Supernova Light-Curve Time Dilation

Distant Supernova

Redshift z 0.50

Rest-frame light-curve length 20 d

Prediction Model

Playback speed 1.0×

Live Readouts

Observed duration

30.0 d

Rest-frame duration

20.0 d

Stretch factor (1+z)

1.50×

Luminosity distance

2260 Mpc

Flux vs. nearby SN

1 / 2,650

Comoving distance

1510 Mpc

How it works

A Type Ia supernova's brightness rises and falls over a fixed number of days in its own rest frame — always about the same shape, which is exactly why they make reliable "standard candles". If the universe is expanding, every photon's wavelength stretches by a factor (1+z) on its way to us, and so does every time interval between wave crests — including the interval between the supernova getting brighter and dimmer. The observed light curve should therefore be time-dilated by the same factor as the redshift:

T_observed = T_rest × (1 + z)

Flat ΛCDM comoving distance:
  D_C(z) = (c/H₀) ∫₀^z dz' / E(z'),   E(z') = √(Ωm(1+z')³ + ΩΛ)
Luminosity distance:
  D_L(z) = (1 + z) · D_C(z)
Bolometric flux:
  F ∝ L / (4π D_L²)

This isn't a small effect: the D_L² in the flux law already carries two hidden factors of (1+z) — one from each redshifted photon losing energy, one from photons arriving less often — on top of ordinary geometric dilution. Redshift slider sets z for the distant supernova. Light-curve length sets its true rest-frame duration. Prediction model switches between the real expanding-space prediction and the historical "tired light" alternative, which claimed redshift comes from photons slowly losing energy in static space with no time dilation at all — it predicts T_observed = T_rest regardless of z.

Real Type Ia supernova surveys (Leibundgut et al. 1996; Goldhaber et al. 2001; Blondin et al. 2008) measured light-curve widths across a wide redshift range and found they stretch as (1+z)¹·⁰±⁰·¹³ — matching the expanding-space prediction and ruling out tired light as an explanation for cosmological redshift.

Nearby SN (z ≈ 0.01) Distant SN (slider z)

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