Wikipedia:Reference desk/Archives/Science/2008 December 18

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December 18

Brazilian copperfish

Hi guys, an anon added a message to the Brazilian copperfish article saying it was a hoax, and I'm certainly finding it hard to find evidence that it isn't. Any of you guys have a big book of south american fish or something? --fvw* 01:25, 18 December 2008 (UTC)

I can't find it on FishBase, which is usually pretty good for piscine problems. DuncanHill (talk) 01:46, 18 December 2008 (UTC)

Good enough for me, AfDed it. Thanks! --fvw* 02:34, 18 December 2008 (UTC)

The article has no references to check. There are exactly TWO Google hits for the fish (either in English or Portugese) - this Wikipedia page and this odd page www.mydearvalentine.com/valentine-vacations/rio-%20de-janeiro.html (which is blacklisted here on Wikipedia) that uses almost the same odd phrasing:

MyDearValantine.com: "If you are in a mood for fishing then catch a plethora of the famous Brazilian copper fish which are in abundance in the river and makes fishing a popular activity in Brazil."

Our article: "In Rio de Janeiro, one can expect to catch a plethora of famous Brazilian Copperfish."

But that's IT. The fish is not mentioned at on any of the many [1] fishing web sites devoted to the Rio de Janerio area), no hits for the supposed discoverer, no hits for the Genera it's supposed to be a member of. It's supposed to be moderately closely related to the Piranah (according to the classification on that page) - yet the fish in the photo looks nothing like a Piranah. The sole author of the article has been accused of vandalism half a dozen times and has shown no previous interest in working on articles about fish. Given the political turmoil and tension between the urban and rural parts of Brazil in 1936 - it seems a doubtful destination for a field trip by "Nature enthusiasts". The language of the article is peppered with phrases like "Believe it or not" - which (along with the zero references and the utter non-notability of the subject) would be enough to justify deletion even if it wasn't a hoax. Yeah - take it down. SteveBaker (talk) 04:18, 18 December 2008 (UTC)

We need some sort of "This article was deleted with help from the RefDesk" thingy, like the one for articles we helped improve! DuncanHill (talk) 04:21, 18 December 2008 (UTC)

For the sake of the record, the (now closed) AfD is at Wikipedia:Articles for deletion/Brazilian copperfish. DuncanHill (talk) 04:27, 18 December 2008 (UTC)

Actually - I was kinda annoyed at how quickly it vanished - I wanted to see from the edit history whether this user had collaborators or sock-puppets and perhaps thereby track down any other hoaxes from the same source that might have gone unnoticed. The connection to the 'MyDearValantine.com' site is particularly interesting. I also found a company CALLED "Copperfish" who promote web sites by bumping their Google search results...it seemed possible that this hoax article was somehow related to their activities. I was happily doing my Sherlock Holmes thing - when all of the evidence was suddenly evaporated! Oh well...next time maybe. SteveBaker (talk) 20:31, 18 December 2008 (UTC)

Maybe a friendly admin would email you a copy of the edit history of the article? DuncanHill (talk) 20:33, 18 December 2008 (UTC)

Looks like almost all of the article text came from User:Vinegar. Kaldari (talk) 23:09, 18 December 2008 (UTC)

A kindly passing admin gave me a copy of the article - I'll go and play detective for a while. SteveBaker (talk) 04:14, 19 December 2008 (UTC)

So would you say, on the whole, that the article is (was) fishy? —Tamfang (talk) 18:58, 28 December 2008 (UTC)

Perhaps it is not a hoax because many fish exist in the Amazon rainforest that are often not documented in western fish encyclopedias such as FishBase and some have not even been scientifically classified as species, also i found one travel website that mentions the Brazilian copperfish as the local delicacy of the city Rio de Janeiro and an additional website that says the Brazilian copperfish is the official food of the Brazilian national team. --Apollonius 1236 (talk) 01:18, 26 December 2008 (UTC)

• There's another person on wikipedia who knows the person who made it (I merely know someone who knew the creator). In any case, read the AfD log - it's pretty obvious it's a hoax. --V2Blast (talk) 07:34, 25 January 2009 (UTC)

cheap lead testing

After reading a previous question about lighting and turtles, I had an idea for a student's school science experiment and I was wondering if it is possible... Every year, there are recalls for toys that have lead paint. It is possible to spend a lot of money to send every toy you have to a lab for testing, but what about home testing? Using only products easily purchased at a common grocery or department store, is it possible to effectively test for lead? Right now, I'm going through the standard cleaners and looking for one that has a chemical that will change colors, produce smoke, or smell real bad if mixed with lead. -- kainaw™ 13:54, 18 December 2008 (UTC)

This Consumer Product Safety Commission report says that the home lead test kits you can buy are unreliable, and their manufacturers don't have the "made with common ingredients" constraint that you do, so I imagine the answer is "no". --Sean 15:21, 18 December 2008 (UTC)

What's really disturbing about that report is that the vast majority of errors are false negatives (50% of the samples that were positive by reference test were missed). A qualitative screening test should always be designed to err on the side of caution, since it can be followed with a more reliable test for a "confirmed result." Given that a consumer is unlikely to even consistently perform the test correctly, they're even more suspect. One point of methodology that may be of interest. The kits given are most likely swab tests. Destructive testing (i.e. grind up the toy) is more likely to give thorough results, though it has obvious problems if you wanted to play with said toy... SDY (talk) 19:32, 18 December 2008 (UTC)

Could high energy alcohol be used as a jet fuel?

I'm particularly asking about 2-Ethylhexanol. Sure with proper jet engine redesign / modifications. 2-Ethylhexanol should contain more energy per kilogram then jet fuel/gasoline (failed to find numbers using Google, but looks like it). And it even denser. And in comparetion to 9+ carbon alcohols 2-Ethylhexanol have low melting/freezing point. Even lower then jet fuel. Cost of production is irrelevant to this question - just imagine that we can get 2-Ethylhexanol at same or a bit lower price then jet fuel. What would prevent use of it as a fuel for airliners? Vitall (talk) 16:17, 18 December 2008 (UTC)

I don't know about that particular fuel, but here are some other things to consider for a jet fuel in general:

1) It must have a high boiling point so it doesn't boil off before using it. This is a deficiency in liquid hydrogen.

2) It must not thicken up at cold temps. This can be a deficiency in bio-diesel fuels.

3) In addition to having a high energy density per mass, it also needs a high energy density per volume.

4) The ignition temp needs to be within a certain range. StuRat (talk) 00:17, 19 December 2008 (UTC)

Safety is another issue - for passenger airliners, they have to add gelling agents to prevent fuel spills from causing major problems. Boiling at low pressures - causing carb icing in prop planes. How safe is it to store, transport, pump. There are just an enormous number of practical problems.

1) Boiling point of 2-Ethylhexanol is 183-185°C. Even higher then Etanol, and FAR CRY from hydrogen(obviously). Boiling point for real life Jet fuel JP-5, MIL-T-5624M, AVCAT is 156-293°C. Essentially the same.

2) As I mentioned before, freezing/melting point of 2-Ethylhexanol are lower then most of jet fuels(-76°C versus -40°C). Liquids tend to thicken up when they come close freezing point.

3) That very strange point. If energy per mass comparable or close and one substance(2-Ethylhexanol) is denser then another(jet fuel), aren't that void your point?

4) Flash point for JP-5: 60°C. "2-Ethylhexanol is a combustible liquid above 60°C.". Essentially same. And there are jet fuels with different flashing points.

Increasing safety by adding gelling agent most likely won't be needed. So called kinematic viscosity of high carbon alcohols are high. But main question - what the problem with adding different agents, if they needed to be added? Why it is not possible to add them, just like we add them in case of ordinary jet fuel? Some very special chemical properties of 2-Ethylhexanol? Or you think something wrong with alcohols? What?

"How safe is it to store, transport, pump. You think with current technology it not possible to safely store transport and pump 2-Ethylhexanol? but industry produce it thousands of tons annually. You think they did not store or transport ethylhexanol??? Or do they do it in a non safe way? What make you think that???? Vitall (talk) 10:23, 19 December 2008 (UTC)

1) Boiling point of 184°C is a long way from 293°C, so it sounds like your fuel may not work for those applications which result in the most heating of the fuel tanks, such as long, high altitude, high speed flights, at least not without an additive to increase the boiling point. It may still be appropriate for lower, slower, shorter, flights, however.

2) As for viscosity, it's not solely a function of how close you are to the freezing point. Some fuels, like bio-diesel, become unacceptably thick at temps well above the freezing temp.

3) I don't understand what you're saying. My argument is that you must not only keep the plane's weight down, you also need to fit the fuel into the existing tanks to get the same range, regardless of weight. (Although the fuel weight does obviously have an effect on range, too.) So, for example, you couldn't use uncompressed hydrogen gas, regardless of it's energy-to-mass ratio, because it's energy-to-volume ratio is too low.

5) (New item) It must not damage the materials it will contact. For example, ethanol tends to damage rubber. This isn't insurmountable, as all rubber seals can be replaced with silicone, but it is a concern.

6) (New item) It must burn cleanly, not producing tar that will pollute the environment and gum up the engines.

7) (New item) It shouldn't be water-soluble, as that allows large fuels spills on the ground to pollute the water table. The most infamous case of this was the gasoline additive, MTBE.

As for safety, the other poster didn't say that your fuel is unsafe, only that this is a general concern for all fuels. I would add that, in practice, this means that the fuel must not be highly volatile (readily evaporate). If so, any small spill becomes an explosion hazard. Ideally, you should be able to toss a lit match on a puddle of the fuel without it igniting. Only when sprayed through a nozzle should it become flammable. Toxicity is also a concern, as workers are likely to get the fuel on their skin or inhale fumes occasionally. StuRat (talk) 16:22, 19 December 2008 (UTC)

1) 184°C higher then 156°C. JP-5 is in range 156-293°C. Second Google link for "JP-5 boiling point" claim "Initial point: 182°C". 184°C is almost same as 182°C. And JP-5 is not ONLY jet fuel out there.

2) There are additions that could increase lubricity if needed. And in fact they were used in some blends of jet fuels. Plus there is jelling agents, as someone mentioned above. So adjusting that property should not be a problem(if it need to be adjusted of course).

3) That exact point I have clearly addressed in initial question.

5) That is a problem of ethanol, not hi-carbon alcohols. Anyway, I wasn't in any way suggesting to use existing equipment/engines/etc.

6) During burns alcohols produce CO2 and H2O.

7) 2-Ethylhexanol non soluble in water.

Current jet fuels are complex mixture of hydrocarbons that are toxic by definition. And that include dermatotoxicity. I'm not sure what substance more toxic in relation to each other. And about lit match - that totally untrue for current jet fuels. The only one I could recall had such property, was highly specialized fuel for SR-71(Blackbird). Obviously not in use anymore.

Overall, this looks like general discussion of what jet fuel could/should be. Not exactly my question about 2-Ethylhexanol. Vitall (talk) 23:01, 19 December 2008 (UTC)

Well, since you know all the properties of that substance, you can judge for yourself whether it meets the criteria for a jet fuel which we describe.

6) Note that many fuels theoretically burn to produce nothing but carbon dioxide and water. However, in the real world they produce complex hydrocarbons and/or carbon monoxide, due to incomplete combustion. StuRat (talk)

I don't know ALL properties, and that is why I'm asking. My primarily source is Wikipedia(different articles) and secondary Google search. I still hope someone with knowledge of 2-Ethylhexanol will step in. Vitall (talk) 17:15, 22 December 2008 (UTC)

fluorimeter/turbimieter

In the context of measuring the turbidity (haziness) of a liquid, is there any important difference between a dedicated turbimeter and a fluorimeter set to the same emission and excitation wavelength? ike9898 (talk) 16:31, 18 December 2008 (UTC)

Exoplanet detections in next decade

How precise will the orbital elements and physical characteristics of exoplanets will it be determined in next decade from telescopes or ultra-precise astronomical instruments, such as Terrestrial Planet Finder, Darwin, New Worlds Observer, SIM PlanetQuest, and Overwhelmingly Large Telescope?

Will future telescopes and instruments will determine inclination, true mass, radius, density, surface gravity, temperature, appearance, features, composition, detecting whether it has moons or rings, and others for almost all known exoplanets as of the next decade? Knowing the true mass of exoplanets is important about whether some candidate exoplanets are actaully exoplanets or a brown dwarfs. Knowing the appearance of extrasolar planets is important about how will extrasolar planets be look like, along with moons and rings if detected. BlueEarth (talk | contribs) 18:47, 18 December 2008 (UTC)

I don't know the answer to your question - but I think the primary goal is to capture enough light from an exoplanet to do spectrographic analysis of the atmosphere. The idea being that we'd have a chance to detect life by finding some 'signature' molecules in the atmosphere. Another goal is simply to make a gross count the numbers of planets of different kinds so we'd know how unique (or non-unique) the earth is. Knowing the other data is interesting too - but beyond simply hoarding information - I'm not sure how it moves science forwards. SteveBaker (talk) 01:06, 19 December 2008 (UTC)

Expansion of the Universe and Perpetual Motion.

(This is a follow-on from an earlier question which is about to scroll off the top of the desk without getting properly answered.)

User:Tango and I seem to have invented a perpetual motion machine - which is annoying.

Find someplace with a nice hard vacuum and no nearby stars or planets to mess things up. Take two large masses (I'm thinking 'bowling balls') and fling them off in opposite directions at a velocity that's just a little less than the escape velocity due to their mutual gravitation. They fly off in opposite directions and (because they aren't all THAT heavy - and they have to move very slowly to avoid hitting their mutual escape velocity) it takes a l-o-n-g time for them to slow down and start falling back towards each other. During this time, the expansion of the universe is gradually increasing the distance between them - so that on the way back towards the starting point, they have to travel a tiny bit further than they did on the way out. This means that the total momentum when they eventually collide is a little more than the momentum we had to give them to launch them off in the first place. Since that extra momentum could be harvested by various means, we get a tiny bit of energy for free...from nowhere.

(We can make a proper perpetual motion machine out of this by using rubber bowling balls which bounce off of each other and head back out again at just the right speed...I'm going to boldly assert that the extra energy we pick up from the expansion of the universe is set up to be exactly enough to overcome annoying things like drag from the interstellar hydrogen and the energy lost in the collision).

Could someone please help us figure out why it can't work? (Or failing that - tell me where the "OFF" switch is - all of these bouncing rubber balls are REALLY distracting?)

SteveBaker (talk) 21:56, 18 December 2008 (UTC)

The expansion of the universe does NOT add momentum to the balls. Momentum is universally conserved even in an expanding universe. Thus, your make an incorrect assumption that they will return to the same point with the same energy as they left. They will have less energy at collision than you sent them off with because the increasing distance between them means that there will be a corresponding decrease in net gravitational attraction (as integrated over the time of travel) than would exist in a "nonexpanding" universe. The increase in distance should be exactly offset by the decreasing gravitational attraction due to that distance increase, and we return to a nice, zero-sum universe again. QED. --Jayron32.talk.contribs 22:15, 18 December 2008 (UTC)

I thought about that - it's OK to boldly assert that momentum is conserved - but how exactly? The universe expands - and to avoid the ball having so much momentum - it has to...what? If I drop a stationary ball from 10 meters - it'll hit the ground faster than one I drop from one meter. I don't see a way to deny that. So if we consider the upward trip of a ball thrown into the air as merely a time-reversal of the downward journey - and we know that the upward leg was a shorter distance than the downward leg because of the expansion of the universe during the upwards and downwards trips. Sure we can ASSERT that it must all sort itself out - and I'm sure it does - I just don't see how. SteveBaker (talk) 00:56, 19 December 2008 (UTC)

Ok. Look at it this way. Why do the balls slow down and start moving back in again? Gravity, right? What is the strength of gravity dependent on? The distance between the objects. Right? So what happens if the distance between the objects increases because of the expansion of the universe? Then the strength of the gravitional force bringing them back together decreases by the same factor. Therefore, the acceleration of the balls towards each other will decrease by exactly the same factor as the rate of expansion of the universe. Thus, they will still be moving at the same speed at collision (assuming of course a spherical cow, erm, a perfect vacuum) as they were at the start of the experiment. Which means the universe is still a zero sum game. All is well, and we can sleep at night... --Jayron32.talk.contribs 01:18, 19 December 2008 (UTC)

Please ignore everything that Jayron has said here, as I would go to far as saying it completely lacks any truth. If you consider that the distance has expanded, and that the masses remained the same then the acceleration will be exactly the same at any given distance between the two objects, but the integral (which relates to the kinetic energy of the two particles) will be slightly larger due to the increment increase is the distance. Also on another note, when you increase the distance between two masses by some factor, the acceleration does not decrease by the same factor as gravity is an inverse square law. Philc 0780 01:29, 19 December 2008 (UTC)

Let's try this a third time.

• Lets consider each effect in isolation. Acceleration refers to an objects change of motion such that its position (distance from starting point) varies with the square of time; that is each successive arbitrary unit of time causes the distance traveled in that time to increase by a constant amount over that time. So if it is accelerating at 1 m*s^-2, after one second, the object has moved 1 meter. After two seconds, it has moved 3 meters, after three meters it has moved 6 meters, etc. etc. Using a little calculus, we find that the time to cover a given displacement decreases with the square root of that displacement. If we increase the distance between our bowling balls, their time to cover that increased distance will be relative to the square root of the distance we added.
• Now, lets consider the effect of gravity. As Phil has already astutely noted, gravitational force (which is the source of our acceleration) is an inverse square effect, thus adding some arbitrary distance between the bowling balls will decrease the force of gravity between those balls the square of the distance we add between them.
• If we consider these two effects on the velocity of balls at our hypothetical "zero" point (i.e. that point we pushed them apart from), lets compare the situation to the "non-expanding" universe. In that situation, the balls should arrive back at the collision point moving the same speed we initially imparted on them. Any recoil energy they get from the collision will be identical to that, so our situation (ignoring friction, and assuming they are moving in the same dimension) will be a perfect harmonic oscilation, with the two balls always moving the same velocity at the instant before the collision point. So what happens in the "expanding" universe. We already determined that the added distance (lets call it x) has decreased the gravitational force by a factor of x² and that the additional distance traveled will mean that we are accelerating by increasing the amount of time required to cover that distance by a factor of x^1/2. Last time I checked, the square root of a square was no change at all, so the balls "act" like no distance has been added. They will strike each other with the same velocity as if the added distance had not been added at all, and we have our nice little harmonic oscilator back again. The universe is safe from perpetual motion, and we are back at our zero sum... --Jayron32.talk.contribs 04:46, 19 December 2008 (UTC)

Your first point depends on the assumption of uniform acceleration (and even then your numerical examples are wrong). Neither that assumption, nor the conclusion that time follows x^1/2 is correct. In fact, the time is proportional to x^3/2 for an inverse square force. Dragons flight (talk) 06:03, 19 December 2008 (UTC)

Are you measuring the distance between the objects as a fraction of the size of the universe? I so this is a very odd thing to do and is clearly the source of the problems. And if you aren't, then why do you assert that its expansion will have affected the distance between the balls. And you are and you assert that it does, by what measure has the distance increased? (or to say, what thing would not have been affected by this expansion) and so the entire reference frame is stretched equally, and so within the frame no stretch at all has occurred. Philc 0780 01:25, 19 December 2008 (UTC)

Why do I assert that the distance between the balls has increased? Because that's what happens to galaxies - they move away from us...why doesn't a bowling ball do the same thing? (That's a rhetorical question - of course it does the same thing - but by a TINY amount - so we don't notice.) SteveBaker (talk) 02:21, 19 December 2008 (UTC)

No, they don't move apart. See below. Dragons flight (talk) 05:50, 19 December 2008 (UTC)

Steve, I think you are essentially asking whether conservation of energy holds, given the the expansion of the universe. I believe your original interpretation (perpetual motion) is tantamount to saying to "energy conservation is inconsistent with an expanding universe." I don't believe that is the standard and generally accepted point of view that most cosmologists hold, but this is most definitely a major un-answered question. See accelerating universe, which clearly needs some expert attention. It is my opinion that there is a great deal of uncertainty regarding some of the astronomical observations upon which some of the basic theoretical claims are made (for example, it is my opinion that quantitative rates of acceleration of the universe expansion are awfully complex derivations from fairly sparse and noisy sets of observational data). Others who specialize in cosmology may disagree with my assessment. Nonetheless, there is some theoretical uncertainty about just which physical "laws" (such as energy conservation) are really universally applicable. Nimur (talk) 04:54, 19 December 2008 (UTC)

If the local space is empty, then the distance between the balls does not expand. Hubble flow describes a solution for the passive evolution of approximately uniform matter under the action of general relativity. However it does not say that the distance between every pair of objects under all possible conditions must expand. In the future, galaxies will be moving away from each other, because they are moving away from each other now, and because they were moving away from each other in the past. The expansion of the distances between galaxies is a natural consequence of their dynamics and occurs in the absence of external forces (strictly speaking I am ignoring dark energy). However, if you take a uniform, isotropic, and expanding universe, and then cut a spherical hole in it to create a region of truly empty space, it follows from general relativity that the expansion occurring outside that hole has no impact on the matter within it. (This is essentially GR's version of the shell theorem.) In particular, you can put a galaxy, solar system, or even a pair of bowling balls in that region of "empty space" and they will not experience Hubble flow. The assumption of locally empty space is incompatible with the assumption of Hubble flow. The alternative is that you are embedded in a medium experiencing Hubble flow and hence necessarily have an opportunity to interact gravitationally with the mass comprising that medium, which implies they you can exchange energy and momentum with it. Dragons flight (talk) 05:50, 19 December 2008 (UTC)

That would certainly solve the problem. It's not something I've heard before, though - how does that tally with the idea that it isn't the matter moving outward but rather the space between them getting bigger? The space between two galaxies is essentially empty, so how come the galaxies move apart? --Tango (talk) 14:55, 20 December 2008 (UTC)

They move apart because they have a relative velocity. There's only one kind of relative motion in general relativity, and it's responsible for both the separation of superclusters and the separation of rubber bowling balls. They were given an initial "push" (by inflation or SteveBaker) and they keep going because of inertia. It's not necessarily wrong to give the two cases different names, but it's like the difference between a tadpole and a frog: the one can be continuously deformed into the other, and any terminological cutoff is going to be arbitrary. -- BenRG (talk) 07:50, 21 December 2008 (UTC)

But that's movement *through* space, rather than space expanding, I thought the whole point was that it's space expanding, not matter within space moving. --Tango (talk) 01:05, 24 December 2008 (UTC)

If you visualise the gravitational field/potential energy contours around the bowling balls it might make things a lot easier. The bowling ball/s start off with an initial velocity which takes them up to a certain contour before they fall back. If they are always given the same initial velocity, they will always reach the same contour (which might now be further out, if an expanding universe is to be believed), but the total kinetic energy gained is dependent only on the potential energy difference between the starting energy contour and the furthest contour reached, and those two shells will remain the same even if the geometry has stretched. In other words, whether the universe expands or not is irrelevant, and gravitational fields remain conservative. Rotational (talk) 08:56, 24 December 2008 (UTC)

But the potential energy is a simple function of distance, so if the universe expands the potential energy should increase. --Tango (talk) 23:06, 25 December 2008 (UTC)

If the geometry remains static, then the potential energy would be a simple function of distance, but you are postulating an expanding universe, so that gravity is steadily diluted and as a result the contour intervals are constantly increasing. The balls have further to go before they stop, since the gravitational gradient is flatter. To use a model, you've lowered the inclined plane slightly allowing the ball to go further, but the final height it reaches above the starting plane is going to be the same. ciao Rotational (talk) 14:27, 26 December 2008 (UTC)

Mathematical Modeling

Regardless of the final solution, I'm curious as to how one would go about calculating the time evolution of such a system. Assuming a symmetrical system of two masses m, each moving away from a stationary reference gnat at position x=0 with velocity v, it was relatively straightforward to calculate for the non-expanding case. Using Newton's second law and Newton's law of gravitation, the time evolution of the position of one of the masses should follow $F=mx''=Gmm/r^{2}$ giving us the second-order ordinary differential equation $x''=Gm/4x^{2}$, with $x'(0)=v;x(0)=0$. However, I have no clue on how I would even start to incorporate the metric expansion of space into such a calculation. I surmise this is because I'm trying to use the tools of classical mechanics to work on a relativistic problem. How would someone versed in general relativity approach calculating this problem? -- 128.104.112.113 (talk) 16:15, 19 December 2008 (UTC)

I should think that Newtonian Mechanics would not be able to model such a system as one of the features of newtonian mechanics is the conservation of energy, something which this hypothetical system attempts to violate. —Preceding unsigned comment added by 92.3.10.246 (talk) 13:44, 20 December 2008 (UTC)

There is a Newtonian version of big bang cosmology and you can derive a version of the Friedmann equations within it (see here). You can probably get some insight into the original question from this model. Two test particles of negligible mass moving collinearly (no orbital angular momentum) in a Newtonian big bang will satisfy

$r''={\tfrac {1}{3}}(\Lambda -4\pi G\rho )\,r$

where r(t) is the distance between the particles and ρ(t) is the density of the dust (ordinary and dark matter). If you also include a 1/r² force between the particles (hereafter "balls") then you get

$r''={\tfrac {1}{3}}(\Lambda -4\pi G\rho )\,r-Gm/r^{2}$

where m is the total mass of the balls. Unfortunately I don't think this can be explicitly solved even for simple choices of ρ(t) (like ρ(t) = 0), but you can get a sense for the solutions by starting at the point of maximum separation (where r'(t) = 0) and extending forward and backward in time. If ρ(t) = 0 then the equation is time-reversal symmetric, so the future and past halves of the trajectory look the same. That means that in an empty de Sitter universe (which is roughly what we're destined for in the future according to ΛCDM), the two rubber balls will neither gain nor lose speed with each bounce. In an expanding universe with nonzero density, ρ(t) is larger for the past half of the trajectory and the attractive force is correspondingly larger, so the balls will collide sooner and with greater speed in the past direction. In other words, the balls lose speed with each bounce in this scenario. They would gain speed in a contracting universe. So where does that energy come from (or go to)? I don't think there's any great mystery here. The balls are simply getting a kind of gravity assist from the dust. They will in turn (Newton's third law) disturb the motion of the dust, which I ignored in my model. If I hadn't ignored it, the apparent violation of the conservation laws would presumably disappear. -- BenRG (talk) 07:18, 21 December 2008 (UTC)