Wikipedia:Reference desk/Archives/Science/2018 December 24

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December 24

Do things "really" fall into black holes, and is the EPR diagram like a gravity well?

I ran across a news article saying that using loop quantum gravity it turns out nothing really falls into the singularity after all. The article is here but it is formidably armored; they say the singularity is avoided but I don't know how. Still, it gets me going on a far cruder point from long ago...

The major issue I have with the idea of a black hole is that it seems well agreed you can see a photon from infalling matter at any time, with no upper limit. Sometimes this is presented as being the "ghost" of something that has "already fallen" into a black hole, but this seems clearly unsupportable -- nothing can fall in faster than a photon, no matter how much gravity pulls on it, so surely the photon's emission takes up the shorter part of the time involved from the perspective of an outside observer. I don't see any way to avoid concluding that whatever was dumped into the hole has to "actually" be there, somewhere outside the event horizon.

The classic Schwarzschild metric diagram gives what looks like a nice explanation for the reason why. Space becomes infinitely curved at the event horizon -- not the singularity. Which means that no matter how fast something falls in, it is limited to travelling at the speed of light through an infinite amount of space. I am tempted to compare this to the classic rubber-sheet model of geodesic motion through spacetime -- the marble bends into gravity wells, or collides into planets should the wells be filled, or starts falling down a black hole and never stops... but never reaches the center either.

Problem with this is that someone has modified our articles on stuff like Wormhole and Schwarzschild metric and I think gravity well also to say that the classic diagrams of spacetime curvature and EPR bridges have absolutely nothing to do with gravity wells, that one is a Flamm's paraboloid that is totally not the same as a gravity well because it's a spacelike surface (though I have to say, I thought the same might be true of gravity wells). There are an abundance of citation needed tags in some of those sections.

I see a similar debate playing out at [1] with one guy saying what I am here, and true, more than one disagreeing, which doesn't bode well but I am short of convinced. But nobody there pulls out the Flamm thing.

If I could take an EPR bridge as a valid diagram, then it would suggest a very intuitive basis for black holes, white holes, wormholes etc. where things falling into heavy gravity simply encounter lots of extra space, which may curve to allow them to use the energy they gained infalling to carry them away. (A black hole should certainly be a "white hole" in the later universe when mass and light are very rare and even the faintest Hawking radiation is warmer than everything else) It would seem like spacetime simply "defends itself", with a time delay, to avoid an ugly singularity. Even if something is stuck "near" (in a 2-D sense) the event horizon, in virtually flat spacetime, when a massive object plunges into the far end of the black hole and expands the event horizon, it should be very difficult for the gravity from that object ever to reach the infalling object! And if it could, I'd think the expansion of the event horizon would mean the outward displacement of the vertical neck of the EPR bridge?

I understand of course that from the point of view of the person falling, they could pass the event horizon in the sense that after an infinite time on ice around a perpetual non-evaporating black hole they would reach the horizon, having experienced almost no subjective time in the duration.

Anyway, I at least want clarification on how to reestablish a sense of a rubber sheet model and make direct comparisons between gravity wells and black hole curved spacetime, and whether c explicitly applies to any motion on the rubber sheet and whether down is really "down" in wormholes. Wnt (talk) 14:45, 24 December 2018 (UTC)

I will make a comment that a rubber sheet is not the best to model time dilation and moving at the speed of light. A black hole could bend the rubber sheet down, and a white hole could pull the sheet up. A wormhole is like connecting two points with a rubber tube. Graeme Bartlett (talk) 12:04, 25 December 2018 (UTC)

ADM formalism perhaps? They recently have a boundary term for modified gravity theories based on it. --Askedonty (talk) 21:19, 25 December 2018 (UTC)

Wnt, you probably won't like my advice, and you probably know what I'm about to say already, but... if you want to understand general relativity, you're going to need to learn and use a lot of very difficult math.

A great place to start is chapter 12 and 13 of Jackson. These chapters cover the interaction of a photon with an inertial reference frame, and then with a non-inertial reference frame, and they prepare the student for more elaborate study of the topic in the context of non-trivial gravity fields (typically presented in greater detail in other books). Normally, people read this book after they have completed a full four or five years of prior full-time preparation as full-time undergraduate physics students, because many very smart people find this mathematical content to be just at the limit of their mental capacity for comprehension after four or five years of full-time preparation. If you are not presently writing and solving wave equations for electrodynamics in conventional cases, you probably are not going to have great success writing and solving wave equations for nontrivial relativistic cases; and if you plan to understand general relativity without solving any equations, you're not going to get very far.

You can try to learn this stuff on your own, but I don't think it will be productive. What you really need is a great book and a great, professional tutor - somebody whose professional career revolves around teaching this type of material. That person would be called a "professor" and you would need to enroll in their university and follow their curriculum. At best, our Wikipedia articles provide an informal introduction; and they serve as helpful reminders about the details for people who have already learned this stuff more comprehensively. As you know, our articles on such topics leave much to be desired for the introductory readers: we simply do not have the critical mass of good editors to write excellent-quality encyclopedia articles on such topics. Consider how few good commercially-available texts exist - and think about how few professional physicists have the luxury to volunteer the extensive time and effort to curate an encyclopedia for zero dollars! Like many topic-areas in our encyclopedia, this material is just arcane enough that our articles can't be built up - and kept up - in a manner suitable for general audiences.

Ultimately, though, there is no way to present general relativity in a manner that is both mathematically sound and easily-accessible for general audiences. This is why so many popular presentations use dramatic simplifications like the "rubber sheet." These are analogies presented to make the broad concept seem interesting; but they are not useful models for predicting behaviors.

Nimur (talk) 16:59, 26 December 2018 (UTC)

It's one thing to say the math is hard. It seems like quite another to have a plot of a number you've calculated and nobody seems to know what it means. The one may be a matter of math, but the other is just a matter of explanation. I mean, is the asymptotic collar of curved surface in the plot something that an object can only fall down at a rate of c or less (relative to an outside observer) or not? I mean, Richard Feynman famously insisted that anything in physics could be explained to an interested 9-year-old. Wnt (talk) 23:11, 26 December 2018 (UTC)

Richard Feynman also famously made up gibberish nonsense syllables and insisted that people guess whether he was speaking Latin or Italian! Don't believe everything a physicist tells you, and don't take it on faith or authority; and definitely don't get fooled into choosing sides in a false dichotomy.

To make sense of any of the explanations in the original article at issue here, you need to know what every one of these important phrases mean: words like Abelian and gauge are really important, and if you're not already a formally-trained mathematician, it might literally take years for anybody to explain what these words mean in a way you can understand. If you want to study relativistic kinematics, (in other words, if you want to be able to solve for an object's trajectory, ergo, whether it will "fall in"...), Landau and Lifshitz discuss this in Volume 2, Chapter 10; but you'd better be pretty quick with your wacky functional notation and path integrals for differential equations in four-space.

The reason you can't get a simple answer is because this stuff is not simple - and even the experts can't necessarily simplify it in the way that you seek.

Nimur (talk) 07:16, 27 December 2018 (UTC)

Honestly, it sounds like you're making a big mystery out of everything. I mean, my understanding of a gauge theory is simply that you postulate there is some invisible property of space that you could measure on a gauge -- like voltage, for example. (To be sure, sometimes your gauge has to display tensors, but still, not a big deal) AFAIK Gauge fixing means that you say (or make) one particular electrode equal to ground potential, such as with a wire. With black holes, you would speak of "flat space far from the hole" as the zero point to measure gravitational potential energy, but not in a galactic void a trillion miles away either. Abelian I'm less clear on -- I know that anything I somewhat understand will be Abelian, and the other stuff isn't. But I mean, as far as I know nobody is telling me that there's no such place as "where", or that black holes are different depending how you look at them; they are as simple and symmetrical an object as can be conceived, especially if we neglect rotation.

Now I should add that I did overlook a major phenomenon writing above: frame dragging can apparently cause light to pass a large rotating object faster on one side than the other. If light were fighting linear frame dragging, then it could be emitted a long time later without the source having persisted outside the hole. That said, even though spacetime can move around the black hole, AFAICT black holes are not known for eating spacetime at the speed of light so that hapless photons are unable to outrun the space they move through. Anyway, if math really couldn't give a straight answer whether objects in a physical black hole of limited lifespan pass the event horizon or not, I'd say it's not a religion I need to understand, but I think it should. Wnt (talk) 00:36, 29 December 2018 (UTC)