Okay, so, I’ve been reading Lawrence Krauss’s The Physics of Star Trek*, in which he points out an interesting tidbit, one of the details of which I hadn’t ever really collected together before.
As black holes get large (in apparent volume of the event horizon from the outside, I guess, since the volume inside is complicated and can be much larger), their density can decrease. For instance, as Krauss points out, a supermassive black about 100 million solar masses would have an overall density roughly equivalent to water. Put another way, if you collected that much water into a single place, it would become a supermassive black hole. He then went on to point out that a black hole the size of the universe (presumably the visible universe) would have the density of…the universe as it is! So, in principle, we might be living inside a black hole.
That got me thinking. One of the reasons nothing can escape from a black hole is that, within the event horizon, all space time geodesics go toward the “singularity” and presumably end there, though quantum gravity (when we have it) will have something to say about that. So, effectively, the singularity becomes “the future” of anyone or anything within the event horizon, in a real, space time geometry sense, and is inevitable.
But the future is also inevitable in our regular space time environment. The general consensus is that this is a function of the second law of thermodynamics and is a “local” effect due to the presence of the highly unusual, relatively low entropy conditions at or after the Big Bang. But what if the future is inexorable at least partly because we are, effectively, within a mega-super-duper-hypermassive black hole of some kind? Perhaps, outside the cosmic horizon (so to speak) there is a space in which time is not uni-directional, just as space is not unidirectional for us.
Maybe the existence of time itself—as a change-inducing “flow”, anyway—is due to the nature of us being in such a black hole. Maybe time, as we experience it, can only exist in a directional way within such an environment.
There are, of course, many possible objections to this notion. Where (and when?) would such a black hole have arisen? All the black holes we know about are formed within our already existing universe, from some form of material collapse and/or compression. This raises another question: can more localized black holes occur within a pre-existing event horizon if it’s large enough? Intuitively, I don’t see why not, but unfortunately, my expertise in the math and theory of General Relativity is not up to pursuing it rigorously**. Notwithstanding my lack of technical expertise, could there, in fact, be an infinite nested series of black holes of various sizes, one within others, and others within those, ad infinitum?
Of course, this all begs the question of the apparent flatness of space time, according to the best of our measurements, which would imply that the total universe is infinite, or at least much larger than the visible universe. Presumably, if I understand correctly, such a much larger universe-containing black hole should be comparatively less dense than the universe in which we find ourselves. Could the perceived curvature and density be a kind of mirage, caused by local effects giving the illusion of flatness? It feels like special pleading to me, though.
Also, how does “Dark Energy” fit into all this, with its evident consequent expansion of our universe? Could that be a form of illusion also, or just the way things seem from a certain point of view, within the horizon, while from without (if such a perspective were possible) it would look very different? How does it explain the Big Bang, which would have been much more dense (but also smaller!) than the present universe.
I have two textbooks on General Relativity (one of reasonable size, the other frikking huge), but in order to be able to tackle the material within them, I need to create a device to slow down external time relative to me, while allowing myself to achieve more than I would otherwise be able to achieve within a local bubble…giving me effectively more hours in any given day. (I don’t have the time and will to fit the study into my current days, since I need to make a living and I have other compelling pursuits, such as writing fiction.) Unfortunately, to devise such a thing, I would need to master the mathematics of General Relativity, and probably quantum gravity as well. This is unlikely to happen unless and until I have already mastered the subjects and created such a device. Which is a paradox, or at least a contradiction.
Maybe my future self will solve these problems and then will send back such a device for me to use to solve these questions and then to invent said device, thus generating a spontaneous, closed time-like loop. That would be nice. I’ll be waiting. Though, I’d like to think that if my future self had developed time travel technology, he would have attended Stephen Hawking’s time traveler party. But maybe that would have required travel outside the time-like loop, and so would be forbidden by the laws of physics. Or maybe he did attend, but hid all traces, in collusion with Professor Hawking.
More likely, of course—by who knows how many orders of magnitude—is that I will not learn the answer to these or oodles of other questions on related subjects. Oh well. Carl Sagan sadly didn’t even live long enough to learn about “Dark Energy”, which I think he would have found as exciting as I did, if not more so. Nature is not kind, necessarily…but it certainly is interesting. Or, as Einstein metaphorically put it, “God is subtle, but he is not malicious.”
*So, I’m still able to read non-fiction about fiction, at least.
**I take consolation from the fact that Einstein himself didn’t really know the math necessary to construct General Relativity, but had to learn and develop the necessary mathematics, with some difficulty, to properly explore the things his superhuman physical intuition led him to conclude, and in the end to produce the mathematically rigorous theory.
