Further Ramblings

 March 21, 2021

22:36

I kept thinking about A/4 – the black hole entropy value, where the number of bits needed to describe all possible quantum states in the black hole is apparently equal to the area (in Planck units) divided by four. So clearly something’s getting saturated at this point, but why the divide by four? What are the other 75% of bits needed for? I figured it had something to do with orientation – because states are one thing, but what is the overall orientation? And relative to what?

So mucking around with some related bits it struck me how the area of a sphere – 4*pi*r^2 – is four times the area of a circle with the same radius. Four times. Oh, and that circle is the two-dimensional projection of the sphere. Ooohhhh. It’s encoded holographically. I guess that’s where the whole “holographic principal” comes from? Though, I’ve never seen it spelled out that way. Anyway, that’s pretty frickin’ cool.

Other than that, been going in circles (haha) about how to model the information flow through onion layers of planck units and how that might lead to something like the Schwarzschild time dilation function. 

At some point was testing out a possible result and thinking how it could lead to relativistic time dilation as well. If it’s about information flow through an area, then what’s changing – the information? The area? So back to the gravitational time dilation, the area in question would be (in the simple cases at least) related to the smallest possible sphere you could put around that pile of stuff. Now, if that stuff is moving very fast relative to you, it’ll show Lorentz contraction. I’m not super happy about using this, because it is itself an effect based on other deductions and I’d much rather see what follows directly from information flow. But anyway – I do at least think that it is interesting that if you picture the containing sphere becoming an oblate spheroid, then the “worst-case” 2D projection of that (side view) is an ellipse where the long axis is the original r and the short axis has been shortened via *sqrt(1-v^2/c^2). The area of this ellipse is reduced by the same ratio, sqrt(1-v^2/c^2). And that’s the time dilation ratio as well. Well, but this super convenient linear relationship between area/time doesn’t map at all to anything I see so far working on the gravitational effects. 

Finally, a random idea: what if black hole radiation (all black-body radiation? All 2nd law of thermodynamics?) is rounding error? There’s this super-tight link between bits of information in a black hole and the surface area in Planck units. Is the surface itself quantized? Is that bit calculation rounded up? (what I’ve read is pretty definitive about saying it’s A/4 – not “close to A/4”). Anyway I am not sure where this will go exactly, but it seems there’s lots of room between “platonic ideal sphere” and “thing made of integer multiples of anything”. I mean, anything solar-sized compared to the Planck scale will be pretty close to the ideal. But – if this discrepancy causes some sort of erosion – eg “this space here should be inside the event horizon, but it’s not because quantization, so there’s a chance for escape” – then as the BH shrinks it’ll get farther from that ideal shape and erode faster, which is pretty much what they do. The power of BH radiation is inversely proportional to the volume. I think that is the right relationship I’d expect, but I’m not sure. What I’d like to see is something like “the volume loss, in Planck volumes per Planck time, as a function of volume in Planck units”. Actually, after typing that up, yes that’s it. Volume loss is energy release, and per time is power. Wait, crap, did it again. Mass is proportional to radius. So volume loss is what, cube root of energy release? Hmm.

c

March 11, 2021

22:46

Oh, well. So I thought I had a good lead on actually getting somewhere analytically today, but I was crossed up in my head between radius and area. Meaning somehow I’d gotten to thinking that a black hole’s area increased proportionally to mass. No, it’s the radius. If it were area, it’d be a nice correlation to my “it’s a bandwidth thing” post from yesterday. So, not getting where I wanted with that.

However, I was watching the follow-up PBS video about how gravity* bends light, and I did have a bit of an epiphany: the whole “The speed of light is invariant across all observers” isn’t about the speed of light. It’s about the speed of observers. There’s something that limits the ability of anything in the universe to process information, that results in this apparent speed limit. I think it’s fair to say that light doesn’t “move”. 

Black Holes (and not black holes)

 March 10, 2021

23:31

OK, think I have some clarity about things. If you take a bunch of stuff in space (planet, star, cloud, whatever), there are two classes of information involved. The aggregate values that must be conserved: mass, angular momentum, charge. Then everything else. Within a given volume of space, the aggregates don't change over time unless something goes in or out of the surface of that volume. All the other stuff can change.

There is a limit to the amount of this information that can flow through a given area of space. 

The immutable class of information gets dibs. Everything else comes out at the rate allowed by what bandwidth is remaining. 

When there's more going on (more mass-energy) within the volume, there's less of that "remaining" BW for the non-aggregate information. The information rate goes down. I'll go out on a limb here and say that the details of the non-aggregate information are only important in terms of how they are changing over time. (It may be that this class of information distills down to only be defined by changes over time). For an outside observer, this means time appears to slow down inside the volume. 

Eventually, at the Schwarzschild limit, that second class of information stops. 

There's a lot of circular stuff going on with this analysis, so it could easily fall apart. And I am not sure yet how black-body radiation plays into it. 

Entropic Gravity, the Holographic Principle

 March 7, 2021

22:45

So if it is consumption of some resource by the processes inside "stuff" (matter, and the interactions between matter, AKA energy) that creates the time dilation that gives rise to "mass", then what is that resource? Entropy comes to mind - not that it is the resource, but definitely some connection between the two. If something is really being consumed, then there's a directionality there, and well, entropy is the most obvious time-asymmetric thing out there. 

An idea I had, but probably am not anywhere close to being able to follow-through on, is whether you could refactor entropy in a way which would turn things inside out, and show the relationship between space and time. EG if the units are "energy divided by temperature" ... well if energy (mass) is an effect of the process, can we solve for the actual process? And temperature contains time and spatial information to make use of. 

I was also thinking about black holes. Consumption of resources leading to time dilation sounds good in a hand-wavy way, but the simple approach to this should have an asymptotic result - more complexity, slower time. Zero time would only happen with infinite complexity. But with black holes, all of the current theory (which I'm certainly not trying to throw out) says time flow actually reaches zero from an outside point of view. Can we come at them from a different direction - information exchange between the "inside" and the "outside" - and arrive at the same conclusion? EG when there's enough going on within a given volume, does it run up against a fundamental limit of being able to support what the stuff outside that volume needs to know about what's inside of it, and the result of this is that all of the time-variant processes in the stuff inside just have to go away? As an aside this appears to totally contradict my starting point of "it's the time-variant processes that give rise to mass", because of course black holes still have mass. Anyway - it seems like the limiting factor in this case would be the surface area of the black hole, because that is the boundary which would impose this "bandwidth limitation". Which reminded me of how the entropy of a black hole is a function of its (event horizon's) surface area. And also reminded me about the "holographic principal" - which I probably have never properly understood but never been too turned on by. I think I definitely have not understood it before now.

So I ran across this - Entropic Gravity, Erik Verlinde's theory: https://en.wikipedia.org/wiki/Entropic_gravity

Oh - it's only the derivation of the Newtonian gravitational equation from statistical entropy combined with the holographic principle. OK that sounds interesting. And then reading about the holographic principal - OK, so back to black holes: yeah, then when the bits of information within a volume exceeds the ability of the surface area of that volume to represent, is when you get a black hole. Waving my hands a lot here. But at least there's a connection. 

(I think some people have taken all this to mean "you could have an informational black hole - where it's not the mass of stuff that leads to an event horizon, but simply the amount of information encoded in the stuff. Well, I will go out on a limb here and say that's a misunderstanding, and how in the world can you expect your stuff to encode more information then it inherently is made of already?). 

Back to Entropic Gravity - again, I'm not up to speed nearly enough to have an opinion on the critiques of that derivation. But I do wonder - if, instead of deriving the gravitational force with this method, you derived time dilation, would there be fewer pitfalls? Because the "force" of gravity is an effect of the time dilation, so there's more room for hazard when trying to get from A directly to C instead of just to B; when there's already a good way know from B to C. 

time and gravity

March 1, 2021

22:55

Wow, funny how things can go this way. This video just popped up tonight on YT for me, posted last week. Explaining how time dilation is what causes gravity; have to wait for the next part to hear the explanation for how that can be true for something like a photon (in this part it's all about torque-like analogies because parts of the stuff have clocks moving more slowly than other parts of the stuff; and that since the math holds up for stuff of infinitesimal size, that means it works on single particles too. He mentions that nothing can actually occupy solely a point in space (zero size), but there's of course the open question about what actually is occupying that space then, and how parts of it would experience time at different rates). 

https://www.youtube.com/watch?v=UKxQTvqcpSg

Just a few minutes before that I was searching for things along the lines of "refraction causes gravity", meaning the time gradient refracts the wave equation of whatever and bends its path. And, wow - I found some guy's page where he asserts that Einstein was "totally wrong" and there's no such thing as gravitational lensing, it is apparently all just refraction due to the upper atmosphere. Mmmmmkay. I guess he hasn't heard of the HST. But seriously there's something not right with this person. Endless statements of truth/falsity without any actual explanations. It's not quite timecube bad, but yikes. 

Meanwhile, I've been wondering about electrons. Current theory mostly thinks they probably don't decay. It's not been "proven", but there's nothing known that they could decay into without violating some pretty solid constraints (like preservation of charge). So I've been wondering what it could be going on inside them which necessitates the resource draw that leads to mass. That's all; no ideas yet.