From the Planck length to the observable universe

Teaching notes

The rail is linear in the exponent, so equal distances along it are equal factors of ten — 61 decades in all. Each screen shows one decade of field of view; every step right divides the apparent size of everything on screen by ten.

Controls

• ← → move by half a decade, Shift + arrow snaps to the next labelled scale.
• Space starts and stops the automatic zoom.
• Drag the rail, or press a chip to jump.

Where the numbers come from

• Planck length 1.616 × 10⁻³⁵ m; proton charge radius 0.84 fm; nuclear radius R = 1.20 A^1/3 fm.
• Bohr radius 5.29 × 10⁻¹¹ m; DNA helix 2.0 nm wide, 3.4 nm per turn.
• Earth equatorial diameter 1.276 × 10⁷ m; Sun 1.392 × 10⁹ m; 1 AU = 1.496 × 10¹¹ m; 1 ly = 9.461 × 10¹⁵ m.
• Observable universe: 93 Gly across = 8.8 × 10²⁶ m.

Honest limits

The pictures are schematic, not to scale within a frame — an atom's nucleus really is far too small to draw at 10⁻¹⁰ m, which is the point made at 10⁻¹² m. Quarks and electrons have no measured size; the drawing at 10⁻¹⁹ m shows the experimental upper bound, not a radius. Between the Planck length and 10⁻¹⁹ m nothing has been observed directly at all.

Questions worth asking a class

• How many decades separate you from a proton? From the observable universe? Which is the bigger jump?
• If a hydrogen atom were scaled to 100 m across, how big is the nucleus?
• Why does the sequence stop at 10²⁶ m and not go further?

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