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Color
Black
Size
S–5XL
Made
To order · shipping times
Color
Size

Details

Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

Unisex tee size chart, inches
SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

Measurements in inches, ±1.5 in tolerance.

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The physics

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 at a redshift of about 1.8 are crossing our event horizon now. 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.

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

\[d_{\text{EH}}(t) = a(t)\int_{t}^{\infty} \frac{c\,dt^{\prime}}{a(t^{\prime})}\]
\[d_{\text{EH}} \to \frac{c}{H_\Lambda} \quad (\text{pure de Sitter})\]
Symbols
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 \(\mathrm{s⁻¹}\)
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