Someone on EP today that wanted to know more about black holes posted a question asking such. Being a cosmology-nerd as well, I went on and started talking about a few of the existing theories, my own theories, and such. I’m sure this already exists as a theory (I know white holes do, but bear with me), but if, lets say, the graviton actually exists, then perhaps there exists an antigraviton, which would do exactly what it sounds like it would do. Antigravity on a very small scale would be pretty freaking awesome. I wondered howΒ an anti-black-hole would behave next to matter. Assuming it doesn’t annihilate the matter, it’d cause it to fling away VERY fast. I thought about what would happen if this were to meet a black hole before, and I knew it’d release more than just a little bit of energy. I didn’t bother to actually calculate it before, though. But this guy asked me what would happen if the two beasts were to meet.

Of course I’m not going to NOT calculate something like this, especially when someone asked “what would happen if…” Β haha! I’m not sure if what I said was 100% right when it comes to the masses doubling or not, but it’s a scalar increase, and with such giant values, it doesn’t really matter when it comes to the point I was trying to make: it would be really, really, really energetic. The person seemed rather layman about the topic, so I didn’t want to talk about spins and such–the more quantum mechanical aspect of this. But the energy released would make a GRB seem like a camera flash…

Warning: Really Big Numbers lay ahead. Note, I told the guy that I was going to go to bed at 1AM because I could go on and on and on about black holes… AND LOOK WHAT HAPPENED…

If a black hole met a white hole, we’d literally destroy the entire universe due to the ENORMOUS amount of energy produced. It’s a fairly simple calculation. Let’s say both are equally massive, although cancel out each other. The white hole has negative mass. However, because of the way antiparticles and particles behave, it’s still effectively behaves as twice the mass. Theoretically speaking, they’ll simply cancel each other out and leave no mass behind whatsoever. HOWEVER. That mass has to go somewhere. Here’s where Einstein’s most famous equation comes in. Mass can be transformed into pure energy, and the amount of energy stored in a given amount of mass is that mass times the speed of light squared–of course, E=mcΒ². The speed of light is approximately 300,000,000 meters per second, which in scientific notation is written as 3 x 10^8 meters per second, or in calculator shorthand, 3E8. Simple exponent math tells us that this squared is 3E16. A typical black hole has a mass of about 10^31kg, so our mass would be 2E31. So the energy released would be 2E31*3E16, which is 6E47 Joules of energy released all at once.

To put that in perspective, the most powerful explosion in the entire known universe is a gamma ray burst (GRB), only beaten by the Big Bang itself. These release 5E43 Joules of energy. In other words, this explosion would release the energy of about 10,000 GRB from the same place all at once.

To put that in another perspective, the Big Bang itself released E64 Joules of energy. In other words, the CREATION OF THE UNIVERSE ITSELF would only be about 100 quadrillion times the energy released in this one explosion, and, on a cosmological perspective, 100 quadrillion is puny. This is similar to nudging a small marble across the table and a ton of TNT. May seem much, but it’s really not.

Maybe it won’t obliterate the *entire* universe, but it’s certainly enough to destroy a HUGE chunk of it.

Oh, but I do speak only of a *typical* black hole mass. What about a supermassive black hole, like the one at the center of our galaxy? About E37 kg. So what’s E37*3E16? 3E53. Big Bang is only about 100 billion times as powerful.

… it’s 1:38AM. SEE THIS IS WHAT I MEAN THAT I CAN GO ON AND ON AND ON ABOUT BLACK HOLES!

Try and beat that explosion, Michael Bay!

Antimatter doesn’t work this way, really; even anti-particles have positive mass, and are attractive. That is, dumping antimatter into a “normal” black hole will only make it fatter. Black holes only care about their total energy contained inside (even if it’s usually called ‘mass’), and remember, even if you annihilate matter with antimatter, you have just as much energy as before! So the black hole wouldn’t care.

For this reason, also, a strongly repulsive “white hole” of the type you describe would require some substance of /negative/ energy density. No such form of matter has been found (although there are certainly plenty of ideas about it, because it would be very interesting.)

On a different note, “anti-gravitons” are widely believed not to be a thing. Fermions (most “matter”) have anti-particles partners, but gauge bosons in many ways don’t have a very similar notion. Okay, that’s not quite fair:

Antiparticles have the opposite charge and spin, but the same mass and excitation in their field.

What does that means? Positrons are just like electrons, except that they have opposite charge. They have gravity in the same way, and they both have an excitation in the EM field. When they annihilate, that mass gets turned into energy of a different form — the momentum of photons — and the excitation of the EM field is represented into a different form — also photons.

Photons are photons’ antiparticles, and so they can also meet and turn into something else, as long as these quantities are preserved. So they can turn their momentum back into mass (“pair-production” of electrons and positrons), or they could they turn their momenta in one pair of directions into another (scattering/interference), or depending on their energy possibly something more exotic (some other leptons and neutrinos and quarks and who knows what), but you still have the same amount of EM ‘noise’ floating around. But by far the ‘normal’ result is that photon + photon = photon + photon.

A graviton is just a quantum of an [as of yet unobserved] gravitational wave in the same way that a photon is a quantum of an EM wave, and the antiparticle of a graviton is another graviton. When they meet, they … are just more gravitons. Just like the photons. And so a graviton is indistinguishable from an anti-graviton.

The energy you’re describing does occur, though — the Hawking radiation that a black hole gives off before it evaporates entirely is exactly the number you computed! π

Luckily that radiation is fairly slow, or else the rest of the galaxy would have been fried. π

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Wow! Thanks for enlightening me on this! See, they don’t teach this stuff in high school. I wish they did, haha! I’m forced to read up stuff on my own, and most pages are either highly simplified or highly detailed, so I’m not able to get the middle ground I need. I remember the timing formula–it was rather simple, and had a 1/3 and a cubed in there somewhere, as a function of the radius, with a wider radius evaporating faster than a small one (I think). Do you know of any site a sufficiently advanced senior in high school (I know some calculus and physics) can teach themselves this?

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As I’ve found (I was in a very similar position to you not too long ago!), unfortunately, these really cool, exotic topics like black holes and Hawking radiation are actually really not the order you want to be learning things in, at all. Below is a little tour of how you learn about something like Hawking radiation, a little tour of physics.

The very existence of black holes, as a topological shift in space time, is something that requires general relativity. I don’t know how much relativity you’ve had, but the two halves are very very separate. Special relativity is a good enough approximation for any physics you might want to study on Earth. It covers things like length contraction and time dilation as a result of different moving reference frames. It doesn’t concern itself with gravity at all, actually, although it has a lot of interesting interactions with E&M — things where an electric field is both there and not there, for instance, depending on whom you ask. (This isn’t the quantum superposition sense of “both”, just that people in different reference frames have different equally valid measurements.) If you don’t feel totally comfortable with special relativity, I recommend trying to get resources on that. The math is still pretty straightforward and you usually talk a bit about it in AP Physics B, if you take that. No calculus is required.

Then once you have special relativity sufficiently grokked, you can look at things like Minkowski spacetimes, which is the special relativistic structure of spacetime: In special relativity, space is still described as being entirely Euclidean, but /spacetime/ is not so much, and you can pull it around and stretch it in quite a few ways and it still is a valid spacetime. Minkowski spacetime is in this sense a bit more of a mathematical way of looking at these topics.

And then only once this is all stuff that comes reasonably naturally, you can look at general relativity. It’s really miles away from special relativity, it’s founded on largely different principles, and has pretty complicated dynamics. I don’t know if you’ve done differential equations…? You say you’re in AP Calc so you’ve probably seen at least some first-order ODEs in there. If you’ve seen partial differential equations, then you know that those are significantly more complicated. General relativity is dictated by a system of 16 four-dimensional non-linear first-order partial differential equations, and they’re very difficult to solve and simulate. /Very/ difficult. There are, really, only two useful systems we have exact solutions for: A still black hole and a spinning black hole. You can Google “Kerr metric” to see what kind of scary math is involved there.

But, if you get through GR and start to grasp it, then black holes will make sense! You will also by this point have a strong understanding of “energy” and how energy relates to black holes, and why there likely wouldn’t be a “white” hole in the same sense.

But what about Hawking radiation? Well, that involves quantum physics. And you’ll want to learn quantum mechanics to do that. Right next to me for my QM homework I have a copy of Shankar’s “Principles of Quantum Mechanics”, and it’s a very good book, but also very dense. I only recommend trying to teach yourself out of it if you have a *solid* amount of work with eigenvectors and partial differential equations, as these are both really core to everything, /everything/ quantum.

Quantum mechanics is to quantum theory in general what AP Physics C Mechanics is to Classical Mechanics. And I don’t know if you’re aware of what continues in classical mech, but you get lots of fun stuff that completely abandons Newton’s equations. Instead of Newton you have Hamilton and Lagrange, and they’ll show you totally different ways of looking at the world. Instead of being bound by forces, there’s now a world governed by some space-momentum potential function, or one where bizarrely psychic particles carve a path of least resistance from one point to another.

What I mean to say is, quantum mechanics teaches you the principles of quantum behavior, but will still only introduce you, in a purely classical setting. (And, by the way — while there are good quantum analogs for Hamilton and Lagrange, there aren’t any for Newton; so you will want to briefly at least pick those up before doing quantum.) The real peak is quantum field theory, where you do quantum mechanics in a Minkowski spacetime. This is where you get the ideas of Feynman diagrams (by the way. I hit my head one of those the other day. Do not recommend, they’re made of metal), ghost particles, loops, and then the beautiful clusterfuck that is renormalization theory. Quantum field theory is arguably the hardest part of physics that will confident in, and something that is still very very poorly understood. There are ‘hard’ branches like string theory and supersymmetry and quantum gravity, but those are all still very very speculative, and a result it’s not really fair to call them easier or harder since we don’t even know if they correspond to reality, and in what ways they might.

Note! I said that quantum field theory is in a Minowski spacetime. It’s the quantum version of /special/ relativity only. The very easy one (compared to GR). But, alas, no one has any convincing way of bringing quantum theory and general relativity together. And where do you find Hawking radiation? … at the edge of black hole, where spacetime is deformed beyond what Minkowski can account for, and yet it is a purely quantum process.

So Hawking radiation can only be mathematically predicted with some amount of GR+Quantum unification. The current way it’s done is typically to slap quantum field theory onto a “fixed”, curved, spacetime; you assume that the Hawking radiation process won’t actually affect spacetime enough to matter, so you set the shape of spacetime rigidly, and then just quantum field theory on it anyway without really caring about the fact that these two theories don’t actually fit.

Different physicists have different levels of being okay with this. To quote my TA from last week at a 4AM physics rant — “What do you mean, quantum gravity is unsolved? Of course I can do quantum field theory on a curved spacetime! You just do it.” — and he was completely serious (and accurate).

This is Hawking radiation was until very recently still hotly debated. Its existence relied on doing two things together that really don’t have any way to do so, yet.

So. As admirable as it is to want to understand it, I would leave topics like that alone for now. π

Build up a strong math background. Do partial differential equations. I don’t know what kind of book is good for that so much, really — well, first you need partial derivatives. Do you have those? Do multivariable calculus, there’s /tons/ of courses on that kind of stuff online. It might seem a little tedious at first but it will open up a lot more systems to your understanding. There’s a great book called “Div, Grad, Curl” that does E&M with multivariable calc (I haven’t used it myself but I’ve heard great things). I know my school uses it in their freshman year. Learn about the Laplace, Heat, and Wave equations. Learn how they operate in 3 dimensions. Fourier transforms are fantastic! Learn about those. You can get a book on advanced classical mech, my school uses “Structure and Interpretation of Classical Mechanics”. This will require a pretty sturdy grasp on multivar calc also so don’t think you can get by without it. The quantum stuff, like I said, I use Shankar, and it was able to teach me some stuff in senior year of high school, but that’s only with a shitton of math and very painful slogging through. It’s not easy. I don’t know of any easier resources, though, but by that point you’ll probably in college and you can ask a professor. As for learning special relativity solidly, some schools have their lecture notes online, e.g. I was able to find http://physics.nyu.edu/hogg/sr/ and http://www.fourmilab.ch/cship/ as recommendations to accompany my school’s courses, they both seem pretty good.

I … hope that helps! π

And by the way, if you’re wondering what school I’m from — well, I noticed you’re a major fan of MIT. Maybe leave it at, I’ve got plenty of friends at MIT, and each of knows we’re better than each other? π

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Haha you’re at MIT??? That’s so awesome! Well, if I get in, at least I’ll have one friend there π

I know what a manifold is ehehe so is the Minkowski space not a manifold? Ohh I want to learn this all! But unfortunately I barely know vectors. I’ve heard of eigenvectors and sort of understand them, but my school is rather crappy (I mean, it’s good for a FLORIDA school, but again, Florida) and my physics teacher last year is the only teacher that actually knew what he was talking about. He’s a trig professor at the local community college Valencia, which is really crappy–but anything’s better than what my teachers basically do. Really, I probably know more math than my current math teacher–that’s how bad he is. He got his degree in sports medicine… So even if I want to ask him questions about eigenvectors, he wouldn’t be able to answer me. He didn’t even understand integrals or Taylor series in the beginning of the year when I asked him about it… I watched the OpenCourse lectures of integral calculus before school started, hehe. I’m able to pick things up really quickly if I put my mind to it (unfortunately I can’t concentrate in my room or anywhere near here which is why it’s extremely difficult for me to study). And I mean really, really quickly xD So if I get the right source, I’d be able to learn the eigenvector and partial differential equations stuff on my own. I wish I could get the books you are talking about but I guess that’d have to wait until I’m in college (hopefully that college would be MIT in which I’d probably need to get the books anyways).

On a random note, how did you find my blog? As soon as I made the blog, a crapton of people into the stuff I post started following me, faster than I’ve ever gained followers before. I’m getting an average of about one follower per day, and this blog is hardly a month old. So I’m wondering how people found my blog. π

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Ah, noo noo noooooo!!! xD I mean to say that I’m not at MIT, I’m at its sort of twin twin school, Caltech. π It’s way better than MIT, trust me. … like, actually, it’s more fun.

Okay, they’re pretty similar.

Either way! Apply to Caltech as well as MIT.

As for books: Yeah, getting books physically isn’t easy, but very very many of them can be found online in PDF form legally. Like, just Google “multivariable calculus PDF” gives me http://people.reed.edu/~jerry/211/vcalc.pdf right away. I mean, I don’t know this book at all, but it’s certainly /a/ textbook that will walk you through the stuff you need. If you get through the first half you’ll have everything you need to last you for a good while. Similarly, Googling “classical mechanics PDF” will give you http://www.physics.rutgers.edu/ugrad/494/bookr03D.pdf . You won’t get much anything out of it without the multivar calc background, but it’s there for when you want it!

If you want to look at more interesting math, group theory is a great place to get started, and has almost no co-dependence on the “normal” math track. Dummit & Foote is the book we use, and you can get it at http://zeth.ciencias.uchile.cl/~cortiz/Apuntes/ebooks/Abstract%20algebra%20-%20Dummit%20and%20Foote.pdf

There’s a lot of free legal textbooks online! Take advantage of them! π

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I AM applying to CalTech! And I mean that in present tense. I’m rushing to finish all my applications today… xD

I bookmarked all of the links you sent me ^_^ when I have the time and am not rushing to get all of my apps done, I’ll read through them. π

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Er… I’m just wondering… would you be able to refer me at CalTech? I didn’t get into MIT, and I’m worried that I’ll get rejected from CalTech too, since my grades are bad… I mean, clearly I’m not like other girls… I’m just wondering if that’s an option… it’d mean a lot to me…

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Oh man, to be honest I’m not really sure to what degree that’s a thing … like, I’ve never heard of “referrals” before at Caltech and I don’t think I can. Sorry!

Just apply to a lot of good schools and I’m sure you’ll get into some!!

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Hmm… I do hope I get in somewhere good… :c

Hmm I’m just curious. Do you have any famous professors? Like… you know, the ones you see on cosmology documentaries? Ahh… CalTech would be even more perfect for me than MIT since CalTech has professors I’ve revered since I was in early middle school… xD

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