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I Twist Space Itself

Spacetime Distortion Physics

\[\alpha = \frac{4GM}{c^{2}b}\]
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Size guide S–5XL · inches

Space is not a rigid stage. Put enough mass on it and the stage bends. Mass curves spacetime and light follows the curve: gravitational lensing, from general relativity. I Twist Space Itself wears it in pixel art on a unisex tee. The physics panel below has the equation, every symbol and the sources.

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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

पैमाने के लिए: साइज़ M की चौड़ाई 20 in (50.80 cm) है, यानी लगभग 3.143 × 1034 प्लांक लंबाई (lP = 1.616255 × 10−35 m)। इंच-टेप ज़्यादा जल्दी काम करेगा।

Measurements in inches, ±1.5 in tolerance.

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The physics

Mass curves spacetime, so a ray of light passing the Sun follows a bent path. General relativity predicts a bending angle of 4GM/(c²b), twice what Newton's gravity gives for light treated as particles, and eclipse measurements agreed with Einstein's value.

The Twister does not push light. Light goes straight. The Twister changes what straight means.

Send a ray past the Sun and it bends. Newton's physics can be made to predict this, if you treat light as fast particles that feel gravity: grazing the edge of the Sun, the bend comes to about 0.87 arcseconds. Einstein's general relativity, in its finished form of 1915, predicts twice that, about 1.75 arcseconds. The first formula on this page has a 4 where the Newtonian version, the second line, has a 2.

Where does the extra half come from? Near a mass, gravity in Einstein's theory does two things. It slows clocks, and that part alone reproduces the Newtonian answer. It also curves space itself, and the curvature adds an equal share. A beam of light, which always takes the straightest available path through spacetime, picks up both.

Stars beside the Sun show only during a total eclipse. On 29 May 1919, British expeditions organised by Frank Dyson and Arthur Eddington photographed the stars around the darkened Sun from Sobral in Brazil and the island of Príncipe, and compared them with the same stars at night. The shifts favoured Einstein over Newton. How cleanly they did so has been argued ever since: the plates were difficult, and one Sobral set that leaned toward the smaller value was set aside for a focusing problem. Later radio measurements, timing quasars as the Sun passed in front of them, confirmed general relativity far more precisely.

Today the effect is a tool. Galaxy clusters bend the light of galaxies behind them into arcs, and the arcs weigh the cluster, including mass that gives off no light at all.

The Twister never touches a photon. They are only heavy, and nearby.

Equations

\[\alpha = \frac{4GM}{c^{2}b}\]
\[\alpha_{\text{Newton}} = \frac{2GM}{c^{2}b} = \tfrac{1}{2}\,\alpha\]
Symbols
SymbolMeaningUnit
\(\alpha\) deflection angle of light passing a mass \(\mathrm{rad}\)
\(G\) gravitational constant \(\mathrm{m³·kg⁻¹·s⁻²}\)
\(M\) lensing mass \(\mathrm{kg}\)
\(c\) speed of light \(\mathrm{m/s}\)
\(b\) impact parameter (closest approach) \(\mathrm{m}\)

Source Einstein, A. (1916). Die Grundlage der allgemeinen Relativitätstheorie. Annalen der Physik 354, 769–822.doi.org/10.1002/andp.19163540702 (opens in a new tab)

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