The Complete Guide to Electromagnetism & Relativity

1. The Bookbinder's Apprentice

Faraday has no mathematics, and sees what nobody else can.

He was a blacksmith's son with four years of schooling, apprenticed at thirteen to a bookbinder. He read the books he was binding. He talked his way into a series of public lectures by the most famous chemist in Britain, wrote up three hundred pages of notes, bound them beautifully and sent them to the lecturer as a job application. He got the job — washing bottles. He became the greatest experimental physicist of the century.

Michael Faraday (1791–1867)

Almost no formal education and almost no mathematics, and he found the electric motor, the generator and the field.

Faraday's lack of mathematics is usually mentioned as a limitation. It may have been an advantage: unable to reach for equations, he thought in pictures, and the picture he invented — invisible lines of force filling the space around a magnet — turned out to be the deepest idea in nineteenth-century physics.

The starting point was an accident. In 1820 the Danish scientist Hans Christian Ørsted noticed that a compass needle twitched when he switched on a nearby current. Electricity and magnetism, previously separate curiosities, were connected. Nobody knew how.

Faraday realised the magnetic force around a wire did not point towards it or away from it — it circled it. So he built an apparatus in which a current-carrying wire rotated continuously around a magnet. That is the first electric motor, in 1821: the first time electricity was turned into continuous mechanical motion, and it came from taking the shape of the force seriously.

Then he spent ten years chasing the reverse. If electricity makes magnetism, magnetism should make electricity. It kept failing, because he was using steady magnets. In 1831 he found the missing condition: the magnetic field has to be changing. Move a magnet through a coil and a current appears; stop moving it and the current dies. That is electromagnetic induction, and it is the principle behind essentially every power station on Earth.

Field: Faraday's great concept: space itself is not empty but carries a condition — a strength and direction at every point — that tells objects in it how to behave. Iron filings around a magnet reveal it. Before this, forces were thought to act instantly across empty distance; afterwards, the field is a real physical thing that carries the influence and takes time to do it.

Asked by a government minister what use electricity could possibly be, Faraday is said to have replied that one day the minister would tax it. The anecdote may be polished, but the point stands: induction was a laboratory curiosity for decades before it lit a single house.

What just happened

• Ørsted found in 1820 that a current deflects a compass needle
• Faraday built the first electric motor in 1821 from the circular shape of the force
• In 1831 he discovered induction: a changing magnetic field generates current

The field concept is the single most important idea Faraday contributed, and it is what made the next chapter possible.

Faraday could not write his insight as mathematics. A Scottish physicist twenty years younger read his papers and decided that it deserved to be.

2. Four Equations, and What Light Turned Out to Be

Maxwell unifies electricity, magnetism and optics on paper.

James Clerk Maxwell (1831–1879)

Took Faraday's pictures seriously enough to write them down, and found light hiding inside.

Maxwell was an unusual combination: mathematically formidable and willing to trust an experimentalist's intuition over the fashionable theory. He also worked out the physics of gas molecules, produced the first colour photograph, and explained Saturn's rings. He died of cancer at forty-eight.

By the 1860s the separate laws were known: charges produce electric fields, magnets have no isolated poles, a changing magnetic field induces an electric one. Maxwell wrote them all in one framework and found the set was inconsistent — it violated conservation of charge in a specific circumstance. So he added a term: a changing electric field must produce a magnetic field, mirroring Faraday's law.

The consequence is one of the most beautiful results in physics. A changing electric field makes a magnetic field; a changing magnetic field makes an electric field. So a disturbance can sustain itself, each field generating the other, and propagate through empty space as a wave. Maxwell calculated its speed from two constants measured in laboratory experiments with wires and magnets — quantities with nothing to do with optics — and got about 300,000 kilometres per second. The known speed of light.

“We can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena.”

This is the moment optics stops being a separate subject. Light is an electromagnetic wave — deduced from equations about wires, not from any experiment on light.

It also predicted that visible light is a tiny slice of a much larger spectrum, with waves of every other wavelength possible. In 1887 Heinrich Hertz generated and detected radio waves in his laboratory, exactly as predicted. Asked what use they might have, he reportedly said none whatsoever. Within twenty years Marconi was sending signals across the Atlantic.

What the four equations say, in words

• Electric charges create electric fields — and the field spreads out from them
• There are no magnetic monopoles — cut a magnet in half and you get two magnets, never an isolated north pole
• A changing magnetic field creates an electric field — Faraday's induction, the basis of every generator
• Currents and changing electric fields create magnetic fields — Maxwell's added term, the one that lets waves exist

What just happened

• Maxwell unified the known electrical and magnetic laws and added a missing term
• The equations predicted self-propagating waves travelling at the speed of light
• Hertz generated radio waves in 1887, confirming the whole framework

This is the first great unification in physics: three subjects — electricity, magnetism and light — turn out to be one subject. Every later physicist has been trying to repeat the trick.

There was one problem, and physicists spent thirty years trying to make it go away. The equations gave a speed for light — but a speed relative to what?

3. The Speed of What, Relative to What?

An experiment that failed, and the failure that mattered most in physics.

Every wave physicists knew travelled through a medium. Sound needs air; ripples need water. Maxwell's waves were assumed to travel through a medium too — the luminiferous aether, an invisible substance filling all space. It had to be rigid enough to carry very fast waves and thin enough that planets moved through it without slowing. Nobody was comfortable with it, but the alternative seemed unthinkable.

If the aether exists, the Earth moves through it, and light travelling with that motion should measure slightly faster than light travelling across it — the same way swimming with a current is faster than swimming across it. In 1887 Michelson and Morley built an interferometer of extraordinary sensitivity, floated on a bath of mercury so it could be rotated, to detect the difference.

There was no difference. None, in any direction, at any time of year. The speed of light was the same however the apparatus moved. It is the most famous null result in the history of science, and for eighteen years physicists tried to explain it away with increasingly desperate proposals — including the suggestion that moving objects physically contract by exactly the amount needed to hide the effect.

Albert Einstein (1879–1955)

Could not get an academic job, so he examined patent applications and rewrote physics in his spare time.

Einstein had graduated without distinction and was working as a technical examiner third class in the Bern patent office. In 1905 — his 'miracle year' — he published four papers: on the photoelectric effect (which won him the Nobel Prize and helped launch quantum theory), on Brownian motion (proving atoms are real), on special relativity, and on E = mc². He was twenty-six.

His move was to stop treating the constancy of light's speed as a problem to be explained and start treating it as a fact to be built on. Two postulates: the laws of physics are the same for all observers moving at constant velocity, and the speed of light in a vacuum is the same for all of them regardless of how they or the source are moving. The aether is not disproved so much as made unnecessary.

What just happened

• Maxwell's waves were assumed to travel through an aether filling space
• Michelson and Morley found no variation in light's speed in any direction
• Einstein took the constant speed of light as a starting assumption rather than a puzzle

This is a model case of how science advances: an experiment fails to find what everyone expected, and eighteen years later someone realises the expectation was the mistake.

Hold light's speed constant and something else has to give. What gives is more alarming than anyone expected.

4. Then Time Has to Bend

What special relativity actually claims.

Speed is distance divided by time. If everyone measures the same speed for light no matter how they are moving, and speeds normally add — a ball thrown forward on a train moves at train speed plus throw speed — then something in that sentence must give. Einstein's answer: distance and time are the things that give.

The standard thought experiment — A train carriage with a light clock

A pulse of light bounces between a floor mirror and a ceiling mirror. To a passenger it goes straight up and down. To someone on the platform watching the train pass, the same pulse travels a longer zig-zag path, because the mirrors move sideways while the light is in flight. Both must measure the same speed of light. The only way a longer path takes the same speed is if the observer on the platform measures more time between ticks. The moving clock runs slow — and not by illusion. It genuinely does.

The instinct at this point is to assume there must be a trick — that the clock only appears slow, the way a distant person only appears small. There is no trick. Every physical process that could be used to measure time slows in step: a pendulum, an atomic transition, a chemical reaction, a heartbeat, the decay of a radioactive particle. If anything ran at its normal rate, you could use it to detect your own motion, and the whole edifice of relativity says you cannot. Time itself is what is running differently.

This is genuinely difficult, and it is worth being honest that physicists found it difficult too. What makes it bearable is that the disagreements between observers are not chaotic. There is an exact set of equations relating one observer's measurements to another's, so everyone can calculate what everyone else will see and all of them agree about it. Reality does not fracture; only the assumption of a single universal clock does.

Time dilation: Time passes more slowly for something moving relative to you. The effect is negligible at everyday speeds and enormous near the speed of light. It is symmetrical for steady motion: each observer sees the other's clock as slow, and there is no contradiction, because they also disagree about which events are simultaneous.

What else follows

• Length contraction — moving objects are measured as shorter along the direction of travel
• Loss of simultaneity — two events that are simultaneous for one observer are not for another. 'Now' is not universal
• Mass–energy equivalence — E = mc². Mass is a form of energy, which is why the Sun shines and why nuclear weapons work
• A universal speed limit — accelerating a massive object towards light speed requires ever more energy, tending to infinity. Nothing with mass gets there

Commonly believed: Relativity means everything is relative and any viewpoint is as valid as another.

Actually: Almost the reverse. The theory is built on things that are absolute — the speed of light and the laws of physics, identical for every observer. What turns out to be observer-dependent is only measurement of space and time intervals, and even those are related by an exact, agreed transformation. Nothing here supports 'it's all relative' in the everyday sense.

Muons created by cosmic rays high in the atmosphere decay so fast that almost none should reach the ground. Far more arrive than should. From our frame, their internal clocks run slow; from theirs, the atmosphere is contracted. Either way the arithmetic works out, and the particles land. Relativity is measured every day in laboratories, not merely believed.

What just happened

• Holding light's speed constant forces time and distance to be observer-dependent
• Moving clocks run slow and moving objects contract along their direction of travel
• E = mc² identifies mass as a form of energy, and c as a universal speed limit

Special relativity dismantled the assumption every previous physicist had made without noticing it: that time is a universal background ticking identically for everyone.

Special relativity has a gap in it: it says nothing about gravity or acceleration. Closing that gap took Einstein ten more years and produced something stranger still.

5. Gravity Is Not a Force

The happiest thought of Einstein's life.

Einstein's starting point was an observation he called the happiest thought of his life: a person falling freely feels no weight. Not less weight — none. And someone in a sealed windowless box accelerating steadily through empty space would feel pressed to the floor exactly as though the box were sitting on a planet.

The equivalence principle: Being at rest in a gravitational field is locally indistinguishable from accelerating in the absence of one. No experiment inside the sealed box can tell you which situation you are in. This is where Newton's unexplained coincidence — inertial mass equals gravitational mass — becomes the foundation of a theory instead of an oddity.

From that, Einstein reached a conclusion that reads like a contradiction and is not. Gravity is not a force at all. Mass and energy curve spacetime, and objects simply follow the straightest available path through the curved geometry. The Earth is not being pulled by the Sun; it is travelling as straight as it can through a region the Sun has bent. The classic image is a heavy ball on a stretched rubber sheet — imperfect, because the real curvature is four-dimensional and includes time, but it is the right idea.

The theory made predictions Newton's could not. Mercury's orbital anomaly fell out exactly. Light, having energy, must follow the curvature too — so starlight passing close to the Sun should be deflected by a specific angle, twice what a naive Newtonian calculation gives.

29 May 1919 — Príncipe, off West Africa, and Sobral, Brazil

Arthur Eddington leads expeditions to photograph a total solar eclipse — the only way to see stars near the Sun. The plates are compared with photographs of the same stars taken at night months earlier. The positions have shifted, by close to Einstein's figure. The Times announces a revolution in science, and an unknown German physicist becomes the most famous scientist in the world in a week, four years after his country and Britain had been at war.

This is not remote. Satellite navigation depends on it. The satellites' clocks run slower because of their orbital speed and faster because they sit higher in Earth's gravitational well, and the two effects do not cancel — the net drift is about 38 microseconds a day. Uncorrected, positions would be wrong by roughly ten kilometres within twenty-four hours. Your phone applies Einstein's corrections continuously.

The theory also predicted objects so dense that nothing escapes them, and ripples in spacetime itself from violent events. Einstein doubted both were physically real. Black holes have now been imaged, and in 2015 detectors measured a gravitational wave from two black holes colliding over a billion light years away, stretching a four-kilometre instrument by a fraction of the width of a proton. He was right and his doubts were wrong, which is roughly the best outcome a physicist can hope for.

What just happened

• The equivalence principle makes gravity and acceleration locally indistinguishable
• General relativity describes gravity as curved spacetime rather than a force
• The 1919 eclipse confirmed light-bending; satellite navigation corrects for both effects daily

Newton described what gravity does; Einstein explained what it is. It remains the deepest description of gravity we have, and it has passed every test devised for it.

Now you know the story

Every wireless signal you have ever used is a prediction of Maxwell's equations. Every satellite navigation fix you have ever taken depends on correcting for relativistic time dilation. Two men who never met, working on problems that looked purely theoretical, built the physics your daily life runs on.

• Explain what a field is, and why Faraday's idea was as radical as any equation
• Say what Maxwell's unification achieved and how it revealed what light is
• State what special relativity actually claims — and what it does not
• Explain why gravity, in Einstein's account, is not a force at all

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Beyond the specification. Special relativity is not on Pearson Edexcel International GCSE Physics. This course is for learners who want to see where the International GCSE material leads.