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Where the model stops

Every picture in physics has a domain of validity, and the interesting physics usually lives at its edge.
sourcesourcesolid: waves arrive in stepbetween them they arrive opposed Waves

When two waves meet, they simply add

Waves pass through each other unchanged and their displacements add point by point. From that one impoverished-sounding rule comes interference, beats, and the evidence that light is a wave at all.

40°25.4°n = 1n = 1.5some light always reflects as well Optics

The bend at the boundary, and what it is really about

Light changes direction when it changes speed. Snell's law is the geometry of that statement, and it can be derived without knowing anything about light at all.

020406080020406080incident angle (degrees)critical angle 41.8°beyond this, nothing emergesdashed: no bending at all Optics

The angle past which light cannot leave

Snell's law asks for the sine of an angle greater than one, and no such angle exists. What happens instead is a perfect mirror made out of nothing but a change of speed.

+ Electromagnetism

Field lines are a choice, not a discovery

Nothing in space is arranged in lines. The lines are a drawing convention — and an unusually good one, because three separate facts about the field survive the translation.

+lines and arrows are the same fielddrawn two ways Electromagnetism

The field before the lines were drawn on it

A field is a vector attached to every point of space. Drawing it as arrows on a grid is honest and ugly; drawing it as lines is beautiful and throws information away.

0123456700.20.40.60.8speedT = 0.5T = 1T = 2T = 4no molecule has the average speed; most are near it Thermodynamics

The speeds in a still room

The air in a quiet room is not still. Every molecule in it is moving at hundreds of metres per second, and temperature is a single number summarising an entire distribution.

123400.511.5volumepressure1234net workhot isothermcold isothermadiabatic steps Thermodynamics

The ceiling on every engine, set before it was designed

There is a maximum efficiency no heat engine can exceed, and it depends on nothing but two temperatures. Not the fuel, not the working substance, not the cleverness of the engineer.

xctlightct′x′here, nowfuturepastunreachableγ = 1.155 — the axes close on the light line together Relativity

Two axes, one speed, and a diagram that does the arguing

Put position across and time up, insist that light travels at forty-five degrees for everyone, and nearly every result in special relativity becomes something to read off rather than derive.

xctsame time, for one observersame time, for the otherABneither slicing is the right one: that is the content of relativity Relativity

Now is a choice of slicing

Two events happening at the same time is not a fact about the events. It is a fact about who is asking, and different observers slice spacetime at different angles.

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