I'm Heart, your friendly neighbourhood admin!

[Kelly]

Heart and michaeld, Physics Girl suggests that a proton or neutron can have more that three quarks each. Is that believable?

[Heart]

The only rule to small things that are governed by quantum mechanics is that nothing is impossible except the one thing you took for granted as true :P

I had never heard this theory, but from the video, I can't see anything wrong with it. This could be so cool... I'm going to spend some time researching this more later when I have some time!!! :D :D

[Dodecahedron314]

The quark and antiquark pairs are completely fine, because they instantly cancel each other out. I believe this is probably considered Hawking radiation (same concept as what's been causing all the confusion over black holes with the information paradox), but don't quote me on that--I'm not entirely certain whether that's only in empty space, or whether it includes all particle-antiparticle pairs no matter where they are. Anyway, essentially it's like having the number of up quarks be written as 2 + 0 + 0 +... (however many zeroes you want), and then realizing that's the same as having 2 + (-1 + 1) + (-1 + 1 ) +... (however many 0 = -1 + 1 repetitions you want).

As a not-quite aside, the whole concept of mass-energy (the thing that makes it so the protons are so massive in comparison to the three valence quarks) is a really interesting one, because it's kind of physics's way of throwing its hands up at higher energy levels and doing really weird things, and yet it makes perfect sense with Einstein's equation. It's the same reason why when everyone was going nuts over the Higgs boson in 2012, you might have heard the figure "126 GeV" thrown around a lot (that was the figure from the ATLAS experiment, anyway, we now know it's closer to the value given by the CMS experiment of about 125 and change). GeV = gigaelectronvolts, and that handily tells us both the mass and the energy where elementary particles are concerned, because really they're the same thing.

(I know I'm not anywhere near as qualified as Heart or michaeld to answer this question, I'm just a first-year physics major being bored out of their mind in the middle of nowhere for another few weeks until orientation week and as a result will take any opportunity to talk physics or math. Also, the Higgs boson version of that exact visualization of LHC data at the end of the video was the background on my school computer for most of junior and senior year of high school, until I got accepted to my current college and switched to really pretty pictures of campus instead.)

[Emery.]

The quark and antiquark pairs are completely fine, because they instantly cancel each other out. I believe this is probably considered Hawking radiation

Heisenberg's uncertainty principle IMO, not enough time for force interaction with the rest of the world, but enough to bend spacetime and give inertia (?). No, really, I'm not sure it has any impact on mass. It is the gluons that give most of it in the end. And virtual particles are literally everywhere (protons -yes, vacuum - yes, anywhere else - yes), given the condition they disappear fast enough and borrow only as much energy as stated in the uncertainty principle. Someone please correct me if I'm wrong. I don't even have a bachelor's degree in it and nobody has taught me that

Hawking radiation is the thing escaping from a black hole :P

[michaeld]

Heart and michaeld, Physics Girl suggests that a proton or neutron can have more that three quarks each. Is that believable?

Yes but they're virtual (not stable, off-mass-shell and not directly detectable). A gluon mediating the strong interaction within the hadron can split into a quark-antiquark pair and vice versa. They are part of the quark-antiquark sea

Same basic idea as Hawking radiation yeah though as Emery says that's in the context of a black hole, and we're usually talking about photons.

[Dodecahedron314]

The quark and antiquark pairs are completely fine, because they instantly cancel each other out. I believe this is probably considered Hawking radiation

Heisenberg's uncertainty principle IMO, not enough time for force interaction with the rest of the world, but enough to bend spacetime and give inertia (?). No, really, I'm not sure it has any impact on mass. It is the gluons that give most of it in the end. And virtual particles are literally everywhere (protons -yes, vacuum - yes, anywhere else - yes), given the condition they disappear fast enough and borrow only as much energy as stated in the uncertainty principle. Someone please correct me if I'm wrong. I don't even have a bachelor's degree in it and nobody has taught me that

Hawking radiation is the thing escaping from a black hole :P

My uncertainty (no pun intended) was whether all the virtual particles were considered Hawking radiation or if it was just the ones associated with black holes. This is what happens when all of my physics books are already packed because I didn't think I would be coming back home before college :P

Yes, the gluons do contribute significantly to the mass of the proton if I'm not mistaken, but again, the idea of "mass" is kind of a weird one at this small of a scale because mass and energy are the same thing. So while the virtual particles might not be "massive" enough in the material sense to do much on that end, they're still fundamentally a brief fluctuation of energy, and that's the contribution to mass Physics Girl was talking about in the video. (Unless I'm conceptually wrong, which is entirely possible. Again, I'm not in the least qualified in terms of classical (pun kind of intended) training to answer most of this, this is just me sifting through all the random physics concepts that have implanted themselves in my brain since I first started reading about it when I was about 10. I technically had two years of higher-level physics in high school, but in actuality that was just me sitting in the back of a math class with a physics textbook and a computer and somehow managing to get a 6 on the IB exam, so taking real physics classes in college is going to be interesting.)

[Heart]

Wow! I think everyone explained things a lot better than I could. Thank you Dodec, Emery and Mic! It's so nice to be surrounded by you guys <3

And Dodec, you're on the right track, but traditionall Hawking radiation only refers to black holes. All the phenomena are related of course, but it's named Hawking radiation specifically because it was one of the things Stephen Hawking predicted when he (and many others) tried to understand the information loss problem with black holes. Interesting story: I ended up doing my undergraduate thesis on a theoretical approach to the information paradox. And, years later, I still don't understand it fully :P

OMG DODEC, I RE-READ YOUR POST, CONGRATULATIONS ON THE 6 IN PHYSICS IB!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! So amazing, you must be so proud!!!

[michaeld]

There's also the related Unruh radiation, theorised to occur not outside a black hole (like Hawking radiation) but from the perspective of an observer in an accelerating frame. It was actually hypothesised before Hawking radiation. The interpretation is somewhat controversial (though I think the difference of opinion really is just a matter of interpretation, nothing more). https://en.wikipedia.org/wiki/Unruh_effect

Another accessible math puzzle I just saw on another board. (By the way I meant to comment on the stones puzzle, see here for the puzzle and here for Heart's spoilered analysis on it. Any more thoughts on that annnnyone before I give a full solution and further background?)

Here it is:

0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0

You have a 4by4 array with all 16 squares at value 0.
Pick any square: all the squares in the same row and column,
including the square you picked, will change values:
0 becomes 1, and 1 becomes 0.
What is the minimum number of picks to end up with:

0 1 0 1
1 0 1 0
0 1 0 1
1 0 1 0

And I'd like to ask a followup for people who solve it. What if you generalise this in the obvious way to an m x n grid?

[Emery.]

My uncertainty (no pun intended) was whether all the virtual particles were considered Hawking radiation or if it was just the ones associated with black holes. This is what happens when all of my physics books are already packed because I didn't think I would be coming back home before college :P

Yes, the gluons do contribute significantly to the mass of the proton if I'm not mistaken, but again, the idea of "mass" is kind of a weird one at this small of a scale because mass and energy are the same thing. So while the virtual particles might not be "massive" enough in the material sense to do much on that end, they're still fundamentally a brief fluctuation of energy, and that's the contribution to mass Physics Girl was talking about in the video. (Unless I'm conceptually wrong, which is entirely possible. Again, I'm not in the least qualified in terms of classical (pun kind of intended) training to answer most of this, this is just me sifting through all the random physics concepts that have implanted themselves in my brain since I first started reading about it when I was about 10. I technically had two years of higher-level physics in high school, but in actuality that was just me sitting in the back of a math class with a physics textbook and a computer and somehow managing to get a 6 on the IB exam, so taking real physics classes in college is going to be interesting.)

The problem with mass of those fluctuations is that they can have negative energy=mass. Wierd thing, isn't it? So, em, taking this Hawking radiation (it's one of my favourite things in physics ;)) - you have some field fluctuations which produce a virtual pair particle-antiparticle that has to disappear quickly, but the gradient of acceleration is so high near the black hole that one of the virtual particles falls on it, while the other escapes its gravitational field. I'm not sure why, but the particle falling onto the black hole is said to have negative energy (probability of this particle having negative energy would be simply 1/2, but there must be a factor I'm not aware of), so that's why black holes can "evaporate" - their mass decreases and they finally can disappear after enough time given. The other particle is said to have positive energy and hence sort of "carries away energy/mass from the black hole. In conclusion, energy can be negative, at least one can encounter such a concept. So, if no other factors are taken into account, why should mass of a proton increase due to virtual particles, if they have equal probablity of having positive and negative energy and hence cancel out or nearly cancel out? Or am I wrong in some assumption? E.g. cancel out =/= nearly cancel out, i.e. x->0 =/= 0, or negative energy is pure speculation :P together with evaporating black holes which in fact should become bigger as they take the ex-virtual particles in.

I did the IB too, BTW :)

Is it 8, Michael? If so, I would have to think how to generalise it.

[Dodecahedron314]

My uncertainty (no pun intended) was whether all the virtual particles were considered Hawking radiation or if it was just the ones associated with black holes. This is what happens when all of my physics books are already packed because I didn't think I would be coming back home before college :P

Yes, the gluons do contribute significantly to the mass of the proton if I'm not mistaken, but again, the idea of "mass" is kind of a weird one at this small of a scale because mass and energy are the same thing. So while the virtual particles might not be "massive" enough in the material sense to do much on that end, they're still fundamentally a brief fluctuation of energy, and that's the contribution to mass Physics Girl was talking about in the video. (Unless I'm conceptually wrong, which is entirely possible. Again, I'm not in the least qualified in terms of classical (pun kind of intended) training to answer most of this, this is just me sifting through all the random physics concepts that have implanted themselves in my brain since I first started reading about it when I was about 10. I technically had two years of higher-level physics in high school, but in actuality that was just me sitting in the back of a math class with a physics textbook and a computer and somehow managing to get a 6 on the IB exam, so taking real physics classes in college is going to be interesting.)

The problem with mass of those fluctuations is that they can have negative energy=mass. Wierd thing, isn't it? So, em, taking this Hawking radiation (it's one of my favourite things in physics ;)) - you have some field fluctuations which produce a virtual pair particle-antiparticle that has to disappear quickly, but the gradient of acceleration is so high near the black hole that one of the virtual particles falls on it, while the other escapes its gravitational field. I'm not sure why, but the particle falling onto the black hole is said to have negative energy (probability of this particle having negative energy would be simply 1/2, but there must be a factor I'm not aware of), so that's why black holes can "evaporate" - their mass decreases and they finally can disappear after enough time given. The other particle is said to have positive energy and hence sort of "carries away energy/mass from the black hole. In conclusion, energy can be negative, at least one can encounter such a concept. So, if no other factors are taken into account, why should mass of a proton increase due to virtual particles, if they have equal probablity of having positive and negative energy and hence cancel out or nearly cancel out? Or am I wrong in some assumption? E.g. cancel out =/= nearly cancel out, i.e. x->0 =/= 0, or negative energy is pure speculation :P together with evaporating black holes which in fact should become bigger as they take the ex-virtual particles in.

I did the IB too, BTW :)

The particle falling in having negative energy makes sense from a theoretical standpoint because of conservation of energy, but is still extremely strange from a practical point of view. I did some citation-diving from the Wikipedia article on Hawking radiation and found the paper that it appears most of the article was copied and pasted from, and the impression I got was that the whole reason Hawking radiation exists is something along the lines of how the infalling negative particle is kind of the equivalent of another positive particle actively leaving the black hole, even though there's already a positive particle floating around out there wondering where the heck its negative counterpart went...??? That's most likely completely and utterly wrong, but that's the only way I've managed to rationalize it so far in my current state of limited knowledge.

Applying all this strangeness (wait, protons don't have strange quarks, never mind :P ) to the topic at hand, really all I can think of at this point is that the actual fluctuation of energy itself that creates the virtual particles in the first place has something to do with it? And perhaps that instantaneous change is all that's being considered, and then the annihilation happens after another pair of particles has already been created by another fluctuation somewhere else so there's still a net positive effect on mass-energy? That's probably grasping for straws, but the real reason is beyond me at the moment. Reality is weird.

It's strange how many IB alums we have on this thread! (Then again, the program at my school was tiny--though not as tiny as that of someone from a different school whom I met over the summer--so maybe I'm just used to us being a rarity.) What classes did you take?

Wow! I think everyone explained things a lot better than I could. Thank you Dodec, Emery and Mic! It's so nice to be surrounded by you guys <3

And Dodec, you're on the right track, but traditionall Hawking radiation only refers to black holes. All the phenomena are related of course, but it's named Hawking radiation specifically because it was one of the things Stephen Hawking predicted when he (and many others) tried to understand the information loss problem with black holes. Interesting story: I ended up doing my undergraduate thesis on a theoretical approach to the information paradox. And, years later, I still don't understand it fully :P

OMG DODEC, I RE-READ YOUR POST, CONGRATULATIONS ON THE 6 IN PHYSICS IB!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! So amazing, you must be so proud!!!

Thanks! ^_^ I didn't do quite as well as I would have liked in most of my other classes by a markband or two (although in all fairness my high expectations for history, at least, were directly informed by my teacher repeatedly telling me I was going to get a 7...I think he jinxed me into getting a 5), but I was also pleasantly surprised by somehow getting a C for my EE, the Epic Topology Paper of Doom where I had absolutely no idea what I was getting into when I picked my topic. (Especially since apparently the EEs got graded brutally this year according to a lot of people both inside and outside my school.)

[Emery.]

More IB alums? Who else?

Me? HL Physics & Math :P

###

Coming back to Hawking radiation....

It makes sense, but the weak point IMO is that if there are two virtual particles creating a pair, the one falling onto the black hole has equal probability of being negative as well as positive (when existence of negative energy assumed), at least from a logical and clear standpoint. So... em... if it is so, they black hole won't evaporate (bacease the probability of a "negative" partile falling on it is equal to the probability of a "positive" particle falling on it) and negative (like, half of them should be negative) particles leaving the black hole will anihilate with anything they meet I haven't read of this happening... or we just don't notice stuff disappearing into nowhere because it gives out no signs of such anihillation (I guess I have just used the word "anihillation" improperly, because it often refers to a pair particle-antiparticle transforming into two photons, and my "anihillation" means the simplest disappearance).

But assuming that energy can be only positive ('cause e.g. it's an absolute value or square of something else), why should black holes "evaporate" in the first place? They take in positive energy. So they take in mass. But there is no problem with "anihillation"®.

Unfortunately, this area of Physics is still ahead of me in my course. I feel like I'm missing something important in here. All I know is some probability theory and stuff from some books for hobbyists.

[Dodecahedron314]

Heart also did IB, and got crazy-amazing scores on everything naturally. I did English and history because they were required HLs at my school, and then math and physics. I only had an idea for mine because reading about hyperbolic geometry in Roger Penrose's book The Road To Reality (one of my favorite nonfiction books out there) really messed with my head and I wanted to learn more about how it works. My math IA topic (Fourier transforms) also came from that book, incidentally. :P

The Hawking radiation paper I read said that the particle that falls into the black hole is automatically assumed to be the negative one. Personally that seems almost like questionable theoretical fudging to me (why is this necessary for conservation of energy? One would think the energy would still be there, just as part of the black hole as opposed to in virtual particle form), but the problem is that you're exactly right as far as I can tell with your assessment that if there was really an equal probability of the particle falling into the black hole being positive or negative, there would be no reason for the black hole to evaporate if that's the only thing that could cause it to do so. Black holes can emit high-energy X rays IIRC, but I'm not sure that's due to the same process of negative-energy particle annihilation you're talking about (as far as I know annihilation is any destruction of antimatter and matter when they come in contact with each other, not just with paired particles).

I'm not "there yet" academically either. I read almost everything in the very limited physics section of the local library from when I was about 10 to when I was about 13, managing to pick up a concept here or there without the math to back it up, then high school happened and all I really had was The Road to Reality and my typo-ridden physics textbook because I was too busy to make it out to the library anymore.

[Heart]

The key with black holes and those pairs of particles is that, by definition, the particle falling into the black hole is accelerating away from you. Which is the same thing as you accelerating away from it.

Most of people's physics knowledge is about inertial reference frames, because that's just what we know most about. But Unruh's big contribution to this whole thing (he actually works at the university I did my undergrad at, by the way, and is a pretty cool guy) was to say that accelerating reference frames are weird when it comes to particles and mass. Basically, if you accelerate a particle detector through a vacuum, then you'll detect particles that wouldn't be there if you were just moving through with constant velocity. There's a lot of weird math in there, which I won't get into here, but basically these particles have imaginary mass; in an inertial reference frame, they don't exist, but in an accelerating one, they do.

So, because one particle in the black hole scenario is in an accelerating reference frame compared to you, the observer (who is presumably not falling into the black hole), and the other is in an inertial frame compared to you, then one is always the one with "imaginary mass". The one with imaginary mass, according to our reference frame of being outside the black hole, is the one that falls inwards.

As such, the black hole gains no real mass, but it does lose real mass.

I hope that helps....

And yay for more IB people! I did HL French, Physics, History, English and Biology. I had to do SL Math Methods because they stopped letting me sign up for HL's ;) And of course the lovely ToK.

PS - I LOVE Penrose! He came to give a talk at my old university during my undergrad, and I went to see him. I've never read any of his works, but he has mad presentation skills, and I can only imagine that his books must be amazing too. The talk I saw was about the big bang theory, the oscillation of the universe, and infinities. So cool.

PPS - Go ahead and post the answer Mic! School's about to start again, and my to do list is long, so I don't know if I'll get back to the stone game. I am really interested in seeing the full solution! :D

[Emery.]

Yay, thank you Heart! :) I think... I got what you wrote :D A whole new level of everything being relative :P Thanks for explanation :) It makes clear why negative mass is assumed for the particles falling onto the black hole.

I can't believe it: Heart and IB :D It must be the influence of ToK that gets us question even our own gender :P

###

They required HL History at your school, Doc? Why on Earth? English - they required at least B HL at my school so I can see the motivation, but if they required A HL - why on Earth, again?

Or maybe you're both in America and everythng functions differently there, even the IB?

ToK was quite nice I must say - we had a whole lot of heated debates, which was quite fun.

[Kelly]

*envies Heart for meeting Unruh and Penrose*

I imagined that the reason why a former virtual particle that falls into a black has negative energy is that a pair of virtual particles has zero energy. They can pop into existence as a pair (no energy needed) and then annihilate each other without giving off any energy (energy is conserved; zero energy with which to begin and end). Each particle themselves has some energy, since it exists. It may and likely does have mass, too (else they would travel at the speed of light, in opposite directions, I assume, and never recombine unless with another virtual particle from another pair).

When one of the pair falls into a black hole and the other escapes and cannot recombine with its sister, then energy is still conserved. The energy required to compensate for the energy of the escaped particle belongs to the black hole. Thus, the black hole looses energy (and mass) equal to and opposite (negative) to the escaped particle.

[Dodecahedron314]

I should probably spoiler for length if I'm going to keep serial-quoting people. I've gotten kind of bad about that lately.

*envies Heart for meeting Unruh and Penrose*

I imagined that the reason why a former virtual particle that falls into a black has negative energy is that a pair of virtual particles has zero energy. They can pop into existence as a pair (no energy needed) and then annihilate each other without giving off any energy (energy is conserved; zero energy with which to begin and end). Each particle themselves has some energy, since it exists. It may and likely does have mass, too (else they would travel at the speed of light, in opposite directions, I assume, and never recombine unless with another virtual particle from another pair).

When one of the pair falls into a black hole and the other escapes and cannot recombine with its sister, then energy is still conserved. The energy required to compensate for the energy of the escaped particle belongs to the black hole. Thus, the black hole looses energy (and mass) equal to and opposite (negative) to the escaped particle.

I was under the impression that since a fluctuation of energy at the quantum level was what created the virtual particles, that energy was released back into the universe when the particles annihilated each other and energy was conserved that way. I could very well be wrong. I really need to take an actual physics class so I can stop being wrong about things. (Sadly, classes don't even start for another three weeks :( ) So what you're saying is that since the infalling particle gets eaten by the black hole, it automatically has to be negative because its counterpart still exists and conservation of energy makes it so? I think I might be able to wrap my head around that. (...and I only just now realized how weird of an idiom that really is. )

The key with black holes and those pairs of particles is that, by definition, the particle falling into the black hole is accelerating away from you. Which is the same thing as you accelerating away from it.

Most of people's physics knowledge is about inertial reference frames, because that's just what we know most about. But Unruh's big contribution to this whole thing (he actually works at the university I did my undergrad at, by the way, and is a pretty cool guy) was to say that accelerating reference frames are weird when it comes to particles and mass. Basically, if you accelerate a particle detector through a vacuum, then you'll detect particles that wouldn't be there if you were just moving through with constant velocity. There's a lot of weird math in there, which I won't get into here, but basically these particles have imaginary mass; in an inertial reference frame, they don't exist, but in an accelerating one, they do.

So, because one particle in the black hole scenario is in an accelerating reference frame compared to you, the observer (who is presumably not falling into the black hole), and the other is in an inertial frame compared to you, then one is always the one with "imaginary mass". The one with imaginary mass, according to our reference frame of being outside the black hole, is the one that falls inwards.

As such, the black hole gains no real mass, but it does lose real mass.

I hope that helps....

And yay for more IB people! I did HL French, Physics, History, English and Biology. I had to do SL Math Methods because they stopped letting me sign up for HL's ;) And of course the lovely ToK.

PS - I LOVE Penrose! He came to give a talk at my old university during my undergrad, and I went to see him. I've never read any of his works, but he has mad presentation skills, and I can only imagine that his books must be amazing too. The talk I saw was about the big bang theory, the oscillation of the universe, and infinities. So cool.

PPS - Go ahead and post the answer Mic! School's about to start again, and my to do list is long, so I don't know if I'll get back to the stone game. I am really interested in seeing the full solution! :D

Yeah...I remember getting sucked into a Wikipedia wormhole when michaeld posted the link to the article about Unruh radiation...I might have understood it for one brief and shining moment when I had another 5 tabs open explaining different aspects of the theoretical framework, but it appears as though that moment has passed. I can accept that it happens, but I can't for the life of me recapture the knowing why. I get the feeling I need math beyond just BC calc to understand this. Anyway, so...because Unruh radiation is a thing, that means accelerating reference frames have particles that stationary ones don't...*lightbulb spontaneously appears above head*...so that means from the infalling particle's reference frame, the stationary frame has particles that it doesn't, and so that makes the infalling particle's mass/energy relatively negative and that's why the black hole loses mass?

Waiiiiit...you did 5 HLs??? That's not even possible, I thought! Maybe it's changed since you graduated, but the max we could take was 4. I had to fight for my Physics HL because it wasn't an actual class that was offered at my school before I requested it by sending painfully formal and laughably ambitious emails to my guidance counselor as a sophomore. (Well, now that I think about it, my promise that I would get a 7 wasn't all that far off...) It was especially difficult to convince the administration because I was also taking Math HL, the class with the highest drop rate in the entire program, and I was told physics wasn't much of a safety net to make sure I still had enough HLs if I dropped to math SL. Also, I am infinitely jealous of you for getting to meet Sir Penrose. He has a really clear way of not only explaining things, but connecting them to each other (there's lots and lots of cross-referencing between different sections to make the connections clearer)--The Road To Reality basically builds physics from first mathematical principles, and the way he goes about it helps you realize the supremely logical progression from simple concepts to explaining beautiful complicated reality.

Yay, thank you Heart! :) I think... I got what you wrote :D A whole new level of everything being relative :P Thanks for explanation :) It makes clear why negative mass is assumed for the particles falling onto the black hole.

I can't believe it: Heart and IB :D It must be the influence of ToK that gets us question even our own gender :P

Alright, anyways... Physics, History and Biology together. Wow, they didn't alow this combination in my school. If you did Physics, you could choose only Econ, Geo, Chemistry and a Language B. I'm not sure about matching History with Biology, but HL classes of the two collided for sure.

And I though I'm a wierdo because of doing 4 HLs and I didn't write it, but it seems that it's not that abnormal here :D As everyone's writing what HLs they did, I did Econ and English at HL apart from Math and Physics. I did German B and Literature at SL. They didn't want to allow me to take 4 HLs :( But I did it anyway, hahaha ;) I just went to the Econ teacher in the beginning of the school year and signed up for HL class. He asked me if I'm crazy but agreed.

They required HL History at your school, Dodec? Why on Earth? English - they required at least B HL at my school so I can see the motivation, but if they required A HL - why on Earth, again?

Or maybe you're both in America and everythng functions differently there, even the IB?

ToK was quite nice I must say - we had a whole lot of heated debates, which was quite fun.

My SLs were music and Spanish (the former of which was another independent study and the latter of which was, again, required...I mean, you could take Spanish HL if you really, really wanted to, but the teacher was terrible so nobody (not even the native Spanish speakers) ever did. The only language B we had was Spanish because we're lame. :P ). We had silly requirements for classes because the program was so tiny, we could only offer so many classes and some could only exist at certain levels. We only had a few IB teachers, so they all had to teach multiple classes for the most part because they were basically the only people in the county who were not only qualified to do so, but inclined to on a public school teacher's pitiful salary. (For the longest time we had the same teacher teaching both HL and SL bio, and HL and SL chem, AND the sophomore pre-IB chemistry class.) And yes, I'm in America, but I don't think IB works differently because the idea is that it works the same regardless of location. My school was just special in its absurdity and illogicality as far as IB was concerned. (Well, also most other things as well, but what do you expect from an underfunded public school.) Our TOK was a very interesting class, but we only had it for one year rather than the recommended two because of our schedule, which was another reason everything class-wise was messed up. I was really glad I'd had it as soon as I took my first college humanities class over the summer, because my university tends to treat those as sort of über-TOK.

[Emery.]

My school was special in its chaos too :P *Sighs* Did I mention that playing on mobile during classes was fun? ##

[Heart]

The key with black holes and those pairs of particles is that, by definition, the particle falling into the black hole is accelerating away from you. Which is the same thing as you accelerating away from it.

Most of people's physics knowledge is about inertial reference frames, because that's just what we know most about. But Unruh's big contribution to this whole thing (he actually works at the university I did my undergrad at, by the way, and is a pretty cool guy) was to say that accelerating reference frames are weird when it comes to particles and mass. Basically, if you accelerate a particle detector through a vacuum, then you'll detect particles that wouldn't be there if you were just moving through with constant velocity. There's a lot of weird math in there, which I won't get into here, but basically these particles have imaginary mass; in an inertial reference frame, they don't exist, but in an accelerating one, they do.

So, because one particle in the black hole scenario is in an accelerating reference frame compared to you, the observer (who is presumably not falling into the black hole), and the other is in an inertial frame compared to you, then one is always the one with "imaginary mass". The one with imaginary mass, according to our reference frame of being outside the black hole, is the one that falls inwards.

As such, the black hole gains no real mass, but it does lose real mass.

I hope that helps....

And yay for more IB people! I did HL French, Physics, History, English and Biology. I had to do SL Math Methods because they stopped letting me sign up for HL's ;) And of course the lovely ToK.

PS - I LOVE Penrose! He came to give a talk at my old university during my undergrad, and I went to see him. I've never read any of his works, but he has mad presentation skills, and I can only imagine that his books must be amazing too. The talk I saw was about the big bang theory, the oscillation of the universe, and infinities. So cool.

PPS - Go ahead and post the answer Mic! School's about to start again, and my to do list is long, so I don't know if I'll get back to the stone game. I am really interested in seeing the full solution! :D

Yeah...I remember getting sucked into a Wikipedia wormhole when michaeld posted the link to the article about Unruh radiation...I might have understood it for one brief and shining moment when I had another 5 tabs open explaining different aspects of the theoretical framework, but it appears as though that moment has passed. I can accept that it happens, but I can't for the life of me recapture the knowing why. I get the feeling I need math beyond just BC calc to understand this. Anyway, so...because Unruh radiation is a thing, that means accelerating reference frames have particles that stationary ones don't...*lightbulb spontaneously appears above head*...so that means from the infalling particle's reference frame, the stationary frame has particles that it doesn't, and so that makes the infalling particle's mass/energy relatively negative and that's why the black hole loses mass?

Waiiiiit...you did 5 HLs??? That's not even possible, I thought! Maybe it's changed since you graduated, but the max we could take was 4. I had to fight for my Physics HL because it wasn't an actual class that was offered at my school before I requested it by sending painfully formal and laughably ambitious emails to my guidance counselor as a sophomore. (Well, now that I think about it, my promise that I would get a 7 wasn't all that far off...) It was especially difficult to convince the administration because I was also taking Math HL, the class with the highest drop rate in the entire program, and I was told physics wasn't much of a safety net to make sure I still had enough HLs if I dropped to math SL. Also, I am infinitely jealous of you for getting to meet Sir Penrose. He has a really clear way of not only explaining things, but connecting them to each other (there's lots and lots of cross-referencing between different sections to make the connections clearer)--The Road To Reality basically builds physics from first mathematical principles, and the way he goes about it helps you realize the supremely logical progression from simple concepts to explaining beautiful complicated reality.

). We had silly requirements for classes because the program was so tiny, we could only offer so many classes and some could only exist at certain levels. We only had a few IB teachers, so they all had to teach multiple classes for the most part because they were basically the only people in the county who were not only qualified to do so, but inclined to on a public school teacher's pitiful salary. (For the longest time we had the same teacher teaching both HL and SL bio, and HL and SL chem, AND the sophomore pre-IB chemistry class.) And yes, I'm in America, but I don't think IB works differently because the idea is that it works the same regardless of location. My school was just special in its absurdity and illogicality as far as IB was concerned. (Well, also most other things as well, but what do you expect from an underfunded public school.) Our TOK was a very interesting class, but we only had it for one year rather than the recommended two because of our schedule, which was another reason everything class-wise was messed up. I was really glad I'd had it as soon as I took my first college humanities class over the summer, because my university tends to treat those as sort of über-TOK.

Yes, technically 5 HLs are "illegal". But I did them anyways, and then just ended up taking the French SL test after going through the HL class. So on my transcript, it says French SL, but only because I'm not allowed all 5 HLs. I'm actually pretty fluent in French, and it was the French as a second language SL too (not French literature), so it was so easy. I remember making a bet with some friends: they betted that I wouldn't be able to use one specific word in the final exam. They would pick a word, and tell it to me one hour before we had to write it. They picked vivimes, the past narrative tense of the verb "to live". The narrative tense is a bit tricky, because we don't have an analogue in English, at least not perfectly.

But anyway. The writing part at the end of the exam asked us to write a letter to a celebrity to ask them to perform in a charity event. we had to do all the corny things like describe what the charity was for. So I decided to write to Celine Dion to ask her to sing at a charity event for a made-up village in Asia, which I decided to inflict ALL OF THE NATURAL DISASTERS ON! They had a 7 year drought, so a recent earthquake set off a landslide because all the dirt was too dry to stick in its shape, and the landslide bowled over the village, and then a hurricane came and I think even a few other things... Basically it was "Heart shows off their fancy French vocabulary". But then I ended it off with a Haiku. Nothing less than a Haiku poem, in French where there are extre strict rules about syllable counting (like, there are some words that are two syllables in the middle of a line but three if they are the last word in the line!). And the last word in the Haiku? Vivimes!

That was possibly the smuggest I've ever been. My friends owed me dinner after all the exams were done :D

As for how it was organised in my school, the HL and SL topics were typically taught together. Then the HL kids came in once a week after school for an extra hour of instruction on the HL stuff, for one of the two years. That way, we all got the same education, but the "extras" for the HL class were just done in that extra time. So the same teacher would teach both the SL and HL typically :)

There's also the related Unruh radiation, theorised to occur not outside a black hole (like Hawking radiation) but from the perspective of an observer in an accelerating frame. It was actually hypothesised before Hawking radiation. The interpretation is somewhat controversial (though I think the difference of opinion really is just a matter of interpretation, nothing more). https://en.wikipedia.org/wiki/Unruh_effect

Another accessible math puzzle I just saw on another board. (By the way I meant to comment on the stones puzzle, see here for the puzzle and here for Heart's spoilered analysis on it. Any more thoughts on that annnnyone before I give a full solution and further background?)

Here it is:

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

You have a 4by4 array with all 16 squares at value 0.

Pick any square: all the squares in the same row and column,

including the square you picked, will change values:

0 becomes 1, and 1 becomes 0.

What is the minimum number of picks to end up with:

0 1 0 1

1 0 1 0

0 1 0 1

1 0 1 0

And I'd like to ask a followup for people who solve it. What if you generalise this in the obvious way to an m x n grid?

I'm waiting for that answer to the stone problem by the way ;) I want to see how close I got and if I was on the right track!

[Kelly]

That was awesome, Heart.

[Dodecahedron314]

EmeryRipley: No, we had HL and SL as totally different class periods, so the teacher I mentioned who taught sophomore chem, chem SL and HL, and bio SL and HL had a class every single class period of the day, if I'm not mistaken. Not to mention that every single person in our IB program (except for me, because I'd had a standing grudge against that teacher ever since sophomore chem because we had very different ideas of what constituted "teaching"...it's a long story...also, physics just coincidentally happened to be the one science he didn't teach at the time we picked our HLs and SLs because our school didn't get Environmental Science until I was a senior) was in one of those classes, so over the course of a day he would see two IB graduating classes' worth of students. And our TOK didn't end before January of the second year...we did all of it essentially in the first semester of second year and then the second semester was given over mostly to the IA and EA, the former of which we spent way too much time on and therefore we had absolutely no warning or instruction on the latter. Also, it seems as though playing cards is the official IB pastime, judging by how well our school bridge team of four of my IB friends has done over the past few years, and how many obscure card games I learned in the back of my physics classroom and on free days in history. How to make friends in IB: always have a deck of cards in your backpack. :D

Heart: That's awesome, but also French sounds really really confusing and I'm now thinking twice about learning it at some point if even syllables are that complicated. (Also, way too many vowels.) Is the past narrative tense in French kind of like the past imperfect in Spanish? It roughly translates to "I was <verb>ing" followed by the statement/implication that something else happened while you were <verb>ing. I'm trying to remember how to conjugate vivir for that...the Internet says it's vivía. (Hey, I might have gotten a 6 on my SL exam, but I never claimed to be fluent. Also, this is something I learned the year when we went from having a really good teacher the previous year to one with no idea what she was doing, towards the end of the year when she realized she should probably teach us something other than tons of useless vocabulary from her completely random monthly obsessions that she called "units" and so spent about the last month and a half teaching us all the obscure tenses she could think of, all while also having us make an hour-long movie entirely in Spanish.)

[Heart]

Heart: That's awesome, but also French sounds really really confusing and I'm now thinking twice about learning it at some point if even syllables are that complicated. (Also, way too many vowels.) Is the past narrative tense in French kind of like the past imperfect in Spanish? It roughly translates to "I was <verb>ing" followed by the statement/implication that something else happened while you were <verb>ing. I'm trying to remember how to conjugate vivir for that...the Internet says it's vivía. (Hey, I might have gotten a 6 on my SL exam, but I never claimed to be fluent. Also, this is something I learned the year when we went from having a really good teacher the previous year to one with no idea what she was doing, towards the end of the year when she realized she should probably teach us something other than tons of useless vocabulary from her completely random monthly obsessions that she called "units" and so spent about the last month and a half teaching us all the obscure tenses she could think of, all while also having us make an hour-long movie entirely in Spanish.)

Don't get intimidated! The syllable counting thing is only relevant if you want to become a poet, and honestly? Most of the native French speakers I've met don't even know how to conjugate the past narrative tense. Most of them will know the present tense of that narrative tense, but it's becoming an "old-fashioned" thing. It's not necessary in any way in life :P And I'm afraid I don't know any spanish, but that sounds about right :)

[nerdperson777]

Well since I don't have IB at my school, I can just say that my AP Biology class was crazed with playing Yu-Gi-Oh cards. Originally the teacher was fine but on the weeks before the AP Exam, he said that the middle aged side of him is getting irritated by that for no reason so they should study unless they're sure that they'll get 5's on the exam. I didn't pass the exam and I didn't even play. I think some of them didn't even take the test I think.

There was one time that I felt good for deciphering a language. I bought burritos with my dad and there was one labeled "poco beans". We weren't sure what it meant. Then I remembered in music notation poco a poco was "little by little", basically gradually. Then I shouted out "little beans"! There were less beans in that burrito. I didn't know any Spanish but music theory is Italian so I guess it helped a little. Tiny achievements.

[Heart]

Well done nerd!! That's an amazing feeling, isn't it? :D

[Dodecahedron314]

There was one time that I felt good for deciphering a language. I bought burritos with my dad and there was one labeled "poco beans". We weren't sure what it meant. Then I remembered in music notation poco a poco was "little by little", basically gradually. Then I shouted out "little beans"! There were less beans in that burrito. I didn't know any Spanish but music theory is Italian so I guess it helped a little. Tiny achievements.

Being a band geek was so helpful when I was learning Spanish. Well, more specifically being a band geek who actually bothered to remember the literal translations of the notation and was generally the designated person whom everyone else in the section would turn to and say "what's this one mean again?" in junior high school. It's kind of odd that the menu wasn't just labeled "poco frijoles" though...

[CosineTheCat]

I kind of want to show, I can now make some really cool things :P

I might just be showing off my new calculus abilities that are still very weak. xD (I'm really enjoying the program MAPLE)

[Kelly]

Awesome. And yay that you are learning MAPLE.

[Amorphous]

I had no idea there were so many physicists here! I just started working on my MSc project and hope to find somewhere to do a PhD next year. My field is nowhere as cool as working with antimatter at CERN, though, as I'm just a lowly condensed matter theorist looking to make the world a better place by explaining phenomena in new materials (right now I'm looking into stanene).

Oh, and, technically, I have a BSc in physics, but my MSc diploma is going to say nanoscience because I just spent a year despecializing myself with a mixture of courses in biology, chemistry and physics. No regrets, though!

[Heart]

I kind of want to show, I can now make some really cool things :P

I might just be showing off my new calculus abilities that are still very weak. xD (I'm really enjoying the program MAPLE)

SO COOL! I never learned Maple, but I really want to. Next time you're in my neck of the woods, you'll have to show off your skills ;)

I had no idea there were so many physicists here! I just started working on my MSc project and hope to find somewhere to do a PhD next year. My field is nowhere as cool as working with antimatter at CERN, though, as I'm just a lowly condensed matter theorist looking to make the world a better place by explaining phenomena in new materials (right now I'm looking into stanene).

Oh, and, technically, I have a BSc in physics, but my MSc diploma is going to say nanoscience because I just spent a year despecializing myself with a mixture of courses in biology, chemistry and physics. No regrets, though!

Hi! :D

I worked ever so briefly in a nanotechnology institute, with nanobeads of diamond. The jokes when I gave a solution of them to one of my partners.... And he'll never be able to give me as many diamonds as I gave him! No matter how hard he tries ;) Nanotech though is so cool.

Random celebration though! Guyz, I am officially a PhD student!!!!!!!!!!!!!!!!!!!!! :D :D :D The paperwork came through, and I have the official designation (and paycheque raise ;) ) now :3

[Kelly]

Totally awesome news, Heart! :)

Welcome, Amorphous. My MSc is physics, but after 20 years of working on particle accelerators, I have accepted a position at a medical company. I will be making diabetes care more accurate and precise. My father is a Type I diabetic, and my work will directly help him and others. I am excited.

More math please (and physics)! :)

[Heart]

I'm still waiting on Mic's stone game solution ;)

And congrats on the job Kelly!! I think you were looking for one once upon a time, not that long ago? I'm so glad you found such an amazing one