Subtitles section Play video Print subtitles 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. 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 book “The Power of Habit” by Charles Duhigg, which explores how we form habits, how to break them, and how to use them to your advantage – it’s a good one. You can listen to “The Power of Habit” or another book of your choice, with a free 30-day trial at Audible.com/minutephysics. Thanks again for watching, and thanks to audible for supporting these videos.

B1 jupiter audible invisible mathematical quantum galileo How Perspective Shapes Reality 20 1 林宜悉 posted on 2020/03/28 More Share Save Report Video vocabulary