Illustrated Physics
physics, drawn
Concept

Clocks — where it appears

Devices that count a periodic process, from a pendulum to an atomic transition, and so define time locally. Comparing two clocks, rather than reading one, is what exposes gravitational redshift, time dilation, and any failure of every clock to slow by the same amount.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The figure a static field is not allowed to close. A spacetime diagram of two clocks held at fixed heights 22.5 metres apart, drawn as though spacetime were flat: time upward, height to the right, light at forty-five degrees. The lower clock sends two pulses; the upper clock receives them. Because the field does not change with time, nothing about the second pulse's journey differs from the first's, so the two null lines are congruent and the four worldlines bound a parallelogram. Opposite sides of a parallelogram in flat spacetime have equal length, so the proper time between emissions must equal the proper time between receptions, and the two clocks must agree. They do not: the measured fractional difference across a tower this tall is 2.455e-15, which Pound and Rebka established in 1960 and Pound and Snider confirmed to one per cent in 1964. Every step above is either a definition, an assumption of staticity, or a theorem of flat geometry — so the measurement refutes the flatness. No field equation has been written down, and none is needed: a laboratory result twenty-two metres tall is already incompatible with a flat spacetime.

The parallelogram that will not close

Two clocks twenty-two metres apart in a lift shaft run at different rates, by two parts in a thousand million million. That measurement, on its own, is enough to prove that spacetime cannot be flat — and the proof needs no field equation, no curvature tensor and no astronomy. It needs one drawing and the fact that opposite sides of a parallelogram are the same length.

astrophysics · Gravitational redshift Both clocks move, and their ratio does not. Two years of a clock's fractional frequency against a distant clock (upper panel), and of the ratio of two unlike clocks kept side by side (lower panel). Above, both clocks slow as the Earth nears the Sun, with an amplitude of 1.65·10⁻¹⁰, and if the redshift is universal the two curves are one curve. Below, the ratio: the flat line is what universality predicts, and the sinusoid is what a clock responding to the potential 10⁻⁶ more strongly than the other would produce — an annual term of 1.65·10⁻¹⁶, a million times smaller than the shift both clocks share and within reach of clocks that compare to parts in 10¹⁷.

The clocks that must all slow together

Every clock on the Earth runs slower in January than in July, by three parts in ten thousand million, because the orbit carries the planet deeper into the Sun's potential at perihelion. No clock on the Earth can see this, and that invisibility is the claim worth testing. If the redshift is a property of time rather than of clocks, two clocks built on different physics must slow by exactly the same fraction, and their ratio must not move with the seasons. A ratio that did move would mean the constants of nature depend on where they are measured.

astrophysics · Gravitational redshift

Named alongside it

The objects these essays reach for when they reach for this one.

Equivalence principleGeneral relativityGravitational redshiftEccentricityFine structure constantGeodesicLight coneLocal position invarianceMetricNull testPotentialPrecision

All concepts