The More Precisely We Measure Gravity, The Less We Understand It

At a glance

Isaac Newton wrote the law of gravity without the number in it. The first person to measure that number worked alone in a garden shed in 1798, and in the 228 years since, as the instruments improved beyond anything he could have pictured, the answers did not converge. They spread apart, until in 1998 the international body responsible for the constants of physics had to widen its own uncertainty by a factor of roughly twelve and state plainly that nobody could say why. This two hour film from Sundown Science walks the whole record: Henry Cavendish reading a rod through a hole in a wall, Charles Vernon Boys drawing quartz fibres by firing an arrow across a room, a team inside a hill in Wuhan spending thirty years to produce two answers that formally exclude one another, and the consequence nobody mentions in school, which is that no one on this planet can tell you what the Sun weighs to better than about four digits.

From there it follows the failure outward rather than letting it sit in the laboratory. The inverse square law has only been checked across a narrow band of distances with darkness at both ends: below about 52 micrometres nobody has looked, and out at the scale of a galaxy the law gives the wrong answer unless you add five times more matter than you can see or change the rule. At the scale of the universe the sign flips entirely and gravity pushes, and our best theoretical account of the thing doing the pushing is wrong by something like 120 orders of magnitude. Underneath all of it, general relativity, the most accurately confirmed theory in the history of physics, does not say what gravity is, cannot be quantized, and points at a carrier particle that serious people argue is undetectable in principle.

The closing argument is the part worth staying for, and it inverts the usual reading. We did not fail to converge because our instruments are not good enough yet. The disagreement grew because the instruments got better. Blurry results agree; it takes precision to disagree properly. Precision is not a way of getting closer to an answer, it is a way of finding out whether you understand something, and what 228 years of sharpening has been measuring is the size of the gap between what we can describe and what we can explain.

The cold open: two bags of sugar and a few dozen blood cells (0:00)

The film opens with an instruction rather than a claim. Hold two bags of sugar, one in each hand, a metre apart.

There is a force between them. It is real. It has never once switched off, and it is pulling those two objects toward each other right now. Its strength is roughly the weight of a few dozen blood cells.

That force is gravity, which is the first thing you ever learned about physics and the one you are most certain is finished. And then the four sentences that set up the entire two hours. Nobody knows how strong it is. Newton wrote his law without the number in it. The first person to measure that number worked alone in a garden shed in 1798. And in the two centuries since, as the instruments improved beyond anything he could have pictured, the answers did not converge; they spread apart until the body responsible for the constants of physics had to widen its own uncertainty by a factor of twelve and admit that nobody could say why.

So the question, stated in the narrator's own framing: how does the most measured force in the universe end up with the worst known number in science? Settle in. And the promise attached, which the film delivers on literally: by the end of this you will not be able to say what the Sun weighs, and neither will anyone else.

Part one: the force you think is finished (1:26)

Gravity is the one you were never asked to wonder about, and the film's first move is to explain why by contrast.

Everything else in physics arrives with a warning attached. Quantum mechanics comes wrapped in paradox. Relativity comes with the caution that your intuition will not survive it. The interior of a star, the behaviour of light, the structure of an atom, the beginning of the universe: all of these are introduced to you as things that will be difficult, things that will require you to set down what you thought you knew.

Gravity is introduced differently. Gravity is introduced as furniture. It was here before the lesson started and it will be here after things fall. You have known this since before you had language for it, and every experience you have had since has confirmed it without a single exception.

And there is a story attached which makes it feel even more finished. A man sits under a tree in the English countryside. An apple comes loose. He looks up and then out, and understands in one motion that the thing pulling the apple down is the same thing holding the Moon in place.

The film is careful with this. It is a good story, and parts of it are even true. Newton did discuss an apple late in his life as a way of describing how the idea first came to him, and the insight underneath it was genuinely one of the most consequential any human being has ever had. The force that makes an object fall off a table and the force that keeps a moon in orbit are not two different forces. They are one force operating on two scales. And the difference between a falling apple and an orbiting moon is nothing more than how fast you were going sideways when you started.

In 1687 Newton published that idea in the book we now call the Principia, and in doing so he did something no one had managed before. He wrote down a rule that applied to the entire universe at once. Two objects attract one another. The attraction grows with the product of their masses. It weakens with the square of the distance between them. Double the distance and the pull drops to a quarter; triple it and the pull drops to a ninth.

That relationship, once you have it, lets you calculate the orbit of a planet, the arc of a cannonball, the shape of the tides, and the return of a comet, all with the same handful of symbols. It was the first time anyone had shown that the sky and the ground obey the same law.

So the file gets closed. Newton solved gravity in the 1680s. Albert Einstein came along a little over two centuries later and refined it, replacing the idea of a force reaching across empty space with the idea of curved spacetime. That refinement was profound, but from the outside it looks like a finishing touch on something already essentially complete. Gravity gets shelved. It becomes the settled one, the one that does not need you, and every other strange thing in physics gets to have the attention.

What the story leaves out (4:50)

Here is what that story leaves out. Newton never knew how strong gravity is.

The film wants to be precise about that, because it sounds like a trick and it is not. Newton's law is a statement of proportionality. It tells you exactly how the force changes when you change the masses and the distance. It does not tell you the size of the force. Written in the form you may have seen, there is a term sitting at the front of the equation, a constant of proportionality, and its entire job is to convert the proportionality into an actual number of actual newtons of actual pull.

That term is not in Newton's work. He did not have a value for it. He could not have had one, because measuring it requires detecting the gravitational attraction between two ordinary objects in a room, and nothing in the 1680s was capable of doing that.

What Newton had was a shape. He knew how gravity behaves. He did not know how much of it there is.

Why the absence went unremarked for a century (5:58)

You can go remarkably far without that number, which is part of why its absence went unnoticed for so long. Astronomy in particular gets along beautifully without it.

If you are tracking a planet around the Sun, the missing constant and the mass of the Sun always appear multiplied together as a single package, and that package is what orbital motion actually responds to. So you can predict eclipses to the second, navigate a spacecraft across the solar system, and calculate the return of a comet a century in advance, and at no point will anyone hand you the strength of gravity, because at no point do you need it. The number hides inside another number and does its work invisibly.

This becomes the hinge of Part nine, so hold on to it. For now the film notes only the exception. The moment you want to step outside that arrangement, the moment you want to know what the Earth actually weighs, or what the Sun actually weighs, or how hard two objects on a table are pulling on one another, you need the constant on its own. And to get it on its own, someone has to go into a room with two lumps of metal and measure a force so faint that nothing in ordinary human experience prepares you for it.

1798, and the thing nobody expected (7:06)

That measurement was first attempted successfully in 1798, roughly 111 years after the Principia. It was carried out by a man working alone in a shed using an instrument built by somebody who had already died. It was, by the standards of its era, one of the most careful pieces of experimental work anyone had ever performed, and it got within about one percent of the modern answer.

And then something happened that nobody expected and that nobody has been able to explain since.

Over the following two centuries, as instruments improved beyond anything that eighteenth century experimenter could have imagined, as laboratories were built underground to escape vibration, as lasers replaced telescopes and computers replaced eyes, the measurement of gravity's strength did not converge. It did the opposite. The individual answers got sharper and sharper, each one claiming greater precision than the last, and as they sharpened they spread apart. They began to contradict one another by amounts far larger than any of them admitted was possible.

The strength of gravity is today the worst known number in fundamental physics. Not one of the worst. The worst, by a margin so wide the film says it is difficult to convey. And the reason is not that nobody has tried. The reason is that a great many extremely capable people have tried for 228 years with progressively better equipment, and the harder they have looked, the less they have agreed.

That is the thing the film sets out to walk through. Not the story of how we solved gravity, because we did not. The story of how we measured it more and more precisely and understood it less and less as we went. And it starts in a garden shed in South London with a man so shy he communicated with his own household in writing.

Part two: the man who weighed the world (9:11)

Henry Cavendish was one of the richest men in Britain and one of the least visible.

He was born in 1731 into an aristocratic family, inherited an enormous fortune, and spent almost none of it. He wore the same style of faded violet coat for decades. He had a staircase built at the back of his house so that he could come and go without encountering anyone. He communicated with his female household staff by leaving written notes on a hall table, because speaking to them directly was more than he could manage. At meetings of the Royal Society, colleagues learned that the way to get an answer out of him was to stand near him and address the general air, never his face, and wait. If you looked directly at him, he would leave.

He was also, by a considerable distance, one of the finest experimental scientists who has ever lived. He worked out the composition of water. He isolated hydrogen. He measured the electrical properties of materials with an accuracy that would not be matched for another century, and then, characteristically, did not publish most of it. James Clerk Maxwell went through Cavendish's unpublished notebooks in the 1870s and found result after result that had been independently discovered by other people decades after Cavendish had quietly written them down and put them in a drawer.

In 1797, at the age of 66, Cavendish took on the problem that would carry his name.

The instrument belonged to a dead clergyman (10:20)

The instrument was not his. It had been designed and built by John Michell, a clergyman and geologist in Yorkshire, who was one of the most quietly original thinkers of the eighteenth century.

Michell had, among other things, worked out that if a star were massive enough its escape velocity would exceed the speed of light and nothing it emitted could ever leave it, which is a description of a black hole written in 1783. He built an apparatus to weigh the Earth and then died in 1793 without ever using it. The instrument passed to another man and then to Cavendish, who took it apart and rebuilt most of it.

The torsion balance, and why it works (11:29)

The design is called a torsion balance, and the film calls the idea behind it beautiful in its economy.

You take a thin wire and hang a light horizontal rod from its centre, so the rod dangles like the beam of a scale that has been turned on its side. At each end of the rod you fix a small lead ball. The whole assembly can now rotate freely, twisting the wire, and a wire resists twisting only very slightly.

That slightness is the point. A wire that barely resists will respond to a force that barely exists.

Then you bring two much larger lead spheres close to the small ones, positioned so their gravitational pull acts to rotate the rod. The rod turns, the wire twists, and it twists until the wire's resistance exactly balances the gravitational attraction, and then it stops. If you know how stiff the wire is and you can measure how far the rod turned, you can work backwards to the force. From the force you can get the strength of gravity.

The numbers, because the numbers are the point. The small spheres weighed about 1.6 pounds each. The large ones weighed roughly 350 pounds each. The rod was about six feet long. And the force being measured, the actual physical quantity that had to move that rod, was smaller than the weight of a grain of sand.

Which is why the entire experiment is really an exercise in getting everything else out of the way.

Picture the shed (12:58)

It is on Cavendish's property at Clapham, on the southern edge of London, and it is winter. Inside the shed is a wooden case, sealed, and inside the case is the balance. The large spheres hang from a pulley system whose ropes run out through the wall of the building, because Cavendish has understood something that took other experimenters years to learn the hard way.

He cannot be in the room.

His body is warm. A warm body on one side of a sealed case sets up a slow convection current inside it, and that current pushes on the rod with a force many times larger than the gravity he is trying to detect. So he stays outside. He turns the pulley from outside, and he reads the deflection through a telescope aimed through a small hole drilled in the shed wall, with a lamp arranged so that he can see the scale without opening anything.

He turns the spheres. Nothing appears to happen. The balance has a natural swing period of about fifteen minutes, so the rod does not simply move to a new position. It begins a slow oscillation that takes hours to settle. And Cavendish's job is to sit outside in the cold with his eye at a hole in a wall and record where the rod is, again and again, while it drifts through an arc smaller than the width of the pencil he is writing with.

He runs the experiment seventeen times. He accounts for the gravitational pull of the case itself. He accounts for the magnetism of the iron in the apparatus by swapping in different materials to check. He accounts for the temperature.

And then he does not calculate the gravitational constant (14:24)

This is the part the film says always surprises people. When it is finished, Cavendish does not calculate the strength of gravity. He never computed the number we now call the gravitational constant. It did not exist as a concept he was pursuing and he showed no interest in inventing it.

His paper is titled, in essence, an account of experiments to determine the density of the Earth, and that is exactly what he wanted. He wanted to know what the planet is made of. Because if you can measure the gravitational pull of a lead sphere of known size, and you already know the gravitational pull of the Earth, you can compare them, and the comparison tells you how dense the Earth must be relative to the lead.

His answer was that the Earth is 5.48 times as dense as water. The modern value is 5.514.

He was off by about one percent, in 1798, in a shed, using an instrument built by a dead clergyman, operated through a hole in a wall, by a man who could not bring himself to speak to his own cook.

Newton's guess (15:51)

There is a small grace note attached, and the film gives it its moment. Newton himself, in the Principia, had guessed at the answer. He reasoned about the density of ordinary surface rock, thought about how much heavier the interior of a planet ought to be under all that pressure, and put the Earth at somewhere between five and six times the density of water.

He offered it almost in passing, as the kind of thing a careful person might estimate on the back of an argument. He was right. He had no instrument capable of testing it, no way of checking, and no expectation that anyone would check within a century of his death. And he landed inside the correct range.

Cavendish's contemporaries understood what had happened. Somebody had weighed the world. Not a mountain, not a region, not an estimate from surface rock. The entire planet put on a scale by measuring how hard a lump of lead pulls on another lump of lead in a garden building. And the number that came out was good enough that it stood essentially unimproved for close to a hundred years.

Then the film plants its first flag. Hold on to the phrase weighing the world, because we are going to come back to it, and by the time we do it will not mean what it means right now. There is a detail hiding inside Cavendish's triumph that nobody in 1798 had any reason to notice, and it is the detail that everything else in this story grows out of.

He had measured a density. He had compared one gravitational pull to another gravitational pull, which is a ratio, and ratios are forgiving. Sometime later, other people would want the raw quantity itself, stripped out and standing alone in units, as a number. And that turns out to be a very different kind of problem.

Part three: the number nobody named (17:48)

For most of the nineteenth century, the strength of gravity did not have a name. The film insists this sounds like a technicality and is not. It is a clue about how physics actually developed and about why this particular quantity ended up so badly served.

Nobody set out to measure the gravitational constant, because for a very long time nobody was thinking in those terms at all. The question people asked was how heavy the Earth is, or how dense it is. Those are questions about a specific object. They are answerable with ratios and comparisons, and ratios are comfortable. You do not need to commit to a universal quantity to say that the Earth is about five and a half times as dense as water.

The shift happened gradually, over roughly the middle decades of the 1800s, as physics acquired a taste for universal constants. The speed of light became a thing people measured for its own sake. So did the mechanical equivalent of heat. There was a growing sense that the universe had a small number of fixed quantities written into it, and that finding them and pinning them down was the central work of the discipline. Under that view, Newton's law contains one, and it had been sitting there unexamined for nearly two hundred years.

The first serious attempts to pull it out and state it as a number in its own right came in the 1870s, with Cornu and Baille in France, among the earliest to compute something recognizably like the modern quantity from a Cavendish style experiment. The symbol itself, the capital G we now use without thinking, settled into place through the following decades and was firmly established by the 1890s.

Boys, quartz, and the arrow (19:43)

That decade also produced the first genuine improvement on Cavendish in nearly a hundred years, and it came from a man named Charles Vernon Boys.

Boys understood something that turns out to matter enormously. Cavendish had hung his apparatus from a wire, and a wire is not a perfect spring. Metal has a memory. When you twist it and hold it and let it go, it does not return exactly to where it started, and it does not resist twisting by exactly the same amount every time. Those imperfections are tiny, and in almost any other application they would be invisible. In this experiment they are the enemy, because the force you are measuring is also tiny, and the two are comparable in size.

So Boys replaced the wire with fused quartz. He learned to draw quartz fibres so fine they were nearly invisible by attaching molten quartz to an arrow and firing the arrow across a room. Quartz behaves far better than metal under torsion. It is closer to a perfect spring.

And having a better fibre let him do something counterintuitive: he made the whole apparatus much smaller.

That seems backwards. A bigger apparatus with bigger masses generates a bigger force, and bigger forces are easier to measure. But a bigger apparatus also means the masses are spread over more space, and every other object in the room, the walls, the floor, the experimenter, pulls on the different parts of a large instrument by different amounts, and those differences do not cancel. Shrink the instrument and the unwanted gradients shrink faster than the signal you want.

Boys built an instrument you could hold, and got a better answer than a man who had used 350 pound spheres.

What the number actually is (21:38)

Now, what actually is this number once you have it? The gravitational constant tells you how much gravity you get per unit of mass at a given distance. Written out, its value is

6.6743 × 10⁻¹¹ cubic metres per kilogram per second squared.

The units look strange because they are the units required to take two masses in kilograms and a distance in metres and hand you back a force in newtons. The part the film wants you to hold on to is that leading factor of 10⁻¹¹. That is a decimal point followed by ten zeros before you reach the first meaningful digit.

Every other headline constant in physics has a value that sits somewhere reasonable when you write it in the units human beings actually use, or has been redefined so that it does. This one is buried eleven decimal places down. That is not a formatting inconvenience. It is a direct statement about how faint the effect is, and therefore about how hard the measurement is going to be.

The structural problem baked into the units (22:51)

And there is a deeper problem sitting inside the units themselves, which the film pauses on because it explains most of what follows.

Look at what the constant is made of: length cubed, divided by mass, divided by time squared. There is a mass in there. Which means that to determine the constant you must independently know a mass precisely, in kilograms. You cannot escape it.

Any experiment that gives you the strength of gravity is also unavoidably an experiment in weighing things, and it inherits every difficulty that weighing things involves. How uniform is the density of your sphere? Is there a void inside it? Is the surface oxidized? What exactly is the distance between the centres of mass of two objects whose centres of mass you cannot see?

This is why gravity's constant is different in kind from the others, and the comparison the film draws is the sharpest line in Part three. When physicists measure the electron's magnetic moment, they are comparing one quantum property against another quantum property, and quantum properties are identical everywhere and forever. When physicists measure the strength of gravity, they are comparing a force to a specific lump of metal that a specific person machined on a specific afternoon.

And the lump of metal is the weak link.

By the end of the nineteenth century, then, physics had a name for the number, a symbol for it, a technique for measuring it, and a value accurate to a fraction of a percent. Everything was in place. The obvious expectation, the one that every other quantity in physics had already met, was that the twentieth century would take that fraction of a percent and grind it down, decade by decade, into ever finer agreement.

For about eighty years, that is roughly what appeared to be happening.

And then the good equipment arrived.

Part four: how weak is weak? (24:40)

Before going any further into the measurements, the film stops to sit with the size of the thing being measured, on the grounds that nothing else in the story makes sense until you have felt it.

Everyone knows gravity is weak. It is one of those facts that gets stated so often it stops landing. Gravity is the weakest of the four fundamental forces, people say, and you nod, and you file it next to the other things you have agreed to accept. But the word weak is doing an enormous amount of work in that sentence and it is not doing it honestly, because weak is a human word calibrated to human experience, and this is not a human scale weakness. This is a weakness of a kind that ordinary language was never built to carry.

Two bags of sugar, done properly (25:30)

So let us do it properly. Take two one kilogram weights. Hold one in each hand. A kilogram is a bag of sugar, a large bottle of water, something with real presence in your palm. Now hold them a metre apart, one hand out to each side, and stand still.

There is a force between them. It is real. It is happening right now, and it has never once switched off in the entire history of the universe. Every particle in the weight in your left hand is pulling on every particle in the weight in your right hand, continuously, and has been since those atoms formed inside a star.

That force is about 6.67 × 10⁻¹¹ newtons, which means nothing to you. So the film converts it, in stages, and the stages are worth keeping in full:

• A newton is roughly the weight of a small apple resting in your palm. This force is about one hundred billionth of that.
• If you wanted something to weigh what these two objects pull on each other with, you would be looking for an object with a mass of around seven billionths of a gram.
• A grain of table salt weighs about 60 micrograms, which is around ten thousand times heavier than that.
• A single human red blood cell weighs roughly 100 picograms, and you would need something like seventy of them to match it.

So the gravitational attraction between two bags of sugar held a metre apart is comparable to the weight of a few dozen blood cells. And that is what has to be detected. Not inferred, not calculated. Physically detected, as a real deflection of a real object, against a world that is shaking, warming, cooling, and pulling in every other direction at once.

The fridge magnet against the planet (27:12)

Now compare it to its neighbours. Take two protons and set them next to each other. They repel each other electrically and they attract each other gravitationally, both at the same time, and the two effects are in direct competition.

The electrical repulsion wins. It wins by a factor of about 10³⁶, which is a one followed by thirty six zeros. The film says, correctly, that it does not think that number can be felt as a number. So here is the version you already know without having thought about it this way.

Go to your fridge and take a magnet off the door. It weighs a few grams. Hold it above a steel paperclip and watch the paperclip jump up to meet it.

In that moment, the electromagnetic field of a small piece of iron you could lose in your pocket has defeated the entire gravitational pull of a planet that weighs six thousand billion billion tons. Not narrowly. It is not close. The planet was never really in the contest.

The two properties that ruin everything (28:22)

That is the force we are trying to measure, and it comes with two properties that no other force in physics has, and both of them are catastrophic for an experimenter.

The first is that you cannot shield it. Electricity can be shielded: put a sensitive experiment inside a metal box and the external electric fields simply stop at the wall, because the charges in the metal rearrange themselves to cancel the field inside. That is a Faraday cage. Magnetism can be shielded with the right materials. Sound can be shielded. Light can be shielded. Vibration can be damped.

Gravity cannot. There is no material in existence that blocks it, and as far as anyone can tell there is no material that could. Whatever you build your walls out of, you have added mass, and mass pulls. Shielding a gravity experiment from gravity makes the problem worse by definition.

So everything in the room is in the experiment. The concrete floor is in the experiment. The steel in the building's frame is in the experiment. The water table under the foundations rises and falls with the rain and it is in the experiment. The experimenter's own body, standing three metres away, exerts a pull on the apparatus that is a genuine calculated correction in modern work, which is why in some laboratories the people running the measurement stand on marked positions on the floor and do not move. The Sun is in the experiment. The Moon is in the experiment, and the Moon moves.

The second property is worse: you cannot turn it off.

Think about what precision measurement normally looks like. You want to measure a magnetic field, so you record what your instrument reads with the field on, then you switch the field off and record what it reads with the field absent, and the difference between those two readings is your signal. Everything that was contaminating both readings equally has just cancelled. That subtraction is the backbone of experimental physics. It is how you find out what your instrument is doing wrong.

There is no off switch for mass. You cannot run a control. There is no configuration of the apparatus in which gravity is absent, so you can see what your errors look like on their own. Every reading you ever take contains the signal and the contamination together, permanently fused. And the only way to separate them is to build a model of every contaminating influence and subtract it by calculation, which means the quality of your answer depends entirely on the quality of your model of everything else in the world.

Random errors are friendly. These are not. (31:02)

And here is the consequence, which the film flags as the hinge of the whole story.

In most experiments, the errors that matter are random. Random errors are almost friendly. They scatter your readings symmetrically around the truth, and if you take enough readings they average away. More data always makes you more right.

In this experiment, the errors that matter are not random. They are systematic. They come from your particular apparatus, your particular fibre, your particular spheres, your particular room, and they push your answer consistently in one direction. Taking more readings does not remove a systematic error. It just makes you more confident in a wrong number.

Which means that when two laboratories using different equipment get different answers, averaging them together does not give you the truth. It gives you a number in the middle of two mistakes, with an error bar that is now lying to you about how well it is known.

That is the trap. And in the 1980s and 90s, physics walked straight into it with the best equipment it had ever built.

Part five: the disagreement (32:17)

By the middle of the 1980s, the situation looked good.

The Committee on Data for Science and Technology, an international body usually referred to simply as CODATA, exists to do a specific and rather thankless job. Every few years it gathers every credible measurement of every fundamental constant, weighs them against one another, and publishes a single recommended value for each with an uncertainty attached. When a textbook prints a constant, this is where the number came from. When a spacecraft navigation team needs a figure, this is the figure they use.

In its 1986 adjustment, CODATA recommended a value for the gravitational constant of 6.67259 × 10⁻¹¹, with an uncertainty of 128 parts per million.

128 parts per million means the value is trusted to about one part in 8,000. By the standards of the rest of physics that is poor. By the standards of this particular quantity it was the best anyone had ever done. And, more importantly, it looked like the middle of a trend. Measurements from different laboratories were clustering. The error bars were shrinking. The story appeared to be following the normal arc, the arc that every other constant had followed, in which the twentieth century slowly and steadily squeezed the uncertainty down.

Then a generation of new experiments arrived, built with better materials, better electronics, better vibration isolation, and better ideas.

They did not cluster.

Germany: remove the fibre entirely (34:04)

In 1995 and 1996, a team at the Physikalisch-Technische Bundesanstalt in Braunschweig, Germany, the national metrology institute and one of the most respected measurement laboratories on Earth, published a result using a method nobody had tried before.

Rather than hanging the balance from a fibre and letting the fibre's stiffness set the scale, they floated the whole apparatus on a bath of mercury and used electrostatic forces to servo control it, holding it in place and reading off the electrical effort required. The idea is elegant: if the fibre is the untrustworthy component, remove the fibre.

Their claimed uncertainty was a few parts in a hundred thousand, which would have made it competitive with anything in the field. Their value came out about seven tenths of one percent higher than the accepted figure.

The film makes sure the scale of that lands. Seven tenths of one percent is 7,000 parts per million. They were claiming a precision of a few tens of parts per million and landing 7,000 parts per million away from where everybody else was. That is not a disagreement. That is a result sitting so far outside the established range that either the entire prior literature was wrong, or something in this beautiful new method was badly misunderstood, and no one could say which.

Nobody found the error. Nobody found it in the German result and nobody found a reason to throw it out. It was a careful measurement by careful people at a serious institution, and it simply did not fit.

Seattle: make sure the fibre never twists (35:51)

Meanwhile, other groups were producing results that were individually excellent and collectively incompatible.

At the University of Washington in Seattle, a group known as the Eöt-Wash Collaboration, named partly for the Hungarian physicist Loránd Eötvös, who had pioneered torsion balance work a century earlier, attacked the fibre problem from the opposite direction.

Instead of removing the fibre, they arranged for the fibre never to twist. Their apparatus sits on a turntable, and as the source masses pull on the pendulum, the turntable accelerates to follow it, keeping the fibre at exactly zero twist at all times. If the fibre never bends, its stiffness never enters the answer, and the whole family of errors associated with it disappears. What you measure instead is the angular acceleration of the turntable, which is a much better behaved quantity.

That result, published in 2000 by Gundlach and Merkowitz, claimed one of the tightest uncertainties yet achieved.

Paris and Boulder, in opposite directions (36:51)

At the International Bureau of Weights and Measures outside Paris, the institution that for over a century physically held the master kilogram, a team led by Terry Quinn built an apparatus that could be run in two different modes, both the classical deflection method and an electrostatic servo method, so that the two could be cross checked against each other inside one instrument. They published in 2001 and again in 2013. Their values sat high, near the top of the published range.

At JILA in Boulder, Colorado, Parks and Faller took a completely different approach again, using laser interferometry to track the motion of pendulums with extreme precision. They published in 2010. Their value sat low, near the bottom of the range, many standard deviations away from the Paris results.

The great hope from outside: cold atoms (37:44)

There was one more hope and it came from an entirely different direction. Atom interferometry does away with lead spheres and hanging rods altogether.

You cool a cloud of atoms until they are barely moving. Drop them, and use laser pulses to split each atom's quantum wave into two paths that travel slightly different routes before recombining. The interference pattern that results is exquisitely sensitive to the gravitational field the atoms fell through. Put a large mass nearby and the pattern shifts.

This method shares essentially no systematic weaknesses with any torsion balance ever built, which made it the great hope for breaking the deadlock from outside. It has produced good results. It has not yet produced results precise enough to settle anything.

Two families of experiment, systematically offset (38:38)

There is also a pattern in the failures that nobody has been able to cash in.

Broadly, the experiments split into two families. One family times things: you measure how the oscillation period of a pendulum changes when you move the source masses. The other family holds things still: you measure the force or the torque required to prevent motion from happening at all.

Historically, these two families have produced results that sit systematically offset from one another. That is exactly the kind of clue that ought to lead somewhere.

It has led nowhere yet.

Twenty sigma as the background condition (39:18)

Line them all up and this is what you see. Each group has spent years, often decades, on a single number. Each has published an uncertainty in the range of tens of parts per million. And the answers are spread across a band roughly 500 parts per million wide, which means the extremes differ by around five hundredths of one percent.

Five hundredths of one percent sounds small until you set it against the error bars. A group claiming 20 parts per million precision, whose result differs by 400 parts per million from another group's, is not making a slightly different measurement. It is making a measurement that formally excludes the other one twenty times over.

In any other area of physics, a twenty sigma discrepancy would be treated as an emergency or a discovery. Here it is simply the background condition of the field.

They cannot all be right. That is not an opinion, it is arithmetic. And the uncomfortable part is that there is no obvious candidate for the one that is wrong:

• You cannot point at the outlier and dismiss it, because there are several outliers and they are outliers in different directions.
• You cannot appeal to which laboratory is more prestigious, because they are all national institutes and major universities.
• You cannot appeal to which method is more trustworthy, because the whole reason there are multiple methods is that each was designed to avoid the weaknesses of the others.

Vagueness had been holding the field together (40:52)

So the field arrived at a strange and rather quiet crisis. The individual measurements were the best that had ever been made. The spread between them was wider than it had been a generation earlier, when the measurements were worse.

The number gets sharper and the disagreement gets wider.

The film asks you to hold that sentence, because it is going to be the shape of everything that follows, and by the end it turns out to be the answer to the question the film started with rather than just a description of the problem.

For now, notice only how backwards it is. In every other corner of science, better instruments produce closer agreement. That is what better instruments are for. That is the entire justification for building them. Here, better instruments produced sharper individual claims that contradicted each other more violently than the blurry old ones ever had, because the blurry old ones had error bars wide enough to overlap.

Vagueness had been holding the field together. Precision pulled it apart.

Somebody was eventually going to have to stand up and say so officially. In 1998, somebody did.

Part six: the year the uncertainty went up (42:09)

Everything described so far is the kind of thing that could stay inside the field. Disagreements between laboratories are normal. They get worked out in conference sessions and letters and eventually in somebody finding the mistake. Physics is comfortable with unresolved discrepancies for a while, because a while is usually all it takes.

What is not normal, what has essentially no precedent among the fundamental constants, is for the disagreement to become so unresolvable that the official record has to be rewritten to admit it.

That is what happened in 1998.

CODATA published its adjustment that year and, for the gravitational constant, it recommended a value of 6.673 × 10⁻¹¹ with an uncertainty of 1,500 parts per million.

Twelve years earlier the figure had been 128.

The uncertainty had not been reduced. It had been multiplied by roughly twelve.

Sit with what that actually is (42:54)

The film asks you to sit with it for a second, because it is easy to hear it as a technical adjustment and miss what it is.

This is the international body responsible for the numerical constants of physics publishing its considered judgment. And its considered judgment was that after more than a decade of additional work by the finest measurement laboratories in the world, using equipment that did not exist in 1986, humanity's knowledge of how strong gravity is had got worse.

Not stalled. Worse. The honest interval around the answer was now twelve times wider than the interval that had been published before all that work was done.

The reason given was stated plainly, and it is worth hearing in something close to its own words: the large increase in uncertainty was necessary because no explanation had been found for the large differences obtained in the presumably more accurate measurements carried out since 1986.

Read that phrase again. The presumably more accurate measurements. There is a whole worldview quietly collapsing inside the word presumably.

These experiments were more accurate. Everyone involved could describe exactly why they were more accurate, component by component, and the descriptions were correct. Better fibres, better isolation, better electronics, better modelling of the surroundings. Each individual improvement was real. And the collective result of all those real improvements was a set of answers that agreed with each other less well than the cruder answers had.

So CODATA did the only defensible thing. It refused to pretend. It could have picked a favourite result and published a tight uncertainty around it, and nobody outside a small community would have noticed. Instead it published a number with an error bar wide enough to contain the mess, and said, in effect: we do not know why these disagree, so we are going to stop claiming we know this as well as we said we did.

The film's verdict on that is generous and accurate at the same time. It is intellectual honesty of a fairly high order. And it is also one of the strangest sentences in the modern history of physics, because there is no other fundamental constant for which this has happened. Not one. Every other number on the list has followed the expected path, tightening decade after decade as instruments improved. Gravity's constant went backwards, in public, in the official record, and it went backwards precisely because the measurements got better.

If you want a single moment where the claim in the title of this video stops being a way of speaking and becomes a documented historical event, this is it. In 1998, more precise measurement of gravity produced formally less certain knowledge of gravity. It is written down. You can look it up.

A constant that will not sit still (46:20)

And the instability did not end in 1998. Watch what the recommended value itself has done since:

• 19866.67259, with an uncertainty of 128 ppm. The best anyone had ever done, and apparently the middle of a converging trend.
• 19986.673, with an uncertainty of 1,500 ppm. The uncertainty is multiplied by roughly twelve because the better measurements will not agree.
• 20026.6742. The value moves in the fourth decimal place.
• 20066.67428. Up again in the fifth.
• 20106.67384. Back down, by more than some of the quoted uncertainties that preceded it.
• 20146.67408. Climbing again.
• 20186.67430, with an uncertainty of 22 ppm, which is where it remains.
• 2022CODATA publishes again and leaves the value exactly where it was, because in the four years since the previous adjustment no new determination of the gravitational constant had arrived that was good enough to move it.

Look at what those digits are doing. This is supposed to be a fixed feature of the universe, and the official value for it has wandered up and down the fourth and fifth decimal places for four decades, sometimes moving by more than the uncertainty that had been quoted for it the time before.

The film's reading of that is the correct one. A constant that will not sit still is not misbehaving. The universe is not changing its mind. What is moving is us, and the movement is a record of which measurements happen to be included in which adjustment.

Kuroda, and the flaw hiding in plain sight for 200 years (47:36)

There was one genuine piece of insight that came out of this period, and the film says it is worth understanding because it shows both how the field made progress and why the progress did not help as much as it should have.

In 1995, a physicist named Kuroda pointed out something about torsion fibres that had been hiding in plain sight for two hundred years.

Remember that a whole family of these experiments works by timing. You measure how long the pendulum takes to swing back and forth, then you move the big masses and measure how the period changes, and the change gives you the force. The method assumes the fibre behaves as an ideal spring, storing and returning energy perfectly.

Real fibres do not do that. Real materials are slightly anelastic, which means that when you twist them, a small part of the energy is not stored elastically but dissipated internally, and the fibre's effective stiffness depends very slightly on how fast you are twisting it. At the frequencies these pendulums swing at, that effect is small.

It is also, Kuroda showed, systematically biased in one direction. Not random. Biased. Time of swing measurements would consistently come out too high, by an amount that depended on the fibre.

That single observation retroactively put a question mark over an entire generation of published results. It did not tell you what the right answer was. It told you that a specific large group of measurements shared a common flaw, which meant that averaging them together, which everyone had been doing, made things worse rather than better, because the flaw did not cancel.

And it explains why the very best modern experiments are designed the way they are. The Seattle turntable that keeps the fibre at zero twist. The Paris servo that holds the balance still with electrostatic force. The German mercury bath that removed the fibre entirely. These are all answers to Kuroda.

The field understood the problem and engineered around it. The engineering worked.

The disagreement stayed.

Which is what makes the next chapter of this story so difficult to shrug off. Because eventually a group would take the two best techniques available, the two designed most carefully to avoid each other's weaknesses, and run them both in the same laboratory with the same masses under the same conditions by the same people. You would expect that to settle it. There is essentially nothing left to blame.

It did not settle it.

Part seven: two answers in one cave (50:23)

There is a hill in Wuhan in central China with a laboratory inside it.

It belongs to Huazhong University of Science and Technology, and it exists because of a decision made decades ago by a physicist named Jun Luo, who concluded early in his career that if you are serious about measuring gravity you cannot do it in a normal building.

Normal buildings breathe. They warm in the afternoon and cool at night. Traffic outside shakes the floor. Machinery in the basement hums at frequencies that couple into anything hanging from a wire. Air conditioning moves air, and moving air moves apparatus.

So the group went underground, into space carved out beneath a hill, where the rock above holds the temperature nearly constant year round and the ground is quieter than anywhere at the surface. The environment does not fluctuate. It just sits there, at a stable temperature, in the dark, and the experiment can be left alone for as long as it needs.

It needed about thirty years.

Thirty years, in human terms (51:31)

The film insists on putting that in human terms, because it is easy to say a group worked on something for three decades and hear it as a summary rather than a life.

A person begins this work in their thirties. They design an apparatus. They discover it is not good enough and design another. They train students who arrive as undergraduates, complete doctorates, and leave for their own careers, and they train the next batch. Above them, the city of Wuhan grows from one thing into another. Underground, the balance swings.

And the object of all of it is a number in the fifth decimal place.

Picture the room during a run. The apparatus is a torsion pendulum, and everything around it has been engineered to disappear. The temperature is held constant to a small fraction of a degree, because a temperature gradient across the apparatus would drive convection and convection would swamp the signal. The source masses are spheres whose density has been mapped and whose geometry has been measured to a precision that took years of separate work to achieve. The fibre has been characterized, tested, and characterized again. There is nobody in the room, because a person in the room is a mass in the room and a heat source in the room.

The spheres are the hard part (52:57)

And a great deal of the thirty years went not into the pendulum at all, but into the spheres. This is the part the film says nobody imagines.

To extract the strength of gravity you must know the mass of your source objects and the distance between their centres of mass, and both of those are far harder than they sound.

A metal sphere is never perfectly uniform inside. There may be a void you cannot see, a variation in density from how the metal cooled, a slight departure from roundness at the level of micrometres. The centre of mass of an object is not a thing you can look at. It has to be inferred from measurements of shape and density, and every imperfection you fail to notice shifts it. A shifted centre of mass changes the distance in the equation.

And the distance is squared.

Teams working on this problem have spent years characterizing a handful of metal balls. As the film puts it: the gravity part of a gravity experiment is often not the hard part.

The rod turns through an angle you could not see with your eye against any reference you could name. A sensor reads it. Data accumulates for weeks. Nobody touches anything.

Two methods, chosen because they fail differently (54:08)

And here is what makes this experiment different from every other one in the story so far. The group did not run one method. They ran two, and they chose the two best techniques available deliberately, on the grounds that the techniques fail in different ways.

The first was the time of swing method, the one Kuroda had warned about, but with the fibre's anelastic behaviour now measured and corrected for directly, using fibres whose properties had been studied specifically for this purpose.

The second was the angular acceleration feedback method, in which the whole apparatus sits on a turntable that continuously accelerates to cancel any twist, so that the fibre's stiffness never enters the answer at all.

These two methods share almost nothing. They depend on different physics, different sources of error, different corrections, different assumptions. If a hidden systematic error were lurking in one of them, there is no reason at all for it to lurk identically in the other. That is the entire point of doing both.

It is the cleanest cross check anyone had ever set up on this quantity. And it was being run by one team, in one place, on one set of masses, in one stable underground environment, with a single shared understanding of every correction being applied.

Whatever excuses had been available before were now gone. You could not say the laboratories were different: it was one laboratory. You could not say the masses were different: they were the same masses. You could not say the standards or the technique culture or the local gravity model differed between groups. There was one group.

August 2018 (56:00)

In August 2018 they published the results in Nature.

The time of swing method gave 6.674184 × 10⁻¹¹, with a relative standard uncertainty of 11.64 parts per million.

The angular acceleration feedback method gave 6.674484 × 10⁻¹¹, with a relative standard uncertainty of 11.61 parts per million.

Those are the two most precise determinations of the gravitational constant that have ever been made. Both of them. Nothing before or since has been tighter.

And they do not agree with each other.

The gap, and what makes it heavier than every gap before it (56:40)

The gap between them is about 45 parts per million. Each of them claims to know its own answer to about 12 parts per million. So the two results are separated by something close to four times the uncertainty either one of them is willing to admit to.

Both values sit within about two standard deviations of the internationally recommended figure, so neither one is an embarrassment against the wider field. That is not the problem. The problem is that they are an embarrassment to each other.

Two methods chosen precisely because they cannot share a mistake, run by one team who wanted them to agree, produced answers that formally exclude one another.

What they did next (57:21)

There is something admirable in what happened next and the film gives it its weight.

The team published both numbers. They did not average them into a single value and quote a comfortable uncertainty. They did not hold the results back until the discrepancy could be resolved. They did not quietly favour the one that fitted better with the literature. They put both answers in a major journal, side by side, with the disagreement visible, and left the field to deal with it.

That is what science is supposed to look like. And it is also why this result is so much heavier than the ones before it.

When two different laboratories disagree, you can always tell yourself a story. Someone's mass metrology was off. Someone's local gravity model was incomplete. Someone had a fibre problem they did not know about. There is always an explanation waiting to be found, and the search for it feels like progress.

When one laboratory disagrees with itself, using two methods designed to have nothing in common, after thirty years of preparation, in a room inside a hill built specifically to remove every excuse, the space where the explanation was supposed to go is empty.

Nobody has filled it since.

And that is the point in the story where the question quietly changes shape. Up to here you could reasonably think of this as a hard measurement problem: difficult, embarrassing, unresolved, but the sort of thing that better technique eventually cracks. Thirty years, two methods, one cave, and a 45 part per million gap suggests something else. It suggests that the trouble might not be in the instruments at all.

Which raises a question the film says it has been avoiding and can avoid for only a little longer. If our best measurements of gravity keep failing to agree, is it possible that the problem is not how we are measuring it, but what we think we are measuring?

Before it gets there, it wants to show how far the consequences of this one uncertain number actually reach. And the answer reaches further than gravity.

Part eight: the constant that refused (59:38)

The film steps back at the halfway mark and puts the pieces on the table together, because the shape of it has been building quietly:

Newton wrote a law with a missing number. Cavendish, alone in a sealed shed, measured the density of the planet to within one percent and never calculated the missing number at all. The nineteenth century extracted it, named it, and improved it. The twentieth century built extraordinary machines to pin it down, and those machines disagreed with each other more violently than the crude ones had. In 1998 the official uncertainty was multiplied by twelve because nobody could explain why. And in 2018 a group inside a hill in Wuhan ran the two best techniques ever devised, deliberately chosen so they could not share a mistake, and got two answers separated by four times their own error bars.

The number gets sharper and the disagreement gets wider.

20 May 2019: the day gravity was left outside (1:00:51)

Now the film shows what that has cost institutionally, because there is a moment where physics had to formally acknowledge this in the structure of measurement itself.

On the twentieth of May 2019, the International System of Units was redefined. This was one of the largest changes in the history of measurement and it received a fraction of the attention it deserved.

For most of the modern era, some of our base units were defined by physical objects or physical procedures. The kilogram was the worst offender. Until 2019 the kilogram was a lump of platinum iridium alloy sitting in a vault outside Paris, and the definition of a kilogram was literally the mass of that object. If it gained a fingerprint of contamination, the kilogram got heavier everywhere in the universe, by definition. Copies of it distributed around the world had drifted measurably away from the original over a century, and nobody could say whether the copies had gained mass or the original had lost it, because there was nothing more fundamental to check against.

The 2019 redefinition ended that. Instead of defining units by objects, physics turned the logic around and defined units by constants of nature, fixing those constants to exact values with no uncertainty at all, forever:

• The Planck constant was fixed to an exact number, and the kilogram now follows from it.
• The elementary charge was fixed exactly, and the ampere follows.
• The Boltzmann constant was fixed exactly, and the kelvin follows.
• The Avogadro constant was fixed exactly, and the mole follows.
• The speed of light had already been fixed exactly back in 1983, which is why the metre is now defined as the distance light travels in a specified fraction of a second.

These constants are no longer measured. They are decreed. Their uncertainty is precisely zero, because they are definitions, and everything else in metrology is built on top of them.

Newton's gravitational constant was not included. It could not be.

To fix a constant by definition, you have to know it well enough that fixing it does not create absurdity. And gravity's constant is not known anywhere near well enough. Twenty two parts per million is not a foundation.

So when physics rebuilt the entire structure of measurement on a bedrock of exactly known constants, gravity was left standing outside the building. Still an experimental quantity. Still something you have to go into a room and try to measure. Still uncertain.

It is, in that specific sense, the last one. The great project of the twentieth century was to replace measured standards with fixed natural constants, and it succeeded almost completely. Gravity is the holdout. The oldest force in physics, the first one described mathematically, the one everybody thinks is finished, is the one that could not be brought inside.

Dirac, and a constant that changes (1:04:07)

This is exactly the sort of situation that attracts alternative explanations, and the film deals with those honestly rather than pretending they do not exist, because some of them come from serious places.

The most persistent is the idea that the constant is not constant. That gravity's strength changes over time, and the reason laboratories disagree is that they are measuring a moving target.

This is not a silly notion and it did not originate at the fringe. Paul Dirac, one of the founding figures of quantum mechanics, proposed something along these lines in 1937. He had noticed that certain enormous dimensionless numbers you can construct from physical constants come out suspiciously similar in magnitude, and he suggested this could not be coincidence, and that the way to make it non coincidental was for the strength of gravity to decrease slowly as the universe ages. That is the large numbers hypothesis.

It was a serious idea from a serious person, and it made a testable prediction. It has been tested thoroughly and it fails.

The most elegant test uses the Moon. The Apollo missions left retroreflectors on the lunar surface, arrays of corner mirrors that bounce a laser pulse straight back to its source. Fire a laser from Earth, catch the returning photons, time the round trip, and you can measure the Earth to Moon distance to within centimetres. Do that for decades and you have a record of the lunar orbit of extraordinary precision.

If the strength of gravity were weakening, the Moon's orbit would slowly expand in a very specific way. It does not. Lunar laser ranging constrains any fractional change in the gravitational constant to well under one part in 10¹³ per year. Binary pulsar timing gives an independent constraint. The physics of the early universe gives another.

So we arrive at a genuinely strange position, and the film states it as a pair:

• We can demonstrate that the strength of gravity is not changing to a precision of better than one part in ten trillion per year.
• We cannot say what the strength of gravity is to better than about one part in fifty thousand.

We know it is not moving far, far better than we know where it is.

Cycles, and gravity shielding (1:06:18)

There is a related claim that surfaces periodically, suggesting the historical scatter in gravity measurements shows a hidden pattern, sometimes proposed as a cycle linked to the length of the day. These analyses have not survived examination. The apparent pattern depends heavily on which measurements are included and which are left out, and no mechanism has been offered that has any independent support.

And then there is the oldest one, the idea that gravity can be blocked or reversed by some device. Claims of gravity shielding recur every couple of decades, usually involving spinning something. None has ever been replicated by an independent laboratory, and careful attempts to reproduce the most publicized case found nothing at all.

The film's read on all three is worth quoting in substance, because it is generous without being soft. Each is an attempt to convert a boring and humiliating truth into an interesting one. The boring truth is that this measurement is genuinely, structurally, brutally hard, and that a hundred careful people can fail at the same task for two hundred years without anybody hiding anything.

But there is one consequence of that boring truth that is not boring at all. Because if you do not know the constant, there is something enormous that you also do not know. Something you were told in school, something you have never once doubted, and something nobody on Earth has ever actually measured.

Part nine: we do not know what the Sun weighs (1:07:59)

Here is a fact you have almost certainly been told, probably more than once, and have never had any reason to question. The Sun has a mass of about 2 × 10³⁰ kilograms, roughly two thousand billion billion billion tons. It is in every textbook, every reference table, every documentary. It is one of those numbers that feels like bedrock.

Nobody has ever measured it.

The film is careful about what it means by that. Not that nobody has measured it very well. That the quantity astronomers actually determine when they study the solar system is not the mass of the Sun, has never been the mass of the Sun, and cannot be made into the mass of the Sun without passing through the least reliable number in physics.

Where the loss happens (1:08:59)

Go back to Newton's law. The force between two objects is the gravitational constant, times the first mass, times the second mass, divided by the distance squared. Now put a planet in orbit around a star and ask what determines the orbit.

The planet's own mass drops out of the problem almost entirely, for the same reason a heavy ball and a light ball fall at the same rate. What is left governing the motion is a single combined quantity: the gravitational constant multiplied by the mass of the star.

That product has a name. It is called the standard gravitational parameter, written as GM. And here is the crucial thing about it. When you watch an orbit, that product is what you are measuring. Not the constant. Not the mass. The two of them fused into one number. And there is no observation of orbital motion, however precise, that can pull them apart, because orbits simply do not care how the product is divided between its factors.

Now, we can measure that product superbly.

For the Earth, the standard gravitational parameter is known to something like two parts in 10⁹. Two parts in a billion. That precision comes from decades of tracking satellites with laser ranging, from spacecraft telemetry, from radar, from the accumulated work of a thousand people who needed to know exactly how the Earth pulls in order to put things in orbit and keep them there. It is one of the best determined quantities in all of physical science.

For the Sun, the equivalent parameter is known even better. Spacecraft have been navigating the solar system for over sixty years and their trajectories are exquisitely sensitive to it. We know the Sun's gravitational parameter to something like ten significant figures.

So we know the pull of the Sun to ten digits.

Now try to get the mass. You take that beautifully determined product and you divide it by the gravitational constant. And the gravitational constant is known to 22 parts per million.

Every digit beyond the fourth or fifth is destroyed instantly. It does not matter that the numerator was known to ten figures. When you divide a number known to ten figures by a number known to five, you get a number known to five. The precision does not survive contact.

Every mass in the universe inherits it (1:11:02)

So the mass of the Sun, and the mass of the Earth, and the mass of Jupiter, and the mass of every star whose weight has ever been inferred from the motion of a companion, are all known to roughly one part in ten thousand. Four digits.

And every single one of those numbers is limited by the same thing. Not by our telescopes. Not by our spacecraft. Not by our theory. By two lead spheres on a bench that nobody can agree about.

The film asks you to sit with that. The Sun is the most observed object in the history of human attention. We have watched it every day for as long as there have been eyes. We have instruments in orbit around it. We have flown a probe through its outer atmosphere. We can tell you the composition of its surface, the temperature of its core, the frequency of its oscillations, the age of it to within a few tens of millions of years.

We cannot tell you what it weighs to better than four figures. Not because the Sun is hiding anything. Because 1798 happened in a shed and the problem it opened has not been closed.

The gap between the two numbers is not a fact about the Sun at all. It is a fact about us.

Astronomy sidestepped the problem before anyone knew it was one (1:13:04)

There is a lovely historical detail buried in here, which is that astronomy figured out how to route around the damage long before anybody understood it was damage.

Kepler's third law, in its exact modern form, contains the standard gravitational parameter rather than the mass. So the entire edifice of celestial mechanics, all the way from the seventeenth century through to the space age, was built on a quantity that never required knowing the strength of gravity.

This is why Cavendish could be a century late to the party without holding anything up. It is why mission planners today work in units of the gravitational parameter and never convert to mass, because converting would only lose them precision they need. The whole discipline roots around the damage without comment, as a matter of ordinary professional practice.

Which means that if you are a navigator flying a spacecraft to Jupiter, you genuinely do not care what Jupiter weighs. You care how hard it pulls. You know that superbly. And the mass is a piece of trivia you would only need if somebody asked you at a party.

Where the mass itself is the thing you want (1:14:25)

The trouble arrives the moment the mass itself is what you want to know. And there are places where that matters enormously.

Stellar physics depends on mass. How a star burns, how long it lives, whether it ends as a white dwarf or collapses further, all of it is set primarily by mass. Models of stellar structure are built and tested against measured masses, and those masses carry gravity's uncertainty inside them.

The same is true one level up, where the mass of a galaxy is inferred from the motion of the things inside it, and one level up again, where the mass of a cluster of galaxies is inferred from the motion of the galaxies. The uncertainty propagates outward quietly, all the way to the largest structures we can see.

Every mass in the universe, as we have written it down, rests on a number that two laboratories in the same cave could not agree on.

And that would be the end of it if the constant were the only thing in doubt. But the constant is only the front of the equation. Sitting behind it is the law itself, the inverse square, the relationship Newton actually discovered. And there is a question about that which is much less comfortable than anything so far.

How much of the range of distances in this universe has that law actually been tested across?

The answer is a narrow band in the middle with darkness at both ends.

Part ten: the law at the edges (1:15:55)

Newton's inverse square law says that gravity weakens with the square of distance. Double the separation, quarter the force. The film has been treating that as given all night, as everyone does, and now asks the obvious question about it: over what range of distances has anyone actually checked?

The small end: everything else wins down there (1:16:26)

Start at the small end. Testing gravity between objects a few centimetres apart is already the delicate business this whole film has been describing. Push the separation down to a millimetre and it becomes far worse, because as the gap shrinks, other forces that were negligible start to dominate completely:

• Static electricity on the surfaces.
• Patch potentials, which are tiny variations in the electrical character of a metal surface from one spot to the next, invisible and unavoidable.
• At the smallest separations, the Casimir force, a genuine quantum effect in which two closely spaced plates are pushed together by the structure of the vacuum between them, and which rises steeply as the gap closes.

Every one of those is larger than gravity in that regime. So the experiment becomes a matter of building shields, choosing coatings, and designing geometries that cancel the interlopers, in the hope of exposing a gravitational signal underneath.

52 micrometres, and then nothing (1:17:24)

The group that has pushed hardest at this is the Eöt-Wash collaboration in Seattle, the same people who built the turntable that keeps the fibre at zero twist.

Their short range work uses pendulums shaped like discs with holes bored through them, so that as a source disc rotates beneath the pendulum the gravitational pull rises and falls at a known frequency, letting them pull the signal out of the noise by looking only at that frequency.

In a result published in Physical Review Letters in 2020, they tested the 1/r² behaviour of gravity down to separations of about 52 micrometres, which is roughly the width of a fine human hair.

Down to that distance, gravity behaves exactly as Newton said it does. No deviation.

Below it, we do not know. Not because anyone doubts it. Because nobody has been able to look.

Extra dimensions, and the ugliest open problem in physics (1:18:21)

And that unexamined region is not theoretically empty.

In the late 1990s, a proposal from Arkani-Hamed, Dimopoulos and Dvali suggested that there might be additional spatial dimensions curled up small, which gravity can spread into but the other forces cannot. If that were true, then at separations smaller than the size of those dimensions, gravity would appear to strengthen faster than the inverse square, because the field would be spreading into more directions than we can see.

The motivation for the idea is one of the ugliest open problems in physics, and the film names it here because it comes back at the end. Gravity is roughly 10³⁶ times weaker than the other fundamental forces. Nobody knows why. There is no mechanism in any accepted theory that produces a number like that. It is not derived. It is observed, and it sits there as an enormous unexplained ratio at the centre of the discipline. This is called the hierarchy problem, and extra dimensions were one attempt to dissolve it by proposing that gravity is not actually weak at all, but merely diluted, leaking into dimensions we cannot access.

Short range experiments have squeezed the room available for that idea substantially. Work of this kind has established that no extra spatial dimension can be larger than a couple of hundred micrometres across.

Which sounds like a loose constraint until you remember that a decade earlier the honest answer was that nobody had any idea, and that a dimension a millimetre wide was a live scientific possibility. That is real progress. It is also progress by elimination, which tells you where something is not and never where it is.

They have not closed it. Below 52 micrometres, the law is a reasonable assumption rather than a measured fact.

The large end: the law gives the wrong answer (1:20:21)

Now go the other way. Out at the scale of a galaxy, the inverse square law does not merely become untested. It gives the wrong answer.

The observation is straightforward and has been for a long time. Take a spiral galaxy. Measure how fast stars orbit at different distances from the centre and compare that to what the visible matter should produce.

In the solar system, planets further out move more slowly, which is exactly what gravity predicts. In a galaxy, they do not. The rotation curve flattens out. Stars in the outer regions move about as fast as stars much further in, and far faster than the visible mass can account for. At those speeds they should have been flung out into intergalactic space long ago. They are still there.

Fritz Zwicky noticed a version of this for clusters of galaxies in the 1930s and coined a term for the missing mass. He was largely ignored. In the 1970s, Vera Rubin and Kent Ford measured rotation curves for individual galaxies carefully enough that the result could no longer be dismissed, and the field had to reckon with it.

Two ways out, and physics has been arguing ever since (1:21:32)

There are exactly two ways out.

The first is that most of the matter is invisible. There is five or six times as much mass in a galaxy as we can see, made of something that does not emit, absorb, or reflect light, and interacts with ordinary matter essentially only through gravity. This is dark matter, and on the largest scales the evidence for it is strong.

The Bullet Cluster, catalogued as 1E 0657-56, is the case usually cited. Two clusters of galaxies that have collided, in which the hot gas, which is most of the ordinary matter, has been slowed by the collision and left behind in the middle, while the gravitational mass measured by lensing has sailed straight through and sits out with the galaxies. Mass and visible matter have been physically separated. That is difficult to produce with any modification of gravity's law.

The second way out is that there is no missing matter and the law of gravity is simply wrong in this regime. In 1983 Mordehai Milgrom proposed modified Newtonian dynamics, which keeps the matter we can see and changes the rule instead.

The proposal identifies a characteristic acceleration around 1.2 × 10⁻¹⁰ m/s² and says that above that acceleration Newton holds, while below it gravity falls off more slowly than the inverse square. That acceleration is absurdly small: it is roughly the rate at which your speed would increase if it took you about 250 years to reach walking pace. Nothing in the solar system ever gets that low, which is why the solar system shows no sign of any of this.

The honest scorecard (1:23:19)

The film refuses to flatten this, because it is a real dispute between serious people, so it gives a scorecard.

Modified dynamics does something genuinely remarkable at the scale of individual galaxies. From the visible matter alone it predicts the rotation curve, including detailed wiggles that track the visible structure, with a single parameter. Dark matter models can reproduce those curves too, but generally by fitting a halo to the data afterward rather than predicting it in advance. There is a documented regularity here, often called the radial acceleration relation, showing that the observed acceleration in a galaxy is tightly determined by the visible matter alone. Modified dynamics predicts that relation as a matter of course. Dark matter has to explain why it emerges.

And then modified dynamics fails. It does not work on clusters of galaxies without adding some unseen mass anyway, which rather defeats the purpose. It has no clean account of the detailed structure of the cosmic microwave background, which dark matter models fit with startling accuracy. It struggles with how structure formed in the early universe.

Meanwhile dark matter succeeds everywhere modified dynamics fails, and has one enormous problem of its own. After four decades of increasingly sensitive searches, in shielded underground detectors, in particle colliders, and in the sky, nobody has ever directly detected a particle of it. The experiments have grown more sensitive by many orders of magnitude and returned nothing. The space where the particle was supposed to be has been narrowed and narrowed, and the particle has not appeared.

So the position, honestly stated, is this. One explanation works beautifully on galaxies and fails on everything larger. The other works beautifully on everything larger and has never been seen.

Both are, at bottom, admissions of the same thing applied to a galaxy: our description of gravity does not close. It needs either an ingredient we cannot find or a modification we cannot justify.

The film began unable to say how strong gravity is. It has now arrived somewhere considerably less comfortable, which is that we may not be certain of the shape of the law either, above and below a fairly narrow band of distances in the middle where all our tests happen to live.

And there is one more scale to check. The largest one. Because when you go all the way out, past galaxies, past clusters, to the universe itself, gravity does something that ought to be impossible.

It stops pulling.

Part eleven: the force that pushes (1:26:16)

In 1998, two independent groups of astronomers set out to measure how much the expansion of the universe has been slowing down.

The question seemed settled in advance. The universe has been expanding since the beginning. Everything in it has mass. Mass attracts. And so the expansion must be decelerating. The only real question was by how much, and the answer to that would tell you the fate of everything: whether the universe expands forever at an ever slower rate, or eventually reverses and falls back together.

The exploding stars that would not cooperate (1:26:55)

To measure it, both teams used a particular kind of exploding star. A type Ia supernova occurs when a white dwarf accumulates matter until it crosses a threshold and detonates, and because that threshold is essentially the same everywhere, these explosions have close to the same intrinsic brightness wherever they happen.

That makes them a distance marker. Compare how bright one looks to how bright it should be, and you know how far away it is. Measure the stretching of its light and you know how much the universe has expanded since it exploded. Do that for enough supernovae at enough distances and you can reconstruct the expansion history.

Both teams found the same thing, and neither of them believed it at first. The distant supernovae were fainter than they should have been. Not by much, but consistently, and in a pattern that had only one straightforward reading.

The expansion of the universe is not slowing down. It has been speeding up.

Something is pushing.

The language matters here (1:28:01)

The film is careful about the language, because this is a place where casual description does real damage.

Nothing is literally shoving galaxies apart like a hand. What is happening is that the expansion of space is accelerating, and in the mathematics of general relativity that requires a component of the universe's contents with a strange property.

Ordinary matter and radiation have positive pressure. This component has negative pressure. And in Einstein's equations, negative pressure produces repulsive gravitation.

So at the largest scale, the dominant gravitational effect in the universe is not attraction. It has the opposite sign.

Five percent (1:28:45)

The name assigned to whatever is doing this is dark energy, and the name is a placeholder standing in for our ignorance in exactly the same way dark matter is. What we can say is how much of it there is:

• Dark energy accounts for roughly 68% of the total energy content of the universe.
• Dark matter accounts for around 27%.
• Everything else, every star, every planet, every cloud of gas, every atom in your body, and every atom that has ever been detected by any instrument, makes up about 5%.

The whole of the material universe, as we have ever known it, is a rounding error in the accounting.

Einstein's term, put in for the opposite reason (1:29:20)

In general relativity there is a natural way to write this in. Einstein's field equations permit an extra term, a cosmological constant which acts uniformly everywhere and produces exactly this kind of behaviour.

Einstein put it in himself in 1917, for the opposite reason. He wanted a static universe, and the equations without it insisted on a dynamic one, so he added a term to hold everything still. When the expansion of the universe was demonstrated observationally, he took it out again.

It came back in 1998, doing the reverse of the job he had first given it.

The worst quantitative prediction in the history of science (1:30:06)

And here is where this becomes a story about our understanding rather than about the universe.

If there is a constant energy associated with empty space, quantum field theory ought to be able to tell you how large it is. Empty space in quantum field theory is not empty. It has structure. Fields exist everywhere and they fluctuate, and those fluctuations carry energy, and that energy should gravitate.

So you calculate it, and the calculation gives a number.

The number is wrong. Not slightly wrong. It exceeds the observed value by something in the region of 120 orders of magnitude.

The film does not try to soften that, and it does not try to find an analogy, because there is no analogy that survives it. 120 orders of magnitude is a one followed by 120 zeros. If you try to compare it to the size of the observable universe measured in the width of a proton, you have used up about 40 orders of magnitude and you are nowhere near. There are fewer atoms in the observable universe than this, by a very wide margin.

It is routinely and fairly described as the worst quantitative prediction in the history of science, and the description is not a joke at anyone's expense. The calculation is done using our best theory of matter, applied to the simplest possible situation, empty space, and the answer is off by a factor with 120 zeros in it. There are technical arguments about the right way to do the sum and whether the discrepancy should be quoted as 120 or some smaller enormous number. None of them makes it small.

The blunder that probably was not said (1:31:45)

There is a story repeated often that Einstein called the cosmological term his greatest blunder. The film handles it properly: the phrase reaches us secondhand through George Gamow, and historians have never been able to confirm he said it.

What is documented is that he abandoned the term once the expansion was established, and considered the episode a mistake of judgment rather than of mathematics. The term was never wrong. He had simply used it to hold the universe still, and the universe declined.

Something is very badly wrong in how quantum theory and gravity are being made to speak to each other, and this is the loudest available signal of it.

The coincidence problem (1:32:27)

And there is a second oddity layered on top, which physicists sometimes call the coincidence problem.

Dark energy has a roughly constant density as the universe expands, because it is a property of space itself, and there is always more space. Matter does the opposite: as space stretches, the same matter is spread thinner, so its density falls.

That means the two have been on opposite trajectories for the whole history of the universe. Early on, matter overwhelmingly dominated. Far in the future, dark energy will overwhelmingly dominate. There is only one relatively brief window in the entire history of the cosmos in which the two are comparable in magnitude.

We are in it.

That may be a genuine clue, pointing at some mechanism that links the two. It may be pure selection, in the sense that this is also roughly the era in which stars and planets and observers exist, so perhaps no one was ever going to be around to notice any other epoch. Or it may be a coincidence, which is the least satisfying answer available and cannot be ruled out.

Nobody knows which.

Three scales, three completely different kinds of failure (1:33:40)

Now the film puts the three scales side by side, because the pattern is the point.

And notice something about the middle of that list. The uncertainty in the gravitational constant, the thing the film has spent most of its time on, does not even matter at the largest scales. Twenty two parts per million is nothing next to a factor with 120 zeros. The measurement crisis and the cosmological crisis are not the same size at all. They are not even in the same universe of size.

What they share is their direction. And the reason the film wants them lined up like that is that it starts to look less like a series of unrelated technical problems and more like one problem seen from three angles.

In each case we have a description that predicts behaviour superbly within the range where it was calibrated, and breaks down or requires unexplained additions the moment it is taken outside that range.

That is what a description does. It is not what an explanation does.

Which brings us to the thing the film has been circling all night without saying directly. We have been talking as though the difficulty is measuring gravity, or testing gravity, or extending gravity to new scales. Underneath all of that is a simpler and more uncomfortable fact about the theory itself.

General relativity is the most accurately confirmed theory in the history of physics, and it does not say what gravity is.

Part twelve: a theory with no mechanism (1:35:55)

The film wants to be completely fair to general relativity before saying anything critical about it, because its record is extraordinary and nothing in what follows is a complaint about its accuracy.

The record (1:36:11)

Einstein published the field equations in 1915. Almost immediately they explained something that had been quietly bothering astronomers for over half a century.

The orbit of Mercury precesses. The whole ellipse slowly rotates around the Sun, and most of that rotation is accounted for by the pull of the other planets. But a residue of about 43 arcseconds per century had refused to be explained. People had proposed an undiscovered planet to account for it, given it a name, Vulcan, looked for it, and not found it.

General relativity produced the missing 43 arcseconds with no adjustable parameters. The theory was not fitted to that result. The result fell out.

Then the predictions started arriving:

• Light bends when it passes a massive body, and by twice the amount Newtonian reasoning gives. Confirmed by observation of a solar eclipse in 1919 and refined a thousand times since.
• Clocks run slower in stronger gravitational fields. That sounds like an abstraction until you remember that the satellite navigation system in your pocket would drift by kilometres per day if the effect were not corrected for continuously.
• A rotating mass drags spacetime around with it. Frame dragging was measured directly by a dedicated satellite mission and by laser ranging to others.
• Massive objects can collapse to a state from which nothing escapes, and we have now photographed the shadow of two of them.
• Accelerating masses radiate ripples in spacetime that carry energy away. The orbital decay of a binary pulsar matched the predicted rate to within a fraction of a percent for decades before anybody detected those ripples directly.

Every one of those was a prediction first and an observation second. That is as good as physics gets. By the standard of predictive accuracy, general relativity may be the most successful theory human beings have ever produced.

And it does not say what gravity is (1:38:19)

Now here is the thing nobody tells you about it.

General relativity says that mass and energy curve spacetime, and that objects move along the straightest available paths through the curved geometry that results. It specifies the relationship between the contents of a region and the curvature of that region with total precision, and from that specification everything above follows.

But ask the next question. Why does mass and energy curve spacetime? By what mechanism? What is the process by which the presence of a lump of matter causes the geometry around it to change?

General relativity has no answer. It does not attempt one. The field equations are a statement of correspondence, not of causation. They tell you that this amount of energy goes with that amount of curvature, the way an exchange rate tells you what a currency is worth without telling you anything about why.

The comparison that makes it obvious (1:39:24)

This is genuinely unusual, and the comparison with the other forces makes it obvious.

Electromagnetism has a mechanism. Charged particles interact by exchanging photons. That is not a metaphor or a bookkeeping device, it is a physical account of what is happening, and it makes quantitative predictions of terrifying accuracy. The electron's magnetic moment has been calculated from that account and measured experimentally, and theory and experiment agree to twelve significant figures. That is the most precisely verified prediction in all of science, and it rests on a story about what the force actually is and how it is transmitted.

The strong and weak nuclear forces have equivalent accounts with their own carrier particles.

Three of the four forces have a description and an explanation. Gravity has a description of unparalleled quality and no explanation at all. It is a theory that tells you what and refuses to tell you why.

The film asks you to hold that phrase, because it comes back at the end and means something larger there.

Why quantizing it has never worked (1:40:35)

The obvious move, the one physics has been attempting since roughly the 1930s, is to give gravity the same treatment that worked for the others. Quantize it. Find its carrier particle. Write down a quantum field theory of gravity, run the machinery, extract predictions.

It has never worked, and the technical reason has a name: renormalization.

When you calculate anything in quantum field theory, you find yourself summing over an infinite range of possible intermediate processes, and the sums come out infinite. This happens in electromagnetism too. The trick that rescues electromagnetism is that all those infinities can be absorbed into a finite number of measured quantities, like the electron's mass and charge. You measure those once, experimentally, and every infinity in the theory disappears into them. After that the theory predicts everything else cleanly and forever. That is what it means for a theory to be renormalizable.

Gravity is not renormalizable in that sense. When you attempt the same procedure, the infinities do not fall into a finite set of buckets. Each order of the calculation produces new kinds of infinity requiring new quantities to absorb them, and the number of quantities you would have to measure experimentally is unbounded.

A theory that requires infinitely many measured inputs before it can predict anything is not predicting anything.

The conflict of temperament (1:42:00)

Underneath the technical failure sits a conflict of temperament between the two theories, and the film says it is worth seeing plainly because it is the reason the marriage has never taken.

General relativity is a theory of smooth, continuous geometry. Spacetime in general relativity is a surface, differentiable everywhere, with a definite shape at every point.

Quantum mechanics is a theory in which definite values are the exception. Things do not have positions until something forces the question. Quantities fluctuate, and the fluctuations are not ignorance about a hidden truth. They are the truth.

Where is the curvature? (1:42:50)

Now put the two together and watch what happens.

Take a single atom and place it in a superposition of two locations, which is an ordinary laboratory procedure done thousands of times a day. The atom has mass. Mass curves spacetime.

So where is the curvature?

There is no available answer:

• You cannot say the curvature is in both places, because general relativity does not permit spacetime to have two shapes at once.
• You cannot say it is in neither, because the mass is real.
• You cannot say the atom's position resolves first, because nothing in quantum mechanics privileges gravity that way.

The question is perfectly reasonable, requires only physics that both theories claim to govern, and cannot be answered by either. That is not a gap in a calculation. That is two descriptions of reality that cannot both be about the same world.

The hope that closed in 1986 (1:43:51)

For a while it was possible to hope that the divergence was an artifact of doing the calculation badly, and that at some order things would tidy themselves up. In 1986, Goroff and Sagnotti carried out the calculation for pure gravity at second order and showed explicitly that the divergence is there and cannot be absorbed.

The hope closed.

That result is why the serious candidate theories look the way they do. String theory proposes that the fundamental objects are not points but extended, which softens the short distance behaviour that generates the infinities. Loop quantum gravity proposes that spacetime itself is granular at the smallest scale, so that the infinitely small distances driving the divergences do not exist to begin with.

Both are enormous intellectual structures built by serious people over decades. Neither has produced a single prediction that has been experimentally tested and confirmed.

The film is explicit that this is not an accusation of failure on the part of the theorists. It is a statement about where the relevant physics lives. The energy scale at which quantum gravitational effects should become obvious is something like fifteen orders of magnitude beyond the reach of the most powerful particle accelerator ever built. Closing that gap with current approaches would require an accelerator of a size that is not merely expensive but geographically implausible.

So the situation is this. We cannot measure the constant reliably. We cannot verify the law at the smallest and largest distances. We cannot explain why the force is so weak. We cannot say what the force is. And we cannot quantize it, because the mathematics refuses and the experiments are out of reach.

At which point a reasonable person asks the obvious question. If we cannot get at this theoretically, can we get at it experimentally from the other end? Forget the accelerator. If gravity is quantized, there should be a particle. Find the particle.

There is a name for it. It has been named since the 1930s. And there is a very good argument that we will never catch one.

Part thirteen: the particle we may never catch (1:46:14)

If gravity is a quantum field like the others, it has a quantum: a smallest possible unit, a particle. And we know a surprising amount about what that particle would have to be like, purely from the behaviour of gravity itself, without ever having seen one.

Massless, and spin two (1:46:58)

It has to be massless, because gravity reaches across the entire universe without weakening beyond the inverse square. A force carried by a massive particle has a limited range, which is why the weak nuclear force does not reach past the inside of a nucleus. Gravity reaches everywhere. Its carrier weighs nothing.

It has to have a spin of two, and that is the more interesting requirement. Spin in this context is a property describing how a particle's field behaves under rotation, and it determines something you would not expect it to determine: who attracts whom.

A spin one carrier, like the photon, produces a force in which like charges repel and opposite charges attract. That is why electricity comes in two flavours that cancel. A spin two carrier produces a force in which everything attracts everything, with no cancellation available, because there is only one kind of gravitational charge and it is positive mass energy.

Why the weakest force built everything (1:47:40)

That single fact explains something about the universe you have taken for granted your whole life.

Electromagnetism is by far the stronger force. And yet the universe is not organized by it, because positive and negative charges sit next to each other and cancel out almost perfectly at any distance. Gravity has nothing to cancel against. Every gram adds.

So the weakest force, given enough matter and enough time, is the one that builds planets and stars and galaxies, simply because it never stops accumulating while the strong one keeps neutralizing itself.

The graviton, and Dyson's conjecture (1:48:19)

The particle even has a name, which it acquired in the 1930s, long before anyone had a coherent theory to put it in. It is called the graviton.

Nobody has ever detected one. And there is a serious argument, made by serious people, that nobody ever will.

The argument is usually traced to Freeman Dyson, who was blunt about it. His position was not that graviton detection is technically difficult. It was that no conceivable experiment in the real universe could accomplish it, which is a much stronger claim, and one that would place the question permanently outside the reach of science rather than merely beyond our current means.

Rothman and Boughn worked it through (1:49:01)

The claim was examined properly rather than left as an aphorism. Tony Rothman and Stephen Boughn worked through it in detail in a paper published in Foundations of Physics in 2006.

Their finding was carefully stated and the film repeats it accurately: it is possible, they concluded, to construct an idealized thought experiment in which a single graviton is detected, but once anything remotely resembling realistic physics is taken into account, the detection becomes impossible. Their assessment was that Dyson's conjecture is very likely true.

The obstacles compound almost comically (1:49:43)

And the way the obstacles compound is almost comic:

• Gravity's coupling to matter is so absurdly feeble that the probability of any given atom absorbing any given graviton is beyond negligible. So your detector has to be enormous.
• Make it enormous and it becomes massive. And if you keep going, a detector of sufficient mass concentrated in one place simply collapses under its own gravity into a black hole, which is not a useful instrument.
• Meanwhile, any environment producing gravitons in quantity is also producing neutrinos in overwhelming quantity, and neutrinos interact far more readily than gravitons do. So the signal you want arrives buried under a flood of something you do not shield against the neutrinos, and you have added more mass to a detector that was already collapsing.

The problem is not engineering. Every approach fails for a different reason, and the reasons are all reasons of principle.

So this is the position. The theory cannot be quantized mathematically. The energy scale where it would matter is fifteen orders of magnitude beyond our reach. And the particle that would settle the question by direct evidence appears to be undetectable, not because we are not clever enough yet, but because the universe seems to be arranged so that it cannot be caught.

There are cleverer indirect approaches under development, aiming to demonstrate that gravity is quantum without ever catching its quantum, by showing that gravity can do something only a quantum field could do. Those efforts are real and ongoing and some of them are beautiful. None has succeeded yet, and the required sensitivities remain far beyond current capability.

The alternative nobody states (1:51:35)

The film pauses on the alternative, because it is rarely stated and it is not absurd.

Everyone assumes gravity must be quantum, on the grounds that everything else is, and the universe presumably does not run on two incompatible operating systems. But that is an assumption, not a result.

A minority of physicists have taken seriously the possibility that gravity is genuinely classical all the way down: that spacetime really is a smooth continuous thing, does not fluctuate, and that the correct picture has quantum matter sitting on a non quantum stage. Most of the field regards that as thoroughly unattractive and there are strong arguments against it.

But notice the shape of the situation. We cannot prove gravity is quantum. We cannot catch the particle that would prove it. And we cannot rule out the alternative either.

The most basic question you could ask about this force, whether it belongs to the same category of thing as everything else in physics, is open.

The fridge magnet, again (1:52:51)

And underneath all of it, unexplained, sits the number the film has brushed past twice and now looks at directly.

Go to your kitchen, take a magnet off the fridge. It is a small thing, a few grams, a piece of plastic coated ferrite, or a rare earth disc. It has no power source. Nothing is being spent to keep it working. It has been holding a shopping list to a metal door for years and it will keep doing so for decades.

Hold it a centimetre above a steel paperclip lying on the counter, and watch the paperclip jump.

Now consider what just happened. Beneath that paperclip is the entire Earth. Six thousand billion billion tons of iron and rock and water, every atom of it pulling downward on that scrap of steel continuously, with the full and undivided strength of planetary gravity. That pull is the reason you cannot jump more than a metre off the ground. It is the reason the atmosphere stays. It holds the oceans in their basins and the Moon in its orbit.

And a few grams of iron in your fingers beat it without effort. Not narrowly. There is no contest, no moment where the paperclip hesitates between the planet and the magnet. The planet was never a serious competitor.

The electromagnetic force between two protons exceeds the gravitational force between them by something on the order of 10³⁶, which is why an object you could swallow can overrule a world.

Nobody knows why that ratio has the value it has.

What kind of ignorance this is (1:54:00)

The film is careful about what kind of ignorance this is, because it is not the ordinary kind.

This is not a quantity we have failed to measure precisely. We have measured it fine. It is not a quantity that is hard to define. It is perfectly well defined. It is a number that appears in nature, that no accepted theory derives, that no principle explains, and that seems arbitrary in a discipline whose entire premise is that nothing fundamental is arbitrary.

It has a name, the hierarchy problem, and the name is a piece of politeness. Naming something does not explain it.

The extra dimensions from Part ten were one attempt to dissolve it, by proposing that gravity is not weak at all but merely diluted across directions we cannot access. Other attempts exist. None has been confirmed.

The complete inventory of failure (1:55:15)

So the film lays out the case against ourselves plainly before turning the corner:

• We cannot agree on gravity's strength on a bench.
• We cannot test its law below the width of a hair, or above the size of a galaxy, without it failing or needing help.
• We cannot explain why it is 36 orders of magnitude weaker than everything else.
• We cannot say what it is.
• We cannot quantize it.

That is a fairly complete inventory of failure for the first force anybody ever wrote down.

Which makes what comes next very difficult to explain. Because in the middle of all this, physics also performed the single most precise measurement of anything, ever. And what it measured was gravity.

Part fourteen: a thousandth of a proton (1:56:06)

On the fourteenth of September 2015, two machines separated by thousands of kilometres of American landscape twitched seven milliseconds apart, which is about how long it takes something travelling at the speed of light to cross the distance between them.

Inside the detector (1:56:30)

The film takes you inside one of them. The detector is an L with each arm four kilometres long.

Down each arm runs a steel tube more than a metre wide, pumped down to one of the largest and emptiest artificial vacuums on Earth, because a stray air molecule drifting across the beam would ruin everything. A laser is split at the corner and sent down both arms at once. At the far end of each, a mirror weighing 40 kilograms hangs from a cascade of pendulums designed to isolate it from the ground, because the ground is never still. The light bounces back and forth hundreds of times, then returns to the corner, and the two beams are recombined so that in the ordinary case they cancel each other out perfectly and the detector sits in darkness.

That darkness is the measurement. Any change in the relative length of the two arms lets light through.

At that moment in September, a signal swept up through the detector's sensitive band, rising in frequency and amplitude over about two tenths of a second, and stopped. The same pattern appeared at the second detector in the other American state seven milliseconds later.

What had arrived (1:57:30)

What had arrived was a gravitational wave. The event is catalogued as GW150914, and it was detected by LIGO.

1.3 billion years earlier, two black holes of roughly 36 and 29 times the mass of the Sun had spiralled into each other and merged, converting about three solar masses of material into pure gravitational radiation in a fraction of a second. For that instant, the collision radiated more power than all the light of every star in the observable universe combined.

Then the ripple spread outward for 1.3 billion years, thinning as it went, until it reached a planet where in the meantime life had arisen and worked out what to build.

The stretch it produced in those four kilometre arms was about one part in 10²¹. In physical terms, the length of each arm changed by a distance thousands of times smaller than the width of a single proton.

We built something that could feel that. And we did not merely detect it. From the shape of the signal we read off the masses of both black holes, the distance to them, and the spin of what they became.

Now hold that beside the other thing (1:58:40)

In a quiet laboratory, in a stable room, with two spheres of metal sitting on a bench about ten centimetres apart, we cannot agree on how hard they pull on each other to better than a few hundred parts in a million.

Those two facts are true at the same time, on the same planet, in the same decade, often in the same institutions.

We can hear two black holes collide across 1.3 billion light years by measuring a change in length smaller than a proton. And we cannot settle an argument about two lead balls on a table.

And it is not only the waves (1:59:30)

The MICROSCOPE satellite spent two and a half years in orbit doing one thing: watching two test masses, one titanium alloy and one platinum alloy, fall around the Earth together, checking whether different materials fall at different rates.

Its final result, published in 2022, found no difference at the level of a few parts in 10¹⁵. Galileo's proposition that all things fall alike, the equivalence principle, has now been confirmed to a precision of one part in a thousand million million.

And lunar laser ranging, as we saw, shows that the strength of gravity is not drifting over time to better than one part in ten trillion per year.

Every triumph is a relationship. Every failure is a quantity. (2:00:14)

So here is the shape of it, and this is the answer to the question the film started with.

We can measure that gravity is not changing, superbly. We can measure that all things fall alike, superbly. We can measure the ripples gravity makes across a billion light years, superbly.

What we cannot measure is gravity itself.

Every triumph on that list is a measurement of a relationship, a comparison, a ratio, a difference. Every failure is an attempt to get at the thing on its own, in units, as a quantity.

Which means the precision never failed.

The turn (2:00:51)

The film says most people reaching the end of a story like this would conclude that our instruments are not good enough yet, and that one day a better machine will come along and close the gap. That is the natural reading and it is the wrong one.

Look at the record again. The instruments have been improving continuously for 228 years and the disagreement has grown alongside them. In 1998 the official uncertainty was multiplied by twelve, and it was multiplied by twelve precisely because the new measurements were better. In 2018 the two finest determinations ever made contradicted each other, and they could only contradict each other because they were so sharp.

Blurry results agree. It takes precision to disagree properly.

The number gets sharper and the disagreement gets wider. That sentence has been sitting in the film since Part five, and here is what it actually means, because it is not a description of a problem. It is a definition.

Precision is not a way of getting closer to an answer. Precision is a way of finding out whether you understand something.

When you understand a thing, sharpening your instruments produces convergence, because everyone's errors are shrinking toward a shared truth. When you do not understand a thing, sharpening your instruments produces divergence, because each experiment's hidden assumptions become visible as its random noise falls away, and hidden assumptions do not agree with each other.

The disagreement was never noise obscuring the answer. The disagreement is the answer. It is the sound of a description being pushed past the edge of its own explanation.

And gravity is the place where physics has pushed hardest and found the edge closest.

What and why, from Newton to now (2:02:48)

Which brings back a phrase from earlier: general relativity is a theory that tells you what and refuses to tell you why. The film offered that as a criticism of one theory. It is not. It is the description of our entire relationship with this force, and it has been from the beginning.

Newton told us what gravity does and said openly that he would not pretend to know why. Einstein told us what gravity does in far greater detail and also declined. Every measurement since has been another statement of what, made more precisely, with the why untouched underneath.

228 years ago a man sat outside a shed in South London with his eye at a hole in the wall, watching a rod turn through an angle he could barely see, and people said he had weighed the world.

We are still weighing the world. The shed has become a chamber under a hill in Wuhan and a four kilometre vacuum tube in the Louisiana pine forest. The lead spheres are still lead spheres. And the answer is still not settled. Not because we have been careless, but because we have been so careful that our carefulness has started reporting back on us.

That is why the more precisely we measure gravity, the less we understand it. Not because the measurements are failing. Because they are working exactly as designed, and what they are measuring is the size of the gap between what we can describe and what we can explain. Every time we sharpen the instrument, we see the gap more clearly.

It has never once let you go (2:04:25)

The closing lines, which are the best thirty seconds in the film:

You will feel it in a few hours when you stand up. Something will hold you to the floor, as it has every second of your life. With a strength nobody on this planet can state to more than five digits, by a mechanism nobody can name, obeying a law nobody has tested across most of the distances it claims to cover.

It has never once let you go.

Key takeaways

• Newton's law has no strength in it. It is a statement of proportionality: it tells you exactly how the force changes when you change the masses and the distance, and nothing about how big the force is. The constant that converts the proportion into actual newtons is not in his work, and could not have been, because nothing in the 1680s could detect the attraction between two objects in a room.
• Cavendish never calculated the gravitational constant. He measured the density of the Earth, got 5.48 times water against a modern 5.514, and did it by comparing one gravitational pull to another. That is a ratio, and ratios are forgiving. Extracting the raw quantity in units is a different and much harder problem.
• The units are the trap. The constant is length cubed per mass per time squared, so determining it means independently knowing a mass in kilograms. Every measurement of gravity's strength is also a measurement of a machined lump of metal, and the lump is the weak link. That is what makes it different in kind from constants that compare one quantum property to another.
• Gravity cannot be shielded and cannot be switched off. So everything in the room is in the experiment, and you can never take the control reading that would show you what your instrument is doing wrong. The errors that dominate are systematic, not random, which means more data makes you more confident rather than more right, and averaging two disagreeing laboratories gives you a number in the middle of two mistakes.
• 1998 is the documented event. CODATA multiplied its own uncertainty for the gravitational constant from 128 to 1,500 parts per million and stated the reason plainly: no explanation had been found for the large differences obtained in "the presumably more accurate measurements". No other fundamental constant has ever gone backwards in the official record.
• 2018 removed the last excuse. One team, thirty years, one underground laboratory, one set of masses, two techniques chosen specifically because they cannot share a mistake. Time of swing gave 6.674184 at 11.64 ppm, angular acceleration feedback gave 6.674484 at 11.61 ppm, and the 45 ppm gap is roughly four times either error bar. They published both.
• Nobody has ever measured the mass of the Sun. Orbits respond to the product of the constant and the mass, never to either alone. We know that product to about ten significant figures, and dividing by a constant known to five leaves a mass known to five. Every stellar, galactic and cluster mass ever written down inherits that ceiling.
• The inverse square law has been checked across a band with darkness at both ends. It holds exactly down to about 52 micrometres and nobody has looked below that. Out at galactic scale it returns the wrong answer unless you add five or six times more matter than you can see, or change the rule. At cosmological scale the sign flips entirely.
• General relativity describes gravity perfectly and explains nothing about it. The field equations are a statement of correspondence, not causation. Three of the four forces have a mechanism with a carrier particle; gravity has predictive accuracy of the highest order and no account of why mass curves spacetime. It cannot be renormalized, its energy scale is fifteen orders of magnitude out of reach, and its carrier particle may be undetectable in principle.
• The closing argument is the point of the whole film. Precision is not a way of getting closer to an answer, it is a way of finding out whether you understand something. Understanding produces convergence as instruments sharpen; misunderstanding produces divergence, because hidden assumptions surface once random noise falls away. The disagreement is not noise obscuring the answer. It is the answer.

Chapters

• 0:00 Two bags of sugar, and the number Newton never had
• 1:26 Part one: the force you think is finished
• 4:50 Newton's law is a proportionality, not a strength
• 5:58 Why astronomy never needed the constant
• 7:06 1798, and the thing nobody expected
• 9:11 Part two: the man who weighed the world
• 10:20 The instrument belonged to a clergyman who had died
• 11:29 The torsion balance: a wire that barely resists
• 12:58 Picture the shed. He cannot be in the room.
• 14:24 Seventeen runs, and no gravitational constant
• 15:51 Newton's back of the argument guess at the density of the Earth
• 17:48 Part three: the number nobody named
• 19:43 Boys, fused quartz, and the arrow fired across a room
• 21:38 What the number actually is: 6.6743 × 10⁻¹¹
• 22:51 The mass hiding inside the units
• 24:40 Part four: how weak is weak?
• 25:30 A grain of salt, and seventy red blood cells
• 27:12 The fridge magnet that beats a planet, 10³⁶ to one
• 28:22 You cannot shield it, so everything in the room is in the experiment
• 29:51 You cannot turn it off, so you cannot run a control
• 31:02 Random errors are friendly. These are systematic.
• 32:17 Part five: the disagreement
• 32:59 CODATA 1986: 6.67259, and 128 parts per million
• 34:04 Braunschweig floats the balance on mercury, and lands 7,000 ppm away
• 35:51 Seattle builds a turntable so the fibre never twists
• 36:51 Paris sits high, Boulder sits low
• 37:44 Cold atoms: the great hope from outside
• 38:38 Two families of experiment, systematically offset
• 39:18 A 500 ppm band, and twenty sigma as the background condition
• 40:52 Vagueness had been holding the field together
• 42:09 Part six: the year the uncertainty went up
• 42:54 "The presumably more accurate measurements"
• 46:20 Four decades of a constant that will not sit still
• 47:36 Kuroda, anelasticity, and a bias that does not cancel
• 50:23 Part seven: two answers in one cave
• 51:31 Thirty years underground, in human terms
• 52:57 The spheres are the hard part, and the distance is squared
• 54:08 Two methods chosen because they fail differently
• 56:00 Nature, August 2018: 6.674184 and 6.674484
• 56:40 The gap, and why it is heavier than every gap before it
• 57:21 They published both numbers
• 59:38 Part eight: the constant that refused
• 1:00:51 20 May 2019: the SI is rebuilt on fixed constants
• 1:02:51 Gravity is left standing outside the building
• 1:04:07 Dirac's shrinking G, and the mirrors on the Moon
• 1:06:18 Cycles, gravity shielding, and the impulse behind them
• 1:07:59 Part nine: we do not know what the Sun weighs
• 1:08:59 GM, the product that orbits actually respond to
• 1:11:02 Divide ten figures by five and you get five
• 1:13:04 Kepler's third law sidestepped the problem in advance
• 1:14:25 Where the mass itself is the thing you want
• 1:15:55 Part ten: the law at the edges
• 1:16:26 Patch potentials, static, and the Casimir force
• 1:17:24 The inverse square holds down to 52 micrometres
• 1:18:21 Extra dimensions, and the hierarchy problem
• 1:20:21 Rotation curves: Zwicky, then Rubin and Ford
• 1:21:32 Dark matter, and the Bullet Cluster
• 1:22:32 Milgrom 1983, and an acceleration of 1.2 × 10⁻¹⁰
• 1:23:19 The honest scorecard between the two escapes
• 1:26:16 Part eleven: the force that pushes
• 1:26:55 Type Ia supernovae, and a result nobody believed
• 1:28:01 Negative pressure, and repulsive gravitation
• 1:28:45 Sixty eight, twenty seven, and five percent
• 1:29:20 Einstein's 1917 term returns, doing the opposite job
• 1:30:06 One hundred and twenty orders of magnitude
• 1:31:45 The greatest blunder he probably never called it
• 1:32:27 The coincidence problem
• 1:33:40 Three scales, three completely different failures
• 1:35:55 Part twelve: a theory with no mechanism
• 1:36:11 Mercury's 43 arcseconds, and every prediction since
• 1:38:19 It does not say what gravity is
• 1:39:24 Electromagnetism has a mechanism. Gravity has none.
• 1:40:35 Renormalization, and why gravity refuses it
• 1:42:00 Smooth geometry against a theory of fluctuation
• 1:42:50 An atom in two places. Where is the curvature?
• 1:43:51 Goroff and Sagnotti close the hope in 1986
• 1:46:14 Part thirteen: the particle we may never catch
• 1:46:58 Massless, spin two, and why everything attracts
• 1:47:40 Why the weakest force is the one that built galaxies
• 1:48:19 The graviton, and Dyson's conjecture
• 1:49:01 Rothman and Boughn, Foundations of Physics, 2006
• 1:49:43 The detector that collapses into a black hole
• 1:51:35 The alternative: gravity classical all the way down
• 1:52:51 Six thousand billion billion tons, beaten by a fridge magnet
• 1:54:00 What kind of ignorance the hierarchy problem is
• 1:55:15 The complete inventory of failure
• 1:56:06 Part fourteen: a thousandth of a proton
• 1:56:30 Inside the four kilometre arms
• 1:57:30 GW150914: two black holes, 1.3 billion years, three solar masses
• 1:58:40 Hold that beside two lead balls on a bench
• 1:59:30 MICROSCOPE, and all things falling alike to one part in 10¹⁵
• 2:00:14 Every triumph is a relationship. Every failure is a quantity.
• 2:00:51 The turn: precision is how you find out whether you understand
• 2:02:48 What and why, from Newton to now
• 2:04:25 It has never once let you go

Notable quotes

Gravity is introduced as furniture. It was here before the lesson started and it will be here after things fall. 1:52

What Newton had was a shape. He knew how gravity behaves. He did not know how much of it there is. 5:20

A wire that barely resists will respond to a force that barely exists. 11:45

He was off by about one percent, in 1798, in a shed, using an instrument built by a dead clergyman, operated through a hole in a wall, by a man who could not bring himself to speak to his own cook. 15:00

When physicists measure the electron's magnetic moment, they are comparing one quantum property against another quantum property, and quantum properties are identical everywhere and forever. When physicists measure the strength of gravity, they are comparing a force to a specific lump of metal that a specific person machined on a specific afternoon. And the lump of metal is the weak link. 23:40

The electromagnetic field of a small piece of iron you could lose in your pocket has defeated the entire gravitational pull of a planet that weighs six thousand billion billion tons. Not narrowly. It is not close. The planet was never really in the contest. 27:50

Shielding a gravity experiment from gravity makes the problem worse by definition. 28:40

Taking more readings does not remove a systematic error. It just makes you more confident in a wrong number. 31:20

Read that phrase again. The presumably more accurate measurements. There is a whole worldview quietly collapsing inside the word presumably. 44:00

A constant that will not sit still is not misbehaving. The universe is not changing its mind. What is moving is us. 47:00

The gravity part of a gravity experiment is often not the hard part. 53:40

Neither one is an embarrassment against the wider field. That is not the problem. The problem is that they are an embarrassment to each other. 56:40

When one laboratory disagrees with itself, using two methods designed to have nothing in common, after thirty years of preparation, in a room inside a hill built specifically to remove every excuse, the space where the explanation was supposed to go is empty. 57:50

We know it is not moving far, far better than we know where it is. 1:05:40

Not by our telescopes, not by our spacecraft, not by our theory, but by two lead spheres on a bench that nobody can agree about. 1:11:40

The gap between the two numbers is not a fact about the Sun at all. It is a fact about us. 1:12:30

That is real progress. It is also progress by elimination, which tells you where something is not and never where it is. 1:19:40

One explanation works beautifully on galaxies and fails on everything larger. The other works beautifully on everything larger and has never been seen. 1:24:40

The whole of the material universe, as we have ever known it, is a rounding error in the accounting. 1:29:00

That is what a description does. It is not what an explanation does. 1:34:40

Gravity has a description of unparalleled quality and no explanation at all. It is a theory that tells you what and refuses to tell you why. 1:39:50

That is not a gap in a calculation. That is two descriptions of reality that cannot both be about the same world. 1:43:20

So the weakest force, given enough matter and enough time, is the one that builds planets and stars and galaxies, simply because it never stops accumulating while the strong one keeps neutralizing itself. 1:47:50

Not because we are not clever enough yet, but because the universe seems to be arranged so that it cannot be caught. 1:50:40

We can hear two black holes collide across 1.3 billion light years by measuring a change in length smaller than a proton. And we cannot settle an argument about two lead balls on a table. 1:59:00

Blurry results agree. It takes precision to disagree properly. 2:01:10

The disagreement was never noise obscuring the answer. The disagreement is the answer. It is the sound of a description being pushed past the edge of its own explanation. 2:01:50

We are still weighing the world. The shed has become a chamber under a hill in Wuhan and a four kilometre vacuum tube in the Louisiana pine forest. The lead spheres are still lead spheres. And the answer is still not settled. Not because we have been careless, but because we have been so careful that our carefulness has started reporting back on us. 2:03:40

Something will hold you to the floor, as it has every second of your life. With a strength nobody on this planet can state to more than five digits, by a mechanism nobody can name, obeying a law nobody has tested across most of the distances it claims to cover. It has never once let you go. 2:04:30

Resources mentioned

The video

• The More Precisely We Measure Gravity, The Less We Understand It, by Sundown Science

People

• Isaac Newton and the Principia, 1687, the law without the number in it
• Henry Cavendish, whose 1798 paper measured the density of the Earth, not the constant
• John Michell, who built the apparatus, described a black hole in 1783, and died in 1793 without using it
• James Clerk Maxwell, who went through Cavendish's unpublished notebooks in the 1870s
• Charles Vernon Boys, who replaced the wire with fused quartz and shrank the instrument
• Alfred Cornu and Baille, France, 1870s, among the first to state the constant as a number
• Loránd Eötvös, the Hungarian physicist the Eöt-Wash group is partly named for
• Terry Quinn and the team at the BIPM outside Paris
• Jun Luo, who decided decades ago that gravity could not be measured in a normal building
• Albert Einstein, the field equations of 1915, and the cosmological constant of 1917
• Paul Dirac and the large numbers hypothesis, 1937
• George Gamow, the secondhand source for the "greatest blunder" line
• Fritz Zwicky, who spotted the missing mass in clusters in the 1930s and was ignored
• Vera Rubin and Kent Ford, whose 1970s rotation curves could not be dismissed
• Mordehai Milgrom, who proposed modified Newtonian dynamics in 1983
• Freeman Dyson, whose conjecture is that no graviton can ever be detected
• Galileo Galilei, whose proposition that all things fall alike is now confirmed to one part in 10¹⁵

Papers and results

• Kuroda, 1995, on anelasticity in torsion fibres and the systematic bias in time of swing measurements
• The PTB mercury bath result of 1995 and 1996, which landed about 7,000 ppm high
• Gundlach and Merkowitz, Physical Review Letters, 2000, the Seattle turntable that keeps the fibre at zero twist
• Quinn et al., 2001 and 2013, the BIPM apparatus run in two modes
• Parks and Faller, Physical Review Letters, 2010, the JILA laser interferometry result at the low end of the range
• Li et al., Nature, August 2018, the two HUST determinations, 6.674184 and 6.674484
• Lee et al., Physical Review Letters, 2020, testing the inverse square law down to 52 micrometres
• Arkani-Hamed, Dimopoulos and Dvali, 1998, large extra dimensions and the hierarchy problem
• Goroff and Sagnotti, 1986, showing the two loop divergence in pure gravity cannot be absorbed
• Rothman and Boughn, Foundations of Physics, 2006, on whether a single graviton can ever be detected
• The MICROSCOPE final result, 2022, no violation of the equivalence principle at a few parts in 10¹⁵
• GW150914, the first direct detection of a gravitational wave, by LIGO

Institutions and instruments

• CODATA, the Committee on Data for Science and Technology, which publishes the recommended values
• Physikalisch-Technische Bundesanstalt, Braunschweig, Germany
• The Eöt-Wash Collaboration at the University of Washington
• The International Bureau of Weights and Measures, Sèvres, outside Paris
• JILA, Boulder, Colorado
• Huazhong University of Science and Technology, Wuhan, and its underground laboratory
• LIGO, the four kilometre interferometers in Washington state and the Louisiana pine forest
• The MICROSCOPE satellite
• Lunar laser ranging, using the Apollo retroreflectors
• The Parker Solar Probe, which flew through the Sun's outer atmosphere
• The Event Horizon Telescope, which photographed the shadow of a black hole
• Gravity Probe B, which measured frame dragging directly

Concepts worth following up

• The gravitational constant and the torsion balance
• The standard gravitational parameter, GM, and Kepler's third law
• The 2019 revision of the SI, and the Planck constant, elementary charge, Boltzmann constant and Avogadro constant that were fixed by decree
• Systematic versus random error
• The Casimir effect and patch potentials
• Galaxy rotation curves, dark matter, the Bullet Cluster and the radial acceleration relation
• Type Ia supernovae, the accelerating expansion and dark energy
• The cosmological constant problem, the worst quantitative prediction in the history of science
• Renormalization, the graviton, string theory and loop quantum gravity
• Tests of general relativity, including Mercury's perihelion precession and the 1919 eclipse

Where it stands

Almost everything in this film is documented rather than argued, and it is worth separating the layers, because the closing thesis is doing more work than the history is.

Solid, and checkable. The CODATA record is public: the 1986 uncertainty of 128 parts per million, the 1998 blow up to 1,500, the wandering recommended value, the 22 parts per million that has stood since 2018 and was left alone in 2022. The 2018 Nature paper reporting two mutually exclusive determinations from one group is real and was published exactly as described, with both numbers side by side. The exclusion of the gravitational constant from the 2019 redefinition of the SI is a matter of record and for exactly the reason given: you cannot fix by decree a constant you know to only five figures. The 52 micrometre limit on short range tests, the constraints on any drift in the constant from lunar laser ranging, the MICROSCOPE result, and the GW150914 strain of one part in 10²¹ are all published numbers.

Fairly presented, though the film picks a side. On dark matter against modified dynamics, the scorecard given is honest and unusually even handed for a general audience treatment: it credits modified dynamics with genuinely predicting galactic rotation curves from visible matter alone, and it credits dark matter with the Bullet Cluster and the cosmic microwave background, and it names the four decade failure to detect a particle without pretending that settles anything. Mainstream cosmology is considerably more confident in dark matter than this framing suggests, and the film knows it, but nothing here is a distortion.

The part that is an argument, not a fact. The closing thesis, that divergence under sharpening instruments is a signature of not understanding something rather than a signature of technical difficulty, is a philosophical claim about measurement. It is a good one and the pattern it points at is real, but a working metrologist would offer a duller alternative: that unrecognized systematic errors are exactly what you expect in a quantity requiring absolute mass metrology at the limit, that they are being found and eliminated one at a time, and that nothing deeper needs to be invoked. The film's own evidence is compatible with both readings. Notice too that it briefly conflates scales for rhetorical effect and then immediately corrects itself, pointing out that 22 parts per million and 120 orders of magnitude are not remotely the same size of problem and share only a direction.

One small caution on the arithmetic. Two of the CODATA values are garbled in the video's captions, and the sequence only makes sense with the documented figures (6.67384 in 2010, 6.67408 in 2014), which is what this page uses; the direction the film describes, down and then up and then settling, is correct either way. And the masses of the Sun and planets are quoted as good to about one part in ten thousand, which is a slightly pessimistic rounding of the 22 parts per million ceiling the constant actually imposes. Neither changes anything about the story.

What survives all of that is the thing the title claims, and it survives intact. The oldest force in physics has the worst known number in fundamental physics; the number got worse in the official record because the experiments got better; the two finest determinations ever made contradict each other; nobody can tell you what the Sun weighs to more than four or five digits; and the theory that predicts gravity's behaviour more accurately than any theory has ever predicted anything still does not say what gravity is.