Total energy against speed, in units of the rest energy

At its defaults it draws total energy against speed, in units of the rest energy. The total energy of a moving body divided by its rest energy, against speed as a fraction of the speed of light. The Newtonian answer, one plus half v squared over c squared, is drawn beside it: the two agree to 0.004 per cent at a tenth of light speed and disagree by 39 per cent at nine-tenths. The relativistic curve has a vertical asymptote at c, which is why nothing with mass reaches it.

relativistic-energy is one function in lib/figures/spacetime.js — worldlines, slicing and the factor that governs both. Everything below came out of it during this build, at parameters taken from the essays rather than invented for this page. A figure here is the figure a reader meets in an essay, and if the generator changes, this page changes with it.

The total energy of a moving body divided by its rest energy, against speed as a fraction of the speed of light. The Newtonian answer, one plus half v squared over c squared, is drawn beside it: the two agree to 0.004 per cent at a tenth of light speed and disagree by 39 per cent at nine-tenths. The relativistic curve has a vertical asymptote at c, which is why nothing with mass reaches it.

The total energy of a moving body divided by its rest energy, against speed as a fraction of the speed of light. The Newtonian answer, one plus half v squared over c squared, is drawn beside it: the two agree to 0.004 per cent at a tenth of light speed and disagree by 39 per cent at nine-tenths. The relativistic curve has a vertical asymptote at c, which is why nothing with mass reaches it.

The share of a kilogram's rest energy released by five processes, on a logarithmic axis spanning ten decades. Burning coal converts 3.6e-10 of it; fission 9.1e-4; deuterium–tritium fusion 3.8e-3; annihilation all of it. The equation applies to the chemistry too — the mass change is simply far too small to weigh.

The energy per beam required to reach a given invariant mass, on logarithmic axes, for a stationary proton target and for two beams meeting head on. antiproton, p̄p pair needs 3.8 GeV of invariant mass, which is 1.9 GeV per beam head-on and 7 GeV against a target; the W boson needs 80.4 GeV of invariant mass, which is 40.2 GeV per beam head-on and 3442 GeV against a target; the Z boson needs 91.2 GeV of invariant mass, which is 45.6 GeV per beam head-on and 4430 GeV against a target; the Higgs boson needs 125.3 GeV of invariant mass, which is 62.6 GeV per beam head-on and 8359 GeV against a target; the top quark, in pairs needs 345.5 GeV of invariant mass, which is 172.8 GeV per beam head-on and 63618 GeV against a target. The names on the plot are the products far enough apart in mass to be labelled without collision; the rest are in the list on the right. The antiproton row is the one that was actually built: the Bevatron was designed at 6.2 GeV precisely because the threshold is a kinetic energy of 5.63, and the machine's energy was chosen from this arithmetic before there was anything to find. Above about ten GeV of invariant mass the fixed-target column becomes absurd, and every discovery on the list after the antiproton was made at a collider — not for want of engineering but because the requirement grows as the square of what is wanted.

The invariant mass of a pair of photons of equal energy, in units of E/c², against the angle between them. It is computed from the total energy and the vector sum of the two momenta, and agrees with 2E·sin(θ/2) to 1.0e-14. at 0° the pair weighs 0.000 E/c²; at 30° the pair weighs 0.518 E/c²; at 60° the pair weighs 1.000 E/c²; at 90° the pair weighs 1.414 E/c²; at 120° the pair weighs 1.732 E/c²; at 180° the pair weighs 2.000 E/c². Two photons flying in the same direction have no mass between them at all, because their momenta add to exactly the energy over c; anything else and they do. Nothing has been added: the constituents are massless at every angle, and the mass of the system is a property of the arrangement. At 180° the pair weighs 2E/c², which is every joule it contains — the case of a sealed box of light, where the two beams cancel in momentum and the whole energy shows up on the scales.

Binding energy per nucleon against mass number: how much energy would have to be supplied, per particle, to take a nucleus apart into free protons and neutrons. The curve is the semi-empirical mass formula, evaluated at whichever proton number binds most tightly for each mass number rather than at a guessed one; the points are measured values. It rises steeply at the light end, peaks at mass number 58, and falls slowly thereafter. Everything about nuclear energy follows from that shape and from nothing else. Two light nuclei joined move up the curve and release the difference; one heavy nucleus split moves up it too, from the other side. Both directions are downhill in energy because the peak is in the middle, and the peak is in the middle because two effects fight — the surface term, which penalises small nuclei for having most of their nucleons on the outside, and the Coulomb term, which penalises large ones because every proton repels every other. The energy released is the height climbed times the number of nucleons carried, and it is a million times a chemical bond for the same reason the vertical axis is in millions of electronvolts rather than in single ones.

physicscheck asserts something about relativistic-energy that could fail — it draws it and measures the result against a value reached some other way.

Across the library: 100 interrogated, 2 exercised only, 1 untouched, of 103. Read out of the gate's source by the gate's own two patterns — and the gate's last claim fails the build if that read disagrees with what it was handed while running.