Pedestrian Physics 14

Redshift

A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.
(Max Planck)

The vorpal universe is a many-splendored thing with pirouetting galaxies dancing to the music of the spheres. with maelstroms sucking in energy and matter, destroying and reshaping, dragging the products into the vorpal interior whence they resurface, buoyed by the inflationary forces; but unless the vorpal itself spins, there is no systemic motion. The cosmic redshift phenomenon must therefore be a function of position, not motion.

With few data as a guide, it is a field wide open for speculations. I shall assume that photons follow the curve of the great circle combining source and target. It means, as the voyage progresses, the momentum vector must rotate to be aligned with the tangent.

Rotation requires work and is best described by introducing the concept of torque, ‘τ’:

E = τϴ
E is work done
τ is torque
ϴ is angle rotated

There is no outside energy available, all forces are in balance. The work therefore must be done at the expense of the photon itself.

What causes the energy loss? There is no known equivalent of friction to slow down a photon, A different explanation is available: the extinction theorem. As it applies to photons in space, when a photon interacts with a particle, it is extinguished. If the particle cannot hold on to it, it must eject a new photon. This photon must be ejected with speed ‘c’ relative to the particle. In the process total momentum must be conserved and, depending on the situation, energy may be lost to the intercepting particle. The new photon will have speed ‘c’ but a reduced momentum. Its average speed will remain close to ‘c’ but after death by a thousand cuts, a tired replica of the original photon will arrive. Hence the cosmic redshift.

This scenario permits us to shift the focus to the central angle. Since the linear velocity remains near 'c', the angular velocity is constant, and equal to the rate of rotation of the momentum.

Stipulate that at each encounter the loss is proportional to the arriving mass, and smooth the curve:
dm = -mkdϴ
d(ln(m₀/m_ϴ ))= kdϴ
z + 1 = m₀/m_ϴ = e^kϴ

Set z = 1000 when ϴ = π, then k = 2.2.

The Virgo cluster, at a distance of 50 Mly, is at the limit of distance estimates based on luminosity. The Hubble z-value is listed as 0.004. It corresponds to a central angle in the vorpal model: ϴ = 0.002 radians. With these numbers, the estimate for R, the vorpal radius, is:

R = 25.000 Mly

Luminosity
Plot: y = e^2.2ϴ - 1

Redshift is all about the quality of the arriving photons, luminosity is also about the number of photons arriving.

The inverse square law makes sense in a “flat” three-dimensional space. In the curved skin of the vorpal it works only in close proximity to the source. The density of photons will be reduced more slowly than in flat surroundings and reach its minimum when the central angle is π/2. The photons will then start to converge and arrive exhausted but in full force at the antipode.





The 'cosmic background radiation' is reported to have z-values in excess of z = 1000. In the vorpal model it implies that the origin is close to our antipode. The anisotropy makes sense if the photons are emitted from individual galaxies.

The lower plot shows that out to 200 Mly, or so, it will probably be impossible ever to obtain data that can differentiate the exponential curve from Hubble's linear correlation.