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August 13

Melanin and light absorption

According to melanin, it's able to dissipate over 99.9% of absorbed UV radiation. However, dark colors absorb more light compared to light colors. To what extent melanin offsets more intense light absorption by dark skin and dark hair when compared to light skin and light hair colors? And to what extent black hairs and skin heat up more than their light colored equivalents? Brandmeister^talk 13:31, 13 August 2015 (UTC)[reply]

Some good info in these freely accessible articles - "Optical properties of human skin" [1], "The evolution of human skin coloration" [2], "Spectroscopic characteristics of human melanin in vivo" [3]. SemanticMantis (talk) 14:00, 13 August 2015 (UTC)[reply]

(edit conflict) "dark colors absorb more light compared to light colors": This is true, but UV is not visible light, and low absorption at visible wavelenghts does not always coincide with low absorbtion of UV. According to this article: (Reflection of ultraviolet radiation from different skin types) "Skin types with moderate sensitivity to solar radiation, neither too pale nor too tanned, reflect the greatest UVR."

Also of interest: The Optics of Human Skin (freely available as pdf). It has a remittance spectrum of two different skin types (light and dark). You can see for UV wavelenghts (below 400 nm) total remittance is always below 30%, so at least 70% of UV light is absorbed, even for Caucasian skin type. Hence I think we can safely say that dark skin is more effective at dealing with UV radiation, even considering that it does not reflect as much as light skin. - Lindert (talk) 14:17, 13 August 2015 (UTC)[reply]

Even white skin contains a very effective UV dye ... unfortunately, that dye is DNA (and RNA). See Spectrophotometer for nucleic acid measurements - the absorption of UV radiation is often taken as a pretty good estimate of the nucleic acid in fractions of ground up tissue, to the exclusion of all else. (I suspect that there is a great deal of biology, important in the earliest living organisms, involving the direct absorption ("photosynthesis?") and use of UV energy by RNA; see [4]. But that's actually not relevant. :) Wnt (talk) 16:37, 13 August 2015 (UTC)[reply]

If an alien contacts you and ask what's a kg

How would you tell an alien, who's not on Earth, how to measure a kg?--Scicurious (talk) 14:08, 13 August 2015 (UTC)[reply]

5.97470 x 10²⁶ hydrogen atoms. Looie496 (talk) 14:13, 13 August 2015 (UTC)[reply]

And why don't we uses Looie's definition above, instead of still defining the kg according to an artifact?--Scicurious (talk) 14:26, 13 August 2015 (UTC)[reply]

Because while that's a good definition for some purposes, it also has many problems. Because the CIPM is very careful, and these things take time. We don't want international standards to change quickly. Metrology is hard, and there are seldom easy answers.

Anyway, see Proposed_redefinition_of_SI_base_units, and here [5] particularly on the current work to redefine the Kilogram. They are actually hoping to do it in terms of the Planck constant, see here [6], involving a Watt balance. For more on this, search /electronic kilogram/, which also leads us right back to NIST - [7] SemanticMantis (talk) 14:40, 13 August 2015 (UTC)[reply]

SemanticMantis is the one to read here, but I should explain that the purpose of the standards we use is to make it possible to measure and communicate data as accurately as possible, not to be intellectually pure. It was more accurate to weigh a special ingot than to weigh a hydrogen atom, hence the definition. Of course, if you can't send out standard ingots to your inquisitive friends across the galaxy, you'll happily make do with a less accurate and possibly slightly different definition. Wnt (talk) 16:29, 13 August 2015 (UTC)[reply]

What school is this homework coming from? It is MUCH more interesting than my physics homework! 209.149.114.32 (talk) 15:10, 13 August 2015 (UTC)[reply]

How do you tell an alien what a hydrogen atom is? How do you precisely describe a very large number like 10²⁶ to an alien? The original question, and its first answer, leaves open a lot of questions that are more serious than the simple problem of unit-definition-by-convention. The Pioneer plaque article provides some ideas, but I'm not certain they would work very well in practice. Nimur (talk) 15:32, 13 August 2015 (UTC)[reply]

If you can communicate with the alien, they know what a hydrogen atom is. The universe consists largely of hydrogen. If you can't communicate with them, you can't communicate with them, but hydrogen is hydrogen. Robert McClenon (talk) 18:26, 13 August 2015 (UTC)[reply]

I am pretty sure a real extraterrestrial life form could be literally well beyond our imagination. My question implies an English speaking alien.

For means of communication with an alien civilization, Communication with extraterrestrial intelligence could be of use. The NSA (strange that's not the NASA) also has some information about it: [8]

--Scicurious (talk) 15:44, 13 August 2015 (UTC)[reply]

Just tell the alien it's about 2.2 pounds. ←Baseball Bugs ^{What's up, Doc?} carrots→ 22:13, 13 August 2015 (UTC)[reply]

Yes, that's exactly the sort of accuracy that enabled the alien to travel vast interstellar distances to Earth, way beyond the capacity of Earthlings to reciprocate. -- Jack of Oz ^{[pleasantries]} 22:37, 13 August 2015 (UTC) [reply]

Even King James knows a pint weighs a pound. What the hell weighs the same as a kilogrammme? Certainly nothing known in either of the Testaments. μηδείς (talk) 00:59, 14 August 2015 (UTC) [reply]

A pint of what? Assuming you mean water, that's not true for the British pints and pounds, don't you think a measurement system should be unambiguous? (Actually, it's not true for a US pint either, but it's closer) A litre of water at 4°C weighs a kilo under standard gravity. And recognisability from a centuries old fairytale is not high on the priory list of a measurement system. Fgf10 (talk) 16:43, 14 August 2015 (UTC)[reply]

"A pint is a pound the world around" is about beer, of course. It measures, volume, weight and price. --DHeyward (talk) 21:52, 14 August 2015 (UTC)[reply]

Iregardless of the above, Scurius's question is a rather good one. I think it should be rather easy to display a hydrogen atom, given the masses of an electron and a proton are a known ratio, and that one can depict large numbers as sets of cubes of various numbers of points. (E.g., a cube with 100 dots per edge = 1,000,000 dots.) μηδείς (talk) 01:05, 14 August 2015 (UTC)[reply]

The other alternative, if the aliens are sufficiently advanced to have discovered mass-energy equivalence, is to give it in terms of some standard energy quantum. The Pioneer plaques attempt to do something similar to this: the symbol to the right shows a hydrogen atom going from spin-up to spin-down, which has a very precisely measured energy value of 5.87433 µeV. That's an incredibly tiny weight (on the order of 10^-41 kg), but tell an alien that a kilogram is 9.5493×10⁴⁰ larger, and they should get the idea. A slightly more complex solution, but it would be useful if the aliens are energy beings. Smurrayinchester 13:00, 14 August 2015 (UTC)[reply]

(Or, if you reckon you can convey the more complicated concept of the Planck mass, you could use that as a basis. Some SETI fans suggest that we should use Planck units when trying to communicate with other worlds). Smurrayinchester 13:29, 14 August 2015 (UTC)[reply]

This reminds me of the theory that it is physically impossible to communicate the difference between left and right, if the other part might be living in a place dominated by antimatter and you have nothing observable in common. PrimeHunter (talk) 21:15, 14 August 2015 (UTC)[reply]

Not to worry, we can use CP violation even if they're made of antimatter. --Amble (talk) 21:27, 14 August 2015 (UTC)[reply]

I don't think that's true. The universe we live in is dominated by "normal" matter, with very little anti-matter. I believe he term we use for that is "right handed universe" and it's anti-matter complement would be "left handed". Baryon asymmetry would define handedness for a particular universe. I think it would be easy to convey the mirror aspect of it and naming them would just be convention. But have we found elements of antimatter beyond electron, neutron and proton? Have we ever encountered something like a carbon atom made up of anti-neutrons and anti-protons. The asymmetry in the universe and preference for "right handed" matter is pretty well established, just not understood. We know we are asymmetric and what our preference is so another universe with opposite asymmetry should be judt as obvious. --DHeyward (talk) 21:47, 14 August 2015 (UTC)[reply]

Practically all neutrinos observed have been antineutrinos, and plenty of antibaryons have been seen too (plus all mesons are half matter, half antimatter). Antihydrogen exists, although I don't think anyone has yet managed to bind an anti-proton to an anti-neutron. Anyway, as Amble says, CP violation gives us a way to convey left and right even to an antimatter universe. "Up and down" can be easily described in terms of a gravity well, so we tell our aliens to set up the Wu experiment. By getting them to arrange the coils so that beta rays fly upwards, we can define "clockwise" and "anticlockwise", and then define left and right in terms of the clockwise and anticlockwise movement of a clock hand (or anything that travels in a circle). Duh, that's P-violation, not CP - wouldn't work for communicating with an antimatter universe. You could do something analogous to communicate left and right to an antimatter universe, but you'd need aliens who've built a B-factory particle accelerator. Smurrayinchester 18:34, 16 August 2015 (UTC)[reply]

You don't need a B-factory; some kaons would be good enough and much easier to make. My wife also points out that you could also just point out some features in the CMB. For example, tell them which way Stephen Hawking's initials are written. --Amble (talk) 04:58, 17 August 2015 (UTC)[reply]

But we most certainly would not try to communicate numbers to the alien in decimal. Who knows what base they use? Numerals would be ambiguous symbols, for the base could be anything higher than the number of visible glyphs. Something unambiguously binary would be needed, such as ●●○●●○●○●. → Michael J Ⓣ Ⓒ Ⓜ 22:01, 14 August 2015 (UTC)[reply]

That's nonsense. Suppose an alien sends you !$##$##!$###!!!! - what base do you think he/she/it is communicating in? You don't know for sure that an '@' might not show up soon...but you can certainly guess. Then they send you # $ ! #$ $$ !$ #! $! !! ##$ $#$ !#$...now I think you can figure out which symbols represent which digits - although it might take you a few minutes to realize that they reverse the order of their digits so that the least-significant digit comes first.

Imagine that the first communications with an alien species would result in every scientist, mathematician and cryptologist on the planet trying to be the first to crack that message. With thousands of the smartest people we have working on it, I'm pretty sure we could figure out how they represent numbers. It's safe to assume that any civilization with the ability to receive our message has basic arithmetic nailed down at least as well as we do.

You don't need binary (at least not for that reason) - and binary is far from unambiguous because ordering might matter - or the aliens might use a two-dimensional number representation, wrapping the digits into a spiral or something like that. The old sci-fi trope that first contact is a series of prime numbers makes perfect sense here - and allows you to figure out what's going on without too much trouble.

The real concerns are if the aliens use something messy like roman numerals...or prefer to express their numbers as the sum of two primes, for which they have unique names. If their concept of quantity is represented by strange cultural markers. I'm thinking of that StarTrek episode where the aliens speak English, but use references to stories in their culture as short-hand for meaning. We do that all the time - if I say "Donald Trump earns a boatload of cash for speaking engagements." - then you need to know a lot about boats and how monetary values are established via physical tokens before you stand any chance of decoding what that means. If aliens had established some bizarre scale of magnitudes represented by physical objects in their world, then we might be in real trouble. SteveBaker (talk) 15:19, 15 August 2015 (UTC)[reply]

In fact, humans don't use a simple base 10 system anyway - it gets far to cumbersome for very large and very small numbers. Instead we use a mixture of base 10 and base 1000. If I tell you that a friend of mine earns $120k, you know that I mean $120,000...and in another context, I might say 1.2x10⁵ or 120x10³. SteveBaker (talk) 15:28, 15 August 2015 (UTC)[reply]

The difference between 453 and 467 Hz

Two files of the same piece of recorded music. In one of them the keynote is 453 Hz, in the second the keynote is 467 Hz. How big an interval is the difference, expressed as a fraction or percentage of a semitone? 87.112.218.55 (talk) 15:15, 13 August 2015 (UTC)[reply]

That depends on what the key is, and on what the musical temperament is. Standard Piano key frequencies for 12-tone equal temperament indicate that the difference is something less than a semitone, with A at about 440 Hz and A# at about 466 Hz. --Jayron 32 15:23, 13 August 2015 (UTC)[reply]

Equal temperament please. Looking at them the difference seems to be very close to half a semitone, if A is 440, Bb is 466....453 splits the diff, and 467 only just over 466. My maths isn't up to working out whether its just over or just under a quartertone 87.112.218.55 (talk) 15:27, 13 August 2015 (UTC)[reply]

In equal temperament, the logarithm of the frequency ratio increases linearly with the number of (semi-)tones in the inverval. The natural logarithm of one semitone is 0.05776, and ln(467/453)= 0.03043, which is about 53% of a semitone. - Lindert (talk) 15:38, 13 August 2015 (UTC)[reply]

This looks like a homework question, but lucky for you, you found me wanting to crack some limescale off the old maths... as I understand it, a semitone is 2**(1/12), unless temperament is a factor. Note that (2**(1/12))**12 = 2. (** is exponentiation) Pulling out the handy-dandy R programming language that serves me mostly as a desktop calculator, I get this is 1.059463. The ratio of the tones above is 467/453 = 1.030905. So we want the log_1.030905 1.059463, which is equal to log_x 1.059463 / log_x 1.030905 AFAIR; we'll make x=e and use ln (which in r is actually the default base of log, actually). Anyway, the ratio is 1.897758, and just to check, 1.030905**1.897758 = 1.059463 - kewl. So the percentage is 100/1.897758 = 52.69376%. Wnt (talk) 16:23, 13 August 2015 (UTC)[reply]

How wonderfully thorough all of this is, thank you. And how dare you accuse me of bringing homework here! ;) What happened to Assume Good Faith? (I used to be a WP editor a few years ago) Now I look at these calculations, I remember why I did so badly in my A level maths. This was a real life question. The recording in which the first note of the chorus is 453 is here, and the recording in which the first note of the chorus is 467 is here. And I used a website for tinnitus sufferers to identify the exact frequencies. I'm a musician; a colleague and I were discussing the difference in vocal quality between the two versions despite the change in pitch being fairly slight. The higher (and faster) version was the commerically released version, the lower one appears to be the pitch of the original recording 87.112.218.55 (talk) 18:43, 13 August 2015 (UTC)[reply]

There's a standard measurement for fine musical intervals, Cent (music), defined so that an octave is 1200 cents. To get the cents measurement of an interval, multiply its natural logarithm by 1731.234049 or its decimal log by 3986.313714. The interval in question is 52.7 cents, or 0.527 tempered semitone. —Tamfang (talk) 23:44, 13 August 2015 (UTC)[reply]

Thank you Tamfang, I had never heard of that before 87.112.218.55 (talk) 14:35, 14 August 2015 (UTC)[reply]

Those without perfect pitch can tune within a herz, I believe. A common practice is that tones intermix and the beat tone is discernible. It's a warble. One band member would play a C (or 440 A) and everyone would match the beat tone tone. Octave differences don't produce a beat. --DHeyward (talk) 07:11, 16 August 2015 (UTC)[reply]

Curved spacetime

How does the presence of mass curve the spacetime around it? What is the mechanism?--86.149.101.111 (talk) 16:04, 13 August 2015 (UTC)[reply]

You are referring to the rubber sheet or trampoline analogy. Spacetime is not a rubber sheet. It doesn't actually bend. The purpose of the analogy was not to express how spacetime bends. It was to show that when something warps the sheet, other things can travel in a straight line from their perspective, but move in a curve from another's perspective. 209.149.114.32 (talk) 16:20, 13 August 2015 (UTC)[reply]

In general relativity, spacetime is indeed curved. The question of how or why this happens is a good question, and we have no satisfactory answer. In general relativity, it's just an axiom that G_µν + g_µνΛ = 8πT_µν. That means that a particular representation of the curvature of spacetime (G_µν) is equal to 8π times the stress-energy tensor (8πT_µν), which includes all the mass and energy, with an additional constant term (g_µνΛ). There's no particular reason why these things should be equal, they just are. We assume that there is probably a more fundamental underlying theory of gravity, presumably some form of quantum gravity. There are various possible contenders such as string theory and loop quantum gravity. We don't know which one (if any) is correct, and they give different answers to your question. However, we suppose that there is a massless spin-2 graviton that mediates gravity in a similar way to how photons mediate the electromagnetic force. In summary, nobody knows! But we have some ideas. --Amble (talk) 17:18, 13 August 2015 (UTC)[reply]

Everyone agrees spacetime is curved especially near massive objects. Now since gravity itself can be dispensed with because it is a ficticious force (ie objects follow geodesic lines in curved spacetime), how does the mass curve the spacetime fabric?--86.149.101.111 (talk) 17:26, 13 August 2015 (UTC)[reply]

We don't know the mechanism, and GR gives no answer. Various theories of quantum gravity give different answers. Presumably it involves interactions with gravitons, but we have no experimental data to test this idea so far. --Amble (talk) 18:27, 13 August 2015 (UTC)[reply]

The issue here is the definition of the word "curved." Spacetime is not curved like a trampoline or a rubber sheet. The Earth doesn't cause everything nearby to turn into rubber and bend. Spacetime is curved in that measurements of distance and time are flexible - especially when near highly massive objects. So, when a layman asks "how is spacetime curved?" they are usually referring to the old analogy of a bowling ball on a trampoline. The main problem with the analogy is that the bowling ball is three dimensional and the trampoline is two dimensional. From our perspective with spacetime, mass is three dimensional, but spacetime is four dimensional. So, the "curve" shown in two dimensions is not how you would describe what some like to call "curve" in four dimensions. 209.149.114.32 (talk) 17:35, 13 August 2015 (UTC)[reply]

Except it is exactly a curve, or at least the 4-dimensional Minkowski space analogue of the rubber sheet analogy. The mathematics describing how a sheet curves (and how objects move in relation to that curve) in the two-dimensional sheet example scale up perfectly well (with appropriate mathematics to do so) to the 4d curvature. --Jayron 32 02:42, 14 August 2015 (UTC)[reply]

My problem is with the assumption that the curved 2-dimensional abstract example works in real space limited only to three spacial and one time dimension. The abstract is 2-dimensional, but the curve is in a third dimension. Therefore, if you scale it up to real space, there must be at least one more undetectable dimension to curve into - assuming that it only takes one. What if it takes one per every pair of dimensions? Then, you'd be at seven dimensions. How many times has someone come here and asked something like: "I saw gravity explained on TV. What makes space curve like that?" I feel the best answer is: It doesn't curve like THAT. It curves in a completely different way. 209.149.114.32 (talk) 13:43, 14 August 2015 (UTC)[reply]

But you're the only one talking about the rubber sheet analogy. --Amble (talk) 18:27, 13 August 2015 (UTC)[reply]

The definition of "curved" used here is that of Curved_space - i.e. not Euclidean. SemanticMantis (talk) 18:52, 13 August 2015 (UTC)[reply]

The rubber sheet analogy doesn't work for me anyway. We're told to take a model of the earth, place it on a rubber sheet and observe that it makes a dimple in it...then maybe we roll a ball towards it, and as the ball descends into the dimple, it accelerates towards the earth because the slope of the rubber sheet increases. But the ball only does that if there is gravity! The dimple in the sheet only forms because gravity is pulling our model earth downwards. So this analogy for how gravity works actually uses gravity...and I'm really no better off! SteveBaker (talk) 14:56, 15 August 2015 (UTC)[reply]

"All models are wrong. Some models are useful." --Jayron 32 14:59, 15 August 2015 (UTC)[reply]

The rubber sheet model is wrong as a model of general relativity. It's reasonable as a model of Newtonian gravity. The vertical dimension represents potential energy, while the horizontal dimensions represent position. The potential energy increases linearly with "height". The most familiar example of a potential energy that does that is gravity near the Earth's surface, which goes like mgh. So this is a way of visualizing a less familiar concept (gravitational motion of a test particle in vacuum) in terms of a more familiar one (a ball rolling around on a hill on Earth). The fact that both involve a kind of gravity doesn't really matter.

As a model of general relativity, it doesn't work at all. For one thing, if you invert a valley into a hill, it's the same intrinsic shape, so the shortest paths will be the same either way. If the shortest path in the valley is "attractive" (which it is) then the shortest path on the hill will be too. But a hill in the rubber-sheet analogy is "repulsive". That's correct for a Newtonian potential energy that's locally larger, instead of smaller. It's also not hard to see that if the particle's motion on the rubber sheet were shortest-path, there would be no circular orbits (nor any bounded orbits, I think). -- BenRG (talk) 01:49, 16 August 2015 (UTC)[reply]

General relativity does sort of have two parts: (1) "spacetime tells matter how to move"; (2) "matter tells spacetime how to curve". As far as I know, there is only one logically consistent way to combine (1) and (2) (plus maybe some technical requirements). In other words, the big idea (1) (Einstein's "happiest thought of my life") is enough to fix the exact way in which matter must make spacetime curve. But it took Einstein, who was pretty smart, a decade to find the correct theory, so it may still be interesting to ask what "mechanism" would allow dumb physical processes to get the right pairing. I don't know the answer, though. -- BenRG (talk) 01:49, 16 August 2015 (UTC)[reply]