Tag Archives: Dieu

L’ horizon

http://gregegan.customer.netspace.net.au/SCIENCE/Rindler/RindlerHorizon.html

Imagine that it’s possible to build a spaceship that constantly accelerates. We don’t really care how it does this; this is a thought experiment in physics, not an exercise in interstellar spacecraft engineering. Because we’re dealing with relativistic velocities, we need to be precise and say that the spaceship undergoes constant proper acceleration: passengers will measure a constant inertial force pushing them towards the back of the ship, whereas observers in motion relative to the ship will necessarily describe its acceleration differently.

If we start out by treating the spaceship as a single point, we can describe its world line in an inertial reference frame with coordinates (t,x) as:

x(τ) = (t(τ), x(τ)) = (sinh(a τ)/a, cosh(a τ)/a)

where τ is proper time measured by a clock in the spaceship (set to zero when t=0), a is the acceleration the passengers feel, and we have chosen coordinates so that x=1/a when t=τ=0. (We are using units where the speed of light is set equal to 1, and this means that whenever we talk about an inverse acceleration being equal to a distance, or vice versa, their product will equal c2 in conventional units. For example 1/g, where g is the gravitional acceleration at the Earth’s surface, corresponds to a distance of 9.18 x 1015m, or about a light-year, while 1/x, where x is one metre, corresponds to an acceleration of 9.18 x 1015g.)

The world line of the spaceship is a hyperbola:

Constant aceleration world line

This hyperbola can also be described by the equation:

a2x2 – a2t2 – 1 = 0, or
x.x = 1/a2

The best style is the style you don’t notice. Somerset Maugham

chapitre 3 : désespoir

le fleuve avait décru

et le moteur ronflait agréablement dans le petit matin

l’avion s’aligna sur la piste

chaque fleur ouvrait sa corolle telle un parachute

sous le ciel qui ressemblait à une boîte en gelée

elle jeta le revolver et je me dis que je retournais maintenant au travail de mes pensées

mais quand je m’aperçus que nous tournions le dos à la ville il était trop tard pour faire demi-tour

alors je sortis de l’autoroute et m’appuyai à cet arbre dénudé

rien n’est plus vide qu’une piscine vide si ce n’est une bouteille à moitié pleine

ou un fusil sans les cartouches