynamic behavior in the convection zone and magnetoplasmadynamic processes that generate the ginormous electromagnetic field of the Sun. (It also loses some energy in the form of the momentum given up to the Solar wind, but this is such a tiny fraction of the total energy its hardly worth noting.)
Technically, it is correct so that that the photons being observed as coming from the Sun are little more than eight minutes old–having been emitted as the product of an electron in the photosphere or chromosphere–dropping to a lower energy state and emitting a photon. However, this is clearly not what Bricker intended when he wrote “The sun stops producing new photons, then the light from the sun goes out.” Should the Sun stop producing photons by some mysterious process but continued to be otherwise hydrostatically stable (i.e. not collapse in upon itself from a lack of photon pressure) it would take between 10,000 and 190,000 years for all of the photons or their children currently being produced by fusion reactions to random walk their way out of the core to the photosphere.
Regarding the o.p.'s originaly question, Squink already posted links to several threads which cover this topic in great detail, but without the Sun and thus Earth’s climatological and hydrological cycles that its output drives, complex life on Earth would be gone in a matter of days. For the first few hours it would just be a progressively cold night, but without solar radiation to renew energy being emitted from the oceans global temperatures would rapidly drop and climate cycles would be seriously disrupted. The heat energy that keeps water vapor suspended in the atmosphere would radiate away, and water would condense and freeze, removing Earth’s protective thermal blanket. All the CO[sup]2[/sup] in the world (0.03% of current atmospheric concentration) won’t reflect enough heat to keep the surface warm, and as ocean currents are disrupted from a lack of driving energy the oceans will freeze from the surface down.
Then things get seriously bad. Oxygen and nitrogen condense on the surface as liquids, and what remaining energy there is probably causes massive oxidation reactions, and anything not near a mid-ocean vent or geothermal fault is going to experience cold to make Jack Frost wince.
Your only hope is to get some good mineshaft space. “Mr. President, we must not allow…a mineshaft gap!”
Stranger
Wasn’t the notion that sun’s fusion furnace had shut off a fairly respectable theory not long ago? I thought the idea was that the sun could ‘go out’, then the lack of interior pressure would start a contraction until a certain density was reached, at which point the fusion process would start again. Given the long time delays for the photons created in the center to ‘get out’, and the heat generated by gravitational collapse, we might not really notice the difference, other than to see variability in the sun’s output. I seem to recall that the neutrino detectors were an important tool in disproving this particular theory.
Is that correct? Or was this just a fanciful theory driven by science fiction authors and popular media?
It was one of the possible explanations for the deficit in solar neutrinos up until 2003, when the discovery of neutrino oscillations made everything copacetic again: Solving the Solar Neutrino Mystery
This question is grinding against the limits of my physics memory, which is why I keep reading this thread - I find it fascinating, even if at some point it becomes a question of semantics.
I will stipulate that two photons of the same wavelength are indistinguishable, and therefore a photon that is absorbed and emitted ten thousand times at the same wavelength over ten years can be said to be ten years old, even if the last absorption/emission happened one second ago.
But it seems that in a (roughly) blackbody radiator like the sun, the odds against that happening are so high as to be essentially infinite. Rather, the initial photon is absorbed and its energy is then divided between an emitted photon at a lower wavelength and additional kinetic energy of the absorbing particle (like a free electron or proton). So if an electron absorbs a gamma ray and emits an X-ray and keeps a few eV of extra kinetic energy, that implies to me that a ‘new’ photon has been created.
Perhaps this is overthinking the problem, but I think that if you aimed a magic wand at the sun that forced all charged particle-photon interactions to be 1:1 with regard to wavelength absorbed and emitted, you’d see some immediate and drastic effects - like the sun collapsing. Wouldn’t you be making it impossible for radiation to heat the matter that makes up the sun? You’re talking about some major screwing around with quantum mechanics here.
As an additional digression, is there any emission from the core of the sun that we can observe directly other than neutrinos?
I am basing all of my answers on very dim memories of college physics, so I am eager to have my ignorance fought.
I may have committed the same sin with physics I so often chastise others for here in GQ in law: to wit, talking out of my ass. If so, I am prepared to eat major crow.
However, let me lay out my understanding of the thing, from high-school physics. And if this is in fact wrong, then I am an invenerate butt-muncher, and I apologize unreservedly.
When you say “Photons get absorbed and then immediately re-emitted,” this confuses me. My understanding is that a photon is absorbed by an atom, which kicks an electron in that atom’s shell to a higher energy level. If the atom then “re-emits” a photon, what’s actually happened is that the electron has dropped back to a lower energy level and emitted a new photon. Now, I readily admit that photons lack ID tags, but as I understand it, that’s a new photon, not the same photon bouncing in and out. Thus, we wouldn’t expect to see free photons that are older than 8 minutes hitting the Earth, or old photons “bouncing around” in any real sense.
I await correction and (possibly) well-deserved scorn.
It doesn’t really make sense to talk about photons as if they’re identifiable anyway. The process generating energy output in the sun is happening at its core, and that energy is thought to take a very long time to migrate to the surface to be emitted as radiation.
And that makes sense to me, but the OP presented what he thought was a clever “gotcha:” his claim that most of our sunlight is old photons, not new. If this is true, then my response is wrong and I’m a goat-felcher for posting a confidently wrong assertion in GQ.
But I’m hanging on to the hope that I wasn’t off base: the basis of the OP’s theoretical exercise is the idea that old photons bounce around for years before being shot out on their way to Earth (or to Mercury, or to Phobos, or to Io). My understanding is that there’s no actual bouncing.
Now, in actuality, I’m a goat-felcher either way, because I’m not sure of my confident-sounding answer. If I’m right, though, I’ll at least have the fact that I’m a lucky SOB as a consolation prize.
This is substantially correct for most earthly conditions, and the photospheres of stars. However, it’s pretty warm down in the core of the sun, and things get odd.
From Solar Physics at Montana State:
There’s no atoms down there to have shells and energy levels, so you get photons absorbed by ‘free’ electrons.
Well, color me surprised to be joining up on the Bricker isn’t a goat felcher team, but it seems to me that a response to a trick question with a trick objection is really not all that unrealistic a response.
Now, the general nitpick I have with “magically” stops producing photons as a premise is that, well, either the sun now works in whatever bizarre way the OP wishes, or some other portion of the laws of physics somehow apply after the laws of physics which used to cause fusion to take place have changed. So, either the new laws of physics make the sun collapse, perhaps faster, or perhaps slower, or the sun just sits there glowing at some arbitrary rate, but is held in its prior configuration by the new magic laws of physics. Even as a serious question, the answer is: You are the one imagining the new physics, you decide how it ends.
Tris
“OK,” he said, desperately trying to hang on to being right, “but even so, what I said seems logical: free electrons absorb photons, and then emit photons. That’s still a step away from photons bouncing around for years on end.”
In one of Feynman’s books, I remember his relating a conversation he had with his father. His dad asked him to explain “where the photon came from” when an atom released a photon. Feynman tried to explain that it didn’t “come from” anywhere; it simply didn’t exist beforehand. He gave the analogy of the sounds that came out of his mouth when speaking; before he speaks, where is the sound?
I’m perfectly willing to allow that I have misremembered and misconstrued what I did correctly remember. But I’d like to hear that, definitively, from someone before I put the dunce cap on.
From Bill Arnett’s Nine Planets site, about as authoritative a site as you’re likely to find on the web:
(emphasis mine).
And if the fact that Arnett is a software engineer puts you off (even though vast numbers of college astronomy departments link to his site), here’s the story from real astronomer (and former Doper) Phil Plait:
(emphasis mine)
Now don’t you wish you’d quit while you were ahead?