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Beyond the A-Level spec · Modern Physics

Nothing with mass reaches the speed of light.

Drag the velocity slider toward c and watch a light clock disagree with a stationary one. That disagreement is time dilation — not an illusion, a measured effect.

LIGHT CLOCKγ = 1.00
LORENTZ FACTOR γ
MOVING CLOCK TICKS
LENGTH CONTRACTION
Modern Physics · Special Relativity

Special relativity

Two postulates, both simple to state, force every clock and ruler in the universe to disagree with each other depending on how fast they're moving.

Einstein's theory rests on two postulates: first, the laws of physics are the same in every inertial frame (one moving at constant velocity); second, the speed of light in a vacuum, c, is the same for every observer, no matter how fast they or the source are moving. That second postulate is the strange one — it's what breaks the everyday assumption that velocities simply add.

Lorentz factorγ = 1 / √(1 − v²/c²)
Time dilationΔt = γ Δt₀
Length contractionL = L₀ / γ

The light clock in the simulator makes this concrete: a photon bounces vertically between two mirrors on a spaceship. To someone on the ship, the photon just goes up and down. To someone watching the ship fly past, the photon traces a longer diagonal path each bounce — and since light speed is fixed for both observers, that longer path can only mean more time has passed for the stationary observer per "tick" of the ship's clock. The ship's clock, from outside, runs slow.

Common exam slip — γ is never less than 1, and it's the clock or ruler in motion relative to you that ticks slower or measures shorter, never your own. There's no absolute rest frame to break the symmetry, which is why both observers can correctly say "your clock is the slow one."
PLAYGROUND
LORENTZ FACTOR γ
MOVING CLOCK TICKS
LENGTH CONTRACTION
Bonus · Not on your exam spec

A first look at string theory

This is graduate-level theoretical physics, included here only as extension reading. Nothing in this section will appear on an A-level paper.

Ordinary particle physics treats electrons, quarks and photons as points with no internal structure. String theory's core idea is to replace every point particle with a tiny vibrating loop or strand of "string," far too small to observe directly. Different particles, in this picture, are just different vibrational modes of the same underlying string — much like a guitar string's fundamental and overtones are all the same string, vibrating differently.

The harmonics simulator alongside is a classical stand-in for that idea, nothing more: a real string on a guitar can only vibrate transversely in the three dimensions of ordinary space, while the strings of string theory are conjectured to vibrate through 10 or 11 dimensions, most of them curled up far too small to notice. The motivation for the theory is that it's one of the few frameworks that might unify general relativity (gravity) with quantum mechanics — a unification that special relativity itself doesn't attempt, since it leaves gravity out entirely.

Why it's here at all — special relativity is the last A-level-accessible idea before physics gets genuinely strange. String theory sits right past that boundary: mathematically serious, but currently untested by any experiment. Treat this section as a preview, not revision material.
STANDING WAVE HARMONICSMode n = 1
Fundamental analogy for "particle type"
Nodes (fixed points)
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