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Null Beacon

Cosmic Event Horizon / Causal Disconnect Physics

\[d_{\text{EH}}(t) = a(t)\int_{t}^{\infty} \frac{c\,dt^{\prime}}{a(t^{\prime})}\]
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Size guide S–5XL · inches

Meet Null Beacon. Some galaxies we can see will never hear from us. In an accelerating universe there is a distance beyond which light sent today never arrives: the cosmological event horizon. Today it lies about 16.7 billion light-years away, and galaxies we now see at redshift about 1.9 are at that distance. We still see their old light, but anything they emit today is lost to us. Null Beacon on a pixel-art unisex tee; equation, symbols and sources in the panel below.

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Details

Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

参考尺度：M 码宽 20 in（50.80 cm），约为 3.143 × 1034 个普朗克长度（lP = 1.616255 × 10−35 m）。用卷尺量更快。

Measurements in inches, ±1.5 in tolerance.

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Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

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The physics

In a universe whose expansion is speeding up, there is a largest distance from which light sent today can ever reach us: about 16.7 billion light-years. Galaxies we now see at redshift about 1.9 are at that distance today. We still see their old light; their new light is lost.

Null Beacon keeps broadcasting. Some of the galaxies they can see will never hear it.

In a universe whose expansion is speeding up, there is a distance beyond which light sent today will never arrive, however long it travels: the space in between grows faster than the light can cross it. That boundary is the cosmological event horizon. The first formula on this page computes it. Add up how much distance light can cover from now until the end of time, with every stretch divided by how much the universe will have grown by then, and convert to today's distance. If the expansion slowed enough, that sum would grow without limit and there would be no horizon. Because dark energy is making it accelerate, the sum converges.

Here is the strange part. Galaxies we now see at a redshift of about 1.9 are at our event horizon today. We still see galaxies far beyond that, because we are receiving light they sent long ago. But light those galaxies emit today will never reach us, and a signal Null Beacon sends today will never reach them. We are watching their past with no way to share any future.

The second formula is the long-run limit. If dark energy is a cosmological constant, the universe ends up in a state called de Sitter space, and the event horizon settles at the speed of light divided by the expansion rate.

Worked numbers, for flat ΛCDM with Planck 2018 parameters (H₀ = 67.4 km/s/Mpc, Ω_m = 0.315): the Hubble sphere, where recession speed equals c, is c/H₀ ≈ 14.5 billion light-years away; the event horizon is about 16.7 billion light-years away; and the particle horizon, the edge of the observable universe, is about 46 billion light-years away. These are the three marks on the back of this shirt. In the far future the event horizon approaches c/H_Λ ≈ 17.5 billion light-years.

Wolfgang Rindler set out the distinction between this event horizon and the particle horizon, the edge of what we can see at all, in 1956. Their present size depends on what dark energy turns out to be, and whether it stays constant is an open question.

Null Beacon is not broken. They are only too far from the future.

Equations

\[d_{\text{EH}}(t) = a(t)\int_{t}^{\infty} \frac{c\,dt^{\prime}}{a(t^{\prime})}\]
\[d_{\text{EH}} \to \frac{c}{H_\Lambda} \quad (\text{pure de Sitter})\]
SymbolMeaningUnit
\(d_{\text{EH}}\) proper distance to the cosmological event horizon \(\mathrm{m}\)
\(a(t)\) scale factor \(\mathrm{1}\)
\(c\) speed of light \(\mathrm{m/s}\)
\(H_\Lambda\) Hubble rate of a Λ-dominated universe \(\mathrm{s⁻¹}\)

Sources

  1. Rindler (1956) Visual Horizons in World Models, MNRAS 116, 662
  2. Riess et al. (1998) Observational Evidence from Supernovae for an Accelerating Universe, AJ 116, 1009
  3. Perlmutter et al. (1999) Measurements of Ω and Λ from 42 High-Redshift Supernovae, ApJ 517, 565
  4. NobelPrize.org — The Nobel Prize in Physics 2011 (accelerating expansion)
  5. PDG 2024 review — Big-Bang cosmology
  6. Davis & Lineweaver (2004) Expanding Confusion: Common Misconceptions of Cosmological Horizons…, PASA 21, 97
  7. PDG 2024 review — Dark energy
  8. Planck Collaboration (2020) Planck 2018 results VI. Cosmological parameters, A&A 641, A6

Source Rindler, W. (1956). Visual Horizons in World Models. Monthly Notices of the Royal Astronomical Society 116, 662–677.doi.org/10.1093/mnras/116.6.662

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