Wikipedia:Reference desk/Archives/Science/2007 July 14

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July 14

A wire from head to toe moving through earth's magnetic field

When wiring moves through a magnetic field it generates electricity. Would it be practical to use this to generate a small amount of electrical energy by having a wire or loop running from ones head to ones toes, as this would pass through the earth's magnetic field as you walk about?

Could (or is) the earth's magnetic field be used in any other way to generate 'free' electrical power? I recall that radio aerials on moving ships, for example, can spontaneously get a high voltage. Thanks. 80.2.220.179 00:08, 14 July 2007 (UTC)

I'm not sure how much power you could generate that way, as the Earth's magnetic field is very weak. But in any case it would not be free: the wire would resist your movement, requiring you to expend extra energy equal to the amount of electricity generated. Of course, if you're walking for exercise then you might not mind that. --Anonymous, July 14, 2007, 00:25 (UTC).

Not only is the Earth's magnetic field very weak (30-60 microtesla), it's the change in magnetic field which induces current (as seen through Faraday's law of induction). For a rough calculation, assume you're walking north, with the horizontal component of Earth's magnetic field decreasing from 50mT to 0mT from the magnetic equator to the magnetic pole, over $10000km=1.0\times 10^{7}m$. Assume you walk at $1{\frac {m}{s}}$, and have $100$ loops of $2m^{2}$ wire. That will generate ${\mathcal {E}}=-N{d\Phi _{B} \over dt}=-100\times {\frac {dB}{dt}}\times 2m^{2}=-200m^{2}\times {\frac {dB}{dx}}{\frac {dx}{dt}}=-200m^{2}\times {\frac {5.0\times 10^{-2}T}{10^{7}m}}{\frac {1m}{1s}}=1.0\times 10^{-6}V$
In short, this would be a horrifically ineffective means of generating electricity. However, if you're patient enough, you could mount enormous loops of wire on the surface of the Earth and wait for the magnetic poles to drift, thus extracting energy from this motion (again, this would be extremely impractical). Borbrav 01:49, 14 July 2007 (UTC)

The problem with this is that you can't mount this gadget on the surface of the earth. As the earth spins, the magnetic field lines spin with it - and you spin with that. Your wire loop doesn't cross any field lines - so no electricity is generated. The idea is to put this gadget into orbit - (NOT a geosynchronous orbit) so it's crossing lots of field lines - and for it to be many kilometers long. However, I'm not convinced that there is a net gain anyway - doesn't it require some effort to push the wire loop through the field - so the craft would gradually slow down and drop out of orbit? I don't think there is a 'free lunch' here. SteveBaker 14:02, 14 July 2007 (UTC)

It is another matter if you are moving very fast, because you are the [[Space Shuttle} in orbit and have deployed a long wire (an electrodynamic tether) which stretches away from the space shuttle for a full 20 kilometres. Then, you may get a quite useful energy source. Unfortunately, the tether ripped when they tried it [1]. But I understand that NASA wants to try again. User:sanders_muc 85.127.180.47 07:58, 14 July 2007 (UTC)

If you made a magically strong wire that wouldn't break and placed it in non-geostationary orbit, it would generate electricity as a result of the Earth's magnetic field moving relative to it. It would also produce mechanical drag from the coupling and heat from the resistance. The Earth will slow down imperceptibly. Your wire will be yanked out of orbit and burn up. 76.185.61.24 (talk) 06:02, 20 October 2009 (UTC)

Does the magnetic field strength have to change? I thought it was just moving through a constant field that did it. And what about if you had wire windings attached to the soles of your feet? They move faster - twice the distance in the same time I think - than your body and are orientated differently so maybe more electricity. I was thinking of enough to generate some electricity for an electronic device of some sort rather than an electric heater. 80.0.106.3 13:48, 14 July 2007 (UTC)

It is not necessary for the magnetic field to change, or lots of generators would quit working. The wire will generate electricity proportional to the lines of flux it cuts. If it moves parallel to the lines of flux, no electricity. If it moves across the lines of flux, maximum voltage is generated. Experimenters looked into this kind of phenomena back in the era of Michael Faraday and Joseph Henry. At any location on the Earth, a compass points toward magnetic north (more correctly the North-seeking magnetic end of the compass needle points toward the Earth's South magnetic pole, which is at about 70 degrees north latitude, near the east coast of Greenland) and a Dipping needle shows the angle the lines of magnetic flux make with the horizontal. At that spot near Greenland, the flux enters the earth and the angle is vertical, so a wire connected between your feet would move perpendicular to the flux and produce a bit of electricity. At the equator the flux lines and dipping needle are about horizontal. In the northern United States, it is about 75 degrees. A wire moving transverse to this magnetic flux would thus have a potential created in it. A stationary or moving wire with a current flowing through it would experience a force, and as said previously, if current flowed from induced current, it would resist the movement. The Earth's magnetic field is about .00006 Tesla. A wire 2 meters long (assume the guy is tall) carrying one Ampere perpendicular to the Earth's magnetic field would produce a force of (1 Ampere)*(2 meters)*(.00006 Tesla)= .00012 Newtons or .00043 ounces force, which no one would notice. If you hooked a voltmeter to 2 strips of metal 2 meters apart and perpendicular to the earth's magnetic field, and arranged for your vertical wire attached to the runner to slide along them like trolley wires while he moved perpendicular to the field (perhaps moving in an east-west direction near the equator), then you could generate electricity as proposed. The induced emf would be B*l*v where B is the magnetic field, say .00006 Tesla, l is the length of the moving wire, and v is the velocity. If he moved at brisk walk, 4 miles per hour (1.8 meter/second), he would generate (.00006 Tesla)*(2 meters)*(1.8 meter/sec)=.00021 volts. If he ran at the world's record 100 meter speed of 9.77 seconds for 100 meters, or 10.23 meters/second (22.9 miles/hour), he would generate (.00006 Tesla)*(2 meters)*(10.23 meters/second)=.0012 volts. (I'm not fond of math, so feel free to check it). The amount of current and power which could be produced would depend on the resistance of the wire and connections, but would be too small to run even most small electronic devices. Now work out the details if an ice skater were doing his/her fastest spin [2] (say 308 revolutions/minute) in the same magnetic field while attached to a vertical 2 meter coil of wire. Each turn in the coil would generate the same voltage, which is what(ignoring that the coil would slow them down)? Edison 17:18, 14 July 2007 (UTC)

Rafting ants... why?

Ants rafting in a pool

Why on earth are all these ants "rafting" in a pool? Is this "normal" behavior and they purposely sought out water to raft in en masse, or is it unintentional, like a large number of ants blew into the pool and are simply clinging to one another or anything they can to stay afloat? Sifaka ^talk 06:02, 14 July 2007 (UTC)

I'd assume a serious lack of chlorine... --L^augh! 09:01, 14 July 2007 (UTC)

It's a natural behavior for river crossing - but it seems doubtful that they "decided" to cross your pool that way. An ant colony works by the sum of thousands of tiny (almost mindless) behaviors. If an ant falls into water, it probably has some kind of instinct to paddle to another ant and cling onto it. If a significant number of ants end up in the water - they'll just 'naturally' form a raft to cross that water. Sadly, these kinds of behaviors don't always work - especially in an unnatural environment like a swimming pool. SteveBaker 13:56, 14 July 2007 (UTC)

What's the name of this space telescope?

I remember reading or seeing on TV, a space telescope that is a cluster of satelite telescopes, joined using interferometry. It's supposed to have jawdropping resolution compared to existing telescopes. I have no idea if it was a definite plan or a theoretical one, but I'm fairly certain it had a name. Does anyone here know what that telescope was called?

Apparently, it will be called the Space Interferometry Mission. Clarityfiend 08:22, 14 July 2007 (UTC)

Might also have been the Terrestrial Planet Finder. Both programs have been just about axed, unfortunately. But there's always the very low-cost alternative New Worlds Imager program. — RJH (talk) 18:05, 15 July 2007 (UTC)

Satellite dish

Why is the satellite antenna shaped like a dish?

The "dish" part isn't actually the antenna; the antenna part is the little part that hangs in front of the dish. The "dish" part is a (typically) parabolic reflector. It acts like a mirror to take an incoming signal that's the size of the dish, and reflect it an focus the whole thing down to a small spot that's the size of the (small) antenna part. You may recall old-style home-TV satellite dishes that were 6-8' across, with a little "tube" held in the middle. They would grab 6-8' worth of incoming radio-waves (which travel in a line from the satellite much like invisible "light"), and reflect and focus it onto that little 2-3" tube, which was the actual antenna part. In this way, a relatively weak signal could be magnified, in much the same way that you magnify (or "focus") energy when you use a (say, 6") magnifying glass to focus 6" worth of light into a tiny little dot.

You know how the dot seems really hot? That's because you've put 6" worth of sunlight into 1/4" of space, compressing it greatly. The higher quality the magnifying glass, the more "dark space" you'll see around your dot, because it focuses ALL of the light that hits the lens, with little "slop." In this way, "regular-old weak" sunlight can be made to seem "very powerful", by the focusing.

Same thing with the satellite signal. A relatively "weak" signal can be made to seem "more powerful" by focusing it. The dish is like the magnifying glass, except it's turned the other way because it's also a mirror.

Trick you can do with a flexible mirror (i.e., a strip of that mirrored plexiglass stuff): face the Sun and reflect a mirror sized spot on the ground. Now flex the plexi-mirror so that rather than a mirror-shaped patch of sunlight, you make a teeny-tiny little line (or dot, depending on how you deform the plexi.) The curvature you make when the line/dot is near-perfect in its small&round-ness is the shape of a satellite dish.

Hope that helps! 4.246.42.103 07:37, 14 July 2007 (UTC)

Satellite dishes are actually shaped like a paraboloid, which is generated by rotating a parabola around its axis of symmetry. A parabola is a geometric figure you can create mathematically (for example, by graphing the function y=x^2). The special characteristic of the paraboloid is that all light rays that travel parallel to the axis of symmetry are reflected to the same point. This allows us to focus a large amount of electromagnetic waves to a small detector, mounted at the specific point where the reflected waves converge. --Waldsen 19:56, 14 July 2007 (UTC)

You can just about see the 'squarial' on the wall of this house

It doesn't actually have to be dish-shaped. The BSB system in the UK used a flat, square plate called a 'Squarial'. SteveBaker 01:02, 15 July 2007 (UTC)

Need details about heat-transfer for simplified weather-sim

The first answer given below satisfies the initial question. The text is left as background for the followup question, below.

Short: I'm looking to find details on how energy (heat) is absorbed and released by various materials to do a simplified weather simulation.

Details: I've checked several articles -- for example, <http://en.wikipedia.org/wiki/Specific_heat_capacity> gives a lot of information that is "close" to what I need. The part I'm missing is how to put all the various numbers and coeficients together.

I'm trying to code a simple wx-sim for a game. It does not need to be "exact" like a full-Earth sim, but I'm trying to understand what bits WOULD need to go into a full-Earth sim, so that I can understand how to simplify it and get my "close enough for the game" sim. I'm trying to avoid "pre-programmed" weather, and end up with some realistic-seeming emergent behaviours.

I've got heat coefficients for various materials, latent-heat-of-fusion numbers (i.e., ~80kC/L for water), Solar energy (i.e., 1500-2500kWhr/M^3/yr), etc. So now the part that I'm stuck on is:

If I have a brick (let's say) that's 1cubic-meter, and it's at 20°C (let's say), and I apply 100kW of energy to it for an hour (total energy applied = 100kWhr) -- how does its temperature change over time?

Follow up: now that my brick (or tub of water, or block of salt or whatever) is warmed-up, if I turn off the energy input, and just leave it in a 20°C (dark) room, how does it cool back down, over time?

What are the factors that go into that, and how does the "changes over time" part work?

More fun example (from an apocraphal anecdote which might be familiar): If I have a 5lb roast at 65°F and I want to get it to a uniform 140°F how much energy to I have to put into it? <G> (Assume that roast is mostly-water.)

I think I sort-of get the bit about <substance> + <energy> = rise-in-temp, but I don't get the "temp changes throughout the volume of the substance, over time" part. I guess "conductivity" is in there, somewhere (let's assume that my brick/roast/tub-of-water has no circulation, for the time being. I'll deal with circulation, later.)

Thanks 4.246.42.103 07:26, 14 July 2007 (UTC)

Newton's law of cooling is an excellent first-order equation describing simple heat transfer (so it's suitable for quick programming and fast run-time!). It may be suitable for a "somewhat realistic" simulation, but it will not take into account things like convection, air mass motion, and non-ideal behavior. Nimur 15:30, 14 July 2007 (UTC)

Follow-up question.

Yes, that link (and ones from it) gave me exactly what I was looking for, thank you! I now have a tangential follow-up.

Short: What's the name of the property of a material which relates to how it radiates-out heat? (And where can I find a list of said property for common materials?)

Detail: In this question, we completely ignore both conductivity and circulation -- I'm asking ONLY about radiation. Suppose I have a substance -- say an asteroid in space. It is being radiated by a source, say sunlight. To simplify, let's call the incoming radiation constant and the rock made of homogenous material. At first, my rock heats up with the incoming radiation. After a while, though, it stabalizes, and radiates-out exactly as much energy as is radiated into it. What is that property called? That is: I want to read-up on that property for various substances, so that my Wx-Sim (see above) can properly account for "soaked-up as much radiation as it can, will now begin radiating-out" of water, bricks, etc. So what's the thing I want to read about called?

Color? Nimur 19:32, 14 July 2007 (UTC)

No, color is more related to an object's albedo. I'm talking more about something's "radiation temperature" or some-such. I guess it's related to "color", except that the color can fall way out of the visible light spectrum and is not the every-day use of the word. I'm looking for "how much energy does a brick heated to 150°C radiate?", and color is more like "what wavelengths of white light does a brick reflect?" Except that I'm looking for "how can I calculate the radiated-out energy for a variety of common substances at a variety of Earthly temperatures?" I suspect that, once I find the answer it will be of the form:

* There is some forumla x=yz^k (or whatever) where x=kWatts, y=time and z=size of object.

* The value for constant k for water is 1, brick is 3.2, air is 0.5, wood is 1.1, etc.

"Or something like that." Btw, you (Nimur) seem to know this stuff pretty well, is there a way I can contact you off-wiki? I guess email-posting is discouraged due to spamming -- is there another mechanism? (I suppose I need to create a new account -- I forgot my old password and have no email on file.) Thanks! 67.72.98.25 19:55, 14 July 2007 (UTC)

There's really no reason; use my talk page, (I can respond there faster than I can respond to email anyway). Nimur 17:52, 15 July 2007 (UTC)

Ok, I'm getting closer. I think the thing I'm asking about is Black_body#Equations_governing_black_bodies. I haven't yet found different values for different substances, but maybe I'm about to learn that it's the same for every substance, and the difference is how it absorbs/conducts heat such that the volume changes temperature. Thanks again! (Oh, and I figured out my account :)) Oliepedia 20:17, 14 July 2007 (UTC)

The black-body approximation is the idealization that is independent of materials. (Hence, "black body"). Other materials have non-black-body radiation patterns, but as a first-pass approximation, you can assume that it is a perfect absorber and perfect radiator. The color of an object determines how well it absorbs / reflects at a given set of frequencies (namely the visible spectrum). An abstract generalization of color would be the frequency absorption for any arbitrary frequency of radiant energy. Nimur 00:06, 15 July 2007 (UTC)

The exact quantity you are looking for is emissivity. It's not really analogous to color, because emissivity applies to conditions of thermal equilibrium, but color doesn't. Objects which are strongly colored at room temperature can look quite different when heated - they become "red hot" or even "white hot". Unfortunately, emissivity is itself a function of wavelength, depending on the material, and also the surface shape and texture. Tungsten has an emissivity which is somewhat less than one, which is why a tungsten filament bulb has a color temperature which is different to its real temperature. --Prophys 08:59, 15 July 2007 (UTC)

Levers

If a load 40g that is 6cm away from the fulcrum is balanced by another load 8g that is (a)cm away from the fulcrum, what is (a)cm?

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It's quite easily solved knowing the moment arm formula. Someguy1221 09:47, 14 July 2007 (UTC)

Faster than light travel

iam just an artist.i believe it is possible that a human can travel faster than the speed of light. Simply by thinking of their arrival, at the destination, before the time it takes light to arrive there?Vonvilhelm 08:31, 14 July 2007 (UTC)

Nope, can't travel faster than light. Someguy1221 09:47, 14 July 2007 (UTC)

It's fine to imagine that - but unless you have some actual proof that you can do it - it's just that...imagination. It would great if that were true - teleportation by power of thought at infinite speed would be about the most liberating thing imaginable (insanely dangerous too! Accidentally thinking of arriving on the moon would result in immediate, explosive decompression...not good!). But this kind of wishful thinking is a cause of a lot of pseudo-science and it's crucial to separate out things that you wish were true from things that actually are true because madness (of the Time Cube variety) lies in the other direction. But sadly - it's conclusively, (mathematically) proven that nothing can go faster than "the speed of light in vacuum" - it's not just that we don't know of a way to go faster than light - it's that we've shown that such a way cannot possibly exist. For those of us who would dearly love for humanity to spread through the galaxy - colonise the stars, this is a desperately disappointing fact. Typically when something is proven as convincingly as relativity, scientists accept it and move on - but this restriction is SO frustrating that enormous scientific efforts have gone into trying to find a loophole in that law - but despite the best efforts of many great minds - as yet nothing convincing has been found. SteveBaker 13:43, 14 July 2007 (UTC)

To put one more nail in the coffin, numerous tests of general relativity verify experimentally that the mathematics is pretty solid. In simple terms, First, they thought about faster-than-light travel, and couldn't think of a way it could possibly work. Then, they tested it, and it didn't work. This sequence of steps is pretty much what makes science different from art. Scientists must check their work with verifiable, repeatable experiment. Nimur 15:34, 14 July 2007 (UTC)

That said, the remaining semi-plausible method for very long-distance travel is (as far as I understand) wormholes, although whether these exist or could be made viable for travel is not known by any means. These get round the problem of faster-than-light travel by taking a "short-cut" that does not go through space: imagine going from one side of an apple to the other; if you could cut through it you would seem to be going very fast to those who could only go around the side. Daniel (‽) 16:24, 14 July 2007 (UTC)

Well yes. I can bounce a laser beam off the moon to a spot one meter away from the laser source. I have 2.4 seconds to move that one meter to beat the laser there. I can move faster than light! :D. Capuchin 16:29, 14 July 2007 (UTC)

At best, it's hypothetical. My assessment is that wormholes are a clever science-fiction workaround to the problem of interstellar travel. Nimur 16:27, 14 July 2007 (UTC)

Yes - I agree. Science says that IF a wormhole existed THEN you could use it as a shortcut. It wouldn't let you travel faster than light (because that's STILL impossible) - it just gives you a shortcut that lets you travel a shorter distance. But the only way anyone can envisage a wormhole existing is by mucking about with black holes...this is all very well - but to 'cross' the wormhole would entail flying into the event horizon of a spinning (and possibly electrically charged) black hole - with all of the annoying gamma/Xray irradiation problems, the oh-so-painful spaghettification and that annoying relativity thing that would make everyone else think you're taking an infinite amount of time to reach the wormhole. Not all that practical...and probably impossible. SteveBaker 00:24, 15 July 2007 (UTC)

"...pretty much what makes science different from art..." What a condescending statement about art, and an idealistic statement about science (and a statement which speaks volumes of someone's ignorance about the ways in which science and art have been intertwined for centuries). If I recall much of what is hot in theoretical physics today is totally unverifiable by experiment, and in fact in the history of theoretical physics a great deal of it was done without the slightest collaboration with experimentalists.

To answer it is non-condescending terms: the current model of how the universe works does not seem to allow for faster than light travel. This is not an arbitrary speed-limit set, but is reflective of the fact that space and time are linked in a very deep way, and the speed of light happens to be something reflective of the barrier between them (moving through space faster than light ends up with wonky time problems — events ending before they start, etc.). Our current equations for how things move at sub-light speeds basically preclude any possibility of going faster than light — if you substitute a speed faster than light into a Lorentz contraction, for example, you end up with a nonsensical equation (you end up having to take a square root of a negative number, which ends up with an imaginary number). In addition to this, the equations also tell us that attempting to get to the speed of light requires using an infinite amount of energy — which doesn't exist, and we can't get even close to that amount.

So basically the universe as we know it is divided, speed-wise, into light, things going slower than light, and hypothetical entities which are faster than light, but cannot ever slow down. The equations have so far behaved extremely well experimentally and make a lot of logical sense as well, when you start to take them apart (they are based in relatively common-sense reasoning about the nature of space and time — Einstein's axiomatic approach is generally quite clear and quite straightforward).

All of that being said — could the equations be wrong? Sure. Nothing is more assured in science than the eventual destruction of old understandings (generally known as "progress"). Would any new understandings allow for faster than light travel by humans? Probably not — any new replacement theory would not likely change the way these things operate on scales that we could appreciate much less exploit for practical purposes. (But who knows. The idea of splitting something as massive as a uranium nucleus with something as paltry as a neutron seemed nonsensical even to those who originally proposed it. How quickly we forget how amazing some ideas once were.) --24.147.86.187 17:41, 14 July 2007 (UTC)

Firstly, it's OK to be condescending about some things - all of the politically correct bullshit about having to "respect the ideas of others" is not something I care to deal with - respect has to be earned. The 'intertwining' of art and science is WAY overrated. However, having said that, I do have a lot of respect for art and artists - just so long as they don't start trying to claim that what they have thought up out of thin air and without any evidence is somehow "real". I'm a huge SciFi book fan - they force you to stretch your mind and make you think out of the box. In my imagination - faster then light travel is not only possible - but routine. But a scientist can separate out what is imagination from what is proven. So by all means imagine what it would be like to be able to travel faster than light just by thinking about it - feel free to write great fiction, paint pictures, make sculpture - but please don't start believing it has applicability to the real world. At that point you cross the line between art and reality - and reality demands science and science is just unbelievably tedious and boring about the whole faster-than-light thing. I hate that as much as anyone - it completely sucks - but I hope I'm mature enough to accept it and relegate faster-than-light travel to the unlimited realms of my imagination. This particular imaginative leap had that kind of artistic value. It got me thinking...if it were true - what would it be like? Would I have to be very careful not to look up at the moon and wonder what it's like up there in order to avoid being teleported there and dying a horrible death? Would using this trick to get to work quickly require me to take into account the motion of the earth around the sun in order to avoid arriving where my office was a fraction of a second before and ending up underground? Would my clothes somehow 'know' to come with me when I travelled? What about my stomach contents? If I can travel faster than light then time travel is also real...what does THAT mean?!? So many mind-twisting things to think about...but that doesn't make it real...interesting...but never real. SteveBaker 00:24, 15 July 2007 (UTC)

Could Einsteins equations be wrong? Yes - of course. But they are amongst the best tested of anything we have in science - we've measured time-dilation directly using atomic clocks put on board planes. We've seen the subtle shift in frequency of radio waves coming from deep space probes - we've got photographs of gravitational lensing - the observations of the transit of Venus...utterly concinging. Everything we try at every extreme we can manage works 100% as Einstein said. If there is something wrong with those equations - it's very, very subtle indeed (and it's probably only at the level of Quantum theory that won't help us big, chunky humans much). SteveBaker 00:24, 15 July 2007 (UTC)

I stand by my assertion that art is not bound by the constraints of experimental verifiability. I don't see this as condescending. It's a statement about the different realms in which science and art operate. Artists are rarely asked to "prove" that their art is worthy. This opens up entire avenues for art to explore. Scientists must regularly prove their work has experimental verifiability. Even the "theoreticians" must be held accountable to experimental evidence eventually, or else they are categorically labeled mathematicians, philosophers, or at worst, crank scientists. Nimur 17:54, 14 July 2007 (UTC)

SteveBaker said But sadly - it's conclusively, (mathematically) proven that nothing can go faster than "the speed of light in vacuum" - it's not just that we don't know of a way to go faster than light - it's that we've shown that such a way cannot possibly exist. Actually, I believe that what we've shown isn't possible is for anything to travel AT the speed of light (results in the equivalent of a divide-by-zero in the Lorentz transformation.) Indeed, the big mystery of tachyons is that they appear to travel faster than light and to move backward in time. 67.72.98.25 19:33, 14 July 2007 (UTC)

You say that in a way that makes it sound like tachyons actually exist - for which there is zero evidence - and a very strong reason why they might not. The divide-by-zero problem in the Lorentz transforms doesn't prevent things from travelling at the speed of light (because the photons in a beam of light do exactly that...duh!) - it prevents things that travel at that speed from having non-zero rest-mass or length...which photons do not. Mathematics doesn't disallow dividing by zero - it merely says that the result is undefined. Dividing by zero happens all the time - and it's OK so long as the result is then multiplied by zero so that the undefinedness doesn't show up in the result. Hence zero rest mass and zero lenght for photons.

However, when you plug in v²>c² into the Lorentz transform, you have to take the square root of a negative number - and that results in an imaginary number - which is a big problem. Imaginary numbers are often handy mathematical tricks for getting around notational difficulties - but they never, ever show up in the results of correct calculations. They always get squared again at some later point in the calculations so they disappear again in the results. There is not one single case in all of math and physics where an imaginary number popped out into the "real" world. However, for a tachyon to exist, something imaginary (in the mathematical sense) would have to actually exist in the real world - and that seems impossible. If it were true then imaginary numbers would start popping up all over the place and we'd surely have noticed that in some way.

Scientists use the term tachyon as a convenient hypothetical when discussing theories (we use the term 'tardyon' for all particles that travel slower than light) - but theories that require the existance of these peculiar beasts are generally severely wounded in their credibility because of that. It's like "Oh oh...your theory of quark-meson-wibbloscity implies the existance of a tachyon"..."Oh - crap, you're right. Maybe I'd better try something else.". But even if tachyons did exist, they don't help our questioner. Just as regular tardyon matter can't be accellerated up to the speed of light without using an infinite amount of energy - so a hypothetical tachyon would require infinite energy to be slowed down to the speed of light and it's imaginary mass & length would make it impossible for it to travel slower than light. So it's not possible for tachyone to become tardyons and vice versa. So even if tachyons did exist - they would be of no help whatever to a human wishing to travel faster than light. We can't somehow magically transform ourselves into tachyons - travel to our destination - then change back again because tachyons can't slow down enough.

I blame Star Trek for the popular idea that tachyons are real - they use the word all the time when they need something to shoot at an 'interstellar anomaly' (a wibbly-wobbly green thing that's up there in the forward view screen). SteveBaker 23:55, 14 July 2007 (UTC)

I just want to step on your "Mathematics doesn't disallow dividing by zero - it merely says that the result is undefined. Dividing by zero happens all the time - and it's OK so long as the result is then multiplied by zero so that the undefinedness doesn't show up in the result." An undefined number, multiplied by zero, remains undefined. The rigorous way to absolve this issue is to create an expression for the final, desirable value (mass, length, whathaveyou) such that the limit as the speed approaches the speed of light does not display any undefinedness (if that's a word), if i recall my math correctly. Someguy1221 00:15, 15 July 2007 (UTC)

I disagree. The slope of a ladder is conveniently represented by the height it reaches up the wall divided by the distance from the bottom of the ladder to the base of the wall. If I push the ladder parallel to the wall, the slope is the length of the ladder divided by zero...damn! However, if I wish to use the slope to calculate the frictional forces required to stop the ladder from slipping - the horizontal component of that force ends up being proportional to zero multiplied by the slope of the ladder - which is undefined. Fortunately anything times zero is zero - so we're good to go with a zero as the result...which is correct. Sadly, this is not true for the vertical component of the force where the top of the ladder meets the wall because we have something non-zero multiplied by an undefined number - but that's OK - with the top of the ladder only just barely touching the wall, the vertical friction is indeed a meaningless concept. Math works - often despite the mathematicians. SteveBaker 00:37, 15 July 2007 (UTC)

And as far as my own purposes go, I do agree with you. But given my plentiful interaction with one or more mathematicians, do expect one to slap you if you suggest that zero multiplied by an undefined number is always zero. Even though ultra-strict mathematical formalism is often unnecessary in physics. Someguy1221 01:36, 15 July 2007 (UTC)

SteveBaker's assertions are pretty valid. Indeed, complex numbers are useful abstractions, but observable physical quantities (conveniently called "reality", but also very well-defined in theoretical physics) do not have imaginary components. Nimur 00:23, 15 July 2007 (UTC)

In no particular order: (1) There are useful contexts in which it is meaningful to divide by zero -- see Riemann sphere. (2) Whether it's well-defined to multiply an ill-defined quantity by zero, again, depends. Usually not. But there are situations where you get away with it, and Steve may well have identified one. (3) The claim that it has been "mathematically proven" that nothing can go faster than light is completely wrong. That is not the sort of thing even subject to mathematical proof. --Trovatore 08:41, 16 July 2007 (UTC)

But here's a thought experiment. Imaginary numbers are often used to express frequency domain phenomena to time-domain creatures as ourselves. But wouldn't photon be more of a frequency domain creature and see our world as imaginary anomaly? Also, the energy barrier to exceeding the speed of light is infinite as we know it. But my own feeling is that nature abhors the infinite and that the physical model will break down before that at some point and another theory will be needed. Just a guess but like the elegant laws of Newton, so to will elegant laws of the theory of relativity, need to enhanced. --Tbeatty 05:46, 17 July 2007 (UTC)

Alternative To Evolution

Are there any alternatives to evolution by natural selection that are supported by scientific evidence? The article on evolution says that it is "completely uncontested in the scientific literature" and i was wondering wether this is strictly true Fountainmon

No - that's truly the only theory that's accepted to any degree whatever. There are small variations on the details - for exmple, whether evolution is a continual process of gradual change or whether species stay stable for long periods then evolve relatively quickly as a result of a sudden change - but there is no significant argument about the core principles. Historically, Lysenkoism was an alternative theory - it held that (for example) Giraffes were originally a lot like horses - but as they had to reach up into trees to get food, the necks of living animals would be slightly stretched by doing that activity (just as you can getter at lifting weights by doing that exercise) - and that the offspring of that animal would inherit that slight neck stretch. Hence - kindof like evolution - giraffes would get longer and longer necks as generations passed. As an idea, it's not bad - and it's a lot like evolution - the only problem is that we have no mechanism to explain the inheritance of an aquired-by-exercise ability. We can look at the genes of an animal at birth and again when it reproduces and there are no changes. So that theory was heavily pushed and taught in Russia. But the idea has been conclusively disproved. SteveBaker 13:28, 14 July 2007 (UTC)

You seem to be confusing Lysenko and Lamarck. Eran of Arcadia 16:36, 19 July 2007 (UTC)

Well, in addition to "evolution by natural selection" there's "evolution by sexual selection", but that's not so much an alternative as an additional mechanism. "Completely uncontested in the scientific literature" seems quite proper. - Nunh-huh 14:34, 14 July 2007 (UTC)

Maybe you need a concise definition of natural selection - this will help you see that it is self-evident. Things that die off more often don't stay around for long. Organisms that can live better tend to stick around more often. They have been "selected" naturally. How could it possibly work any other way? Unless... there were an intelligent designer who is super-naturally selecting unfit species who would normally die without some kind of interference? Nimur 15:38, 14 July 2007 (UTC)

Well, the non-self-evident part is that selective pressures are enough to constitute species change. The question never was whether there was truly a "survival of the fittest," just whether that actually accounted for evolution. (And evidence as to how non-self-evident that is can be found in the fact that even after Darwin proposed it, most scientists didn't think natural selection could actually account for evolution until the 1930s!!) --24.147.86.187 16:10, 14 July 2007 (UTC)

You are probably confusing evolution and speciation - related but different concepts. In any case, scientific consensus is that natural selection and genetic variation are sufficient to cause speciation. The speciation article contains many references including this list of observed instances of speciation. Nimur

Well, I'm not confusing them, but that is almost certainly what the poster meant when they said "evolution", and it is what most non-biologists mean. The modern synthesis definition of "evolution" is practically tautological and is not at all what people (including Darwin) meant by "evolution". In any case I am not arguing against natural selection in any way; I am just arguing that it is all as "self-evident" as you'd make it out to be. It's not — which is why it took a long, long time to get to the current theory of it, and why a lot of very smart and very capable people were long opposed to natural selection as the force behind evolution. --24.147.86.187 17:25, 14 July 2007 (UTC)

There are a few scientists who disagreed that natural selection could cause speciation in the long term. Another detail I guess, but already mentioned above. See punctuated equilibrium. Someguy1221 19:10, 14 July 2007 (UTC)

Somethign that I couldnt find with a quick google.

You hear often hear that the tap water you drink has passed through half a dozen (or more/less) people before you. I have no problems believing that but i'd love a scientific source if you can find one? Does it differ for different countries? Capuchin 16:14, 14 July 2007 (UTC)

Half a dozen? Try hundreds. Think about it- you drink five glasses of water. You urinate most of that back out, be it into a toilet, where it is taken to a waste treatment plant, or behind a bush, where it filters through the earth, and eventually joins an underground water source, where it flows out to ponds/oceans where it becomes rain, which falls to earth, etc. Given the Water cycle, it's entirely possible that the water you drink used to be Napoleon's bath water, or part of a soup from some obscure village eons ago. --L^augh! 16:56, 14 July 2007 (UTC)

And of course, the water ends up being thoroughly mixed in the pipes and lakes, so it's not just one bit of water but a great mixture; I remember going to a chemistry lecture where the speaker stated that in a cup of water, every person on the planet, alive and historical, had drunk and passed at least a few of the molecules in the glass (1 tablespoon of water contains about 6 hundred thousand million million million water molecules, so it's not surprising really!). Laïka 17:17, 14 July 2007 (UTC)

Well, the second law of thermodynamics basically implies that you'll never get much of any given bit of water that anybody has previously drunk or used, and the oceans are incredibly vast. So I don't think you can at all say with certainty that a molecule of Napoleon's bathwater is in any given small amount of water. The odds of getting any individual molecule of water are incomparably small, though the odds of getting some molecule of water that was used in the long past are quite high. --24.147.86.187 17:21, 14 July 2007 (UTC)

I seem to recall the lecture addressing this by saying that the oceans contained approximately the same number of litres of water as the bottle contained water molecules, so if you took a one litre sample of water, there should be on average one water molecule in the litre sample for every litre of the original water product; a bathtub contains maybe 100 litres, Napoleon must have had hundreds of baths over his lifetime, so the bottle might contain up to 10000 water molecules from Napolean's bathtub - not much, but still... Laïka 17:29, 14 July 2007 (UTC)

A very similar calculation to the famous "odds of breathing in a molecule of air from Julius Caesar's Et tu Brutus" problem. Conclusion: you don't want to think about how many people your water has passed through. — Laura Scudder ☎ 17:45, 14 July 2007 (UTC)

There is a fallacy in assuming a totally random redistribution of all water-molecules. It would be ridiculously complicated to try to track a single molecule through multiple iterations of the water cycle, but it would be worthwhile to estimate the statistical time-distance propagation constant (i.e. a molecule travels X miles in one week through evaporation, rain, ocean currents... etc). I bet it's fairly localized; if ocean waves are anything to compare, the net propagation of energy does not require mass movement of individual fluid components... but current and wave motion are not identical. (Rivers are a good counter-example, of course). Nimur 17:50, 14 July 2007 (UTC)

Oceanic mixing time is long (i.e. ~2000 years), but atmospheric mixing is rapid (e.g. months). A gentle breeze (e.g. 10 miles per hour) can carry molecules 1700 miles in a week. Dragons flight 17:57, 14 July 2007 (UTC)

Yes of course, by direct multiplication... but does a single molecule travel all 1700 miles? Brownian motion, convection, and other considerations might yield a very complicated and statistical answer. Nimur 18:33, 14 July 2007 (UTC)

Wind is direct mass transfer, so yes the statistical average particle in a 10 mph breeze is advancing at 10 mph. Dragons flight 20:01, 14 July 2007 (UTC)

I would like to add that we can see it happen with large volcanic eruptions as the ash and sulphates disperse globally over a period of months. Dragons flight 20:02, 14 July 2007 (UTC)

In truth, we can't know whether a particular volume of water does or does not contain water that was drunk/bathed in/whatever by someone else in the past. So any definite statement is going to be false a lot of the time and true other times. It is safe to say that if you go far enough into the past (eg Julius Ceasar's bathwater) then it's more likely to be true than for (say) President Nixon's pee-pee! If mixing were essentially perfect then it's true that every day you'd definitely be drinking a few molecules of everyone who ever lived. If mixing is imperfect then it's likely that the water you are drinking has never passed through any other human in history. If you dug down a few thousand feet under the Antarctic ice, grabbed a cupfull of the stuff - melted it and drank it - then I think it's safe to say that no other humans drank it before. If you took a cupful of water from the municipal water supply of a large city - then it's certain that many other humans will have processed much of that water through their bodies before. The truth lies between those extremes - but it's impossible to say where. The adage has value in that it rams home the point that there are a truly insane number of molecules in a glass of water! SteveBaker 23:27, 14 July 2007 (UTC)

Is it worth pointing out that there is no distinguishable difference between one molecule of pristine Antarctic ice meltwater, and one molecule of undiluted Napoleon pee water? --Prophys 09:11, 15 July 2007 (UTC)

Of course that's true - but does it matter? We are interested in the history of those molecules - not whether they are different in any way. SteveBaker 18:49, 15 July 2007 (UTC)

By certain definitions they are the same molecule if they are exactly the same in every way except location. Also, photosynthesis involves breaking up water molecules and reforming them. I don't know how big the effect is, but it could make it improbable that all the atoms in any molecule in your volume of water were in one of Napoleon's water, and it would be even more improbable that they were still in the same molecule. Electrons exchange atoms even more than atoms exchange molecules. — Daniel 03:02, 16 July 2007 (UTC)

Ants

Ants have queens. Do they ever have coups?

There's more to being queen ant than just leading the nest and getting lots of food; queens are made at birth by being fed special food, allowing the queen to develop wings and lay eggs. Normal ants are not given this food, and as a result, they can never lay eggs. If a nest of ants ever managed to get rid of their queen, they'd be stuck - no new ants could be born and the colony would die out. Laïka 18:19, 14 July 2007 (UTC)

Queen ant says that there can be more than one queen in a colony, depending on the species. It doesn't say if they all breed or only one does and the rest are spares. Clarityfiend 20:12, 14 July 2007 (UTC)

Make sure you don't take the political metaphor too seriously... it is a metaphor only, and as such only certain parts of the source domain apply to the destination domain (they don't wear little crowns either, or get their portraits done by Annie Leibowitz). --24.147.86.187 21:50, 14 July 2007 (UTC)

Maybe not in ants, but in stingless bees there are upstarts called dwarf queens. Bendž|Ť 22:59, 15 July 2007 (UTC)

240 V 50/60 Hz

On reading Domestic AC power plugs and sockets, I see that some parts of the world use 240 volts at 50 Hz, while others use 240 volts at 60 Hz. What would happen if you supplied something expecting a different frequency (e.g. 60 Hz on something that wants 50 Hz)? Nothing? Boom? --Tim1988 ^talk 18:23, 14 July 2007 (UTC)

Probably very little; most systems with sensitive electronics use a power supply and convert the AC to DC. Those converters often use a filling (or holding) capacitor, and since 50 and 60 Hz are fairly close anyway, the capacitor will effectively convert to DC. A few AC items such as motors might possibly be sensitive to the frequency deviation, so you should check tolerances for particular devices. Nimur 18:31, 14 July 2007 (UTC)

Nimur is right "in general" however, you probably don't want to risk your electric devices by plugging them into the wrong source. Basically, you'll run into an inefficiency which can lead to heat which can either ruin the device or, in extreme cases, lead to a fire. While technically possible, it's highly unlikely that anything would "explode" ("boom") unless you happen to be on the set of a Hollywood movie ;)

Imagine that there is a vending machine with a candybar behind a door, and the door opens and closes 60x/minute. You have a mechanical arm that you can extend on the 50ths of a second (up to 50x/sec). You want to grab the candy bar. You can see how, while it can be done, you'd be "fighting against your tools", right? Now imagine that, instead of a whole candy bar, there was a teeny-tiny crumb of a bar that, once you had all 10,000 of them, you could assemble them into a whole bar & eat. Door opens & closes 60x/sec, your grabber-arm is on the 50ths, you need to do this 10,000 times.

Very-abstractly, that's what it's like when you plug your 60hz electric razor into a 50hz outlet. It's not so much that you'll "break everything", as that you're putting undue stress on it, making it over heat, aging it beyond its years, etc. So a razor that might normally last 3 yrs might wear out after 3 months or weeks.

(Lost my password, and no email on file. I guess I just create a new account...?) 67.72.98.25 18:48, 14 July 2007 (UTC)

Always check your electrical devices or their power adapters, or their manuals thereof, for their tolerances for electrical input before plugging into a foreign outlet. Someguy1221 19:16, 14 July 2007 (UTC)

Incidently a friend of mine plugged his 50 hz alarm clock into a 60 hz system and the time was screwed up. That might only depend on how this specific clock determined time. As well, our building has elevator motors that are wound for a 50 hz system, but are used at 60 hz, and they apparently produce more heat than designed for because of that - this is according to the elevator tech. Flyguy649 ^talk _contribs 21:28, 14 July 2007 (UTC)

Yes, many alarm clocks use the frequency of the AC as signal to determine time. Because of this power providers are actually required to maintain 60 Hz to a rather high tolerance over the long term. During times of peak demand, the generators may slow down a little due to high load, so you might get 58 Hz for a while, but if this happens the operators are required to spin them up to 62 Hz (etc.) to catch up later in the day so that clocks run right. Dragons flight 21:35, 14 July 2007 (UTC)

I would like to award User:67.72.98.25 the Official Wikipedia platinum plated platic spork award for the most confusing and useless answer in the history of the help desk! WHAT?!?! Most (but not all) 60Hz devices work perfectly at 50Hz (and vice-versa) because the manufacturers want to sell them in markets where they other frequency is standard without having to redesign them. However, you can't rely on this and some products won't work, others will get outrageously hot, and yet others will burn out or catch fire. There is really no way to tell which are which. Being a Brit (240V, 50Hz) who lives in the USA (120V, 60Hz), I have a bunch of gizmos that purport to convert one into the other - but as far as I can tell, they all convert the voltage without changing the frequency. My UK CamCorder charger works fine when plugged into one of these things - my Laptop charger has a 110/220v switch - but not a Hz conversion - and it works just fine. An antique table lamp works - no problems. But the UK charger for my son's R/C car overheated to the point where it burned my finger when I touched it here in the USA on 60Hz/220V and our US cellphone charger didn't charge the cellphone battery at all on 50Hz/110V in the UK. So "your milage may vary". Good luck with that! SteveBaker 23:14, 14 July 2007 (UTC)

Okay, here's how I'd divide things:

• Most purely-electronic things that work on 50 Hz (and don't use the line frequency for timing as many clocks do) will work fine on 60 Hz but the reverse isn't necessarily true.
• Transformers designed for 50 Hz will work fine on 60 Hz, but a transformer designed solely for 60 Hz will may over-heat when operated on 50 Hz.
• In power supply units, bulk-storage capacitors designed for 50 Hz will work fine on 60 Hz, but capacitors sized solely for 60 Hz will be sized too small when operated on 50 Hz and the power supply unit will have too much ripple in its output.
• AC induction and synchronous electric motors operated on the wrong frequency will turn at the wrong speed. 60 Hz motors operated on 50 Hz may overheat.
• AC universal motors will work fine.
• DC motors will work fine if their power supply units work okay.

Nowadays, because manufacturers usually like to be able to ship world-wide, many things are truly universal (100-240 VAC, 50-60 Hz), but the ratings on the manufacturer's nameplate is the best final arbiter of what will work and what will cause the release of the magic smoke.

Atlant 00:38, 15 July 2007 (UTC)

Very good! No platinum-plated spork for you then! One VERY minor quibble. A 60Hz transformer running on 50Hz will certainly get hotter than it would on 50Hz - but whether that is over-heating is not so certain. It may be able to dissipate that heat without problems - in which case it may merely get warm. SteveBaker 00:53, 15 July 2007 (UTC)

Once the core of your transformer becomes magnetically saturated, it stops being a transformer and starts being a short circuit. If your transformer is sized for 60Hz, then 50Hz won't be changing fast enough to prevent this. --Carnildo 22:59, 16 July 2007 (UTC)

Yes in reply to atlant there is a lower frequency limit on a transformer, going below which will release the magic smoke! It occurs when the magnetising current (due to insufficient reactance) increases to such an extent that the pri winding overheats/melts/ bursts into flames! Zero frequency is therefore good to avoid. Tuggy

Shape of raindrops - teardrop shape or spherical?

Has real rain been studied, for example by high-speed photography, and the typical shape of raindrops been found empirically? Is it teardrop or sphere? 80.0.96.159 18:39, 14 July 2007 (UTC)

According to raindrop (which please see for more details), "Small raindrops are nearly spherical. Larger ones become increasingly flattened on the bottom, like hamburger buns; very large ones are shaped like parachutes."--Shantavira|^{feed me} 18:54, 14 July 2007 (UTC)

To be more precise regarding the "very large" raindrops (>4.5 mm or so), they go unstable, become increasingly concave and briefly look like a thick-edged parachute, and then break up into smaller droplets [3]. This instability is because the dynamic pressure of the air in front of the drop (which increases with drop size, partly because the terminal velocity does) becomes larger than the drop's internal hydrostatic pressure caused by surface tension (which decreases with size). --mglg_(talk) 21:19, 14 July 2007 (UTC)

The origin of the teardrop shape is the shape of upside-down accumulated water getting heavier than what the surface tension can stand. The water drop, just before dripping, stretches away of the surface in a teardrop shape, until the surface tension breaks and the water drop stars falling. From there on, the shape should be roughly spherical, as explained. — Kieff | Talk 00:37, 15 July 2007 (UTC)

Even if you don't ever see the raindrops themselves, every time you see a rainbow, it is due to the fact that raindrops are spherical. You wouldn't see the distinct colors if the raindrops were nonspherical. -- JSBillings 02:11, 15 July 2007 (UTC)

I suspect that's not precisely true. The raindrops need only have internally-reflective surfaces and be generally similar in shape. An oblate raindrop will still refract (and internally reflect) light. But the difference is probably negligible if the distortion is minor. — RJH (talk) 17:59, 15 July 2007 (UTC)

And in any case - just as the raindrops aren't spherical - so the rainbow isn't 100% perfect - they are fuzzy, blurry things. Take a look at the spectrum you get out of a glass prism - it's much crisper and richer in colour than natural rainbows. You are seeing the result of reflections and refractions from the AVERAGE of an awful lot of raindrops. SteveBaker 18:46, 15 July 2007 (UTC)

Time Zones

I am curious. What time zone is Wikipedia based on ... and why? I guess I am looking for an answer such as "Wikipedia is on USA Pacific Time because their headquarters are in Los Angeles." --- or whatever. Thanks. (JosephASpadaro 19:03, 14 July 2007 (UTC))

Wikipedia time is Coordinated Universal Time, that UTC next to your sig. I don't know what the specific reasoning for this was, though. Someguy1221 19:13, 14 July 2007 (UTC)

UTC is a pretty standard default time zone. It has the advantage of being theoretically culturally neutral. Donald Hosek 20:33, 14 July 2007 (UTC)

Incidently, both the Wikipedia servers and the Wikimedia Foundation are based in St. Petersburg, Florida, so if they did use local time, it would be UTC-5 (UTC-4 in the summer). Laïka 21:11, 14 July 2007 (UTC)

Culturally neutral? I'd think that would be more like UTC-2 or -11, so one can grab large swaths of ocean where no one lives.  ;-) By contrast, I think the English would be annoyed to know you think they have no culture. Dragons flight 21:26, 14 July 2007 (UTC)

And indeed, the determination of Greenwich as being "universal" was highly controversial! The French wanted it centered on Paris, but the British controlled the shipping... in any case, I'm pretty sure it can be adjusted in one's settings. --24.147.86.187 21:48, 14 July 2007 (UTC)

You have to pick somewhere - and wherever you pick will upset someone. We Brits happened to get the technology that made it matter first - so we win! SteveBaker 23:03, 14 July 2007 (UTC)

How's that again, Mr. CDT? :-) —Steve Summit (talk) 12:00, 15 July 2007 (UTC)

Speaking as a Brit, I just want to point out we are currently on UTC +1. Algebraist 23:34, 14 July 2007 (UTC)

Indeed. If you make the casual assumption that GMT == "British time", you're not alone, but it's quite wrong, and the distinction is more than merely theoretical. There was a minor scandal a couple of years back when it was discovered that in some version of Microsoft Windows or another, the folks in Redmond (in PST/PDT) had made this same assumption, but it meant that you couldn't set the clock forward for summer time in Britain without screwing up GMT, or vice versa. (That is, the relevant timezone dropdown box had only one choice, "GMT", rather than the necessary two, "GMT" and "British time", distinctly separate.) —Steve Summit (talk) 00:02, 15 July 2007 (UTC)

Yes - just because we have arbitarily chosen the little town of Greenwich (specifically center of the brass line that travels through the middle of the old royal observatory there) as 'zero' doesn't in anyway imply that British people use GMT+0 for wall-clock time. We have daylight savings time just like many other countries (except we call it "British Summer Time"). So during the winter, we use GMT+0 and in the Summer, GMT+1 - but there is no particular connection between the time we use and where the meridian happens to be, There have been some fairly serious proposals to switch to GMT+1 in the winter and GMT+2 in the summer. SteveBaker 00:49, 15 July 2007 (UTC)

A follow-up. When it is exactly 0:00:00 in UTC ... it is exactly midnight where? In Greenwich, England? Thanks. (JosephASpadaro 00:58, 15 July 2007 (UTC))

According to this site, a couple of them are Casablanca and Reykjavik. But this would change depending on day-light savings. That's why currently, Greenwich is not at UTC+0 time (as stated by Algebraist above). - Akamad 06:14, 15 July 2007 (UTC)

Not so sure about "no particular connection between the time we use and where the meridian happens to be", Steve. It would be a little odd if the UK was on GMT+7, say. I'm not saying they can't do this, but would they, realistically? -- JackofOz 06:21, 15 July 2007 (UTC)

Well, "no particular connection" might have been a little strong, but it's certainly the case that there are several areas where the time zones depart rather significantly from the nice, regular, 15-degree-centered stripes you might expect. See this excellent map. —Other Steve (talk) 23:52, 15 July 2007 (UTC)

Two small points. First, the Greenwich meridian was chosen as the prime meridian not because of who "controlled the shipping", but because of what existing mapmakers were doing. Not only maps made in Great Britain, but also in the US, the Netherlands, Italy, and Japan, among others, all used the Greenwich meridian. According to figures presented by Sandford Fleming at the International Meridian Conference, 65% of the world's ships (representing 72% of the world's shipping tonnage) used maps based on Greenwich. And the maps used by the other 35% (28%) were divided between many other prime meridians; the Paris meridian was the second most popular, and it had just 10% of ships (8% of tonnage). See Greenwich Time and the Longitude by Derek Howse (1997 edition ISBN 0-85667-468-0).

Second, the prime meridian is no longer actually defined by the old Greenwich Observatory, and in fact is now computed in a way that makes it about 100 m (330 feet) off the old position at Greenwich. See Prime Meridian and World Geodetic System.

--Anonymous, July 15, 08:43 (UTC).

Ah, thank you, Mr. Whoever-you-are, that point needed making. But there's one more point: the whole point of zone time is that it doesn't change the answer. When it's exactly 00:00:00 in UTC (or GMT), and unless summer time is in effect, it is exactly midnight in Greenwich. That is, the arguments in this earlier thread do not apply, and the time in Greenwich is not 100 ÷ 1000 ÷ 40032 × 24 × 60 × 60 = 0.2 seconds earlier, or anything. It's also exactly midnight, of course, in London, Edinburgh, Milton Keynes, Barrow-on-Trent, Weston-super-Mare, and Ashby-de-la-Zouch. And Casablanca and Reykjavik, as Akamad said. And Dublin, Lisbon, Laâyoune, Nouakchott, Bamako, Dakar, Conakry, Abidjan, Monrovia, Freetown, Ouagadougou, Lomé, and Accra. —Steve Summit (talk) 4:57, 15 July 2007 (PDT)

When you talk about 'exactly midnight' it makes me think of solar midnight, which isn't the case for the aforementioned cities. -- JSBillings 14:06, 15 July 2007 (UTC)

If JosephASpadaro was in fact asking about "solar midnight" (which sounds kind of like an amusing oxymoron!), then my answer is incorrect, and it actually ends up being a rather interesting question. I don't know (and our UTC article doesn't say) what the relationship is between UTC midnight and the WGS84 geoid upon which most lat/long measurements are based. So I don't know whether UTC midnight is supposed to correspond to local solar midnight at Greenwich, or at the WGS84 0° longitude (which as our anonymous informant has reminded us is about 100 m off of Greenwich), or somewhere else. In practice, of course, the exact geographical location of UTC midnight wanders around somewhat, due to leap seconds, somewhat as shown here. —Steve Summit (talk) 23:52, 15 July 2007 (UTC)