I've been chipping away at various angles of information theory as a hobby for a few years now, conceptually for me a black hole in the traditional sense is like compressing random bits to a single zero or one - there'd be no way of getting information back out in the original order. Encoding a higher dimensional representation holographically would be like having a side channel of information I guess, so you could have the 0 or 1 as the 'black hole' but still can reference external state data to reconstitute meaning from it. Entropy is preserved, and laws of maths and physics are no longer being broken.
Say, I can divide a sequence of bits by 2 if they're even, or add one then divide by two if they're odd, repeatedly until the result is 1 (after which the sequence repeats indefinitely, but we can stop at 1 - similar but different to the collatz conjecture). If I know the sequence of operations I can rebuild the original data, but encoding that sequence of operations is the exact same amount of information as the original sequence (in my tests at least).
I'm kind of comforted by the fact that it may turn out black holes aren't destroying information, merely transforming it.
I offer my own, within this realm of discussion, layman's perspective that a black hole might be metaphorically similar to an above ground swimming pool with a (small) hole in the side, within a still larger pool. If there is an orderly structure within the small pool the flow will remove structured information from within and spray it back out.
Following the above metaphore and the impression the article gave me: a black hole does something similar but in a more fourth-dimensional hysteresis format. Over time the energy and "information" contained within (or released out as other forms of energy) is observation-ally constant. This would be a lot more like the way a moon can create tides that pull water in and out of a bay.
While I would also love for science fiction toys like the Portal Gun (or other wormholes/gateways) to be a reality, I really doubt they're actually possible and even if they are this would probably be as close to realizing them as discovering the principles of electricity were to creating the microprocessor.
The reduction of information example I thought agreed with the article, because traditionally (or in other words in layman's understanding) a black hole seems to have been represented as thing that removes information from the universe, which would be like taking a sequence of binary and reducing it to a 1 or 0 through some hidden methods. You'd never be able to get back the original data - unless you had some encoding of the steps taken to reduce, i.e. through a transformation.
Genuinely I'm just not quite sure which bit of my analogy contradicts the article, and perhaps I've just not been clear enough in what I am writing, but I appreciate your comment in any regards.
This is how modulus works for hashing. The number of turns around a circle is lost but is computationally accurate and well-formed.
Interesting to think about.
Holocube/Kaluza-Klein Cube: https://www.dropbox.com/s/3o0ovqe41j624wy/image4.jpeg?dl=0
Holo-Fractal Cube: https://www.dropbox.com/s/gmk375cgu2rylcu/image1.jpeg?dl=0
Although Kaluza-Klein theory has been disproven, I can't help but be amazed that solving Einstein's equations in the higher dimensions independently results the equations for electro-magnetism (light). I also can't help but like the idea quatum mechanics is simply physics for higher dimensions, and that all objects we believe are 3D extend both inward into 4D (particles) and outward from the object in 4D (light/electro-magnetism).
Edit: May be more accurate to say solving Einstein equations in 5th dimension independently yield the five-dimensional Einstein equations yield the four-dimensional Einstein field equations, the Maxwell equations for the electromagnetic field, and an equation for the scalar field.
Could you link a source to this? I would love to read about it.
It is my understanding EM is more or less directly relatable to more fundamental forces (or rather derived from it) so even being able to fit EM in it means that the others must fit.
I think its fun and certainly quirky (imagining the light you/every object emits is actually still one and the same as you/the object, its just that part of you/the object transcends 3D into higher dimensional).
As a result I fear it would be considered less as a Flatland style writing (fun, educational story about dimensions) and more of a Flat Earth style conspiracy theory (we are 4D beings and "they" are keeping the truth from us lol). Who knows maybe it would be fun to launch the next flat Earth theory...
It's not "coherent" information. It's the markings caused by a trillion different impacts. And smoothing things out takes energy, so it would be strange if all those marks dissolved away spontaneously.
The statement "the things that fell into a black hole affect the radiation coming out of it" isn't even a weird thing to say!
The reason is that "the things that come out of it" are reference frame dependent. That is, you and I will disagree on what is emitted as Hawking radiation. In fact a free-falling observer will observe NO Hawking radiation!
So Hawking radiation must be determined entirely by spacetime geometry, which depends only on mass-energy-momentum and not things like baryon number.
Oh, and "smoothing things out takes energy" doesn't seem right. Consider the heat equation: a solid with a temperature differential reaches equilibrium while conserving energy.
I mean absent all the exotic physics calculations, since that comment is saying that people are too twisted up in theoretical math. In a very basic sense it seems reasonable.
> So Hawking radiation must be determined entirely by spacetime geometry, which depends only on mass-energy-momentum and not things like baryon number.
I'm not really following that 'so'. Lots of things are reference frame dependent but still depend on exact particles.
You could test learning and understanding by making questions based on these articles where answers are not given in text and I doubt that you could answer any of them. Or they could write two articles where one is carefully crafted nonsense and it would be hard to figure out witch one is true.
It's a conflict in predictions involving different theories - quantum mechanics only, vs. quantum mechanics plus general relativity. It's a "paradox" in the sense that the two approaches reach conclusions that contradict each other - both can't be right.
The conflict implies that one or both theories are incomplete or incorrect in some way - which we already knew, because quantum mechanics and general relativity are known to be incompatible with each other in various ways.
Such conflicts are rich ground for discovering new physics, because they highlight very specific weaknesses in existing theories. That's why people like Hawking, Susskind, and many others have spent so much time on this.
I think physicists will become more and more convinced of this fact -- there can be no impassable communication barrier (no event horizon).
I believe black holes will be understood in the future as simply arbitrarily massive stars with increasing time dilation. That's because historically it was always assumed black holes do exist, and worked from there. Models of collapse were never fully laid out, and most don't consider an external observer as the correct reference. It's essentially analogue to thinking the field of electrons would diverge when sufficiently close to them (and the paradoxes this would bring).
The light escape mechanism will not turn out to be exotic -- it's simply ordinary light being emitted by objects making its way out in an ordinary null geodesic, which is possible since there is not event horizon :)
Confusion arises because theories predict these things, but one has to be careful to distinguish cases where the theory is being used in a regime beyond its effective domain, from other cases where infinities are less problematic. For example:
> in actual observation nothing infinite was ever seen.
"Real" infinities do show up in various places in physics and cosmology, not in the sense of objects with infinite density, but in more abstract ways. For example, it takes infinite energy to accelerate an object with mass to the speed of light - which we interpret to mean that it is not possible to do that.
A more relevant example is that beyond our cosmic event horizon, light that is emitted "now" will never reach us, even if we wait an infinite time. That is another kind of abstract infinity that doesn't pose any serious conceptual problem.
One effective way to model this case is that the light is infinitely redshifted, very much like light from the event horizon of a black hole. In fact, some models equate the two cases.
You can argue that infinitely redshifted light doesn't actually exist, and in a sense you'd be right - but the point is that very good models predict that the light tends towards being infinitely redshifted, and the effect is that we never see it, even after infinite time.
As such, talking about infinite redshift effectively means that the light in question doesn't exist in the region in question, and "infinite redshift" is a consistent way to model that. Infinite redshift also implies zero amplitude, which again implies that the light in question doesn't exist in that region.
(As an aside, Heisenberg tells us there's no such thing as a consistently zero amplitude quantum field, which gives us a direct link to Hawking radiation from event horizons!)
> I think what he meant was that we have no proof that "singularity" even exists.
As I mentioned, that's not controversial. But what the original commenter wrote was "you can escape [black holes] just fine !" That contradicts everything we know about physics, including our observational evidence of actual black holes.
Importantly, the infinities that arise at the event horizon are also observer-dependent. The infalling observer doesn't see anything special at the event horizon, it's only an external observer that observes time and redshift tending towards infinity.
This is again analogous, if not equivalent to, the cosmic event horizon I mentioned - the cosmic event horizon isn't common to all observers. If you could travel to the location of the cosmic event horizon we observe from Earth, you would find nothing special there, and you would observe another cosmic event horizon 46.5 billion light years away. It's similar to the ordinary visible horizon on Earth in this sense.
So there's no fundamental physical problem in this case with taking the infinities literally, as long as you correctly understand what that means. Besides, for the question of escaping a black hole, it doesn't really matter whether these values actually "reach" infinity - you still aren't going to be able to escape a black hole.
Imagine a black hole with mass M and radius R.
Let's assume to have radius R+1m, a black hole has to be of mass M+1kg.
Any falling matter trying to approach R will cross R+1m in finite time. At some moment 1kg of matter will cross R+1m. At this moment, that 1kg will effectively be inside the horizon.
If you (a distant observer) watched your blinking probe approach a black hole, you would see its blinks slow and red shift as the probe approaches the horizon. You cannot see it enter the horizon, as light cannot escape from inside the horizon. There would be a last blink, as the red shift approaches infinity.
If the event horizon were to increase in radius, the effect would be to further slow and red shift the blinks.
I know this stuff is confusing but an explanation would be great :)