Spacetime: Einstein's idea
Gravity is not a pull but a shape. See how mass curves spacetime, why clocks run slower where gravity is stronger, and why your phone would be kilometres wrong without the correction.
THE MOVE
Gravity is geometry
Newton said masses pull on each other across empty space. Einstein said something stranger and more useful: mass and energy bend spacetime, and everything moving through that bent region follows the straightest available path. Nothing is pulling. The floor you are standing on is the only thing pushing, and it is stopping you from following your natural path.
In lesson 03 you saw an astronaut float while falling. Now you can say why it feels like nothing: falling is the natural state. What you feel as weight is the ground interrupting it. The whole of gravity becomes the shape of the map rather than a force on the traveller.
The stretched sheet, and why it cheats
Put a heavy ball on a stretched sheet and roll a marble past it. The marble curves around the dip. That is the picture everyone is shown, and it does get one thing right: the path bends because the surface is shaped, not because the ball reached out. Where it cheats: it uses real gravity to make the dip, so it explains gravity with gravity. It shows only two dimensions of space. And worst of all, it leaves out time, which is the part that matters most. For anything moving slowly, it is the bending of time, not of space, that produces almost all of what you call falling.
Check yourself
Sina says: 'If gravity is not a force, why do I feel heavy standing on the floor?' What is the best answer in Einstein's terms?
- You feel the floor pushing you off your natural falling path
- You feel the Earth's mass tugging on every cell of your body
- You feel the air pressing down on you
- You feel spacetime pulling downward on you
Show the answer
You feel the floor pushing you off your natural falling path
Right. Your natural path is to fall freely, and free fall feels like nothing at all. The sensation of weight is the floor refusing to let you take that path, which is why astronauts in orbit feel nothing: no floor is interrupting them.
THE STRANGE PART
Deeper in gravity, time runs slower
This is not an illusion and not a problem with the clocks. Time itself passes more slowly where gravity is stronger. A clock on the ground floor of a tall building runs slower than one on the top floor. The difference is tiny on Earth, but it is real and it has been measured directly.
Today's best laboratory clocks can detect the difference over a height change of a few tens of centimetres. Lift one off the table and it ticks measurably faster. Near a neutron star or a black hole the effect stops being tiny: close to a black hole's horizon, a clock would appear to an outside observer to almost stop.
a GPS satellite clock, compared with one on the ground:
higher up, weaker gravity -> runs FASTER by 45 microseconds a day
moving at about 14,000 km/h -> runs SLOWER by 7 microseconds a day
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net faster by 38 microseconds a day
how far does light travel in 38 microseconds?
300,000 km/s x 0.000038 sabout 11 km, which is how wrong your position would be after one uncorrected dayPositioning works by timing radio signals, so a clock error is a distance error. Two separate effects are at work here: gravity speeds the satellite clocks up, and their speed slows them down. The correction is built into the system.
Check yourself
Two identical clocks in perfect working order, one flown up on a satellite and one left on the ground, really do end the day showing different times.
Show the answer
True
True, and nothing is wrong with either clock. They are among the most accurate ever made, which is exactly why the effect shows up. Time itself passes at a slightly different rate up there, because of both the height and the speed. Positioning systems correct for the difference; without that correction their fixes would drift by kilometres within a day.
Four things the theory predicted before anyone saw them
- Mercury's drifting orbit
Mercury's closest point to the Sun creeps around by a small amount each century that Newton's law could not account for. Einstein's equations produced exactly the missing amount, with nothing adjusted to fit.
- Light bent by mass
Predicted, then measured at the 1919 eclipse, and now used every day as gravitational lensing to map mass we cannot see.
- Clocks slowed by gravity
Confirmed in a laboratory in 1959 using a tower a few tens of metres high, and relied on ever since by satellite positioning.
- Ripples in spacetime
Predicted in 1916. Inferred from a shrinking pulsar orbit in the 1970s, as you saw in lesson 07, and caught directly by detectors in 2015.
Check yourself
Where does time run faster, and where slower?
- Top floor of a tower
- Ground floor of the same tower
- A satellite 20,000 km up
- Just outside a black hole's horizon
- The surface of a neutron star
- Deep space, far from any mass
Show the answer
Time runs faster here: Top floor of a tower, A satellite 20,000 km up, Deep space, far from any mass
Time runs slower here: Ground floor of the same tower, Just outside a black hole's horizon, The surface of a neutron star
Is Newton wrong?
Newton's gravity
A force between masses. Simple arithmetic, and accurate enough to land probes on other planets. It is what engineers use for almost everything, and what you used in lesson 03. It is not wrong so much as incomplete: an excellent approximation when gravity is weak and speeds are far below light.
Einstein's gravity
Curved spacetime. Harder mathematics, and it only differs measurably where gravity is strong, speeds are high, or precision is extreme. It is needed for Mercury's orbit, satellite clocks, neutron stars, black holes and the universe as a whole. Where they overlap, it reproduces Newton exactly.
Check yourself
- A team sends one atomic clock up in an aircraft for a day and leaves an identical one at the airport. On landing, the two disagree by a few hundred billionths of a second.
- The same team repeats it with the aircraft parked on the runway, engines running, for the same day. The two clocks agree.
What does the comparison show?
- The disagreement comes from vibration in the aircraft
- The disagreement comes from height and motion, not from the clocks or the journey itself
- Atomic clocks drift randomly over a day
- Air pressure changes how fast a clock ticks
Show the answer
The disagreement comes from height and motion, not from the clocks or the journey itself
Right. The second run keeps everything about the aircraft the same and removes only the altitude and the speed. The difference vanishes with them, which points straight at gravity and motion as the cause. Experiments of this kind were done in 1971 and have been repeated since.
What this buys you for the rest of the course
- Gravity as curvature is why light can be bent by mass, which is how we weigh galaxy clusters and find dark matter in lesson 11.
- Curved spacetime is what a black hole is made of, and it explains the shadow in that famous image.
- The same equations, applied to the whole universe, say it cannot sit still: it must expand or contract. That is where lesson 10 starts.
- Still unfinished: general relativity and quantum physics do not fit together. Both work superbly in their own domains, and nobody has a tested theory that covers the places where both matter, such as the centre of a black hole.
Check yourself
Yasaman asks whether relativity is 'just a theory that might be overturned tomorrow'. Which reply is the most accurate?
- It is proven beyond any possibility of revision
- It is untested speculation, since nobody can visit a black hole to check whether any of it is real
- It only applies to black holes and has no effect on daily life
- It passes every test so far, including ones your phone depends on
Show the answer
It passes every test so far, including ones your phone depends on
Right, and that is how physics works. A better theory may come, most likely where relativity meets quantum physics, but it will have to give the same answers everywhere relativity has already been checked, from Mercury's orbit to satellite clocks.
Lesson recap
- Einstein replaced gravity as a force with gravity as the shape of spacetime: mass curves it, and things follow the straightest path through the curve.
- Free fall is the natural path and feels like nothing. The weight you feel is the floor pushing you off it.
- Time runs slower where gravity is stronger. Satellite clocks gain about 38 microseconds a day, and positioning would drift by 10 km a day without the correction.
- The theory predicted Mercury's orbit, light bending, slowed clocks and gravitational waves, and all four were later measured.
- Newton is not wrong, just incomplete: an excellent approximation for weak gravity and slow speeds.