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  • It's well known that gravity pulls two objects together with a force proportional to the

  • mass of one, times the mass of the other, divided by the square of the distance between

  • them.

  • . Anyway, this equation is called Newton's law of universal gravitation, it's taught

  • to school children the world over, and it predicts the motions of the planets and moons

  • and asteroids in our solar system with incredible precision.

  • However, Newton's law of universal gravitation isn't actually a universal law: first, we

  • know that when the gravitational force in question is really strong, Newton's law

  • is just wrong . And second, we know that when the gravitational force in question is really

  • weak , we don't know whether it's right or wrong because gravity gets too weak to

  • measure.

  • Only in between (like, on the scale of the solar system), do we know that thelaw

  • of gravitation reasonably applies .

  • Ok, but if Newton's Law of gravitation has been confirmed so accurately by the motions

  • of planets and moons, how could it be wrong at a different scale?

  • Well, the earth looks flat when you're relatively close to the ground, but zoom out and it looks

  • round, or zoom in and it looks bumpy; thelawdescribing the shape of the earth

  • is different at different scales.

  • Similarly, when the force of gravity is really strong (like near a black hole), gravity is

  • better described by the mathematics of general relativity, and only when the forces in question

  • get a bit weaker (for things farther apart or with less mass) does gravity start to match

  • up with Newton's law of gravitation.

  • But when you go even weaker (with objects even farther away or even less massive ), we

  • get to a point where we don't know whether Newton's law of gravitation applies any

  • more.

  • And yet, even many physicists appear to be ignorant about our ignorance about how gravity

  • works when it's weak - or at least, they ignore our ignorance.

  • It's common to blindly apply -G m M/r^2 to decidedly non-astronomical objects, for

  • which we haven't tested gravitational attraction very well at all: if you have two pieces of

  • tape, you can calculate the gravitational force that they in principle exert on each

  • other according to the law of universal gravitation - but it's far too ridiculously ridiculously

  • small for you to ever have the remotest chance of noticing any effect whatsoever, let alone

  • actually checking that the attraction between them follows the law of universal gravitation

  • as you move the bits of tape farther apart.

  • In contrast, if you stick the two pieces of tape together and then pull them apart, they'll

  • exchange some electric charge and then measurably attract each other; an electrical attraction

  • which is a million billion times stronger than the predicted gravitational attraction

  • , and whose strength has allowed us to confirm Coulomb's law of electrical attraction to

  • a very very very high degree of accuracy .

  • So it makes sense to apply Coulomb's law of electrical attraction to objects at normal

  • human scales.

  • But testing Newton's law of gravitation at these scales requires very delicate experiments,

  • like very very sensitive oscillating pendulums that oscillate slightly differently if there's

  • a heavy mass nearby (and can thus measure the gravitational force with great precision),

  • or incredibly finely-controlled lasers that simultaneously levitate and measure the positions

  • and forces on tiny little beads of glass - these can measure ridiculously faint forces, like

  • zeptonewtons.

  • And so far, for objects a meter apart, we've only confirmed that the gravitational attraction

  • between them follows the law of universal gravitation to within around one one hundredth

  • of a percent . Which is a trillion times less precise than our knowledge of the equivalent

  • law for electricity.

  • And our grasp on gravity gets worse the smaller you go - Here's a plot showing how our uncertainty

  • about Newton's gravitational law varies across a whole range of distances - small

  • distances on the left, big distances on the right; and the higher the line the higher

  • the uncertainty.

  • Which, you will notice, is very high on the left.

  • Our existing experimental understanding of short-distance gravity is so bad that gravity

  • at the scale of the atomic nucleus could actually be as much as a quadrillion quadrillion times

  • stronger than Newton's law of gravitation predicts!

  • That's a HUGE range; it would be like not knowing whether the moon pulls on us with

  • the force of a hundred billion billion tons of rock , or the force of a fruit fly . Or,

  • put another way, at the scale of an atomic nucleus, the law of gravitation could depend

  • instead on the square of one or both masses, or the square root, or the inverse cube of

  • the distance, or G could be a million billion times bigger, or a bunch of other possibilities,

  • and we wouldn't even know it.

  • .

  • The fact that there's so much uncertainty about gravity at short distances means that

  • a lot of interesting truths about our universe could be hiding under our very noses!

  • One possibility, for example, is that there are not just 3 dimensions of space, but an

  • extra one that only the gravitational force can travel through, which loops back on itself

  • at the scale of micrometers or smaller . Just like how the surface of a hair is technically

  • 2-dimensional but hairs look one dimensional from afar, this would mean that at distances

  • much much longer than a micrometer, gravity would act as if space had 3 dimensions and

  • follow a roughly inverse square law (which is what Newton's law of gravitation is),

  • while at distances much shorter, it would behave as if space had 4 dimensions and follow

  • more of an inverse cube law (which we haven't ruled out at particularly small scales) .

  • However, as we've made increasingly precise measurements of the gravitational attraction

  • between small things, we haven't yet discovered any gravitational forces inconsistent with

  • Newton's law of gravitation . so it may be that -G m M over r squared does describe

  • the strength of gravity for very very short distances; but our uncertainty is still very

  • big, and it remains pretty crazy to blindly apply Newton's law of gravitation to things

  • like an electron and proton in a hydrogen atom.

  • This video was made with the support of the Heising-Simons Foundation, which also supports

  • research in precision measurement of the strength of gravity at short distances.

  • These experiments are super cool, because they're small, simple, clever, and are testing

  • our fundamental understanding of physics without the need for giant multi-billion-dollar particle

  • accelerators.

  • Thanks again to the Heising-Simons Foundation for supporting MinutePhysics, and for supporting

  • fundamental physics research.

It's well known that gravity pulls two objects together with a force proportional to the

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我们对重力的无知(Our Ignorance About Gravity)

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    joey joey 發佈於 2021 年 04 月 29 日
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