Red shift

Meaning of red shift

When does a red-shifted photon dissolve into the “vacuum”?

Question.
If a photon’s wavelength keeps increasing with cosmic red-shift, at what point does it become indistinguishable from the background vacuum fluctuations?
In other words: when does a photon “drown” in the quantum sea of space itself?

Physical picture

In quantum electrodynamics the vacuum carries zero-point fluctuations with energy $E_\text{vac} = \tfrac{1}{2}\hbar\omega$ for each field mode.
A photon is a single coherent excitation of that same mode, with energy $E_\text{photon} = \hbar\omega.$

The ratio between them is constant ($E_\text{photon}/E_\text{vac} = 2$),
but as the universe expands, both $E$ and $\omega$ decay exponentially with time:

$$ E(t) = E_0 e^{-H t}, \qquad \lambda(t) = \lambda_0 e^{H t}. $$

Critical scale

When the wavelength approaches the cosmic event-horizon scale

$$ \lambda_c \sim R_\text{EH} \approx 1.5\times10^{26},\text{m} \approx 16,\text{Gly}, $$

the photon’s energy becomes

$$ E_c = \frac{h c}{\lambda_c} \approx 10^{-52},\text{J} \approx 6\times10^{-34},\text{eV}, $$

corresponding to an effective temperature of $T_c \approx 10^{-30},\text{K}$.

At this level, the photon’s coherent energy is far below the amplitude of ambient field fluctuations — it no longer forms a distinguishable excitation.

Interpretation

A photon does not vanish at a fixed distance; its energy decays exponentially as its wavelength stretches.
Once its wavelength exceeds the cosmic horizon scale, its phase and identity blur into the stochastic vacuum field — it effectively dissolves into the background, not by annihilation but by loss of coherence within the universal quantum noise.

Hypothesis summary: Red-shift as photon spreading in a static universe

There is a hypothesis, that the red-shift which is observed of light coming from long distance sources (other galaxies) is not (simply) based on expansion of the universe, but by a continuoes increase in size of the photon.

In this view, the cosmological red-shift does not arise from an expanding space, but from the spreading of each photon as it travels through an otherwise static universe. At the moment of emission, the photon is not launched as an infinitely thin, perfectly defined wave packet, but with a minute angular and spatial uncertainty — a natural blur rooted in the quantization of space itself at the emission site.

Over cosmological distances this infinitesimal uncertainty becomes manifest: the photon’s energy front diverges, its wavelength effectively stretches, and its spectral signature appears red-shifted. What we interpret as “space expanding” is, in this hypothesis, the accumulated geometric consequence of that primordial emission blur — the photon gradually dissolving its coherence into the grain of space.

In such a picture, the red-shift is not the result of galaxies receding, but of light thinning out as it approaches the limit of a finite, static cosmos — a slow diffusion of the photon’s own quantized geometry toward the horizon of existence.

Let’s have a look if this makes sense calculatively.

Observable-universe size

• Diameter ≈ 93 Gly (≈ $8.8\times10^{26}$ m).

How far (as $c\Delta t$) until a photon’s wavelength stretches to that size?

In an exponentially expanding future (set by today’s Hubble rate $H_0$), a photon’s wavelength grows as $\lambda \propto e^{H_0 t}$. The required expansion is $$ N=\ln!\frac{\lambda_{\text{target}}}{\lambda_0},\quad \lambda_{\text{target}}=D_{\text{obs}}. $$ The corresponding “distance” in light-travel units is $$ c\Delta t ;=; N,\frac{c}{H_0};\approx; N\times 13.97\ \text{Gly}. $$

Concrete comparisons (today → until $\lambda$ equals 93 Gly)

So, whichever reasonable photon you pick today, you’re looking at roughly (9–12\times) the observable-universe diameter (i.e., about $900–1,100$ Gly in $c/H_0$ units) before its wavelength reaches the scale of the observable universe.

If you want a one-liner to reuse: $$ c\Delta t ;\approx; 13.97\ \text{Gly}\times \ln!\bigg(\frac{93\ \text{Gly}}{\lambda_0}\bigg), $$ with $\lambda_0$ in Gly (or convert units consistently).

Dismantlement

Scientific view

The static-universe photon–dispersion hypothesis proposes that the observed cosmological red-shift arises not from an expanding spacetime metric, but from a gradual spreading of the photon wave packet as it propagates through an otherwise static universe.

At emission, a photon is assumed to carry an intrinsic angular or spatial uncertainty — a minute spread in its momentum vector — resulting from local quantum indeterminacy or a quantized granularity of space at the emission site. As the photon travels over cosmological distances, this microscopic divergence accumulates. The effective wavefront slowly expands, the average wavelength increases, and the photon energy correspondingly decreases.

The apparent red-shift would therefore be an emergent property of the photon’s propagation geometry in a static metric, rather than a manifestation of metric expansion itself. In this framework, the cosmic red-shift reflects a progressive decoherence or diffusive stretching of the photon field within a quantized spatial substrate.

Assessment from standard physics

Current cosmology and quantum field theory provide several constraints that strongly challenge this model.

(a) Energy and direction conservation

In flat spacetime (Minkowski metric), the energy–momentum four-vector of a free photon is conserved. A spontaneous, cumulative reduction of energy (red-shift) would require a physical mechanism that breaks translational invariance — effectively a frictional or diffusive coupling to space itself. No such coupling is observed in laboratory, astrophysical, or cosmic propagation: photons from distant galaxies and supernovae preserve phase coherence and polarization over billions of years within experimental limits.

(b) Linearity of red-shift

The observed red-shift z follows the metric relation $1+z = \frac{a(t_{\text{obs}})}{a(t_{\text{emit}})},$ which applies uniformly to all wavelengths and correlates tightly with distance. A diffusion-based or scattering-based process would generally produce wavelength-dependent (chromatic) effects — blurring, broadening, or energy-dependent attenuation — none of which are observed in high-resolution spectra from distant quasars or supernovae.

(c) Surface brightness (Tolman) test

A purely geometric spreading of photon energy would predict a different dimming law than the one confirmed by the Tolman surface-brightness test: observations show the (1+z)^4 scaling expected from cosmic expansion, not the (1+z)^2 or exponential fall-off typical of scattering or diffusion models.

(d) Cosmic microwave background (CMB)

The CMB spectrum is an almost perfect blackbody, its temperature scaling with 1+z. A photon-spreading model would have difficulty maintaining the precise Planckian shape under cumulative dispersion, since energy loss and angular diffusion would distort the spectrum.

(e) Quantum-mechanical coherence

A “minute uncertainty at emission” is real — every photon is a finite wave packet. However, quantum mechanics predicts that this uncertainty does not grow in free space beyond the linear dispersion allowed by the wave equation. In vacuum, the photon’s wave packet spreads transversely, but the central wavelength and energy remain invariant unless an external field or curvature acts on it.

Perspective

The hypothesis fits conceptually with a wave-geometric view of the universe: red-shift as an intrinsic property of propagation rather than of space expansion. From a theoretical standpoint it’s elegant in simplicity — it preserves a static cosmos and attributes the observation to the photon’s own geometry. However, the model would need a precise, Lorentz-invariant mechanism for how a photon’s energy decreases in vacuum without scattering, and why this effect is strictly linear with distance and independent of frequency.

Without that, standard cosmology (ΛCDM) remains the only framework that quantitatively matches the entire suite of red-shift-based observations.

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