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Comment: Re:Professors poor in geography (Score 1) 688

by boristhespider (#47063697) Attached to: Professors: US "In Denial" Over Poor Maths Standards

Where do *you* live? That's a genuine question, because here in the UK, South America is that big southern lump featuring the likes of Argentina and Brazil, Central America is the thin wiggly bit featuring the world-famous Panama Canal which is based in Panama, and North America is the big lump on top which Mexico, the USA and Canada call home.

Comment: Re:math? maths? (Score 1) 688

by boristhespider (#47063683) Attached to: Professors: US "In Denial" Over Poor Maths Standards

Actually, sorry, you're wrong about that. The geography skills of the guy who wrote the summary are deeply questionable (Mexico seemed to pull off the trick of joining South America remarkably quietly), but "maths" is the abbreviation of "mathematics" used in the UK. It's not a plural of "math" -- and, after all, we don't call it "mathematic". So I think we've pinned down where "thephydes" is from - he or she is either British, or learned British English.

So I think the main thing we can learn from the summary is that despite the characterisation of Americans has having no knowledge of geography outside their own country, the rest of the English-speaking world is just as bad and should probably stop feeling so damned smug and look at the fucking great log in their own eyes.

Comment: Re:And what about dark matter? (Score 1) 109

by boristhespider (#46871961) Attached to: What Happens To All the Universe's Hydrogen?

Well, I wasn't a particular fan of that comment either... :) But your comments about the conservation of energy are basically wrong -- like I say, the expansion of the universe is governed basically by two equations:

1) The Friedman equation, which is the "Hamiltonian constraint" and which can be interpreted as an energy constraint equation
2) The matter continuity equations, which arise directly from conservation of equation of matter

(Technically, and apologies for the ugly LaTeX notation here, matter is described in relativity by "stress-energy" or "energy-momentum" tensors, which bundle together the classical concepts of energy, momentum flux, energy flow, and momentum flux density. The gradient of the more familiar Momentum flux density produces momentum conservation, while the time derivative and gradient of the energy give, well, energy conservation otherwise known as matter continuity. In terms of the stress-energy tensors, if energy is conserved then the covariant gradient of these is conserved -- written T^{\mu \nu}_{; \nu} = 0 where the \mu and \nu describe the four spacetime coordinates, and the repeated \nu means we sum across them. In Euclidean spacetime this immediately reduces to normal energy and momentum conservation. That semi-colon means "covariant derivative", meaning it has contributions coming from interactions with the spacetime geometry; if instead you insist on writing the conservation equation as a partial derivative (as in familiar classical mechanics and fluid dynamics) then you get T^{\mu \nu}_{, \nu} = [gravitational terms]^\mu and if you were unaware of the form of a covariant derivative this would look like a violation of energy and momentum conservation rather than what it is -- an interaction of the stress-energy of matter with the geometry of spacetime.

(The energy density, with respect to some chosen time coordinate which can be described as the vector n^\mu normal to a purely spatial three-dimensional surface, is found by the contraction \rho = n^\mu n^\nu T_{\mu \nu} which basically just means the scalar product of the stress-energy tensor with the time coordinate, or phrased differently, the stress-energy tensor projected along the time coordinate. This energy is conserved. Similarly, if we take the full Einstein equations they can be written as G^\mu_\nu = 8\pi G T^\mu_\nu where the G^\mu_\nu is the "Einstein tensor" that basically characterises the local gravitational field, and the G is newton's constant which infuriatingly has the same god damned symbol. If we project these equations along the time coordinate then we get out an energy on the right-hand side, and something that therefore can be interpreted as embodying the "gravitational energy" on the left-hand side. The result of this is the Hamiltonian constraint, and in the specific case of a cosmological spacetime the result is the Friedmann equation. Both these equations therefore express energy conservation -- one for the gravitational field, and the other for the matter.)

Said a bit less technically, the second equation is simply what you expect -- for normal matter we except the density changes with scale factor as rho = rho_0 / a^3. That is, the density decays as the volume of the universe increases. For photons we would expect instead rho=rho_0 / a^4, where we've got the normal volume dilution (1/a^3) and, since a photon's energy is proportional to length and the expansion of the universe will stretch that length, we should have an extra decay in the energy of 1/a. So rho = rho_0 / a^4. To a good approximation the same can be said for neutrinos (although to be exact we should make these massive, albeit extremely light.) Put these together and you have rho = rho_matter / a^3 + rho_photons / a^4. This is nothing but what happens when space expands.

That's well and good but it doesn't answer your issue with energy conservation, because it seems to violate it. That's where the other equation comes in, because these equations are only *half* the story. In GR (and other related, geometric theories of gravity) gravity also has an associated energy. It's hard to describe where the Friedmann equation comes from in this picture without the full theory, but it's obvious that if the energy density of photons is being diluted there must be some impact on the geometry that underpins what we call "gravity". In cosmology there is basically one quantity that determines that geometry -- the same scale factor, a. So the energy equation should determine how a evolves in time. Given that we can characterise it with the Hubble rate, which is the change in a with time, divided by a. This doesn't have the units of energy which (since we've set the speed of sound equal to 1, meaning we measure seconds and centimetres with the same stick) has units of 1/time^2. So let's square the Hubble rate to get something in the right units to be an energy. That gives us a crude estimate of the gravitational "energy conservation" as H^2 = ?. First guess for the right hand side has to be to slap in something proportional to the matter energy. This then gives us H^2 = \kappa \rho. This isn't a particularly convincing way to justify the Friedmann equation (which is what that is), but it's better than the usual approach which is to assume an expanding sphere of pure dust and which misses the point of gravitational energy completely.

The point of all of that, both technical and ineptly non-technical, is that while if you just look at the matter sector alone and forget that you have to take the geometry into account, you conclude that energy is not being conserved. However, remembering that in the theory cosmology is based on we have to include interactions with gravity (which can also be described as the "energy" of the gravtiational field though I'd advise caution in taking such interpretations too strongly) everything suddenly falls into place -- the apparent loss of energy from matter is balanced by the gravitational field.

Jesus. Sorry for the length of that one, you didn't deserve that. Oh well, hopefully it interested you -- ultimately I'd agree with the statement "physics has problems too" because if it didn't there'd be one hell of a lot of unemployed physicists mooching about looking unhappy.

Comment: Re:And what about dark matter? (Score 1) 109

by boristhespider (#46870939) Attached to: What Happens To All the Universe's Hydrogen?

It's just how gravity works - if you fill a universe with not quite enough matter to make it collapse it will expand. Meaning if the universe was a bit denser it would collapse, but since it's not it's expanding. Then, as Neil Boekend says, due to something we're currently calling "dark energy" for want of a better term, with the amount of matter we've got we would expect the universe to be expanding but slowing whereas it's actually accelerating.

Sorry I can't give a better answer but really no-one can -- just that given the theory we've got, and the starting point we assume (an initial expansion coming from the point at which the theory simply breaks down), that's how it goes.

Comment: Re:And what about dark matter? (Score 1) 109

by boristhespider (#46862319) Attached to: What Happens To All the Universe's Hydrogen?

Well, we can have a very good bash at it by taking the science we have at the minute, extrapolating back, noting every place where the story seems to get shaky and the edge cases that can arise, and see when things die. Surprisingly, the story of the last five billion years is a hell of a lot shakier than the story from, say, the fifth second up to the ten billionth year. Very early cosmology, yes, I totally agree -- it's speculation, and in particular (the slight overreaction to the BICEP2 results aside) I don't think anyone actually working on inflationary theories would pretend that they are dealing with anything that isn't, strictly speaking, phenomenology. I think most theorists believe something that *behaved* like inflation had to occur, and I would agree with that, but I don't think anyone has made any particularly strong claims for any particular inflationary theory, since they're all by their nature nothing but speculation about how higher-energy theories might act viewed with our current techniques.

But by the time of big bang nucleosynthesis in the first seconds to the first minutes, the science is really well understood -- we have direct evidence from accelerators for how matter behaves at such energy scales, and the very fact that the predictions of the theory based on this match so closely to observation at every point up to (and even beyond) the ten billionth year of the galaxy can give us a hell of a lot of faith that the fundamental picture is (at least phenomenologically) correct. I say this as someone who has chopped away at cosmology's fundamentals for over a decade -- the broad idea of inflation is probably accurate; something that closely resembles a universe composed of "baryonic" (ie normal) matter (about 5% of critical density), cold dark matter (about 25% critical density), photons, and three species of slightly massive neutrinos, *had* to hold between the first few seconds and roughly around the 10th or 12th billionth year, at which point that model breaks down unless one additionally adds in something that looks like a cosmological constant or a dark energy. Whether the physical identifications are actually precise or not is a totally different question -- and they're not, with dark energy on particularly shaky grounds but "dark matter" certainly hiding a world of complication beneath its single boring equation (w = 0) -- but the actual model is far too successful to simply be ignored. And I wouldn't consider using a different model for the period from just before BBN up until around a redshift of, say, 2 or 3, because there would be little to be acheived. Precisely how I generate the different components of course is model dependent, but it will look and act a lot like Lambda CDM.

For lower redshifts, meh, many bets are still off.

Comment: Re:And what about dark matter? (Score 1) 109

by boristhespider (#46862223) Attached to: What Happens To All the Universe's Hydrogen?

Sure but you know what I'm meaning. In physics we have a very distinct hierarchy of descriptions. At the base are the "fundamental" theories, which are assumed to hold for point particles and fundamental forces (ie forces that don't reduce to different ways of viewing another force). These are the likes of the electroweak theory, the strong theory, and any random speculation about quantum gravity that you choose to believe (or not - I don't believe any of the theories of quantum gravity at the minute, though the approaches of loop quantum gravity, dynamical triangulations, or non-commutative geometries are to my mind a lot more promising than the approach of superstring theories; less ambitious and following more closely the ethos that lead to QED in the first place). Above that is the emergent theory of quantum mechanics, which in principle should arise out of QED but which in practice is a staggeringly successful and ultimately phenomenological theory. The two are related, however, and both involve similar quantisations of classical concepts - a Lagrangian density in the case of the "fundamental" theories which are therefore quantum field theories describing the fundamental forces; and a Hamiltonian or Hamiltonian density in the case of quantum mechanics which is therefore a direct quantum theory of particles.

Then above that, quite a long way, sit the likes of thermodynamics and fluid mechanics. Thermodynamics arises by describing a system of interacting particles -- atoms, molecules, what have you -- through a Hamiltonian and then applying a statistical average of this. What emerges is a simple description of the behaviour of vast numbers of particles which is coincidentally the phenomenological theory developed in the 19th century, except that entropy is now a determined quantity rather than defined only to within an additive constant. Fluid mechanics can be recovered by setting up a Boltzmann equation, which is itself a statistical quantity, and then integrating out the lower moments, which become density, momentum, momentum flux etc. Similarly chemistry in principle can be recovered by modelling atoms with Schroedinger equations, and that's certainly done but it's computationally expensive.

Then above *that* (which holds on our scales) lies cosmology. Cosmology is the extrapolation to gigaparsec scales, of all things, of a force known to operate on scales between a millimetre and, with mounting inaccuracy in the measurements, solar system scales. It seems likely to hold on at least parsec scales but the extrapolation to kiloparsec scales is questionable, and the application in galaxies is actually ill-defined (meaning that it is impossible with current knowledge to calculate the mean-field of a galaxy due to the numerous gravitational lenses a galaxy is filled with, and the fact that such lenses break any spatial average we've currently been able to define in metric-based theories; we're also still working on straight statistical averages for gravitating systems). The application up to first mega- and then gigaparsec scales is subject to similar caveats.

So yes, in principle I totally agree wtih you that ultimately all numerical science is phenomenology, but the way the word is typically used in physics is slightly different -- a phenomenology is a theory that is not assumed to be related in any direct way to the theories that are assumed to hold on laboratory or, particularly, atomic scales and below.

There's got to be more to life than compile-and-go.

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