Wikipedia:Reference desk/Archives/Science/2007 May 13

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May 13

Lightning in the snow

Can lightning happen when it is snowing or only during rainstorms? —The preceding unsigned comment was added by M.A.D.M.D. (talk • contribs) 00:13, 13 May 2007 (UTC).

See thundersnow. --Tardis 00:28, 13 May 2007 (UTC)

Yes, but it's not common; link. --TotoBaggins 00:49, 13 May 2007 (UTC)

Here in Toronto I would guess that we typically get about 10 storms a year with significant lightning, mainly in the summer. Lightning in a snowstorm is something I see maybe once every 5 years. --Anonymous, May 13, 2007, 06:09 (UTC).

In several decades I have seen only one spectacular lightning/thunderstorm. Edison 23:09, 13 May 2007 (UTC)

CD-1 Mouse

I have been reading this study about emu oil, wherein emu oil is applied to "CD-1" mice. What makes these mice CD-1? Are there other classifications or grades of lab-mice (CD-2?) or other lab-test animals? Nimur 01:04, 13 May 2007 (UTC)

CD-1 is the designation given to a specific mouse strain. Check here for more info... — Scientizzle 01:09, 13 May 2007 (UTC)

Interesting. I would guess that comparative studies should stick to the same breed/strain for quantitative result comparison? What other scientific implications do these different breeds have? Nimur 01:24, 13 May 2007 (UTC)

See our articles on BALB/c and C57BL/6 for examples. However, Michael Festing's Inbred Strains of Mice is the definitive source, there is a online version here - just select your strain of interest and find out their characteristic of interest. Rockpocket 01:50, 13 May 2007 (UTC)

Limbs falling asleep

What's the term for a limb "falling asleep" when you sleep on it/lean on it/etc.? Basically where the limb goes numb. My leg fell asleep today and to my surprise, I didn't get the tingling sort of "pins and needles" feeling after I moved it. The feeling in my leg simply came back. So I thought that I could maybe find out why it didn't have the tingling feeling that sleeping limbs normally have after they "wake up" but I can't seem to get Google to give me the right page to read. Dismas|^(talk) 01:52, 13 May 2007 (UTC)

Thanks to this thread from back in February, we have learned that two relevant terms are paresthesia and obdormition. (Thanks, Lph!) —Steve Summit (talk) 02:04, 13 May 2007 (UTC)

Thanks, at least now I know what they're called but I still don't know why I didn't get paresthesia after my obdormition... Dismas|^(talk) 03:42, 13 May 2007 (UTC)

passive solar to generate electricity

I had a thought about a system to generate electricity, and would appreciate any comments or criticism. It is designed for a building, and consists of two fairly large transparent plastic cases, connected to each other with two pipes. One case (the hot case) hangs on the south side of the building (or somewhere else exposed to sun, the roof, etc), and the other (the cold case) hangs on the north side or behind a shaded wall, etc. The cold case is higher than the hot case. One insulated pipe travels from the top of the hot case, across the building to the top of the cold case. Another pipe travels from the base of the cold case to the side of the hot case. Perhaps the hot case will also have a reflective material on the base to assist. The whole system is sealed and contains air. So, as the sun hits the hot case, the air will be heated and rise towards the cold case, thus forcing air from the cold case to travel through the other pipe to equalise the pressure. My first question, will this happen? Or will relatively hotter and cooler air molecules simply pass by each other through the same pipe? As you can imagine, my vision is that air will constantly flow in one direction around the device. Because this air will definately not generate enough breeze in the pipe to run a wind turbine, I envisioned a valve which is placed in the pipe somewhere. The pressure builds up, then pops up the valve to allow air through. It drops back down and the cycle continues. This regular jerking motion can be used to spin a turbine (which sits outside the pipe) and generate power. As far as I can tell, the system will be fairly cheap. Can anyone point out any obvious flaws or drawbacks to this system? Will the energy generated be too small so as to not be worth the trouble? Drathr 02:50, 13 May 2007 (UTC)

So basically it's two large radiators which uses convection currents to generate electricity? I would suggest you not to use air as it is fairly inefficient in heat transfer, doesn't absorb all of the sunlight and has a low density. Something like water in a special solar collector would be much more appropriate. A similar system already exists which uses huge reflectors to reflect the sunlight into a a point which boils water and extracts energy from its steam, which is roughly the same as your concept, using water. --antilived^{T | C | G} 03:14, 13 May 2007 (UTC)

Agreed, use water instead. Perhaps add some dye to make it absorb more sunlight. Also use one-way valves to ensure that all flow occurs in the proper direction. StuRat 04:47, 13 May 2007 (UTC)

Thanks for the input. One-way valves would solve one issue. Although air is less efficient for heat convection, I was thinking of ways to construct an extremely low-cost and light system, that would generate a small amount of power on a local scale, not for generating large amounts of electricity. Use of water would make it much heavier (although I have no idea of what case size would be suitable) and also, my impression is that water flowing through a heavy one-way valve would simply keep the valve open constantly, and flow slowly through, while air would build up pressure, then simply rush through at once, allowing the valve to drop back down. Given that the pipe will not contain a turbine to capture energy from the moving gas or liquid, I think this violent motion is necessary to generate electricity. Can anyone tell me if this is correct or if I am missing something?Drathr 05:36, 13 May 2007 (UTC)

Another advantage of water is that it is readily available and inexpensive, so the tanks can be filled with a hose once installed. Why not use a turbine inside the pipes, BTW ? A continuous process is typically more efficient than an intermittent process, so it would be best if the valves stay open when the device is in use. Also, you might consider locating the cooling tank inside the house, so as to heat the house. And, if you really want a very low power output, why not just use solar cells ? The lack of moving parts makes them more reliable (although they do need to be cleaned from time to time). StuRat 05:59, 13 May 2007 (UTC)

The reason I didn't consider placing a turbine inside the pipe, is that I would like the system to be both extremely cheap and fairly easy to assemble from kit form. So I see the pipes as regular 5 cm diameter pipes. I think if a turbine were used inside the pipe, the volume would have to be quite substantial and the water flow quite fast for anything meaningful to be gained in the way of electricity generation. But this would probably make the system too heavy and complicated to fit its original purpose. So although the intermittent action would be less efficient than a continuously rotating turbine, I think it is necessary here to be suitable. I haven't established what the kinetic intermittent energy would be transferred to yet. Also, I intend this to be used in very hot and sunny areas. I understand that solar panelling and battery storage is a fairly easy and reliable method of electricity generation on a house, but I'm trying to theorise whether some system could be set up to generate some energy for a much much cheaper price, like well under a thousand dollars. Drathr 09:28, 13 May 2007 (UTC)

Battery storage is anything but fairly easy. They will cost a lot more than your generation system. But otherwise I think a better approach would be something like a small scale Solar updraft tower (black tarp on some conical support with a turbine on top?). This would solve all the issue of the one-way valves and would only require one large structure instead of two. Although neither are very efficient compared to other things like photovoltatic cells and I doubt it can even supply 1W for a tent sized structure. --antilived^{T | C | G} 10:17, 13 May 2007 (UTC)

I agree. Any mechanical system is likely to cost more per watt than solar cells, not less, and be less reliable. The one advantage of such a system (using water) is that it has the potential to convert a higher percentage of sunlight into usable energy than a solar cell. However, if it costs 10 times as much and produces twice as much energy, that's still less economically efficient. The air filled version would probably produce even less usable energy than solar cells, yet still cost more. StuRat 14:11, 13 May 2007 (UTC)

I am assuming that ease of assembly/repair and durability are also factors - I doubt that energy recovery from a one-way valve can be made mechanically simpler than a pinwheel type turbine. You might see some savings in the charging hardware by trading continuous (during daylight) input at variable power for known impulse power at intermittent intervals, but intuition says no. A [solar chimney] looks feasible and quite simple for remote but sunny areas. You might also want to consider that pretty much any implementation will be more efficient as a single large installation (say, at a village center) than trying to make individual houses self-contained. Eldereft 14:06, 14 May 2007 (UTC)

Fuel Cell

Any idea if we could run a fuel cell in reverse, then would it convert water and CO2 back to fuel??~~ —The preceding unsigned comment was added by 59.92.244.211 (talk) 05:14, 13 May 2007 (UTC).

Not exactly. Fuel cells use hydrogen and oxygen to create energy by combining them to form water. In reverse, water would be split (using energy) to create hydrogen and oxygen. --M1ss1ontomars2k4 ^{(T | C | @)} 05:21, 13 May 2007 (UTC)

i.e. Electrolysis of water -- Consumed Crustacean (talk) 07:37, 13 May 2007 (UTC)

Fuel cells don't produce CO₂ so maybe the question may be "can you run an internal combustion engine backwards?". I don't know the answer, but I would guess that with enough energy/pressure you could... Aaadddaaammm 09:47, 13 May 2007 (UTC)

At one point, you run into the Second law of thermodynamics. Titoxd^{(?!? - cool stuff)} 19:19, 13 May 2007 (UTC)

Fuel cells that run on H2 dont produce CO2, others well do so. The advantage of a fuell cell is that it's effectiveness is not limited by the effectiveness of a carnot process, not that they are more "clean" than a combustation engine. Cells that run on H2 are cleaner only when you put aside the process of the making of H2, which requires energy, from dirty traditional sources. 84.160.200.176 19:24, 13 May 2007 (UTC)

Or from less dirty sources, such as geothermal, nuclear, etc. Power plants are often far higher in efficiency than ICEs as well, even taking into account power loss during transmission. -- Consumed Crustacean (talk) 21:55, 13 May 2007 (UTC)

Water plus electrical energy produses hydrogen and oxygen. In principle, the addition of carbon dioxide and energy should be able to produce hydrocarbons, i.e. fuel. Edison 23:08, 13 May 2007 (UTC)

Respiration and photosynthesis are opposite reactions of I suppose 'natural fuel cells'. Respiration produces carbon dioxide, water and energy from oxygen and sugar, photosynthesis does the opposite, i.e. requires the input of energy from sunlight. Reversing a reaction that produces energy will require energy input, but is probably possible under the right conditions. Cyta 07:37, 14 May 2007 (UTC)

I'm kinda doubtful that you could just run a fuel cell in reverse - but there are certainly other chemical pathways that would allow you to make fuel from the byproducts of a fuel cell. But obviously the energy that would require would be more than the fuel cell generated in the first place (possibly MUCH more!) - so there isn't much in the way of a practical application for this. SteveBaker 01:18, 15 May 2007 (UTC)

Why don't corn cobs burn ?

Most other plant materials are flammable, so why aren't corn cobs, even when dried ? StuRat 06:32, 13 May 2007 (UTC)

If they don't burn, what do they do? Now I can't wait till fall to do some experimenting... Dismas|^(talk) 07:45, 13 May 2007 (UTC)

Well, sure they burn. In fact they make fine charcoal for use in stoves. I recall, but cannot cite, that they were used by many farmers in the era of steam tractors to stretch their coal supply. --BenBurch 19:43, 13 May 2007 (UTC)

They seem to be left, intact, in the ashes after a nice fire. Do you need to soak them in gasoline and burn them in pure oxygen ? StuRat 21:47, 13 May 2007 (UTC)

Make sure they are totally dry! --BenBurch 22:00, 13 May 2007 (UTC)

When Sweet corn is roasted (roastneers), the high moisture content of the cob preserves it somewhat from burning. The rule (only partly in humor) for cooking sweet corn is ideally to have a pan of water boiling, go to the field and pick the corn at the peak of sweetness, and run as fast as you can to the house. If you trip and fall, abandon the sweet corn and go get another batch. The point is that the sweetness and moisture content both decrease after picking. It can be judged in the supermarket by peeling back the shucks and observing whether the kernals are dimpled. If they are, it is too far postmature. It will be older than ideal , but still delicious. Field corn [1] is dried to a low moisture content of 15% to 30% so that the cobs which are left after shelling burn very nicely in cob stoves, which are similar to wood-burning stoves. Stoves of a different design have also been built to burn the shelled field corn itself. The cobs were also used (painfully in my judgement) as a toilet-paper substitute in outhouses. Edison 23:06, 13 May 2007 (UTC)

ring species

Mention above of species problem reminded me of this. There are multiple known species chains, sets of species or subspecies spread out over a long distance such that each can interbreed with its neighbors in the chain but the ends of the chain are clearly distinct. When the ends of the chain overlap in territory, as in the case of a genus of Arctic birds whose name escapes me, it's called a species ring. My question: are there any cases where the ring is truly continuous, where there are no "end" species that can interbreed in only one direction? (Presumably this would be the result of a climate change, or similar event, that made the core of the ancestor's range inhospitable but left it happy in the periphery.) When I've raised this question before elsewhere, I got only blank looks; perhaps I did not make clear the distinction between physical separation and breeding separation. —Tamfang 09:38, 13 May 2007 (UTC)

So you have initially an essentially homogeneous species with a wide range, then drop out the middle? If members tend to breed with geographic neighbors (as opposed to maintaining a central breeding ground, like seals) such that it would take many generations for an advantageous gene to be passed around the ring, I see no reason why the various regions would not begin to speciate. I seem to recall that there are precious few examples of [ring species] of any kind - those gulls, some California salamanders, and the [greenish warbler] runs the gamut of our article and what I recall from last time I looked into the issue. While not an evolutionary biologist, I suspect that the situation would be unstable - even without further habitat-altering events, sexual selection can drive speciation. Eldereft 14:43, 14 May 2007 (UTC)

LUNAR ECLIPSE

WHY LUNAR ECLIPSE IS VISIBLE ON ALL THE PLACES ON THE NIGHT SIDE OF THE EARTH ? —The preceding unsigned comment was added by 202.164.134.90 (talk) 12:01, 13 May 2007 (UTC).

Because the shadow that the Earth casts is much bigger than the moon, no light from the sun falls on the moon. Thus there's nothing to see, from anywhere on Earth. Contrast with a solar eclipse, where only a small shadow is cast, so only parts of the Earth can see it. Rawling4851 12:10, 13 May 2007 (UTC)

Because you can see the Moon from everywhere on Earth which is facing in that direction. During a lunar eclipse, the Sun must be on the opposite side of the Earth to cast the Earth's shadow on the Moon, making it night on that side of the Earth facing the Moon. The Moon is then only dimly lit from light reflected from the Earth and stars. StuRat 14:00, 13 May 2007 (UTC)

For this question, the important difference between a solar eclipse and a lunar eclipse is the effect of parallax. In a lunar eclipse you are seeing the shadow of the earth on the surface of the moon, both in the same plane, and so its appearance doesn't depend greatly on where you are looking from. In a solar eclipse, you are seeing the moon against the background of a much more distant sun, so its appearance changes according to your viewpoint.--Prophys 02:46, 14 May 2007 (UTC)

Do we have any pics of an eclipse as seen from space ?

I didn't find any when I searched, which seems odd. I would have expected many pics of the Earth with the Moon's shadow on it. StuRat 04:43, 14 May 2007 (UTC)

What you want is a picture of a solar eclipse as seen from space. Here's a good one.--Prophys 05:38, 14 May 2007 (UTC)

Thanks. Is it my imagination or is the Moon's shadow a pentagon in that pic ? StuRat 07:06, 14 May 2007 (UTC)

Definitely not just your imagination but I'm struggling to explain it. I'm a bit into astronomy and I've seen a lot of pictures, I'd be inclined to say this is more likely an artefact of the equipment used and conditions wile the picture was taken, rather then some astronomical phenomenon. Sort of like the famous face on mars, we are so hardwired to recognise patterns I think we're just seeing something that isn't really there. What could possibly make a round shadow into a pentagon? I believe the storms on Saturn taking uncannily geometric shapes, but a shadow travelling through space? Generally the only thing which creates geometric shapes with light in pictures is lenses. Vespine 23:47, 14 May 2007 (UTC)

Weird - I did some image processing on this photo and the shadow is definitely hexagonal - it's not an optical illusion - it's really there. It's not a regular hexagon though - the segment on the right side is much shorter than on the left - which is the opposite of what you'd expect due to perspective. I agree that lens effects are generally the cause of hexagonal artifacts (these are 'lens flares') - but I've never seen a dark lens flare. I guess it must be something to do with refraction through the atmosphere. After all, the atmosphere has a different refractive index than vacuum - and it's curved slightly due to curvature of the earth. I suppose it's possible that we're seeing some bizarre lensing effect of the atmosphere. Very interesting! SteveBaker 02:52, 15 May 2007 (UTC)

The ground's color is not even, and therefore the iso-whatsits of the shadow superimposed on that ground are not perfect circles. What's to be surprised of? —Tamfang 05:31, 15 May 2007 (UTC)

Yes, the shadow is falling on an uneven cloud layer, rather than a flat surface. Also the cloud densities vary, so their albedo varies from point to point. You are seeing the effects of patchiness in the cloud distribution. Notice that even where there is no shadow, there is still considerable variation in reflected light intensity between thick cloud, thin cloud and no cloud. The penumbra portion of the shadow is likewise affected. Remember that the shadow, even if it fell on a flat, uniform surface, does not have sharp edges, but grades steadily from none to full shadow at the centre (for a total eclipse). The shadow is falling on a sort of hexagonal-shaped irregularity in the clouds. --Prophys 11:13, 16 May 2007 (UTC)

Then I suppose the new question is: "Why is there a hexagonal-shaped irregularity in the clouds ?". StuRat 23:46, 16 May 2007 (UTC)

Because a hexagonal-flavored irregularity would be just silly. (Now, does someone want to tell me the difference between hexagonal-shaped and just plain hexagonal?) —Tamfang 22:06, 17 May 2007 (UTC)

Falling

I am not sure if I have the physics of this right or not, so I'd like someone to give me a hand here. I was told that the acceleration of a falling body is approx. 5m per second per second, and that there is a maximum speed at which a body which has no specific shape-related drag (i.e. not a feather or piece of paper) can fall. I was also told that that maximum speed was 35m/s. By my calculations, this would mean that a person falling from a height would stop accelerating after just over 2 seconds of falling and would remain falling at the same speed until hitting the floor.

Does this mean that a person will have the same injuries, ceteris paribus, if, a) they fell out of a three-storey window; b) they fell out of a 30-storey window; c) they fell from a plane at 33,000 ft? Manga 12:35, 13 May 2007 (UTC)

You have the concepts mostly correct, but your numbers are not too accurate. Standard gravitational acceleration is 9.8m/s² (not 5); every object (even feathers) has a terminal velocity determined by its aerodynamic properties, the local atmosphere, and its weight (so filling a hollow sphere changes its terminal velocity). There is no single maximum speed; the article gives humans an average of 54m/s, or 89m/s if you're trying. Also, your math doesn't seem to work out; it takes the obvious 7 seconds for an acceleration of 5m/s² to reach 35m/s.

Finally, a falling body doesn't accelerate uniformly up to its terminal velocity and then "stick" there suddenly; instead it gradually accelerates less as it approaches that velocity and, in theory, never actually reaches it. In reality, for long falls (like from the stratosphere), the air pressure is increasing relatively rapidly as the object falls, so the terminal velocity is reduced. This means that at some point a short distance into the fall, the object will actually be falling faster than its terminal velocity (because that velocity dropped) and will spend the rest of its fall decelerating to keep "up" with the air drag. Does that make anything clearer? --Tardis 13:09, 13 May 2007 (UTC)

Yes, it does, thanks. Manga 13:25, 13 May 2007 (UTC)

Also, in addition to shape factors, terminal velocity is also very much influenced by the density of the falling object. Thus, a bowling ball will fall faster than a soccer ball of the same diameter. StuRat 13:56, 13 May 2007 (UTC)

How much would it help to deploy an umbrella (34 inches)? How about a 60 inch beach umbrella? An 11 foot patio umbrella? Edison 22:51, 13 May 2007 (UTC)

They wouldn't work as a proper parachute, and could only hold up a small weight before the forces on the umbrella would break it. However, if it held together, an umbrella would slow the fall of a small object, say a baseball, considerably. StuRat 03:03, 14 May 2007 (UTC)

Rather than an umbrella, you might want to deploy a Drogue 'chute.

Atlant

Yep - you've got to ask yourself how your umberella would stand up to a 100mph wind - 'cos that's what it's gonna be doing if you open it to slow the fall of something like a human being. SteveBaker 21:09, 14 May 2007 (UTC)

Princess Peach did it. - 2-16 12:18, 16 May 2007 (UTC)

No, she used a parasol. 213.48.15.234 14:04, 16 May 2007 (UTC)

Motion through Spacetime (Special relativity)

I understand that all motion is relative, and that there is no absolute motion or rest, but if I am at complete rest relative to the universe, I have motion through time, but no motion through space.

As I move I convert some of that motion through time into motion through space. If I were to convert all that motion through time into motion through space, I would be travelling at the speed of light and time would effectively stop for me (again, I understand that at the speed of light, my inertial mass would be infinite and thus require an infinite force, making travelling at the speed of light impossible).

But say I was to accelerate further, impossible - I know. I would be travelling faster than light, and as the sum of my motion through space and my motion through time is equal to the speed of light, wouldn't travelling faster than light mean that my motion through time is negative, effectively reversing the flow of time? And wouldn't this be a direct violation of the second law of thermodynamics which states that time can only flow in one direction and that entropy increases over time?

Also, what does this mean for the electrons which travel faster than light in water in the Cherenkov effect.

Ignore the last bit, the speed of light in water is of course 0.75c, which particles can easily be accelerated to.

Aiyda 13:06, 13 May 2007 (UTC)

You've almost answered your own question there - you can't accelerate beyond the speed of light, so therefore you can't travel through time in the negative direction, and so you won't break the second law! →Ollie (talk • contribs) 13:22, 13 May 2007 (UTC)

I know that the question which I asked is purely hypothetical, as nothing can travel faster than light, but I am asking if it could, would the second law be broken by a reversal of time. Aiyda 13:26, 13 May 2007 (UTC)

[edit conflict] As far as "relative to the universe", you'll need to define this; the universe hath not a single reference frame. It's really only proper to say that if you observe an object as not moving, its motion is entirely timelike, and to restate the rest of your question in such terms. As far as "infinite force", it's more direct to simply state that a massful object travelling at c has infinite energy (kinetic energy, if you like); how would it acquire that much?

You are correct that the Lorentz factor stops being a positive number at superluminal velocity: in particular, it becomes negative-imaginary. Given a pair of objects moving at relative speed greater than c (which is itself understood to be impossible), we can always find a third object, moving at less than c with respect to one of the objects, which observes it as progessing forward in time and the other as moving backwards (arriving before it departs). Moreover, it is thought that there may exist tachyons which have the properties you describe; however, while in general FTL travel can create 2^nd-law violations, causality loops and a variety of other science-fiction-y complications, the tachyon article says that the special kinematics of tachyons actually make them much less disruptive.

[answering the last bit anyway] Finally, the Cherenkov effect is fortunately not this complicated; in special relativity it is always the true (vacuum) speed of light c that matters, not whatever effective speed it has in some local medium. Such electrons are certainly relativistic, but they are not in danger of youthening; their weird radiative output can be described in a largely classical manner. Does that help? --Tardis 13:27, 13 May 2007 (UTC)

Thanks, although I don't understand everything (currently in year 10 studying physics), I think I get the general drift. thanks for the help Aiyda 13:41, 13 May 2007 (UTC)

This is so widely misunderstood. What special relativity predicts is that an object going faster than light in one frame of reference will go backwards in time in some other frame of reference (moving quickly, but slower than light, with respect to the first one). So (assuming that your FLT drive works in every frame of reference) you could arrange to get back to an earlier time at a "fixed location" (such as Earth) in a two-step process, going faster than light in Earth's frame on the way out, then faster than light in a different frame on the way back. It doesn't predict that going faster than light in Earth's frame means you'll go backwards in time in Earth's frame, and it doesn't predict that you'll get younger on the way. --Trovatore 19:22, 13 May 2007 (UTC)

This question is horribly flawed - to the extent that it can't be answered:

but if I am at complete rest relative to the universe

There is no such thing as 'at rest relative to the universe' - it's a totally meaningless concept. Bits of the universe are moving every which way - there is no 'special' motion that you can count as 'at rest'.

As I move I convert some of that motion through time into motion through space.

That's just nonsense. There is no "conversion" between time and space - that's just meaningless. Time and distance are dilated because of speed - there isn't some kind of exchange between time and distance when you are moving. Meaningless concepts can't generate meaningful answers - so we can't answer that.

I would be travelling at the speed of light and time would effectively stop for me

No - when you are moving close to the speed of light (relative to some other object) - everything seems perfectly normal to you inside your spaceship. Time for you passes normally - it's whatever you are moving fast relative to that seems (to you) to have time dilation.

But say I was to accelerate further, impossible - I know.

It is impossible - but it's not impossible because somehow you can't manage to find enough energy to do it due to mass dilation effects. No, it's impossible because the consequences are impossible. The Lorentz transform is the mathematical description of how time/length/mass are distorted by relative motion. The math is '1/sqrt(1-v²/c²)'. When v (your velocity) is greater than c (the speed of light), v²/c² becomes greater than 1 - which means that (1-v²/c²) is a negative number. But now you have to take the square root of that number...which you can't do and remain within the bounds of 'normal' arithmetic. If you try to take the square root of -1 on your calculator it will produce an error. Mathematicians find it convenient to do math with the square roots of negative numbers - but the way they do that is to use "complex numbers" - which can't describe real world things like length, mass or time. So if you fly faster than light then all of your distances lengths and times are complex numbers. Complex numbers cannot ever happen through calculations of physical quantities because they are purely a mathematical abstraction - but at greater than 'c', they don't cancel out. So asking about what would happen if you flew faster than light is just not a question you can expect an answer to - there is no physical interpretation of a complex number. Time doesn't run backwards because that would require a negative result from the Lorentz transform - and you don't get a negative answer - you get a complex result.

Even moving at the speed of light is a problem - in that case v equals c - so sqrt(1-v²/c²) comes out to exactly zero - but Lorentz requires one divided by that...and once again, math falls apart when you divide one by zero. 1/0 is not infinity - it's undefined. Your calculator gives you an error again. So the math falls apart just before before you get faster than light.

Flying faster than light to cause time travel is pure science fiction - there is no math to support that. There are other ways to imagine that time travel could be possible - but superliminal travel ain't it. The premise behind the question is wrong - and the only valid answer is "You just can't do that" - speculation about what would happen if you did depends on a physical interpretation of complex numbers - which can't exist.

SteveBaker 04:26, 14 May 2007 (UTC)

Steve, I think your analysis relies a bit too heavily on extrapolations of known physics into unknown regimes. It doesn't make sense to say "of course there is no known mechanism to travel faster than light, but if there were such a mechanism, then observers using it would see their clocks move by an imaginary amount". Since we don't have any proposed mechanism, we can't say what observers using it would experience.

On the other hand, we can give some reliable predictions about what observers remaining behind would observe. If the spaceship is moving faster than light in one frame, then there's another frame, moving (slower than light) with respect to the first frame, in which the spaceship would be seen to arrive at an earlier date than it had left. This prediction is completely independent of the unknown mechanism, provided only that the mere fact of the ship's voyage does not affect the measurements of the observers remaining behind. --Trovatore 05:25, 14 May 2007 (UTC)

No - that's my entire point. You fail to notice the key point of special relativity - which is the symmetry between the observer and the observed. If we don't know what the universe would look like in the frame of reference of a spaceship travelling faster than light - then someone here on earth (which would also be travelling faster than light relative to the spacecraft) would have the exact same problems. The result isn't negative time effects - it's complex-number time effects - and that just can't be. The only chance one would have for something 'interesting' to happen would be if the theories of relativity were wrong. There is no evidence for that - so again, you can't speculate as to what the answer might be. SteveBaker 11:28, 14 May 2007 (UTC)

Steve, here what you're doing is conflating the physics that we know from observation, with Einstein's ideology. The physics is well established. The ideology, on the other hand, could easily be wrong.

To go faster than light, we'd obviously have to do something not provided for by known physics. That doesn't mean that known physics keels over and dies, just that it wouldn't apply to our posited spaceship. It would still apply, presumably, to the rest of the universe that's not under the influence of our funky FTL-enabling field or magic spell or whatever.

And that's my point: Provided only that the FTL-enabling effect, whatever it is, is local, then special relativity does in fact make the predictions I described. In a certain frame of reference you do predict the spaceship arriving before it leaves. You never have to take the square root of a negative number, because this second frame of reference is moving sub-light with respect to your original one. This is an easy calculation; I can give details if you want to see them. --Trovatore 18:14, 14 May 2007 (UTC)

I'm gonna have to call you on that one - I think it's B.S. SteveBaker 01:12, 15 May 2007 (UTC)

OK, let's take a simple case. Let's take two frames of reference, which we'll call unprimed and primed, and we'll ignore the y and z coordinates and focus on x and t (or in the primed reference frame, $x'$ and $t'$ respectively). For simplicity we'll use units in which the speed of light equals 1. The "primed" observer is moving at a speed of 0.8 in the positive x direction, as measured by the unprimed observer.

Now consider two event points A and B. The coordinates of A are

x_A=t_A=$x'_{A}$=$t'_{A}$=0.

The unprimed coordinates of B are

x_B=10

t_B=1

That is, B is the event point one year later than A, as measured in the unprimed frame (not the ship frame!), but ten light-years in the positive x direction (still as measured by the unprimed observer).

What are the primed coordinates of B? Just plug it into the Lorentz transform:

$x'_{B}={\dfrac {x_{B}-vt_{B}}{\sqrt {1-v^{2}}}}={\dfrac {10-0.8}{0.6}}=15.33$

$t'_{B}={\dfrac {-vx_{B}+t_{B}}{\sqrt {1-v^{2}}}}={\dfrac {-8+1}{0.6}}=-11.67$

So from the point of view of the unprimed observer, the ship leaves event point A and travels for one year at ten times the speed of light, and arrives at point B, one year later but ten light years away. From the primed observer's point of view, the ship arrives eleven years and eight months before it left.

Note that there is as yet no causal paradox -- there is no forward-facing timelike path from B back to A, so you can't get a causal loop in this one step. But you can get one if the primed observer at point B, on the arrival of the ship, works the same trick and sends a ship back the other direction at ten times the speed of light in the primed frame. This last point assumes that the mechanism works in any reference frame; that point can't be fully justified, since we have no idea what the mechanism might be. --Trovatore 04:08, 15 May 2007 (UTC)

That's bogus! To see why - understand that the 'unprimed observer' has nothing whatever to do with what happens - nothing the magical spacecraft or the primed observer does or sees depends on him. Let's just delete him from the discussion. That shouldn't change what the primed observer sees - because if it does then there are an infinite number of possible observers in an infinite number of frames of reference we could have chosen as 'unprimed' and you'd get different answers for what 'primed' sees depending on which one you choose. Poor old 'primed' can't possibly experience different things depending on where some 'unprimed' physicist doing the math happens to be watching him from! So given that the correctness of the answer cannot possibly depend on the existance of this extra person - we can ignore him. This simplifies things considerably. So now you have your 'primed' observer who might as well believe himself to be stationary - watching a craft shoot off at v=(10c-0.8c) and lo and behold you are back taking the square root of a negative number - as you should be.

If you still think you're right, either explain it to me again without any reference to the irrelevent unprimed observer or explain it again with a 'double-primed' observer who is moving at some other speed relative to primed - remembering that you MUST get the same answer from the point of view of 'primed' or you have an impossible situation that's just as bad as sqrt(-1). SteveBaker 19:46, 15 May 2007 (UTC)

The unprimed observer is not irrelevant -- he's the one from whose point of view the ship is moving faster than light, but forward in time. From the primed observer's perspective it's moving faster than light (by the way, you're using the wrong formula for addition of velocity) but backwards in time. The point of view of someone on the ship is unknown and irrelevant; all we're interested in is reconciling the accounts of the two "normal space" observers.

So it's just as I said -- if from one observer's perspective (unprimed) something is moving faster than light, then from some other perspective (primed, moving sublight with respect to unprimed), that thing is moving backwards in time. That's what I was trying to get across from the beginning. --Trovatore 19:54, 15 May 2007 (UTC)

Infinity and Speed of Light (Theoretical question)

Einstein said that when a body accelerates to the speed of light (theoretically), the body becomes infinitely small. Does it follow, then, if a body is absolutely motionless (i.e. there is nothing around to compare its acceleration with) it becomes infinitely big? Manga 13:20, 13 May 2007 (UTC)

I think it's impossible for any body to be absolutely motionless. It can be relatively (*no pun intended*) motionless, but not absolutely. Therefore, your question is without basis. -- JackofOz 13:24, 13 May 2007 (UTC)

Actually it's possible for a body to be completely motionless in the frame the measurement is made, i.e. motionless relative to the observer. In fact any body can deduce that it itself is completely motionless and everything else is moving. So observations on yourself are in effect observations of motionlessness. This is called the rest frame, as the body seems at rest. You are right, Jack, in the sense that another observer wouldn't necessarily see that body as motionless, but the question makes as much sense as asking what happens at the speed of light, you simply need to specify a frame to measure in. But yeah the correct answer is the Lorentz Factor mentioned below. Maybe see also length contraction and time dilation. Cyta 07:46, 14 May 2007 (UTC)

Doesn't the mass of an object increase while it is moving, as mass is a form of energy and energy a form of mass, as per Special relativity. Aiyda 13:30, 13 May 2007 (UTC)

The OP means absolutely as in "exactly", not as in "without need for a comparator". But no; see Lorentz factor, which controls such effects. It tends to positive infinity at $v=c$, but at $v=0$ it simply gives 1, which means "normal": nothing special happens for "complete" stopping. (So your rolling stops do not have a safety justification!) Moreover, at all small speeds, the limit of the special-relativistic equations is normal Newtonian mechanics, so everything is smooth and well-behaved.

As far as mass increase, this is largely a question of semantics; see relativistic mass. --Tardis 13:34, 13 May 2007 (UTC)

It is not a question of semantics. In relativity there is no physical difference in its descriptions and reality. It makes no difference whether or not the acceleration is due to movement or a fictitious gravitational field. The effects are the same, the reality is thus the same. --24.147.86.187 17:56, 13 May 2007 (UTC)

USA on Fire

I see on TV News that several US states, such as Florida, have fires all over the place. Fires in western states, that take a long time to get put out, have been part of our news for years. Are there credible theories to explain this phenomena of apparently serious fires in many different states of the USA?

Off the top of my head, the possibilities include:

• Forestry practices
• Wetlands removed for development
• Funding cuts for first responders
• Natural weather cycles ... this is not a new phenomena, we just have not witnessed it recently
• Global warming
• This is nothing new, except what the news media chooses to focus on.

User:AlMac|^(talk) 15:40, 13 May 2007 (UTC)

Large wildfires in Florida are also not uncommon. I don't think there are any odd or unusual causes to blame, with the possible exception of the theory that rigid suppression of small wildfires helps set the stage for eventual really big ones. — Lomn 17:39, 13 May 2007 (UTC)

some areas of forest need to be revitalised by fires, so stopping them can badly affect the area.

Just as there are areas which regularly flood (flood plains), there are also areas that regularly burn. This hasn't changed, the difference is that many people now live in those areas, making such fires newsworthy. StuRat 20:16, 13 May 2007 (UTC)

I call it 'summer'. Nothing new or different. The western areas are very large and seemingly close fires to previous years are not. Just random collection. You only have to look at how pine trees fireproof their seeds to see how natural it is. --Tbeatty 04:30, 14 May 2007 (UTC)

It's not some new thing, it perfectly falls into statistical probability and there isn't anything to blame. Sometimes people have a hard time getting past the fact that sometimes there isn't anybody to blame. [Mac Δαvιs] ❖ 07:03, 14 May 2007 (UTC)

Are there any actual data for the acreage burned, number of fires, or property losses/deaths this year compared to previous years, to allow viewing of any trends? The discussion sounds like a lot of hand waving in absence of data so far. The amount and prominence of news coverage can make the ordinary seem extraordinary (and contrariwise). [2] says that this year US wildfires have burned 3 million acres, which is three times the average for this time of year, and that since 1970, the number of wildfire worldwide has "soared." [3] says that 2006 set new US records for number of fires and acres burned, 125% above the ten year average. [4] gives acres burned 1960-2006. [5] has the forecast fire danger as of today. Edison 22:06, 14 May 2007 (UTC)

If you want to learn all about the history of fire, both controlled and wild, in the United States, try the book Fire in America: A Cultural History of Wildland and Rural Fire by Stephen J. Pyne. It is very thorough (although only up to the 1980s or so). Long story short, there are several distinct fire regime regions in the US, some with more frequent (and usually less intense) fires, some with less frequent (usually more intense) fires. The late 1800s and early 1900s saw some of the largest and most intense wildfires in the US. Curiously, during the same period the Forest Service and national forests came into existence.

The page List of forest fires has info on a few of the larger, more famous fires. The Peshtigo Fire of 1871 is particularly amazing to read about. Pfly 02:22, 15 May 2007 (UTC)

Scree plot

Holy cow, no article on scree plot en that with 89000+ hits in google: [6]. I wish I knew what is was/is. Then I could write about it. VanBurenen 18:21, 13 May 2007 (UTC)

Maybe it should redirect to principle component analysis, since it appears to be a graphical representation of this technique. I have never heard of it. Nimur 18:25, 13 May 2007 (UTC)

Newts: friend or foe?

I found a newt in my garden, under a piece of wood, together with some slugs. (With no lake or pond around anywhere.) What do they feed on? Do they eat my seeds like the slugs do? 84.160.200.176 19:27, 13 May 2007 (UTC)

My response has been moved here, where people still appreciate a joke: [7]. StuRat 17:50, 14 May 2007 (UTC)

It had 4 legs and didn't talk about politics. But, who knows if the slugs weren't camuflaged bodygards? Perhaps by suggesting it might by a terrorist I could get some intelligence agency to find out what it feeds on? Salmonella sure gives a link to biological warfare. 84.160.200.176 20:31, 13 May 2007 (UTC)

I believe they are carnivores, eating slugs, worms, and insects. I suppose you might prefer if the earthworms were left alone, to help aerate the soil, but it sounds like they do more help than harm to me. Also, the coolness factor would make me happy to have one in my garden. StuRat 21:38, 13 May 2007 (UTC)

Just to expand on the coolness factor:

"Newts have the ability to regenerate limbs, eyes, spinal cords, hearts, intestines, and upper and lower jaws"

Nice. Vranak

The enemy of my enemy is my friend --- as long as he's small and not numerous enough to gang up against me. I hope it's carnivorious, but I don't know. The soil is heavy and aeration is mostly done by ants, I rearly see earthworms, even by rain or when digging. 84.160.200.176 22:08, 13 May 2007 (UTC)

Thermal expansion

Is there any material which undergoes significant thermal expansion in a relatively small range of temperatures (say, between freezing and body temp)? Preferably, this should be at roughly temp, rather than close to absolute zero or 1000s of degrees C. Laïka 19:46, 13 May 2007 (UTC)

Well, the easy answer is that when any element or substance reaches its boiling point, it undergoes rapid expansion, and that's over a very small temperature change. As to your conditions, I don't have a flat out answer for you, but this article might help: List of elements by boiling point. Anchoress 21:51, 13 May 2007 (UTC)

I don't know what the original question was at, but, if you want a robust and energetically effective shutter for your window, you'll need something that's not as sensitive to pressure as a boiling point. (after edit conflict) 84.160.200.176 22:33, 13 May 2007 (UTC)

Water! When it freezes it expands significantly over a very small range of temperature. --BenBurch 22:18, 13 May 2007 (UTC)

I assumed they meant something that expands as it heats up, not when it cools down, due to a phase change. I could be wrong, though. StuRat 23:05, 13 May 2007 (UTC)

Water is the ONLY thing we know of that expands like that when it freezes, and it is a larger density change over a small range than thermal expansion would ever supply. --BenBurch

Actually, that's a myth. There are some compounds of Tin that behave similarly. SteveBaker 03:47, 14 May 2007 (UTC)

As does Bismuth. Laïka 07:21, 14 May 2007 (UTC)

Our coefficient of thermal expansion article has a list of the thermal expansion coefficients of various substances at 20^oC. Mercury heads the list, with a linear thermal expansion coefficient of 60 x 10^-6/K - hence its use in mercury thermometers. If you want a common material that is solid at room temperatures, lead is high on the list, with a linear thermal expansion coefficient of 29 x 10^-6/K. Gandalf61 10:09, 14 May 2007 (UTC)

Certain waxes have useful expansion properties; see our wax motor and thermostat articles.

Atlant 12:12, 14 May 2007 (UTC)

Taco manufactures "zone valves" for hot-water heating systems. Instead of a motor the valve is activated by heating a solid metal cylinder, causing the cylinder to expand with great force the push on the valve head. The valve operates slowly, taking perhaps thiorty seconds to open or close, the total amount of movement is less than 1/4" (6mm). The metal looks like brass of some kind. -Arch dude 22:07, 14 May 2007 (UTC)

Oh yeah, I knew there was a third article: Zone valve. Thanks for reminding me!

Atlant 00:24, 15 May 2007 (UTC)

Coyote behavior dangerous?

Last night, out walking with my 70 lb dog at about 2 am, we were paced (about a half block back) by a coyote, for about two blocks. When a car and a cyclist crossed its path at the same time, it skedaddled. Now coyotes are very common in Vancouver, and I've never been concerned about their proximity (even when I've seen two together), partly because they are so timid and partly because of my dog. But with it behind us and my dog oblivious (and me in bare legs, a miniskirt and flip flops), I was a bit nervous.

What would make a coyote behave like that? Was I right to be worried? What should I do if it happens again? Anchoress 22:27, 13 May 2007 (UTC)

It obviously just wanted to see you in the miniskirt. —Preceding unsigned comment added by 68.117.135.99 (talk • contribs)

They claim that coyotes do not attack humans. I might surmise that they never leave anyone around to complain. They certainly carry off and devour cats, rabbits, and small dogs. A 70 pound dog should not constitute coyote food. Nor should an Anchoress. Perhaps the wiley coyote was only waiting for the delivery of his rocket powered Acme roller skates, the better to overtake you. Edison 22:43, 13 May 2007 (UTC)

Tee hee. Wyle E. Coyote is my favourite. I think if I were the road runner, I'd let the coyote catch me. Anchoress 23:59, 13 May 2007 (UTC)

"Allow me to present myself (*hands over business card*), I'm Wyle E. Coyote, Super Genius. There's absolutely no point in your attempting to escape, as you simple won't have a chance against my towering intellect. So, why don't you just avoid all the unpleasantness by surrendering right now ?"..."Me-meep (*roadrunner sticks out tongue and runs away*)."StuRat 02:35, 14 May 2007 (UTC)

I live in Texas - we have both roadrunners and coyotes - and I am pretty sure that coyotes can catch roadrunners - because I've seen one of my dogs catch one by sheer speed. However, the coyotes are obviously more cunning about it because I've seen no sign of rocket packs, volcano pills or any crates labelled "ACME" in my back yard. As for coyotes and dogs...any carnivore has to weigh up the risks and rewards of an attack. A coyote would be taking a significant risk of injury taking on a healthy medium sized dog - and even a small dog or a cat might be more than it would want to take on. The risky times must be when they are hungry, desperate or defending their young. SteveBaker 01:07, 15 May 2007 (UTC)

Of course, to know that neither you nor your dog are "food", they need to check you out first, which might be why they were following you. Once they figured that your dog was too large, they likely would have moved on. Another possibility is that they saw your dog as a rival for their territory, and were looking to pick a fight, but weren't going to so long as you were around. To be safe, however, instead of letting them stalk you from behind, I'd suggest you turn around and look at them, so they know they've been spotted. And, wearing that miniskirt, you might just find a wolf on your trail some day. :-) StuRat 22:53, 13 May 2007 (UTC)

That's my take on it too, but I'd rather be sure. Probably the coyote has gotten accustomed to eating what people throw away, and was hoping I'd discard something, but I don't know... maybe it had rabies? Anchoress 23:59, 13 May 2007 (UTC)

It doesn't sound anything like rabies, to me. Affected animals throw caution to the wind, but your coyote sounded as cautious as ever. StuRat 02:29, 14 May 2007 (UTC)

"In California there has only been one documented human death attributed a coyote attack." --JWSchmidt 23:37, 13 May 2007 (UTC)

Yeah, that's also in the coyote article, which also says that attacks on humans aren't unknown. But I was hoping for something to contextualise the info there. Thanks for the link. Anchoress 23:59, 13 May 2007 (UTC)

Wolves don't normally attack humans either, except if they are injured or crazed by hunger, which is commonly caused by injury. Are coyotes common in Vancouver proper? As in the habituated bits? I think you should call someone anyway to make sure, like the animal protection department or whatever you have there. Maybe you and your 70lbs dog are safe but what if that cyclist was a child and the coyote is hungry? Though at least this page seems to suggest rabies is not likely. Either way your local animal handlers will be much more likely to tell you if what you saw was abnormal or reason for concern. Vespine 00:34, 14 May 2007 (UTC)

Thanks for the info; I was thinking of calling it in, but I'm not sure where to. Yes, coyotes are extremely common in Vancouver; I've heard up to 1000 just in the City, thousands in the Lower Mainland. I see them all the time in my (very urban, just outside downtown) neighbourhood, but only at night. Aah well, I guess I'll give the City a call on Monday; they should be able to tell me where to report it. Anchoress 00:44, 14 May 2007 (UTC)

BCSPCA Might not be the right people but i bet they'll know who is. I always thought the moose/coyote thing in Canada was a bit like people saying kangaroos hop around the main streets in Sydney;), guess not.Vespine 02:00, 14 May 2007 (UTC)

Yeah, but if you want to see moose and grizzly bears in the same driveway, you have to go to Alaska. Anchoress 02:11, 14 May 2007 (UTC)

They'd better just hope to the bear doesn't decide to go fishing for salmon in their bathtub next. StuRat 02:54, 14 May 2007 (UTC)

It's possible that it was part of a group, looking to get the dog to chase it so that they could harass and exhaust it so that they could kill it. I recall when I worked on a golf course in Edmonton, hearing coyotes howling at each other for a while before hearing dogs barking and then an aweful noise before silence. Creepy stuff, and enough to keep your dog on a leash when walking through parks.

Thanks to all who answered. I was enlightened and entertained, such a rare occurrence. —The preceding unsigned comment was added by Anchoress (talk • contribs) 18:25, 16 May 2007 (UTC).