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January 11

Electron spin

Some years ago, I visited with friends whose father is a physicist, and he spent a few minutes telling me about some development that I didn't really understand at all. As I understood it, they'd discovered that pairs of electrons could have their movements modified (some kind of "spinning") so that any action on one would instantly be equalled in the other, no matter how far away the two were from each other. Can anyone explain whether this is anywhere close to realistic? I can't get past the second intro paragraph in Spin (physics), and even the first sentence of Electron magnetic dipole moment is too much for me — not to mention that I've had several years in which this already confused memory has been able to get even weaker. Nyttend (talk) 06:52, 11 January 2014 (UTC)[reply]

Quantum entanglement? See also Bell's theorem. — kwami (talk) 07:59, 11 January 2014 (UTC)[reply]

Bell's theorem seems the best way to explain it: basically, it involves the measurement of a property which can take only two values, say up or down; if both entangled particles are measured at the same angle, their spins are always opposite (but to keep the argument simple, lets assume that the result of one of the two instruments is inverted, so with the same angle we get the same spin). If the angles are not the same, the correlation between measurements will be equal to the cosine of the difference between the two angles. So correlation varies between -1 and 1; and at 90° and 270° it is zero, meaning that you get the same spin 50% of the time (and the opposite spin also 50%). In classical physics, you'd expect the correlation at 45° to be 0.5 (75% the same), not cos(45°) (=0.71 or 85.3% the same). In that case locality and counterfactual definiteness would be preserved: you can assume that with the same spin, had you taken the measurements at different angles, you would still get compatible results. In QM this isn't true: with 85.3% of results the same when measuring at 0° and 45°, and 85.3% the same when measuring at 45° and 90°, measuring at 0° and 90° should give the same spin in at least 70.6% of cases. Yet in reality you get only 50%. The only explanation seemed to be (now there are more, like the many worlds theories etc..) that spin is undetermined before the measurements, and once you measure one of the particles the wavefunction collapses and the other particle also gets its "spin value" instantaneously. Ssscienccce (talk) 11:11, 12 January 2014 (UTC)[reply]

My guess is that he was talking about Quantum entanglement, as suggested by Kwamikagami, but perhaps in relation to teleportation as in Quantum_teleportation , since this was a popular subject even outside of realm of physicists a few years back.DanielDemaret (talk) 17:21, 11 January 2014 (UTC)[reply]

Mathematics Problems Related to Medical Sciences

Is there anywhere I can find a list of mathematics problems/research that is relevant to medicine, but is not focused on the medical aspect so much as the mathematical. For example, I recently stumbled on viral tiling, which sounds interesting, but most of what I found seems focused on the values of it or the biology of it, is there anywhere I could find out about the math aspect with the biology as a background? I mean in the same sense that I can find books on group theory that discuss the parts related to chemistry or physics, but are more geared towards someone with a mathematics background. I'm interested in the medical applications, but I am far stronger in mathematics than medicine and feel like I'm coming from the wrong end (it doesn't need to be viral tiling, by the way, just an example). Thank you for any help, I'm seeming to have bad luck with this on my own.Phoenixia1177 (talk) 10:57, 11 January 2014 (UTC)[reply]

There is, of course, Epidemiology and perhaps this will give you some ideas. There's also a discussion here and here. Richerman (talk) 11:22, 11 January 2014 (UTC)[reply]

You might like "Mathematical Models in Biology" By Leah Edelstein-Keshet [1]. There is some population dynamics (relevant e.g. to epidemiology, described above), but also I think a few basic models of cellular processes and tumor formation. It's not "cutting edge" by any means, as but it is a very classic text for late undergrad/early grad courses. Most academic libraries should have it. SemanticMantis (talk) 14:20, 11 January 2014 (UTC)[reply]

One of the biggest mathematical applications I've heard of recently is optical projection tomography,^[2] which uses math to get a whole lot more out of visible light imaging. There are many other imaging applications (confocal microscopy, two-photon excitation microscopy, atomic force microscopy, etc.) where an ambitious mathematician might find a way to make a difference. There may also be opportunities for invention in population biology - currently there are a number of measures like Tajima's D and fixation index that are widely used, but may well be supplanted by something you can invent that has more mathematical sophistication. And while there may be a lot of clever heads and advanced computers on the task, Protein structure prediction remains marginal and could always use someone to make it faster or more accurate. Wnt (talk) 14:27, 11 January 2014 (UTC)[reply]

My own background is similar to yours -- I came close to getting a Ph.D. in math before switching to neuroscience. I think you are going about it in the wrong direction. When mathematicians look to biology as a source of math problems, they usually end up reframing the problems in a way that greatly reduces their biological relevance. The only way to avoid irrelevance is to learn some biology. Pick the area that interests you the most (for me, neuroscience), and start reading about it. Every area of biology and medicine has mathematical aspects, so you really can't lose. If you're like me, you'll find that the more biology you learn, the more mathematical issues you will spot, and the more ideas will occur to you. (For me, the most interesting interaction between math and biology comes in the effort to understand grid cells. But there are hundreds of other important biomath problems.) Looie496 (talk) 17:01, 11 January 2014 (UTC)[reply]

There are several applications in probability and statistics: Bayesian statistics can be used in differential diagnosis, particularly with the development of expert systems. The multiple comparison problem has relevance for medical imaging tests such as the MRI, which must perform thousands of statistical tests per scan. Probably the best match, though is Biostatistics, which is an emerging field with several PhD programs to choose from. OldTimeNESter (talk) 15:46, 13 January 2014 (UTC)[reply]

Thank you for all of the replies:-) After following up on some of these, I definitely need to learn more of the relevant biology; thank you for the advice in that regard, Looie496. The protein structure prediction problem looks interesting, thank you.(Sorry if this reads weird, I just got back from a business trip and am half asleep, but I wanted to make sure I said thank you before this ended up getting archived; I really appreciate all the answers, very helpful:-)).Phoenixia1177 (talk) 06:48, 14 January 2014 (UTC)[reply]

Burning candle efficiently.

Is it possible to burn a candle efficiently with a blue flame? Making it burn more slowly so that the available oxygen was sufficient and no carbon was wasted would be acceptable. --78.148.110.69 (talk) 23:33, 11 January 2014 (UTC)[reply]

I don't know how to burn a candle so that there is less soot, less carbon monoxide, and more heat. But since candles are usually used for light, it isn't enough to just consider how much unburned/partially burned carbon there is. Other hydrocarbon fuels such as white gasoline, propane, and natural gas are often burned in a lamp with a gas mantle which greatly increases the amount of light. So a way to produce more light would be to process the crude oil into fuels that can be burned in a lamp with a mantle, instead of processing it into candle wax. Jc3s5h (talk) 23:50, 11 January 2014 (UTC)[reply]

Have you considered a career in politics? 78.148.110.69 (talk) 02:22, 12 January 2014 (UTC)[reply]

Here's another efficient use of candles.[3] Go to the 1:40 mark. ←Baseball Bugs ^{What's up, Doc?} carrots→ 04:40, 12 January 2014 (UTC)[reply]

In a test of smoke points, it was found that "Soot emission was not possible for any fuel when wick diameter was below 1.7 mm or when wick length was below 5.9 mm." So trimming the wick, or if it's a dripping candle put something around it to keep the molten wax around the wick would help (our article mentions candle followers, didn't know those existed). Not sure what the advantage of a blue flame would be, in a way a yellow flame is more efficient, it's bigger because the center doesn't get enough oxygen, and gives more light due to the glowing soot, but that soot is still burned completely in the outer zone so no carbon is wasted, unless the flame gets too long. Keeping the wick as short as possible by trimming seems the best option, whether you want to avoid soot or have longer lasting candles. Ssscienccce (talk) 12:55, 12 January 2014 (UTC)[reply]