mò Ž·™Fc @s—dZdkTedeeddƒdeeeddƒdeed d ƒee dd ƒƒZ e i d ee i edd ƒdee i e ddƒƒeiieie iƒedeiededeeeeddƒƒZei deeieiddƒdeiƒei deidedeideiddƒdee iddeie iddƒƒeiiededdƒƒƒeie_eie _ ed eed!d"ƒe!ed#e"e#edd$ƒd%ed&de$d'e%e&dd(ƒd)ed*e$d+e'd,ƒƒZ(e(i)i d-eie(i)d.de(i)ƒe(i d/ed0ee(i*eid#dd1ƒd2edd3ee(i*eid4dd5ƒd6ede(i*eiddd7ƒƒed8eed9d:ƒe+ee'dd;ƒd<eed=d>ƒe,e-ee'dddd?ƒƒZ.e.i d@e.i/dAede i0e(i1e.i/ddBƒƒe.i2eie_3ei3e_4dCS(Ds¤Basic physics. See also: http://physics.nist.gov/cuu/Constants/ http://www.alcyone.com/max/physics/laws/ $Id: physics.py,v 1.3 2007/03/24 22:42:21 eddy Exp $ (t*tPlanckf662.60687600000006f5.1999999999999997e-05f9.9999999999999994e-37tdocsqAngular Planck's constant Planck's constant is definitively given by the equation E = h.f relating the frequency, f, of electromagnetic radiation to the amount of energy in parcels (quanta) of which the electromagnetic field's spectral line at that frequency interacts with matter. Properly, f should be recognised as having, as its units, angle/time, or at least cycles/time. In particular, the frequency Planck was refering to was turn/period, one cycle divided by the time taken for the field to return to its prior state. Thus, strictly, the constant of proportionality should be a quantity with units Joule*second/turn. This then represents Dirac's constant `h-bar' as h*radian. For the sake of widely accepted usage which takes h without the turn divisor, I'll reserve the name h for h*turn and use the name Planck for the `correct' quantity, with the turn unit in it. tMillikanf160.21000000000001f0.0070000000000000001s+Millikan's Quantum; size of electron chargeths=Planck's constant See Quantum.Planck's __doc__ for details. thbars<Dirac's constant See Quantum.Planck's __doc__ for details. tct permeabilityf0.40000000000000002sÛMagnetic permeability of free space. The magnetic force per unit length between two long parallel wires a distance R apart carrying currents j and J is j*J/R times the magnetic permeability of the medium between them. tZ0s&Impedance of free space, Z0. This is the square root of the ratio of the vacuum's magnetic permeability and electric permittivity, whose product is 1/c/c. Thus: c*c*epsilon0*mu0 = 1 Z0*Z0 = mu0/epsilon0 whence we may infer: Z0 = c*mu0 c*Z0*epsilon0 = 1 so that c and Z0 suffice to determine the permeability and permittivity of free space. Note that, since c has (by the definition of the metre) an exact integer value and mu0 is (by the definition of the Ampere) exactly pi*4e-7, the values of Z0 and epsilon0 are also exact. tmu0t impedancet permittivityisÍElectrical permittivity of free space. The electrostatic force between two point charges q and Q a distance R apart is q*Q / (4 * pi * R**2) divided by the permittivity of the medium between the charges. talphais¤The fine structure constant. The fine structure constant arises naturally in the perturbation expansions of various physical quantities. It is a dimensionless quantity which expresses the charge on the electron (Millikan's quantum) in terms of the natural unit of charge, sqrt(h/Z0), one can obtain (after the style of Planck's units, see below) from Planck's constant, h, and the impedance of free space, Z0. The definitive formula for the fine structure constant is: e**2 / (4 * pi * epsilon0 * hbar * c) or, equivalently (as 2*pi*hbar is h and epsilon0*c*Z0 is 1): e**2 * (Z0 / h) / 2 as expressed here. I am given to believe that the fine-structure splitting of the spectrum of Hydrogen (and, I am thus inclined to guess, other quantum electrodynamic systems) is expressed as a power-series in 2*alpha, which the latter formula gives as the ratio of e**2 and h/Z0. It is perhaps worth noting that, when Planck's constant is undestood to include units of angle, alpha actually emerges as an angle, rather than being strictly dimensionless. Then again, either G or epsilon0 arguably involves a factor of solid angle, which would complicate the matter even further ... f137.03604000000001f0.00011tGf66.719999999999999f0.040000000000000001isìNewton's constant of gravitation. The gravitational force between two small massive bodies is the product of their masses divided by the square of the distance between them, multiplied by Newton's constant, which is normally called G. tHubblef2.2999999999999998f0.10000000000000001s´Hubble's constant. This describes the rate of expansion of the universe: it is the velocity difference between widely-separated parts of the universe divided by the distance between them. We should probably actually use hyperbolic angles in place of velocities, though. A velocity should be expressed as c*tanh(b) and described in terms of the value of b; the correct relativistic addition of velocities adds these hyperbolic angles. Thus Hubble/c gives the rate of change of the hyperbolic angle b with distance. The Doppler effect that goes with the velocity scales frequencies by the factor exp(b). The Wilkinson Microwave Anisotropy Probe's study of the microwave background (emitted only 380,000 years after the Big Bang) vastly improved the available accuracy of this datum; previously the best estimate's uncertainty included its most significant digit. The new figure is 71 km / sec / Mpc, accurate to 5%. See also planets.universe t temperaturef2.7248000000000001f0.00040000000000000002sƒCosmic Microwave Background Temperature. The after-glow of the Big Band shows itself as an almost uniform background glow in the sky with the spectrum of an ideal black body (one which absorbs light perfectly, regardless of the light's colour) at a temperature of 2.725 Kelvin. Such a close match to the ideal black body spectrum says a lot in its own right: normally, all matter has spectral lines where it is more or less apt to interact with light. We know the radiation has been cooled adiabatically by the universe's expansion since the background radiation fell out of thermal equilibrium with matter (by ceasing to interact with it sufficiently intimately), and this means it's been red-shifted from a much higher temperature black body spectrum when it last interacted with matter. The matter at that time must have had no distinct spectral lines, strongly favouring the belief that it was much hotter than anything we see today - since all matter has spectral irregularities at all familiar temperatures. The background radiation is also extremely close to uniform across all directions in the sky. The principal variation has the form we would expect from a Doppler shift, which tells us our velocity relative to the rest-frame of the background radiation. Once the effects of this are eliminated, a tiny variation remains, of order one part in 10000. For parts of the universe that are now vastly distant from one another to have temperatures so remarkably close to equal would itself be surprising, if they hadn't come from a common past when they were close together. See http://www.astro.ubc.ca/people/scott/faq_email.html for further details. tlengthttimetkappaisÎEinstein's constant of gravitation. One side of Einstein's field equation for general relativity is constructed out of the the metric of space-time (describing distances), the Ricci tensor (which describes space-time's curvature) and the cosmological constant. The other side is just the energy-momentum-stress tensor (which describes matter and related phenomena, such as the electromagnetic field) scaled by Einstein's gravitational constant, usually called κ, which is 8 * pi times Newton's gravitational constant divided by a suitable power of the speed of light. Thus κ has the dimensions of a length per mass, give or take some factors of velocity (which is nominally dimensionless, like angles). tqpermif0.5sA The Einstein/Maxwell Charge-to-Mass ratio. The free-field equations of general relativity with an electromagnetic field can be put in a form which doesn't involve the usual electromagnetic and gravitational constants: (D/g\D)a = 0 (d^a)/g\(d^a) -g.trace((d^a)/g\(d^a)/g)/4 = -R +g.(trace(R/g)/4 -L) where R is the Ricci tensor, L is the cosmological constant and a is the result of multiplying Maxwell's co-vector potential, usually called A, by the charge-to-mass ratio, sqrt(4.pi.G/epsilon0), given here. The use, here, of /g\ means the same as contracting via g's inverse; while the use of /g means the same as contracting with g's inverse (on the right). The D/g\D operator is the usual `box' (or box-squared) operator equivalent to the del-squared operator in three dimensions. Since (modulo factors of c) A has the dimensions of energy per unit charge, this gives a the dimensions of energy per unit mass, i.e. the square of a velocity, which is implicitly dimensionless (because we're working modulo factors of c). Note that R + (d^a)/g\(d^a) is parallel to (i.e. a scalar multiple of) g; and that this says everything the second equation above says - because trace(g/g) is 4 (or, rather, the dimension of space-time) and trace commutes with scaling - whence, in particular, we can infer that L is zero. If we add in charges and currents as sources for the electromagnetic field, the first equation above becomes (D/g\D)a = g.j with j equal to the conventional 4-vector current times a scalar, roughly 9.731 (m/s)**3 /Amp, obtained by dividing the charge-to-mass ratio by the permittivity of free space. The thus-scaled j is, consequently, the cube of a velocity - i.e. dimensionless. If we compare Newton's and Coulomb's force laws for gravity and electrostatics, respectively, this charge-to-mass ratio (about 86.2 nano Coulombs per tonne) also emerges as a natural way of comparing the strengths of the two fields; two objects, each of mass one million tonnes and carrying 86.2 milli Coulombs of charge (almost 0.9 micro-moles of electrons), of equal sign, would repel one another electrostatically with a force equal to that with which they would attract one another gravitationally (regardless of the distance between them). This ratio is equally the Planck charge (see planck.Planck) divided by the Planck mass; but note the non-involvement of Planck's constant. Contrast with the charge-to-mass ratios of the proton (95.79 MC/kg) and electron (-175.9 GC/kg), roughly 1e19/9 and 2e21 times as big. Even the Beauty+2.Truth equivalent of the proton only gets down to around 1 MC/kg, around 1e16 times as high as the Einstein-Maxwell charge-to-mass ratio. One electron's charge is worth the mass of over a million million million nucleons; the mass of a mole of nucleons is worth only a bit over half a million electrons' charge. t SchwarzschildsæSchwarzschild's factor. The Schwarzschild radius of a black hole of mass m is 2.G.m/c/c; outside this radius, the radial co-ordinate is spatial and the time-wards co-ordinate is time-like, as one would expect; inside, they swap. tkf13.805400000000001f0.0018sBoltzmann constanttStefanf56.703200000000002f0.012500000000000001síStefan-Boltzmann constant The total radiant power output per unit area from a black body at temperature T is given by sigma T**4 where sigma is the Stefan-Boltzmann constant, sigma = pi**2 k**4 / 60 / c**2 / hbar**3 See also: Radiator.total, space.hole.BlackHole, below; notably (in the latter) the observation that the above law must clearly be modified when k.T exceeds the rest mass of any type of particle (unless this modification is, for some reason, specific to black holes). t BoltzmanntHawkingsThe Hawking radiation constant. A black hole radiates away energy after the manner of a black body of temperature T given by k T = hbar g / 2 / pi / c = hbar c / 4 / pi / r = hbar / kappa / M where g is its 'surface' gravity G.M/r/r = c.c/2/r and r is its Schwarzschild radius. The product M.T is thus the constant given here as the Hawking radiation constant. N(5t__doc__tstudy.value.unitstObjecttQuantitytsampletJouletsecondtturntzeptotCoulombtQuantumtalsoRtradiantmoltchargetobservetAvogadroRtlighttpitmicrotHenrytmetretVacuumRRRRR R tepsilon0t fineStructuretmillitgramtkilottophattattotHertztKelvintCosmosRR tyoctotnanotWatttThermalRRRRtRt gasConstant(R/R#R9R=((t)/home/eddy/.sys/py/study/chemy/physics.pyt?s^$    ! #    $ " 0