The Hubble Law

The farther a galaxy, the faster it recedes. The recession velocity is linear in distance — v = H₀·d — and it has no centre: every galaxy sees the same law, because space itself is stretching. Rendered, not quoted.

source Hubble, E.P. (1929), A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae, PNAS 15(3), 168–173 · doi:10.1073/pnas.15.3.168

Blue Team · builds & defends
3

The Model

A galaxy at distance d recedes with velocity v set by one constant, the Hubble parameter H₀:

v = H₀ · d (H₀ ≈ 70 km/s/Mpc)

A straight line through the origin. Double the distance, double the speed. The slope is H₀; its reciprocal 1/H₀ is a timescale.

Uniform expansion means a single scale factor a(t) multiplies every separation, so ḋ = (ȧ/a)·d = H₀·d for all pairs at once.

5

The Lineage

Farther is faster. Hubble 1929 turned nebular redshifts into a law: v = H₀d, no centre, Hubble time 1/H₀ ≈ 14 Gyr.

Upstream, the expansion is governed by the-friedmann-equation. Downstream, the stretch is read off light by the-cosmological-redshift. This sphere is the middle term: the observed straight line.

7

The Witness

Live re-check of the engine's invariants. Confirms green; flips red the instant the machine is tampered.

witness idle
The Machine
4

Data In in ↓

A distance d in megaparsecs (Mpc). Drag it. The engine returns the recession velocity live.

d = 500 Mpc
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0

The Panel LIT

v = H₀·d, computed live. The line, the Hubble distance where v = c, and the expanding lattice.

v(d) = km/s
v/c =   
Hubble time 1/H₀ = Gyr
Hubble distance c/H₀ = Mpc
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8

Data Out out ↓

Proven at boot, deterministically:

awaiting selfcheck…
Red Team · attacks & breaks
1

The Adversary WALL

“A recession law implies we are at the centre of an explosion.”

Real objection, real answer. Because v = H₀d is linear and the expansion multiplies every separation by one factor a(t), the same law holds from every galaxy's frame — the vector velocity from B is H₀(r₀₋r_B). No point is privileged; there is no centre and no edge. The redshift is stretched space, not a Doppler flight through it.

2

The Graveyard

  • “Redshift is ordinary Doppler motion through space.” → cosmological redshift is the stretching of wavelengths by expanding space; beyond c/H₀ recession exceeds c with no law broken. [AMBER: interpretation-dependent]
  • “H₀ is a fixed constant of nature.” → H(t) evolves; “constant” means constant over the sky now. Hubble's own slope (~500) was mis-calibrated; the value is still argued (the Hubble tension, ~67 vs ~73). [AMBER]
  • “1/H₀ is exactly the age of the universe.” → only an estimate; the true age depends on the whole expansion history (matter, Λ). It lands near 14 Gyr by coincidence of parameters.
6

The Tamper

Planted void (disclosed): replace the law with v = H₀·d² (quadratic). Now a galaxy twice as far recedes faster, not 2× — a preferred centre reappears and homogeneity dies. The Witness (7) catches it.