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Light Cone Hoodie

ELSEWHERE IS A REAL PLACE | Pixelated Physics

\[ds^2 = c^2dt^2 - dx^2 - dy^2 - dz^2\]
$54.99 USD
$54.99 USD
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Size guide S–5XL · inches

Pick one event: here, now. The light it sends out spreads into a cone in spacetime, the future cone. The light that could have reached it forms the past cone. A Minkowski light cone: future and past, three worldlines through one event, one of them accelerating. Outside the cone is elsewhere. Pixel-art unisex hoodie in black; equation, symbols and sources in the physics panel below.

Shipping calculated at checkout by destinationMade to order, ships in 2–5 business days

Details

Size & fitS–5XL

Unisex Heavy Blend hoodie (Gildan 18500), classic fit.

SizeWidthLengthSleeve
S202733.5
M222834.5
L242935.5
XL263036.5
2XL283137.5
3XL303238.5
4XL323339.5
5XL343440.5

Measurements in inches. Width and length ±1 in, sleeve (from center back) ±0.75 in.

ShippingBy destination

Shipping calculated at checkout by destination.

Delivery times & where we ship

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.

Full refund & replacement policy

The physics

In spacetime, light travels along a cone that separates events you could reach or be reached from (past and future) from those you can't (elsewhere). A rocket with constant acceleration follows a hyperbola that bends toward that cone but never crosses it.

Pick one event: here, now. The light it sends out spreads into a cone in spacetime, the future cone. The light that could have reached it forms the past cone.

Hermann Minkowski drew this picture in 1908. Inside the future cone is everything this event can affect, and inside the past cone everything that can affect it. On the cone itself, ds² = 0.

Everything outside both cones is elsewhere. For those events, observers moving differently disagree about whether they happened before or after now, and nothing can travel between them and here.

The art shows a cone in two space dimensions plus time. Three worldlines pass through the event: one at rest, one at half light speed, and one under constant acceleration that bends but never reaches the cone.

Elsewhere is a real place.

Equations

\[ds^2 = c^2dt^2 - dx^2 - dy^2 - dz^2\]
\[ds^2 = 0\;\text{on the cone}\]
\[x(t) = \frac{c^2}{g}\left(\sqrt{1+\left(\frac{gt}{c}\right)^2}-1\right)\]
SymbolMeaningUnit
\(ds\) spacetime interval \(\mathrm{m}\)
\(c\) speed of light \(\mathrm{m/s}\)
\(t\) time \(\mathrm{s}\)
\(x, y, z\) position \(\mathrm{m}\)
\(g\) proper acceleration of the curved worldline \(\mathrm{m/s^2}\)

Sources

  1. Minkowski (1908) Raum und Zeit, lecture at Cologne, published in Phys. Z. 10, 104 (1909)
  2. Einstein (1905) Zur Elektrodynamik bewegter Körper, Ann. Phys. 322, 891
  3. Taylor & Wheeler, Spacetime Physics, 2nd ed. (1992)
  4. Rindler (1966) Kruskal Space and the Uniformly Accelerated Frame, Am. J. Phys. 34, 1174

Source Minkowski, H. (1909). Raum und Zeit. Physikalische Zeitschrift, 10, 104–111.

Field notes

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