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February 16

Aerial skiing

I have been looking at explanations of how aerial skiers appear to change their rotational motion in mid-air. These describe how orientation can be changed by moving parts of the body separately in sequence, like a self-righting cat, while never actually imparting any overall spin (which would be impossible due to conservation of angular momentum). Yet looking at real footage, it is hard to see that such explanations are correct. For example, see 0:45 to 0:53 here. During the first part of this sequence he has a seemingly clear rotation around his head-to-toe axis, and yet as he comes into the landing this disappears. How is this possible without changing angular momentum? 86.160.221.91 (talk) 01:38, 16 February 2014 (UTC)[reply]

It's very hard for me to fully understand the motion, both because I'm not looking at a full set of slomo options and because I don't know the angle of the photography. But my assumption is that it relies on a basic point that you don't really have angular momentum about two axes at the same time. When he lands, he has a simple head-over-heels angular momentum. When he spins, his body is angled relative to this axis, and he is both spinning head over heels in that other angle, and spinning around his body axis. I assume these vectors add up to the simple head-over-heels vector, even if it's hard for me to understand it visually? Wnt (talk) 05:48, 16 February 2014 (UTC)[reply]

With regard to the video, it appears to me that he could impart a spin to himself aerodynamically, by tucking in one arm while extending the other to serve as a dive brake to increase drag. 67.169.83.209 (talk) 06:56, 16 February 2014 (UTC)[reply]

When skiers launch themselves off the ramp they establish the angular momentum required to rotate about both their head-to-toe axis and one of their lateral axes. After that, they are able to alter the speed of rotation about these axes by altering their moment of inertia about these axes. They do this by retracting and extending their arms, bending their knees etc. Sometimes they move both arms symmetrically, and at other times they retract or extend just one arm. Skiers and divers can position their arms and legs to achieve a significant range of moments of inertia. Theoretically they can display many different maneuvers based on one set of angular momentum vectors (x-axis, y-axis etc.) just by altering their moment of inertia about each axis and this is what makes their performances so inscrutable that they appear to defy the principle of conservation of angular momentum.

A gyroscope can't display a similar variety of different maneuvers because gyroscopes acquire extraordinary stability from their great speed but skiers and divers are turning at speeds much slower than gyroscopes. A gyroscope toppling due to inadequate speed is analogous to the amazing maneuverability of skiers and divers. Dolphin (t) 11:44, 16 February 2014 (UTC)[reply]

Applying Einstein field equations over black hole

Do Einstein field equations also apply on black holes? 182.66.50.164 (talk) 07:51, 16 February 2014 (UTC)[reply]

In fact, what most people describe as a "black hole" is one of several solutions of the Einstein field equations, particularly for the Schwarzschild metric. If the enclosed mass is sufficiently large, there exists a Schwarzschild radius as part of the solution. In the simplest case, that radius defines an event horizon, and that is why people loosely call the region inside that radius a "hole" - things can fall in, but nothing comes out - not even light.

Of course, if you worry about all the confounding details, there are lots of other things to bring up: conservation of angular momentum, electric charge, radiation pressures, quantum-mechanical effects at the edge of the event horizon... leave it to mathematicians to turn a "solution" into a series of more challenging problems!

This is to say nothing of Stephen Hawking's most recent 2014 paper - Weather Forecasting for Black Holes - very probably the one that will be his last contribution to the physics of black holes. I, as a bit of a cynic, read between his lines, and interpreted the paper as a sort of parting volley - "ha ha, physics community! I've mis-led you for forty years, and there is no such thing as a black hole in the first place, the math just doesn't work out!" But, I'm sure you and other readers can read it and make up your own minds... (Incidentally, I downloaded the PDF when it was first published on ArXiV, and read the whole thing on my iPad... I found a typo, and checked the LaTeX source, and the typo is there, too..."7evaporating black hole," an error I can only imagine was due to an improperly formed TeX reference that Professor Hawking's assistive text entry software mistyped... and it must have been a real pain to try to correct that, because no update has been posted for the last few weeks). Nimur (talk) 09:21, 16 February 2014 (UTC)[reply]

Maybe people were too busy soapboxing rather than telling Hawking so he doesn't know? Nil Einne (talk) 13:47, 16 February 2014 (UTC)[reply]

Out of respect, and in the furtherance of whatever may be left in my academic career, I have stopped trying to correct people who have more Ph.D.s than I. Nowadays, I just point out any relevant errors I find, buried among the minor details, and hope that any other interested detail-oriented people will make good judgements. Even I have produced a typo, on rare occasions; but these days most of my publications are in wiki-format and are not widely read by pedantic English-speakers. Nimur (talk) 17:41, 16 February 2014 (UTC) [reply]

So when he says that "inside the event horizon, the metric and matter fields will be classically chaotic", is he saying that the old idea of a singularity in the middle surrounded by a sea of empty space with occasional bits of fast-falling stuff isn't right? In the past I've read that with a galactic black hole you might not even notice when you drop inside the singularity, but here... the inside of a black hole is some kind of ... stuff? Does this mean that when you've dropped far enough in, if somehow you could survive, you'd could see objects flying around, complex matter constructs, somebody who says he's God who wants to talk to Captain Kirk about his warp drive? Also, in that quote when he says "event horizon" he means an approximate event horizon inasmuch as the back traffic is sparse and unpredictable? Oh, yeah, and last but not least -- how close does this push the refined classical view of a black hole to a fuzzball, which is also full of ... stuff? Wnt (talk) 17:47, 16 February 2014 (UTC)[reply]

The below is predicated on clearing up a critical common misunderstanding: stuff falls in to black holes, but it is not correct to say that it can never escape. This effect is called Hawking radiation (in honor of its proponent); and it is responsible for the eventual evaporation of the black hole. So, don't get confused - stuff can and does escape the event horizon - just in a very complex, round-about way.

The energy and length scales of the dynamics inside the event horizon are sufficient to tear fundamental particles apart. The "chaotic" description means that the exact geometries are difficult to predict, and the mathematical explanation is because the disturbances are non-smooth. (That means that no matter how small you zoom in, there is still fluctuation).

The paper essentially says that the radiation emitted from a black hole directly corresponds to the time-reversal of the accretion of mass and energy; but that the internal dynamics make it difficult to correlate any specific ejected photon back to any specific input matter that fell in previously. By analogy to weather forecasting: we know that if a hurricane causes rain to fall, any individual raindrop is full of water molecules that evaporated from some ocean somewhere; but we can not predict the trajectory forward or backward: we can't watch ocean-water evaporate and meaningfully know where it will fall; and we can't catch an individual raindrop and meaningfully know where its constituent water originated. The dynamics inside the hurricane are chaotic but they are not, in principle, any different from the behavior inside the black hole: particles are following complicated dynamic trajectories that are determined by interactions with other particles and mediated via fundamental forces. We can write a geodesic to describe these trajectories, but for chaotic systems, the geodesics are non-smooth. Complexity nothwithstanding, the particles still traverse these trajectories. This is what Hawking means when he says the system is unitary and that it satisfies CPT symmetry. The "apparent event horizon" is simply "the point when the geodesic becomes non-smooth" - and that depends entirely on you, the observer, and the scale length that you can actually resolve. (We do not, categorically, call the edge of a hurricane an "event horizon," simply because we failed to describe the internal dynamics with sufficient precision!)

I should emphasize: we don't know if CPT symmetry must be preserved, at least not any more than we know that energy must be conserved. It is merely a very fundamental way of generalizing the consistency in all other observed phenomena. Another thing we don't know is whether Einstein's field equations actually correspond to a complete description of the real world! To me, it is more reasonable to assume that symmetry is the fundamental principle of our universe. In other words, I believe that conservation of energy and momentum is more fundamental to our universe than some goofy geodesic equation Albert Einstein wrote a hundred years ago - especially now that his equation has been clearly shown to predicts implausible behavior - a fact known to physicists since the 1970s! When Hawking referenced his own 1976 paper, he is essentially saying the same thing: his original statement about black holes is, if nothing else, an indictment of the flaws in general relativity. But everyone else was so excited about the incredible science-fiction applications of the "black hole" that they just kept running with it! Nimur (talk) 20:51, 16 February 2014 (UTC)[reply]

Often chaos isn't all that ... chaotic. For example, two of Saturn's moons apparently have orbital chaos^[1] yet they continue going around and around, and all the physical phenomena involved are continuous. Chaos can be a mere folding and stretching of possibilities, a mere "x modulo epsilon / epsilon" calculation. But the way you describe it, it sounds as if the innards of the event horizon are a place abruptly different from the outside, with Planck scale variations in gravity. Now I'm in absolutely no position to say, but Hawking objected to firewalls saying (which I don't really understand) that "if the firewall were located at the event horizon, the position of the event horizon is not locally determined but is a function of the future of the spacetime." Would the same objection apply to this? Could the chaos be something more mundane (like particles quantum tunneling out of the singularity, though I assume that isn't right)? Wnt (talk) 03:48, 17 February 2014 (UTC)[reply]

For convenience, here is Black Holes: Complementarity or Firewalls?, the paper Hawking cites. It explains the conundrum: three statements cannot simultaneously be true. Among them, "information originates near the event horizon," corresponds to energy that originates near the "edge" and escapes by quantum-mechanical processes. Again, the developments put forth by these scientists don't prove what happens: all they show are what cannot happen, by demonstrating that certain theoretical constructions yield a contradiction. (And to your question about "chaos" - these guys formulate the black hole of mass M as a quantized system that transforms input matter into Hawking radiation via an intermediate system transform, whose entropy - number of available states - is exponential in M, the mass of a black hole. Try tuning a monte carlo simulation to search a problem space that large - it's a little bit worse than an n-body problem like the dynamics of planet-moon orbits!) Nimur (talk) 05:30, 17 February 2014 (UTC)[reply]

I suppose what's throwing me off is that at the highest level, it would apparently resolve the paradox to say that "Hawking radiation is not in a pure state", or "the infalling observer encounters something unusual at the horizon". In Hawking's paper he is saying that the radiation is not in a pure state, but like the weather, but in your interpretation above (in the unlikely event I haven't misunderstood), you seem to be saying that the infalling observer encounters some kind of meat-grinder at some point before hitting the singularity. It still seems like more solutions than necessary. I should not pretend to understand the evolution of the internal quantum state at this point; I don't understand how it predicts what being inside the hole would be like. Wnt (talk) 13:28, 17 February 2014 (UTC)[reply]

Frank Wilczek apparently said of Hawking's latest paper "I think the kind thing to do is to pass this over in silence." That's harsh, but it's a fact that most of Hawking's colleagues haven't paid much attention to his work for decades now. I have nothing against him, but he's not the genius that laypeople imagine him to be, and I think there's no sense in citing any of his recent papers here. The firewall paper did start a debate, which is still unresolved as far as I know, but Hawking isn't a major participant in it. -- BenRG (talk) 06:01, 18 February 2014 (UTC)[reply]

How strong of a handicap is playing chess blindfolded for a chessmaster?

Obviously for a computer it doesn't matter what format they receive the moves, a millionth of a second later they can translate that to their internal data structure representing the board. But for a chess player (grandmaster), how strong of a handicap is it when they play blind? (No board in sight, just told moves algebreically). I mean in quite specific terms, like ELO rating. Any information? --89.132.116.141 (talk) 13:18, 16 February 2014 (UTC)[reply]

It sounds to me like this is the sort of thing which would vary wildly from one grandmaster to the next, as well as how much the attention the grandmaster gives to Blindfold chess. I also wonder if there is enough information to come up with a meaningful figure, for example the now defunct but apparently highest profile blindfold chess tournament is Amber chess tournament which wasn't just blindfold chess but also rapid chess. Nil Einne (talk) 13:44, 16 February 2014 (UTC)[reply]

Most players at the grandmaster level are so good at mentally visualizing the chessboard that having an actual chessboard in front of them means little. It only starts to be important when you get to multiple simultaneous chess games, which impose a load on memory. Looie496 (talk) 14:53, 16 February 2014 (UTC)[reply]

Looie, you've just stated something extremely firmly. Do you have any evidence? I would consider a 200 point drop in ratings to be totally normal if the GM doesn't actually have a board in front of them but has to visualize it. You're saying there is no effect. So, can't you show this with some refernece? Thanks. 212.96.61.236 (talk) 16:36, 16 February 2014 (UTC)[reply]

There are blindfold ratings here: [2]: the OP might like to correlate these with the FIDE ratings of the individuals.--Phil Holmes (talk) 16:48, 16 February 2014 (UTC)[reply]

But if you know anything about how Elo rankings work, you've got a big conundrum: rating calculation depends on measured relative performance among a crowd of others... so, who is wearing the blindfold? Are you suggesting that one person wearing a blindfold has to be compare - not only to opponents who aren't blindfolded - but also compared to other games, where neither competitor wore a blindfold? It is actually not clear whether that comparison is meaningful. Elo style ratings only make sense when there's symmetry between all n members of the sample population so that the performance in any specific game can be compared against other games with other players. Bear in mind that the rating result for the blindfold-game depends on the rating of the un-blindfolded opponent also - and his current rating depends on whether he played previous games against blindfolded or unblindfolded opponents. Nimur (talk) 20:06, 16 February 2014 (UTC)[reply]

I'm actually OP here. So, I actually meant, blindfolded versus a non-blindfolded opponent!!! I was curious how much the blindfold changes pertformance on an absolute scale, i.e. if you are blinded on one game without any other changes (opponent isn't blinded) how much does that make your rating drop? Assume for people like Kasparov, Vishy, or Carlsen 212.96.61.236 (talk) 21:09, 16 February 2014 (UTC)[reply]

Then, the Elo rating system isn't what you want, because it's categorically a relative - not an absolute - scale!

You might be interested to read about certain computer chess algorithms that seek to determine whether a specific move, set of moves, or board-position is "objectively better," (which is related, but distinct, from making progress towards a win). It is actually quite difficult to define "better" for chess (except for the obvious "win/did-not-win" categories). As such, it is difficult to meaningfully measure the performance of one opponent against one other opponent. You could have the two competitors play a large number of games - some with a blindfolded player, and some without - and compare win statistics. But that couldn't be converted into an equivalent FIDE-style rating at all! Nimur (talk) 05:16, 17 February 2014 (UTC)[reply]

Whatever. I (still OP) think you're splitting hairs. I obviously really mean the following: if I were a carbon copy of Kasparov in every way, what would my ELO rating be? It would be the same as Kasparov's, since I am Kasparov in every way and ELO ratings are relative. Now what if I am a carbon copy of Kasparov in every way except that I am secretly blindfolded in a way that nobody knows - I can't see the boards that I play. Now, if I am rated in STANDARD (not blind) chess competitions, would I still have nearly Kasparov's rating? Or would it be expected to be 100 points lower, or 200 points,e tc. Same for others I have listed. What would the average handicap be? (for these experienced blind players). --91.120.14.30 (talk) 10:05, 17 February 2014 (UTC)[reply]

If there were a way to create a "carbon copy" of Kasparov, then his and every other chess player's rating would be different, because there would be two Kasparovs in the rankings pool. Every time any two players play even one single match, that causes everyone else's Elo rating to change. That's how the scoring system is designed! The ranking was designed by chess nerds, for chess nerds, and it has all the messy mathematical complexities that chess nerds thrive on. I think you want a simple answer, but this is a complex problem!

The best way I can describe chess ratings is to consider the scores of every player as a giant simulated annealing problem. You want to invert for the value for each player, so that you can predict the statistical win-loss ratio of any player against any other player. This is effectively using a statistical approach to determine the inverse of an n-by-n matrix for very large n. You have a bunch of prior matches, with win-loss estimates; and from those sample points, you assign a value to every player; then check whether the matrix of all possible match-ups is close to a best-fit with your data; and then you iterate. What set of scores should you assign to every player that yields a matrix whose elements are most consistent with the statistics of all prior games? There's a large null-space, and the problem is degenerate : you can't possibly have data for all n by n elements.

What happens when you add one person who is a clone? Well, the matrix size increases, but its rank does not; the size of the null space increases, and problem of assigning scores becomes more degenerate! So, no, sorry, you can't just assume that a cloned Kasparov has the same chess rating as his original. That isn't how it works! You have to blindfold your clone and then run him through a lot more games, and everyone's Elo rating changes, including the original guy.

One of the best ways I have proven to myself that FIDE-style chess ratings are mostly junk is by playing a bunch of symmetrical chess engines (identical software!) against each other, and calculating the ratings that emerge. I say again, it's like running a simulated annealing algorithm on a degenerate problem. You get an answer, but it's mostly noise. Now that free and open-source chess software is widely available, and powerful computers are cheap and easy to come by, everyone should try this. It's a bit eye-opening. It made me never want to play chess again. The game is not yet solved, but with computers, it has become way too deterministic to be fun for me; and the ratings are really a lot more bogus than most chess nerds will usually admit. Nimur (talk) 05:55, 18 February 2014 (UTC)[reply]

Thanks for completely ignoring my question. Your point is basically irrelevant, as we can simply imagine that the carbon copy of Kasparov starts playing while the real Kasparov is killed - the pool doesn't change. If even that isn't enough for mathematical reasons, then we can start the carbon copy with Kasparov's current rating, while Kasparov is killed. If that STILL isn't enough, then we can simply copy the Universe into two parallel universes. Universe 1 is the current one (control), Universe 2 is where the (there, real) Kasparov secretly is blinded for every one of his remaining matches, without anyone knowing this. Likewise we can create a separate Experiment universe from the Control experiment, in each Universe a top player is secretly blinded. Question: if we repeat this experiment with a separate universe for each player we are testing, then what is the average change in a given top player's ELO reating between the control universe and the test Universe? (We only consider top players, who are experienced blind players.) Example. If instead of blinding them we made the secret change that in each Control universe there would be a small paperclip that is placed under all of the rest chess boards in every game that the person undergoing the experiment plays, then we would find that every test Universe statistically matches the control Universe. A paperclip secretly placed under the chess board does not affect ELO ratings. So, this is my experimental question, and it concerns an actual real-life effect. How much handicap do experienced blind-chess players experience if they are blinded in a normal match? You can mince it however you want, but it's a straight-forward question. --91.120.14.30 (talk) 11:14, 18 February 2014 (UTC)[reply]

Who would win the Super Bowl if Dallas had to play all its games in snow? It's an easy, straightforward question to ask, but it's a hard question to answer. Nimur (talk) 21:34, 18 February 2014 (UTC)[reply]