Unit 12, lesson 59. About 20 minutes.

Einstein's big ideas

Could time really run slower for a fast traveller?

Play

Getting the experiment ready…

Explain

Albert Einstein found something surprising. The speed of light is always the same, however fast you are moving.

That means that time runs more slowly for very fast things. It is a tiny effect in everyday life, but scientists have measured it.

He also showed that mass is a kind of stored energy, and wrote it as E = mc².

Special relativity: the laws of physics and the speed of light are the same for all observers moving steadily.

Time dilation: a moving clock runs slow by a factor of 1 / √(1 − v²/c²). At 0.8c, it is 1.67 times slower.

Worked example: 1 gram of mass has E = 0.001 × (3 × 10⁸)² = 9 × 10¹³ J.

Light speed is fixed
Moving clocks tick slowly
Mass is energy

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At normal speeds the effect is tiny, so Newton's laws work well. General relativity adds gravity: clocks run slower near a large mass. GPS satellites must correct for both effects, or sat navs would soon be wrong by kilometres.

The Formula

energy = mass × the speed of light squared

E = m c^2

$E$: the energy, measured in joules (J)
$m$: the mass, measured in kilograms (kg)
$c$: the speed of light, 3 × 10⁸, measured in metres per second (m/s)

Try the numbers

Mass: 0 kg

Energy: 8.99 × 10¹³ J

The Formula

moving clocks tick more slowly as speed gets close to light

t' = \frac{t}{\sqrt{1 - v^2/c^2}}

$t'$: the time for someone watching, measured in seconds (s)
$t$: the time on the moving clock, measured in seconds (s)
$v$: the speed, measured in metres per second (m/s)
$c$: the speed of light, measured in metres per second (m/s)

Try the numbers

Speed, as a fraction of light: 0.8 c

One second on the ship takes: 1.67 s for us

Try it at home

You need a calculator.

You need: a calculator.

Pick a speed, as a fraction of light, such as 0.6.
Square it, take it from 1, and find the square root.
Divide 1 by your answer.

What's happening: this is how much a moving clock slows down. For 0.6, the answer is 1.25.

Physics is life

Your body

Your body has huge energy in its mass.

The mass of your body stores an enormous energy, according to E = mc².

Daily life

Sat navs use relativity.

Sat navs must correct for relativity to work properly.

Nature

Fast particles from space live longer.

Fast muons from space reach the ground because time runs slow for them.

Space

Black holes bend time.

Close to a black hole, a clock seems to run very slowly to a distant watcher.

Quick check

Question 1 of 3

What did Einstein find about light?

Words to know

Relativity: Einstein's ideas about space, time, mass and energy.

Relativity: Einstein's ideas about space, time, mass and energy.
Energy: What makes things able to happen. It is measured in joules.
Speed: How far something goes in each second.

Meet the scientist

Next up

The tiny world: quantum physics