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Contents 1 March 21 1.1 Free falling human body 1.2 amplifier 1.3 Specific Heat Capacity 1.4 Modeling Friction 1.5 universe 1.6 Boomerang returns in space. Make 'splain that one now! 1.7 Metric expansion of space 1.8 "He's got balls..." 1.9 dimethyl sulfone decomposition

[edit] March 21

[edit] Free falling human body

Let's say that a person is very high up in a building (the 100th floor, 200th floor, whatever). And he falls / jumps / is pushed out of the window and falls to the ground. (No parachute, no nothing.) I have heard that the human body would be dead before it hits the ground. Is that possibly true? In other words, would you die while in mid-air (and of what, exactly?) or does the impact at the ground kill you? When people were falling / jumping from the Twin Towers on 9/11, I remember people saying that they would have been dead before hitting the ground. Shock? Heart attack? Pressure/force of gravity? So, what's the deal with all this? Thanks. (Joseph A. Spadaro (talk) 07:12, 21 March 2008 (UTC))

This idea is a myth, based on poor scientific knowledge and limited reasoning powers, possibly propagated to help the victims' relatives deal with the loss more comfortably. There are many instances of people falling from great heights, for example from flying planes, and surviving.[1] There is also a worldwide sport of deliberate freefalling from planes at high altitude, the participants seem to be able to survive this experience with renewed vigour and an urge to repeat the process. Like the old saying goes 'It ain't the fall that kills ya, it's the stop at the end that does it'Richard Avery (talk) 08:24, 21 March 2008 (UTC)

BTW, according to this [2] (not the best source but I'm sure someone here could calculate it, heck I probably could but I'm lazy) terminal velocity will usually be achieved from a 96 floor jump. Anything higher is therefore irrelevant except it takes you longer to hit the ground. Indeed the terminal velocity article raises another important point. The people who jump off high buildings probably don't even go anywhere nearly as fast as free fall divers since free fall skydivers optimise their body position and clothing to reduce air friction i.e. increase their terminal velocity. People jumping off buildings don't, they may not even have the time to do so that well. Nil Einne (talk) 12:01, 21 March 2008 (UTC)

...free fall skydivers optimise their body position and clothing to reduce air friction i.e. increase their terminal velocity.

Are you sure about that? I thought the standard skydiving position (back arched, pelvis thrust forward) was designed to keep you facing down instead of up at the sky. If you wanted to fall faster, I think you would do it by either curling into a ball and falling buttocks-first, or maybe pointing your arms above your head and falling hands-first. The pelvis-first position doesn't seem particularly optimized for speed. —Keenan Pepper 15:48, 21 March 2008 (UTC)

Like Einstein's Brain, they saved Kittinger's Testicles.

Indeed. This fascinating source says that terminal velocity in normal skydiving position is about 125 mph, but adopting a "balled up" position increases this to about 200 mph. The free fall speed record without special equipment is 321 mph, and Joseph Kittinger reached speeds of over 600 mph in his record-breaking parachute descent in Project Excelsior. Gandalf61 (talk) 16:53, 21 March 2008 (UTC)

A person with a weak heart can, of course, have a heart attack while in suspense about the immediately outcome of hitting the ground. Gravitational acceleration is unlikely to kill because it must be less than one g, half the force delivered on some roller coasters. As for air pressure, at terminal velocity, the force applied by the air is equal to the force applied by gravity; that's why the velocity remains constant. An adult human weighs approximately 75 kg and has a cross-section of about 30 cm x 170 cm, so that's 15 g/cm^2 of pressure. Decidedly not a lot. A person diving head-down would experience 330 g/cm^2 of air pressure, with the reasonable assumption that the head's cross-section is 15 cm x 15 cm and the unreasonable assumption that all air resistance is provided by the head. 330 g/cm^2 is a lot, yes, but I don't think it's enough to kill.

Note that g is a measure of mass, not force or weight, so expressing pressure as g/cm^2 is technically incorrect. I did it to make visualizing the pressures easier. --Bowlhover (talk) 18:16, 21 March 2008 (UTC)

So, basically ... you are alive up until the very moment of impact? And what exactly causes the death at that point? Thanks. (Joseph A. Spadaro (talk) 05:25, 22 March 2008 (UTC))

The Project Excelsior article notes that the reason for Kittinger's high-altitude test jumps was that Air Force scientists were worried that after an ejection at high altitude, a pilot might go into a rapidly rotating fall, at speeds of up to 200 rpm, which could be fatal (I guess they observed this with test dummies) I don't konw if that is a real concern for a person, but that is one potential way in which a person might die before he or she hit the ground. --Bmk (talk) 07:34, 22 March 2008 (UTC)

Bmk - I am confused by your post. What is the potential way? Someone rotating very rapidly at 200+ rpm would (might) die from the rapid rotation itself, you're saying? Thanks. (Joseph A. Spadaro (talk) 21:14, 22 March 2008 (UTC))

Joseph, are you serious? You can take your choice depending on which part of the body hits the ground first. Perhaps a crushed skull with subsequent brain trauma? ruptured heart and major blood vessels? Broken neck and severing of spinal cord? Landing feet first can thrust the femurs up into the chest cavity with consequent damage to the cardiovascular system. I'm sure there are several other serious trauma scenarios that ultimately cause death. Richard Avery (talk) 07:34, 22 March 2008 (UTC)

Yes, I'm quite serious. Why are you suggesting otherwise? Perhaps the question may be worded better. I will assume that the doctor would write _____ on the death certificate. Blunt force trauma? Or what? And is there really any way at all for a doctor to know what killed the person, or would that be impossible to tell ... (i.e., in the resulting carnage, it would be possible / impossible to know which body part actually caused the death?) ...? Thanks. (Joseph A. Spadaro (talk) 21:18, 22 March 2008 (UTC))

For a penny, I once read that throughing a penny off the Empire State Building, it will reach its maximum speed already by falling 500 feet. By the way, Jet Li in a movie once jumped off a building several stories. It looked 5 or 6 stories. He probably jumped the safest and best way possibe. For 1 thing, he didn't fall standing vertically, but horizontally. 2ndly, he was swinging his arms, like in a specific pattern, probably to fight wind resistance. 3rd, he was breathing hardly, probably to fight against wind. And then, he landed on a soft mat. Truly amazing, I thought. Neal (talk) 20:49, 22 March 2008 (UTC).

[edit] amplifier

why amplifier have high input resistanceNippun makkar (talk) 07:34, 21 March 2008 (UTC)

Well, the full answer is that they do not always have a high input impedance. Those that do are designed that way so that the input voltage is not dropped by the input resistance of the amplifier. For instance, if the input impedance was equal to the impedance of the source voltage then the voltage at the amplifier input terminals would be exactly half the sources unloaded voltage. But surprisingly, this might be desirable in some cases. To avoid signal reflection at the input, the amplifier input impedance needs to match the source as closely as possible. In RF applications, amplifiers are often designed in the common base configuration as this results in an input impedance close to the 50Ω characteristic impedance commonly used for RF transmission lines. It can also be desirable to have an input impedance of less than infinity for noise reduction reasons. For the kind of audio frequency amps you are probably referring to, where high input and low output impedances are required, then common emitter is the configuration to use for signal level amps or some kind of push-pull arrangement for power stages. SpinningSpark 09:55, 21 March 2008 (UTC)

[edit] Specific Heat Capacity

In an experiment to find the specific heat capacity of a metal, it is found that 5200 J is needed to raise the temperature of a 2 kg block by 20 oC. How to find the specific heat capacity?

Have you looked at our specific heat article. From that you will see that specific heat is measured in joules per kg per ^oC. Do you see how to calculate it now? SpinningSpark 09:35, 21 March 2008 (UTC)

Heat capacity is Joules per kgram per degree C.

So you need to work out how many joules to raise a block of 1kg the temperaure 1 degree C

eg if it take 100 J to raise the block 3C then in takes 100/3 J to raise it one.

Can you take it from there. (ask again if you get stuck)87.102.16.238 (talk) 12:02, 21 March 2008 (UTC)

[edit] Modeling Friction

Friction is usually modeled by a constant multiplied by a normal force. This is the model used in the friction article, and the one they taught me in high-school physics. It is quite clearly wrong. We all know there's a reason drag racers have big wheels, but with that model of friction it makes no difference. In my robotics class, we once made "robots" go up a slope. They held better when more weight was added. It should be the same. Is it just too complex to make a better model? — DanielLC 16:50, 21 March 2008 (UTC)

Well, for drag racers, the large rear wheels aren't to add weight but to increase surface area and give enough thickness to allow some of the rubber to melt, increasing friction further. This is why you see other auto racers weaving back in forth to melt their tires. -- MacAddct  1984 ^{(talk • contribs)} 17:06, 21 March 2008 (UTC)

There's some discussion of the less-than-ideal nature of friction and the ideas taught in school here. I would suspect that there are so many variables, an overall model is too complex for most uses, but you could probably create a good, useful model for any particular recurrent situation. So you could probably create a useful model for your robots, assuming you don't vary much between trials, but that model probably wouldn't hold for other situations. But I am not a friction expert :) Skittle (talk) 17:14, 21 March 2008 (UTC)

To give credit where it is due to WP, our coefficient of friction article does say that the COF is a system property, rather than a property of the pure materials. As Skittle says, once you have set up your system and chosen the right value of μ, then the simple linear equation is a reasonably good approximation. If you start adding weights and deforming your tyres or creating adhesion, then the equation will cease to apply. That doesn't make it "wrong". --Heron (talk) 10:29, 22 March 2008 (UTC)

Surely adding weights and deforming tyres etc. won't mean the equation ceases to apply, merely that the value of μ in the equation changes? Eve (talk) 22:42, 25 March 2008 (UTC)

To take this into another direction, what you guys were speaking about is essentially sliding friction. There are other kinds of frictions, such as air friction or "drag" (see fluid friction) that aren't modelized in the same way. Stokes' drag usually works mighty fine until you start going at higher speed. Headbomb (talk) 08:50, 26 March 2008 (UTC)

[edit] universe

is there an end to the universe? either way how do you know. —Preceding unsigned comment added by 72.155.39.82 (talk • contribs)

Current theory says yes, and it is ever expanding. See observable universe -- MacAddct  1984 ^{(talk • contribs)} 17:14, 21 March 2008 (UTC)

Another answer would be to say, no, there is no end to the universe, but it is "closed" - if you and a buddy head off in exactly opposite directions, you'll eventually meet up again. From Nature journal: "If the Universe is closed, and has a small enough diameter, we may be able to see right round it because photons can traverse the whole Universe" and "The WMAP data ... suggest that we might indeed live in such a small closed universe". Of course, I'm not all that good at reading this stuff :) Franamax (talk) 20:54, 21 March 2008 (UTC)

[edit] Boomerang returns in space. Make 'splain that one now!

There have been some posts floating about socialbookmarksville relating to a japanese cosmologist's demonstration that a boomerang returns in space. Unfortunately, however, the articles have all been rather sparse on content, and one is at a loss to find any discussion on the matter. The obvious question that arises is: what's goin' on there, then? From my admittedly limited memory, all explanations of boomerang dynamics have involved recount to aerodynamics of the 'leading edge is moving faster through the atmosphere, and so generates more lift' ilk. Having always been rather dubious of the canonical explanations of "wot makes dem aerofoils werk" (planes fly upside down you know, if WWI movies have taught me anything), ones interest is perked as to what possible mechanisms might be put forward for this interesting result. Chards of regards, 83.102.28.140 (talk) 18:30, 21 March 2008 (UTC)

I see no reason why a boomerang would work in space. Boomerangs work by use of an airfoil and lift both of which wouldn't work in a vacuum. Otherwise our spaceships could take off and fly around with wings. -- MacAddct  1984 ^{(talk • contribs)} 18:42, 21 March 2008 (UTC)

Japanese astronaut Takao Doi did not throw the boomerang in space as such. He threw it inside the pressurised International Space Station and thus had all the benefits of aerodynamics to assist its flight. SpinningSpark 18:48, 21 March 2008 (UTC)

Ah, that makes more sense. No gravity, but there is an atmosphere. -- MacAddct  1984 ^{(talk • contribs)} 18:53, 21 March 2008 (UTC)

I would question the wisdom, though, of deploying a hunting weapon on board a spaceship. SpinningSpark 19:48, 21 March 2008 (UTC)

Most commercially available boomerangs aren't useful as hunting weapons. Making them reliably aerodynamic, so they come back, destroys their ability to deal any significant amount of damage. Hunting boomerangs I've seen usually have one end blunted and weighted, making them fly straight and hit hard. A proper throw can make them curve through the air, which probably led to experimentation in design and the more modern-looking boomerang. -- Kesh (talk) 00:32, 22 March 2008 (UTC)

Thinking about it, what would be the point in the first place of having a throwing weapon that returns to the user - if it's only going to be used for hunting animals (I suppose that such a device might have its uses on the battlefield)? If you throw and miss, your prey has more than likely seen your attempt and decided to bolt - whilst you stand there waiting for the thing to come back. It would make far more sense to carry a few 'one way' boomerangs and whang them one after the other in the path of your quarry's flight in rapid succession. --Kurt Shaped Box (talk) 00:52, 22 March 2008 (UTC)

There were two reasons why this was important, both stemming from weapons being expensive (in terms of time invested in making them) back when they were hand-made. Thus, you might not have very many, so didn't want to lose or damage them by having them land who-knows-where. Also, it would take quite a bit of time to track down thrown weapons even if they could be retrieved intact. This is time that could be better spent hunting. StuRat (talk) 03:33, 22 March 2008 (UTC)

Wouldn't the stray hydrogen atoms in the vacuum of space *eventually* have an effect on the boomerang's flight? --Kurt Shaped Box (talk) 20:59, 21 March 2008 (UTC)

I would expect stray rocks and the gravity of large objects to have an effect first. -- kainaw™ 21:11, 21 March 2008 (UTC)

Darn, boring old reality strikes again. 83.102.28.140 (talk) 03:34, 22 March 2008 (UTC) (OP)

No reason to let boring reality get in the way of answering an interesting question. This gives the vacuum pressure of space as 10 pPa. That is a factor 10¹⁶ lower than earth sea-level. Lets say a typical boomerang throw on earth is aimed at a target a distance of 50 feet away and the boomerang travels in a circular path. Distance travelled by the boomerang to return is 300 feet (pi is 3 in my universe). The same throw in space will have 10¹⁶ less "lift" in the direction of curve and consequently the circumference of the curved path is 3 x 10¹⁸ feet or 10¹⁸ metres (there are 3 feet to the metre in my universe). If you threw the boomerang at a velocity of 20 m/s it will return to you in about 88 million years if you manage to miss all the kangaroos and other significant objects in the universe. SpinningSpark 09:47, 22 March 2008 (UTC)

More of an unrelated history answer but..as stated above most boomerangs were the non returning kind that would be used for hunting (mainly) kangaroos and wallabies. The returning kind would be thrown over a flock of birds on a body of water, with the intent (I think) of getting the birds to get scared and fly over the ground where other boomerangs can be thrown at them.--Shniken1 (talk) 12:20, 22 March 2008 (UTC)

If space is curved, surely it will come back to you eventually anyway? Samilong (talk) 05:10, 25 March 2008 (UTC)samilong

[edit] Metric expansion of space

Probably a FAQ but couldn't find what I am looking for!

The metric expansion of space over time is clearly not equivalent to applying an enlargement transformation to all the objects in the universe by a certain scale factor. For example, it doesn't "stretch" the solar system, or pull galaxies apart, or on a smaller scale, tear apart the atoms in molecules (a context where the primary force is not gravitational). However, the distance between distant galaxies does increase.

The intuitive explanation of why in the examples I gave where the distance does not actually increase, is that they were being held together by forces that prevented separation. Distant galaxies are not bound in the same way. Is this intuitive explanation reasonable? Or is it a mistake to view changes to the metric as in some way analogous to the application of a force? IBangMyHead (talk) 19:20, 21 March 2008 (UTC)

On a small scale, whatever the metric of the universe as a whole, space is Euclidean to all intents and purposes. Atoms remain the same size despite the expanding space. Things made out of atoms, like trucks for instance, also remain the same size. Distances between galaxies however are increasing. Think of pieces of broken ice moving apart on an expanding ocean. The ocean is expanding, the distance between the pieces of ice is increasing, but nothing much happens to each individual iceberg. SpinningSpark 19:41, 21 March 2008 (UTC)

Yes - but my question is why clusters of matter that make up the icebergs (stay pretty coherent) behave in a different way to the clusters of icebergs (which spread out). A criticism of the "rubber sheet" analogy is that if you did paint a little picture of the solar system on the sheet as you stretched it, the planets would spread out (and indeed, the planets themselves would enlarge!).

Is it because at a local level, the effects of metric expansion are effectively impossible to observe (the icebergs do expand, but it's harder to observe any change in the icebergs compared to the distances between distant icebergs which clearly grow) or is it because forces that hold the icebergs together counteract the inflationary pressure? IBangMyHead (talk) 19:48, 21 March 2008 (UTC)

User:BenRG is usually good for these kinds of question but he does not seem to have been active on the Reference Desk for a few days. SpinningSpark 19:53, 21 March 2008 (UTC)

As I understand it, it has to do with the different distances on which the forces operate most effectively. Gravity is very weak on small scales compared to electromagnetic forces. Metric expansion of space is only going to be very noticeable on massive scales; on smaller scales, the more locally powerful forces are going to reign supreme. The structure of atoms themselves are regulated by nuclear force, which metric expansion of space couldn't affect even if it wanted to, and the structural integrity of molecules is going to preserved by the electromagetic force. Does that explain things? Different forces are powerful on different scales, and that's why something that can move entire galaxies is not going to affect things within those galaxies. --Captain Ref Desk (talk) 20:04, 21 March 2008 (UTC)

1. If the answer is to do with the big bang 'throwing out matter spherically' then one would expect a universe that has the galaxies concentrated at the edge.

2. Another answer could be that the theory is simply inconsistent.

3. Another answer would be that everything should be explanding equally but the forces between 'bonded' matter (ie the icebergs) stops them doing so (as you say). ie/eg gravity affects the expansion - regions with more gravity expand less. ie the gravity forces between galaxys is very weak.

3a. Think in terms of weak springs and strong springs holding everything together - the strong springs are under tension but do not expand much eg molecules/icebergs. The weak springs are under tension but stretch lots - hence galaxies are far apart - In this case it helps if you assume that the expansion of space is accelerating.87.102.16.238 (talk) 20:14, 21 March 2008 (UTC)

3a (sub) You don't need to throw away standard euclidean space in 3a. This model works using simple concepts such as spring constant - which can be directly related to electromagnetic and gravitational forces. The only requirement for success is that the lengths are increasing and the rate of increase is increasing eg the metric is accelerating as it increases in length eg L=lenght dL/dt>0 AND d²L/dt²>0. I can't emphasise this enough!

[edit conflict] You may be right, Captain, based on this, but if so I don't understand why, because metric expansion isn't a force. (Is it?) And excellent question, IBangMyHead. --Allen (talk) 20:21, 21 March 2008 (UTC)

Yes - metric expansion can cause a force - see above comment 3a, 3a(sub) - that would go some way to explaining things - no idea if that is really true.87.102.16.238 (talk) 20:23, 21 March 2008 (UTC)

It looks like the simplest explanation for this phenonama would be that all things in the universe experience an additional force (additional to the ones you know eg gravity,electro ) that is universally repulsive. Only strongly bonded things can resist this force. What is the name if this force?87.102.16.238 (talk) 20:43, 21 March 2008 (UTC)

There's no reason to think it's not a force just because nobody else has stated it is or isn't - it acts like a force therefor it is a _____.87.102.16.238 (talk) 20:45, 21 March 2008 (UTC)

Here is some perfectly relevant discussion from Argonne National Lab, inspired by our own article. Apparently even (non-cosmologist) physicists can be confused by this question. --Allen (talk) 21:14, 21 March 2008 (UTC)

And Michael Pierce seems to agree with you, 87, although he doesn't name the force resulting from expansion. --Allen (talk) 21:20, 21 March 2008 (UTC)

It's interesting that both my question and the one raised on the Argonne Lab page were inspired by the same Wikipedia article, and by the comparison of the "raisin" and "rubber" models in particular. Captain Ref Desk's point that "The structure of atoms themselves are regulated by nuclear force, which metric expansion of space couldn't affect even if it wanted to, and the structural integrity of molecules is going to preserved by the electromagetic force" is one that I had alluded to in my question - one of the things that had caused me to ask the question was that I had in fact considered this, and on thinking about it, it seemed that the internal structure of a basic molecules could be computed (e.g. internal distances for a stable molecule) so any separation caused by inflationary pressure would end up being reversed by the internal forces anyway (and in practice the "spring" would not expand and then contract - merely resist) but this seemed to suggest the idea itself that there is an internal "reactive force" counteracting an "inflationary force" - the fact that distant galaxies have no equivalent possibility for a "reactive force" could then explain why they were affected by the inflation. But as I couldn't find anything written about this force - or at least analogy to a force - I came to the refdesk. In particular I'm not sure just how sound the analogy (or literal truth of inflationary "forcehood") is, and what consequences it has. For example, if you view it as a force, does it mean that the "springs" of atomic bonds are somehow in (very slightly) more "tension" as a result? And if it is a force, then does this have any energy implications (not all forces have an energy associated with them, but some obviously do)?

One thing that was maybe too subtle for both me and Captain Ref Desk is the comment in the Argonne link that "If everything (and I mean everything) were changing with time, such that the universe, the yard-stick, and the relative force strengths (the coupling strength) were all changing in the same way and proportionally, then there would be no way to measure such a change" which is rather insightful. You obviously can't make the universe twice as big in any meaningful way by getting ISO to define "1 new metre = 2 old metres" because, for example, formulae for gravitational attraction would simply change from F_old = GMm/r² (r measured in "old metres") to F_new = GMm/R² (R measured in "new metres" so R = 2r; the two forces would actually have different but convertible units) and there would be no observable difference. (Mental note: when metric conversion finally happens, switching from yards to metres will not increase the size of the universe by around 10% and my waist will not be 10% larger...) When we say "the metric changes" we obviously don't mean it in this naive way. Stretching my intuitive understanding a little bit, is a reason that we might look at inflationary pressure as a force, that the formulae for e.g. inverse square attraction/repulsion somehow don't change their distances, but the distances themselves should change - and if the distance doesn't change, it is apparently because a reactive force has constrained it from doing so? 87.113.64.15 (talk) 22:11, 21 March 2008 (UTC)

Note to 87.113 - by the time the USA finally switches to the metric system, I pretty much guarantee that your waist -will- be 10% larger :) Franamax (talk) 00:55, 22 March 2008 (UTC)

There is nothing pushing the galaxies apart (ignoring for the moment the cosmological constant, about which more later). The galaxies are moving apart because of inertia. They were moving apart in the past, and nothing has stopped them—gravity has only slowed them down a bit, and the other forces don't operate between galaxies at all. The galaxies have been moving apart since they formed, because they condensed from matter that was moving apart, and they acquired the average velocity of that matter. But they did condense; that means that local gravitation overcame the initial separating velocities, just like the gravity between the earth and an upward-thrown ball overcomes their initial separation velocity. Once the initial separation has stopped, that's that. There's nothing trying to make the ball fly away from the earth again, it just happened to be flying away to begin with in the unexplained initial conditions of the problem.

Aside from making galaxies and clusters condense out of the primordial Hubble flow, gravity also makes the Hubble expansion as a whole slow down. Absent a cosmological constant, the recession speed of a typical pair of galaxies can only decrease with time. But the more they recede from each other the weaker the attraction between them becomes. If the matter density of the universe is high enough (above the critical density), then the attraction wins out and the universe recollapses (i.e. the ball falls back to earth). If it's not high enough then the galaxies disperse too fast for gravity to pull them back together (i.e. the ball exceeded the escape velocity). In the latter case the recession velocities approach a limiting value and the galaxies simply recede linearly away from each other forever, with essentially no further gravitational interaction since they're so far apart.

Okay, now add a cosmological constant to this. Probably the best way to think of the cosmological constant is as a correction to the gravitational force. Along with an attraction proportional to m/r², you also have a repulsion proportional to r. At small separations the attaction wins out; at larger separations the attraction decreases and the repulsion increases until eventually there's a crossover point and the repulsion dominates. With regard to the overall motion of the universe the situation is not much different from before; there's still a critical density below which the attraction wins and above which it doesn't, except that now if the attraction doesn't win, the far future motion is exponential instead of linear (because the solution to the differential equation is exponential). But again this only affects large clusters of matter which are still moving in the aggregate with the Hubble flow. For things which have condensed out of the Hubble flow, like our galaxy, the short-range attractive force dominates to such an extent that you can't even detect the repulsive term with the most delicate experiments. About the only visible consequence of the runaway separation is that you lose sight of other galaxies (and the CMBR). This eventually happens even without the cosmological constant, but it takes a lot longer. Other than that, life continues as normal until heat death (sorry, I know it's a downer). One caveat is that it's not clear yet whether the dark energy actually behaves like a cosmological constant. If it doesn't, there are other scenarios like the big rip. -- BenRG (talk) 00:19, 22 March 2008 (UTC)

Excellent answer, BenRG; thank you. But it leaves me confused about where "metric expansion" fits into the picture. I had the impression that for most of the 20th century, metric expansion was accepted based on Hubble's observations, but that the cosmological constant was rejected until the 1990s. So metric expansion != cosmological constant, therefore your first two paragraphs must be dealing with metric expansion. But you make it sound like a simple matter of galaxies flying apart in a Newtonian sort of way, whereas metric expansion is supposed to be spookier than that, as in space itself expanding... whoa! Is there a straightforward way to relieve some of my confusion? (I'm mindful that if one keeps asking physics people seemingly logical cosmological questions, one will eventually be told, "Sorry, beyond this point there's no substitute for learning the math.") --Allen (talk) 01:14, 22 March 2008 (UTC)

I think some confusion here arises from thinking of space and time as a static stage on which objects such as galaxies are placed. In general relativity, space-time is shaped by matter and energy, so it is not a static backdrop. Most distributions of matter and energy give rise to very complex space-time configurations. However, if we assume a particularly simple case in which the distribution of matter and energy is both homogeneous and isotropic, the equations of general relativity can be solved, resulting in the Friedmann equations. These say that the metric or scale of space (as determined by a yardstick based on the wavelength of light) is changing over time in a way that is determined by just three numbers - the average density of matter and energy; the average curvature of space and a cosmological constant. Depending on the values of these parameters, the space-time metric may expand forever, or may go through an initial expansion followed by a subsequent collapse.

The assumptions of homogeneity and isotropy on which the Friedmann equations are based are only correct on very large scales. Within our solar system, and even within a single galaxy, the distribution of matter is far from homogeneous, and the Friedmann equations do not apply. However, if we observe distant galaxies then we reach a scale at which the universe is approximately homogeneous and isotropic. Light from these galaxies is red-shifted by an amount that is proportional to their distance - this observational law is called Hubble's law. This redshift is a result of the metric expansion predicted by the Friedmann equations. We don't observe this metric expansion when looking at nearer objects (i.e. anything in our solar system or our galaxy or nearby galaxies) because the Friedmann equations do not apply at smaller scales.

We can measure the constant of proportionality between red-shift and distance, which is called the Hubble parameter. We can estimate the average density of matter and energy in the universe. And the age of the universe means that the average curvature of space must be very close to 0. These facts are all consistent with a version of the Friedmann equations in which the metric is expanding, but the cosmological constant is 0. So, yes, the expansion of the space-time metric can happen even without a cosmological constant, and cosmologists originally left the cosmological constant out of their models because there was no good reason to complicate matters by including it. However, by observing distant galaxies very carefully we can tell how the Hubble parameter has changed over time, and recent observations show that the expansion of the metric is actually accelerating. This is not consistent with a cosmological constant of 0. So the most-favoured current model of the large-scale evolution of the universe, the Lambda-CDM model, has a non-zero value for the cosmological constant. Gandalf61 (talk) 13:07, 23 March 2008 (UTC)

The expansion is just galaxies flying apart. But it's not entirely wrong to say that space is expanding, because in the case of perfect isotropy and homogeneity the matter pretty much is the spacetime. Normally there are extra degrees of freedom in the geometry beyond the ones which depend directly on the local distribution of matter. They describe what's normally thought of as the gravitational field (which extends into the empty space surrounding the gravitating matter), and gravitational waves (which can propagate through vacuum). But the extra degrees of freedom always violate homogeneity and isotropy, so when matter is homogeneous and isotropic spacetime can't "do" anything independent of the matter in it. You can read the local shape of spacetime straight off of the local stress-energy tensor. Technically the Weyl curvature is zero.

Here's the 1+1 dimensional case (or its Euclidean version, anyway). The Gaussian curvature of a location in spacetime equals the mass-energy density there. So take a little piece of two-dimensional space with positive Gaussian curvature. Homogeneity implies that the matter density is the same a little way to the side, so attach another piece of space with the same shape next to the one you already have so that they fit together smoothly. Keep doing this (sideways), and the overall shape will inevitably curl into a circle, in the same way as the surfaces in this thread. Now extend this upward (into the future) and, if you like, downward as well. You might think that you'll end up with a sphere, and you would if not for the fact that the mass-energy density doesn't remain constant. If you draw a bunch of lines perpendicular to the circle of symmetry, representing the paths of individual particles, the paths will converge (increasing the density) if the circle gets smaller and diverge if it gets larger. Overall the matter density, hence the curvature, will be inversely proportional to the radius of the circle of symmetry. (With three spatial dimensions it's inversely proportional to the cube of the radius.) Note that the circle itself and its radius are physically meaningless—just an artifact of the embedding—but they happen to be a convenient way to see the overall density. The physical reason for the change of density is the local convergence or divergence of the lines.

The completely general form of this kind of geometry is a sort of extruded circle whose radius is a function of time (only). I can parametrize this with a coordinate t measured vertically along the surface (not in the embedding space) and an angular coordinate θ, and the distance between points on the surface is then in the Euclidean case, or in the Lorentzian case. That's the FLRW metric. It's simply the most general possible geometry with this kind of symmetry.

So there's clearly a sense in which "space is expanding": the lines are diverging and (therefore, necessarily) the circle is getting larger. But at the same time it's a strange thing to say, because space isn't a substance that changes over time. The space at a later time is different space, and there's nothing that inherently relates it to space at an earlier time. What does persist with time is the matter, and the real physical content of the expansion is the divergence of the matter lines.

This may not sound much like inertia, but it's exactly the same thing. Locally the surface is roughly flat and diverging lines are just objects moving away from each other. Our lines of "constant time" were chosen on the basis of the global symmetry. Whenever we have objects locally moving away from each other we have a local Hubble-like expansion with a geometry that's locally FLRW-like, and we can choose a local cosmological time (generally not aligned with the global one) that respects the symmetry of that local expansion.

This also may not sound much like Newtonian physics, but again it's almost exactly the same thing. You can, though I don't know the details, rephrase Newtonian gravity in the same kind of geometric language. What I do know how to do is quantitatively derive the Friedmann equations from a Newtonian big bang model, so let me do that. (This is going to be a long post.)

Suppose we have infinitely many particles with uniformly distributed velocities in a Newtonian universe. At time t = 0 they're all at the origin, but an instant later they're uniformly distributed through all of space. In the absence of gravity they'll separate linearly forever. What's the effect of gravity? Well, consider a spherical region of matter centered at x₀ with radius r. Its total mass is , where ρ is the mass density of the particles (at a given time), and so it causes a gravitational acceleration of on a particle at the edge of the sphere. The rest of the matter in the universe has no effect at all, because it can be considered as a collection of concentric spherical shells around our sphere, and a uniformly dense spherical shell of matter has no gravitational field inside. (If this argument sounds a bit dubious, note that you can get the same answer with less handwaving by solving the gravitational Poisson equation.) So for a particle at x the vector acceleration is . But there's a serious problem here: x₀ was arbitrary, so we've just derived a force of arbitrary magnitude pointing in an arbitrary direction. This has led people sometimes to claim that Newtonian gravity doesn't work for unbounded distributions of matter. But those people are wrong, because there's a hidden gauge freedom in Newtonian gravity. A constant gravitational field accelerates everything in exactly the same way, and when everything accelerates in the same way you can't tell that anything is accelerating at all. So you can add an arbitrarily time-varying spatially constant vector field to any gravitational field without changing any of the physical predictions of the theory. And all of our solutions differed by a spatially constant vector field, namely . So they are all really the same solution. Gravity just makes the particles attract each other with a relative acceleration proportional to distance, without any particular center. Since it doesn't matter where the center is, I'm going to take .

We can add a cosmological constant to this. The cosmological constant adds a term to the gravitational acceleration that's proportional to distance, changing it to − Gm / r² + (Λ / 3)r, where I've arbitrarily (but with malice aforethought) chosen a proportionality constant of Λ/3. For our distribution of matter this gives an acceleration of , where I've picked the origin for the Lambda term to be 0 (I can do this for the same reason as before). So the equation of motion of a particle at distance r from the origin is

or with a bit of rearrangement

,

which you might recognize as the or limit of the second Friedmann equation.

Now, ρ changes with time, and not independently: it's inversely proportional to r³, where r is the distance between any two particles moving with the overall flow. So let's substitute ρ = k/r³ in the equation of motion:

multiply by 2r':

integrate:

divide by r²:

and that's the first Friedmann equation. I don't actually know the significance of the curvature term showing up as a constant of integration; I've been assuming no curvature.

Notice, incidentally, how this gauge freedom in the gravitational field gets us general covariance. In the absence of gravity, Galilean relativity says that we can treat any uniformly moving object as our standard of "rest at the origin". With gravity we can extend this from uniform motion to arbitrary motion. We get rid of the second and higher time derivatives by adding a uniform gravitational field proportional to the second derivative, and then eliminate the first and zeroth derivatives with a Galilean transformation and a translation. I believe there's another gauge freedom which can be used to relativize rotation as well. In fact all of this works better in Newtonian gravity than in general relativity, where all kinds of problems crop up that have no Newtonian analogue. The twin paradox shows the failure (in a certain sense) of Einstein's general principle of relativity in a Lorentzian world. In a Newtonian world, of course, the twins are always the same age when they rejoin, and there's a true equivalence of all paths.

We can also introduce perturbations. Because like attracts like, gravitation is inherently unstable; it tends to magnify small variations in the density instead of smoothing them out like electromagnetism does. So we get clumping. The clumping is probably happening everywhere, but since we can choose the origin to be anywhere, let's look at clumping around the origin. We can still use the concentric-shell argument to ignore most of the matter in the universe; it no longer applies exactly but it becomes more and more accurate as the shell size increases. The Λ term is negligible since it's proportional to distance from the origin, so the clumped matter pretty much follows the usual rules of Newtonian gravity as though it were alone in the universe. You get stars, galaxies, planetary orbits, and so on, but the aggregate motion is still roughly zero—that is, still roughly with the Hubble flow. There's nothing to give it a significant velocity in one direction or another. This applies to all of the clumps everywhere in the universe. The characteristic clumping scale will increase with time, but the Hubble flow and overall homogeneity will always persist at larger scales.

There's one important feature of general relativity which doesn't show up in the Newtonian case: the local light cones. The fact that light moves locally at c with respect to the local Hubble flow is a nice realization of Mach's principle. This has no analogue in Newtonian gravity as far as I know.

It's also worth looking at a special relativistic big bang. Again say we have an infinite collection of particles at the origin with evenly distributed velocities, but now they're evenly distributed over the hyperbolic space of SR velocities. In the 1+1 dimensional case, this means evenly distributed rapidities. After a time t has elapsed the particles form a sphere of radius ct, with the density approaching infinity near the edge. This is a lot like what many people imagine big bang cosmology to be. But t is not a very nice time coordinate, because it doesn't respect the inherent symmetry of this setup. A better time coordinate is based on the proper time of each particle, that is, . This is the cosmological time. The locus of points at a particular τ is a spacelike surface which is hyperbolic and filled with particles at a uniform density out to infinity. The particles have time-invariant recession speeds which obey Hubble's law at any given time (with a time-varying Hubble constant). This is, in fact, the ρ = 0 case of the FLRW cosmology—just a coordinate reparametrization of Minkowski space. This is why space is hyperbolic for low densities (below the critical density).

The Euclidean version of the special relativistic cosmology is polar coordinates, with τ being the radius. If your whole universe has spherical symmetry then global polar coordinates make sense. If you locally have some uniformly diverging lines then local polar coordinates make sense (which probably won't coincide with the global coordinates, though they might). Add gravity and you get global/local curvature, giving a global/local FLRW shape, which makes it sensible to use "longitude" and "latitude" lines (FLRW coordinates), which are the curved-space versions of the polar coordinates. -- BenRG (talk) 18:59, 23 March 2008 (UTC)

[edit] "He's got balls..."

Is there any real correlation between human testicle size and the propensity for bravery and courage? --81.77.147.21 (talk) 22:27, 21 March 2008 (UTC)

The verifiability and falsifiability of a claim would be in question. Mac Davis (talk) 00:28, 22 March 2008 (UTC)

It's fairly well established that high testosterone levels cause aggressive and risk-taking behavior. However, the link between testicle size and high testosterone level is less certain. In the case of athletes taking steroids, for example, they often have high testosterone levels and small testicles. StuRat (talk) 03:01, 22 March 2008 (UTC)

For what it's worth, our article on testosterone claims that it's low levels that cause aggression. --Milkbreath (talk) 03:23, 22 March 2008 (UTC)

The IP who inserted that information (without references) in October has a string of vandalism warnings around the same time and was then blocked. I would suggest that can safely be put down to vandalism and 82.42.171.4's other edits should be reviewed at as well. SpinningSpark 08:49, 22 March 2008 (UTC)

Of course there is - but only in men. silly.87.102.16.238 (talk) 11:41, 22 March 2008 (UTC)

[edit] dimethyl sulfone decomposition

Does dimethyl-sulfone (MSM) decompose in household storage, or is it stable? Would it be an oxidation or reduction reaction?

If you keep it in the bottle it should be fine. It should stay that way for years. Mac Davis (talk) 23:56, 21 March 2008 (UTC)

Are you asking again with different words? We don't offer advice on how things work inside your body. Even if it's not a medical compound, really, ask a pharmacist. Franamax (talk) 00:39, 22 March 2008 (UTC)

It is kept in the bottle in a cupboard and opened daily, with a bit spooned out. The spoon is always clean and dry, but the powder balls up a little due to attracting moisture in the air. Someone reported the same "balling up", but they also said that dimethyl-sulfone does not decompose significantly over time.

The question is straightforward and not about physiological application. I am sure the WP community has thousands of participants of any given background, but anyone knowledgeable about the stability and/or reactivity of dimethyl-sulfone at room temperature can address my question. Thank you.

dimethyl sulfone should keep for a long time when stored correctly eg in the dark, stopper on. Just how long I don't have the answer. But it is in general stable (like sugar etc)87.102.16.238 (talk) 11:50, 22 March 2008 (UTC)

Yeah make sure it is in the dark. Double bonds never like UV light.--Shniken1 (talk) 12:10, 22 March 2008 (UTC)