Space and time as one, in 3D
Spacetime
Space and time are one thing, and mass bends it. Here it is in live 3D: light cones, the twin paradox, the true shape of curved space, the inside of a black hole and the ripples LIGO caught.
Above is a slice of space round a dense star, curved the way general relativity says it is. Each section below takes one idea about spacetime and makes it something you can turn and slide. In the diagrams light always moves at 45°, which puts time and space in matching units: a year of time and a light-year of distance.
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Your light cone divides the Universe
The idea
Space and time together make spacetime, a four-dimensional map in which every event has a place and a moment. From any event, light spreads out as a cone. Everything you can ever affect lies inside your future cone, and everything that could have affected you lies inside your past cone1.
Reading the cones
Drawn here with two directions of space across and time going up, so light travels at 45°. Events inside your cones can be linked to you by something slower than light, and everyone agrees on their order. Events outside are "elsewhere": light cannot connect them to you, and observers moving differently disagree about whether they come before or after your now.
The numbers
The Sun is 8.3 light-minutes away2, so the Sun you see is on your past light cone, as it was 8 minutes ago, and whatever it does in the next 8 minutes is elsewhere for you. Proxima Centauri is 4.25 light-years away3: a question sent there today cannot be answered in less than 8.5 years.
Where the idea came from
Hermann Minkowski joined space and time into one geometry in 1908: "Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."1
Try it
Drag the event outside the cone and the readout turns red: nothing, light included, can link you to it.
02 / 5
The twin who travels comes home younger
The idea
In spacetime the time a clock measures is the length of its path, measured with spacetime's own rule, in which the straight path between two events is the longest. The twin who stays home follows the straight path and ages most. The traveller's bent path is shorter.
The numbers
To a star 4.2 light-years away and back at 80% of light speed: 10.5 years pass at home and 6.3 for the traveller. At 99% the trip takes 8.5 years at home and only 1.2 for the traveller.
Why it is not symmetric
Only the traveller turns round, swapping from one frame to another. At the turn the traveller's "now at home" (the dashed lines) jumps forward by years, and that jump is where the home twin's extra ageing comes from.
Try it
Push the speed to 0.99 c and watch the traveller's dots spread apart: each is one year of their life.
03 / 5
What curved space really looks like
The idea
Mass curves spacetime. The usual picture is a heavy ball on a rubber sheet. The embedding diagram on the right is the faithful version for space: the true shape of a slice of space round a ball of mass, worked out by Ludwig Flamm in 19166.
What the sheet gets right
Mass changes the shape of what is round it, more mass makes a bigger change, and moving things follow curved paths near it.
What the sheet gets wrong
The ball sinks because the Earth's gravity pulls it down, so the picture uses gravity to explain gravity. It also shows only space. Near the Earth almost all of gravity is the curving of time: clocks lower down run slower, and falling things head toward slower time7.
What the embedding shows
The circles are spaced by their circumference. Near the mass there is more distance between neighbouring circles than flat space allows, and that extra distance is the curvature. For the Sun it is tiny, about 4 millionths of a black hole's8; a white dwarf like Sirius B reaches about 0.05%9, and a neutron star nearly a third10.
See it in 3D
Slide all the way to a black hole and the surface turns into a throat. Our viewer's black hole bends the real sky round itself.
04 / 5
At a black hole, the future points inward
The idea
Near a black hole, light cones tip toward the centre. At the event horizon the outward edge of the cone stands still, and inside it every possible future, light's included, leads to the centre. In there, the centre lies in your future.
Reading the diagram
Across is the distance from the centre in Schwarzschild radii (rs), up is time, in coordinates that stay smooth through the horizon. The cones tip further the closer they are. A falling astronaut feels nothing special at the horizon: they cross it without noticing, and only then is the way out gone11.
The numbers
The horizon's radius is 2GM/c²: 2.95 km for the Sun's mass, if it were squeezed that small8, and 8.9 mm for the Earth's. The black hole in the galaxy M87 has 6.5 billion times the Sun's mass and a horizon about four times as wide as Neptune's orbit12.
How we know
In 2019 the Event Horizon Telescope imaged the shadow of M87's black hole: a dark centre ringed by light bent round it, the size general relativity predicts for its mass12.
See it in 3D
Light near our black hole is traced step by step through the curved space round it.
05 / 5
Spacetime ripples
The idea
When heavy objects swing round each other they shake spacetime, and the ripples spread out at the speed of light. A passing wave stretches space one way and squeezes it the other, then the reverse.
How we know
On 14 September 2015 both LIGO detectors in the United States caught waves from two black holes, of 36 and 29 times the Sun's mass, merging 1.3 billion light-years away. The signal swept from 35 to 250 hertz in a fifth of a second13.
The numbers
The waves stretched space by 1 part in 10²¹, so LIGO's 4 km arms changed length by about 4 × 10⁻¹⁸ m, a few hundred times smaller than a proton. In the merger, about three Suns' worth of mass turned into gravitational waves13.
The ring of masses
The ring on the right is what a detector feels. LIGO uses laser light to compare two arms at right angles, and a passing wave lengthens one while it shortens the other.
Spacetime is measured
Spacetime began as a way of drawing special relativity and became the stage general relativity is built on. Its predictions, from clocks running slower in gravity to black hole shadows and gravitational waves, have all been measured15.
Questions
What is spacetime?
Space and time combined into one four-dimensional geometry, in which every event, a place at a moment, is a point. Observers moving differently split spacetime into space and time differently, so neither one on its own is the same for everyone1.
Is spacetime really curved?
General relativity describes gravity as the curvature of spacetime, and its predictions match every measurement so far: starlight bent by the Sun14, Mercury's turning orbit15, clocks running slower lower down16 and gravitational waves13.
What is wrong with the rubber sheet picture?
It needs gravity underneath to make the ball sink, and it shows only space. Most of what makes things fall near the Earth is the curvature of time: clocks run slower closer to the ground, and free objects move toward slower time7.
What is a light cone?
All the paths light can take from one event, spreading out in every direction. Inside the future cone is everything that event can affect; outside lies everything it can never reach.
What happens at the event horizon?
For someone falling in, nothing they could feel there: the horizon is where the way out closes. Inside it, every direction into the future leads to the centre11.
How fast do gravitational waves travel?
At the speed of light. In 2017 gravitational waves and gamma rays from one neutron star merger arrived 1.7 seconds apart after 130 million years on the way, which shows the two speeds are equal to about one part in 10¹⁵17.
Sources
- Minkowski, H. (1908), Space and Time (English translation)
- IAU 2012 Resolution B2: the astronomical unit is 149,597,870,700 m
- Proxima Centauri, 4.2465 light-years away
- Hafele, J. C. and Keating, R. E. (1972), Around-the-World Atomic Clocks: Observed Relativistic Time Gains, Science 177, 168
- Bailey, J. et al. (1977), Measurements of relativistic time dilatation for positive and negative muons in a circular orbit, Nature 268, 301
- Flamm's paraboloid: the shape of space round a mass (Flamm, 1916)
- Pound, R. V. and Rebka, G. A. (1960), Apparent Weight of Photons, Physical Review Letters 4, 337
- NASA Sun fact sheet (mass, radius, luminosity, apparent size)
- Bond, H. E. et al. (2017), The Sirius System and Its Astrophysical Puzzles, ApJ 840, 70 (Sirius B: 1.02 Suns, 0.0081 solar radii)
- Riley, T. E. et al. (2019), A NICER View of PSR J0030+0451, ApJ Letters 887, L21 (1.34 Suns, radius 12.7 km)
- Eddington-Finkelstein coordinates: light cones through the event horizon
- Event Horizon Telescope Collaboration (2019), First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole, ApJ Letters 875, L1
- Abbott, B. P. et al. (2016), Observation of Gravitational Waves from a Binary Black Hole Merger, Physical Review Letters 116, 061102
- Dyson, F. W., Eddington, A. S. and Davidson, C. (1920), A Determination of the Deflection of Light by the Sun's Gravitational Field, Philosophical Transactions of the Royal Society A 220, 291
- Will, C. M. (2014), The Confrontation between General Relativity and Experiment, Living Reviews in Relativity 17, 4
- Chou, C. W., Hume, D. B., Rosenband, T. and Wineland, D. J. (2010), Optical Clocks and Relativity, Science 329, 1630
- Abbott, B. P. et al. (2017), Gravitational Waves and Gamma-Rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A, ApJ Letters 848, L13
The scenes run on the formulas in their readouts. The embedding diagram is drawn deeper than life whenever its readout says so, and the gravitational waves are drawn about 10²⁰ times stronger than the ones that reached the Earth.