It seems as if I need two more Karma (somehow), or I will have to wait five days.
Have some upvotes then :-)
Your insight about system entropy being limited by surface area was precisely one of the missing puzzle pieces I wanted to find. I do not yet know what to make of it, but perhaps it would be obvious to you.
The intuitive explanation for this is that a black hole is a maxentropy state, because you have the minimum possible information about its internal structure and composition. You can know its mass, momentum, and net charge, and that’s it. You can’t look at a black hole and infer anything else about the composition and structure of the matter that went into its formation. Hawking radiation complicates this a bit—I think there’s some quantum information theory result that it necessarily somehow encodes the information about the matter that went in (IIRC because the virtual particles that cross beyond the event horizon annihilate normal matter instead of their virtual partners that escaped, in a way that matches the energy/charge/parity of the escaped matter?)? And you can theoretically, maybe, use something like the Penrose process to extract the energy from the rotational momentum and charge, thereby eliminating that gradient. At that point you only have the mass, and kinda (AFAIK) have to just wait the ridiculous amount of time it takes the black hole to evaporate into a similarly maxentropy gas in a post-heat-death cosmos.
With the CMB it is a bit different, since the CMB is present everywhere coming from all directions. If one could isolate the CMB photons in the atmosphere they would add energy based on atmospheric volume (I suspect), not area.
In the limit, however, with a sufficiently thick gas and large volume (if you could even get such a thing), you would get absorption of all CMB-photons deep inside the atmosphere, and then you would be limited by surface area, not volume. Rather than the CMB giving a volume based black body radiation you would get a more standard flux situation, limited by area.
I could be wrong, but I was under the impression that the CMB (a photonic gas) is composed of primordial photons; that they’re not still being generated. In which case, for any concentration of matter (like the Earth’s atmosphere), the CMB photons initially present will have either rapidly passed through and out (since the atmosphere is pretty transparent to microwaves) or else the local matter will have long since absorbed the local CMB photons and re-emitted their energy as part of a thermalized blackbody radiation of their own at the local temperature, such that there is no internal flux. Instead you have the gas emitting its own blackbody radiation out through its boundary, and the unabsorbed CMB passing out of the boundary, and the external CMB coming in across the same boundary. I think? In which case this is something that happens and reaches equilibrium very quickly—faster than you can actually form such a gas, since the CMB moves at light speed and matter does not. In any case it should all balance.
In the context of normal matter, the CMB sets a kind of minimum cold reservoir temperature for heat pumps that do net work—generating a colder cold reservoir takes more work than you can extract by dumping heat into them—but a minimum that decreases with time as the universe expands and cools.
Things get a little wonky with black holes, which are much much colder than the CMB. I am a bit unsure whether black holes break this in some way, since they get colder as you add matter to them. But I think that’s balanced by the frictional heating and other effects that happen as matter approaches the event horizon? And also by relativistic effects that mean that matter takes infinite time (from the reference frame of a distant observer) to cross the event horizon as it falls in? We still don’t have a good understanding of quantum gravity, either, which could have a lot of implications for the metric effects that happen near black holes and for the long-term future of the cosmos.
Maybe the reset time would diverge into infinity, and the last conscious thought, the last computation, will be broken, just hanging there, never finished.
Both of those thought experiments involve versions of this. Dyson’s Eternal Intelligence assumes exponential slowing of computation over time, in order to produce infinite computation over even-more-infinite time using finite extropy. It is set in an ever-expanding,ever-cooling cosmos. Omega Point is set in a collapsing cosmos, performing infinite computation in finite time using finite extropy. Both involve decoupling objective from subjective time, since the computation/simulation happens much slower or faster than linearly, respectively. I don’t think very many people seriously think that we, from within the universe, could set things up with the perfect precision needed to make either scenario work enough to do actually-infinite computation? More like you can stretch the efficiency of computation to be arbitrarily high the more precisely you can set things up.
Keep in mind I’m not any kind of cosmologist or theoretical physicist—just someone who once thought he wanted to be. I am a materials scientist, but one who hasn’t worked in a lab in 15 years, and in any case we’re way beyond that context now.
Thanks! Actually, your materials scientist perspective is perfect for a few of the questions I have been wondering about.
I could be wrong, but I was under the impression that the CMB (a photonic gas) is composed of primordial photons; that they’re not still being generated.
This is my understanding as well. I switched into a thinking mode that explores limits without bothering with what can be achieved in reality. Kind of like how gas volume decreases as temperature goes down. Reality dictates the gas will turn solid at some point. But what if it didn’t? You are much more firmly rooted in reality compared to me, I think.
Have some upvotes then :-)
The intuitive explanation for this is that a black hole is a maxentropy state, because you have the minimum possible information about its internal structure and composition. You can know its mass, momentum, and net charge, and that’s it. You can’t look at a black hole and infer anything else about the composition and structure of the matter that went into its formation. Hawking radiation complicates this a bit—I think there’s some quantum information theory result that it necessarily somehow encodes the information about the matter that went in (IIRC because the virtual particles that cross beyond the event horizon annihilate normal matter instead of their virtual partners that escaped, in a way that matches the energy/charge/parity of the escaped matter?)? And you can theoretically, maybe, use something like the Penrose process to extract the energy from the rotational momentum and charge, thereby eliminating that gradient. At that point you only have the mass, and kinda (AFAIK) have to just wait the ridiculous amount of time it takes the black hole to evaporate into a similarly maxentropy gas in a post-heat-death cosmos.
I could be wrong, but I was under the impression that the CMB (a photonic gas) is composed of primordial photons; that they’re not still being generated. In which case, for any concentration of matter (like the Earth’s atmosphere), the CMB photons initially present will have either rapidly passed through and out (since the atmosphere is pretty transparent to microwaves) or else the local matter will have long since absorbed the local CMB photons and re-emitted their energy as part of a thermalized blackbody radiation of their own at the local temperature, such that there is no internal flux. Instead you have the gas emitting its own blackbody radiation out through its boundary, and the unabsorbed CMB passing out of the boundary, and the external CMB coming in across the same boundary. I think? In which case this is something that happens and reaches equilibrium very quickly—faster than you can actually form such a gas, since the CMB moves at light speed and matter does not. In any case it should all balance.
In the context of normal matter, the CMB sets a kind of minimum cold reservoir temperature for heat pumps that do net work—generating a colder cold reservoir takes more work than you can extract by dumping heat into them—but a minimum that decreases with time as the universe expands and cools.
Things get a little wonky with black holes, which are much much colder than the CMB. I am a bit unsure whether black holes break this in some way, since they get colder as you add matter to them. But I think that’s balanced by the frictional heating and other effects that happen as matter approaches the event horizon? And also by relativistic effects that mean that matter takes infinite time (from the reference frame of a distant observer) to cross the event horizon as it falls in? We still don’t have a good understanding of quantum gravity, either, which could have a lot of implications for the metric effects that happen near black holes and for the long-term future of the cosmos.
Both of those thought experiments involve versions of this. Dyson’s Eternal Intelligence assumes exponential slowing of computation over time, in order to produce infinite computation over even-more-infinite time using finite extropy. It is set in an ever-expanding,ever-cooling cosmos. Omega Point is set in a collapsing cosmos, performing infinite computation in finite time using finite extropy. Both involve decoupling objective from subjective time, since the computation/simulation happens much slower or faster than linearly, respectively. I don’t think very many people seriously think that we, from within the universe, could set things up with the perfect precision needed to make either scenario work enough to do actually-infinite computation? More like you can stretch the efficiency of computation to be arbitrarily high the more precisely you can set things up.
Keep in mind I’m not any kind of cosmologist or theoretical physicist—just someone who once thought he wanted to be. I am a materials scientist, but one who hasn’t worked in a lab in 15 years, and in any case we’re way beyond that context now.
Thanks! Actually, your materials scientist perspective is perfect for a few of the questions I have been wondering about.
This is my understanding as well. I switched into a thinking mode that explores limits without bothering with what can be achieved in reality. Kind of like how gas volume decreases as temperature goes down. Reality dictates the gas will turn solid at some point. But what if it didn’t? You are much more firmly rooted in reality compared to me, I think.
Since I can (thanks to you), I have now posted my next part here.