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  • When Galileo pointed his telescope at Jupiter in 1610, he was the first person to see the

  • giant orbs attached to it by springs.

  • His actual drawings, compared night after night, show these bright spots moving back

  • and forth past Jupiter, exactly the same as if they were balls hanging off of springs.

  • I mean, yeah Galileo was looking at the moons of Jupiter, but if you plot their motion back

  • and forth and back and forth over time, it forms a sine wave.

  • And that motion is mathematically identical to the motion of something bouncing up and

  • down on a spring with a linear restoring force - also sine waves over time.

  • From a side-on perspective that projects two dimensions down to one, things in circular

  • orbits look exactly like theyre springing back and forth on giant coils of wire.

  • Now, I’m not saying that we should think of the moons of Jupiter as being held on by

  • giant invisible springs, but it’s a valid mathematical model when viewing them from

  • a distanceitll make the same predictions about the motions of the moons as theorbiting

  • in circles due to invisible gravitymodel, and one can be mathematically transformed

  • into the other.

  • The moons of Jupiter aren’t alone in having multiple mathematical descriptions: projectiles

  • and storms on earth experience a force (called the Coriolis effect) that causes them to turn,

  • but viewed from an external perspective, the projectiles and storms are what goes in a

  • straight line while the earth turns beneath them.

  • Both models, if you use them carefully, make correct predictions about reality.

  • And quantum phenomena can be modeled in at least three different ways that all give the

  • same predictions: as a particle being guided by a spread-outpilot wave”, or as a

  • spread out probability wave that collapses to a single point, or as a particle exploring

  • all possible paths it could take and interfering with itself along the way.

  • All three of these mathematical models suggest different ways of thinking about what’s

  • actuallygoing on in quantum mechanics, and the fact that all of them give the same

  • experimental predictions suggests that perhaps none of them is therightway to picture

  • what’s happening in quantum systems.

  • Mathematical models give us nice, easy-to-digest pictures of how the universe works: moons

  • orbit around planets, atoms bind together into molecules, electrons are clouds of probability,

  • and so on.

  • But we need to be careful how much weight we give to the models in our heads (or on

  • our blackboards, or computer screens).

  • Do Jupiter’s moons move like theyre pulled back and forth by the invisible force of springs?

  • Or held in orbits by the invisible force of gravity?

  • Or are they following helical paths which are actually straight lines in curved spacetime?

  • The way we describe the world influences the way we think the world is, even when there

  • are other, equally correct ways of describing the world that paint entirely different pictures

  • from our own.

  • That’s not to say we should accept wrong ideas, but we should be aware that sometimes

  • a different correct picture, one we haven’t considered, is the one we need to see.

  • Hey, Henry here, thanks for watching.

  • This video has been supported by Audible.com, as you may know, a leading provider of audiobooks

  • including fiction, non-fiction and periodicals.

  • You can get a free 30-day trial at audible.com/minutephysics, and I’d like to recommend the bookThe

  • Power of Habitby Charles Duhigg, which explores how we form habits, how to break

  • them, and how to use them to your advantageit’s a good one.

  • You can listen toThe Power of Habitor another book of your choice, with a free

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When Galileo pointed his telescope at Jupiter in 1610, he was the first person to see the

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