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 they’re 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 distance – it’ll make the same predictions about the motions of the moons as the “orbiting

in circles due to invisible gravity” model, 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-out “pilot 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

“actually” going on in quantum mechanics, and the fact that all of them give the same

experimental predictions suggests that perhaps none of them is the “right” way 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 they’re 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.

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