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3 months agoI found some under the couch cushions! 
cosecantphi [he/him]
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Joined 4 years ago
Cake day: July 27th, 2020
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Understanding classical waves better is what helped me wrap my mind around the physical meaning of the uncertainty principle. It’s not a technical limitation, and it’s not just because you need to interact with something to measure it. It’s just a property of waves. Since small enough particles exhibit the properties of waves, it only makes sense that we can’t know their location and momentum at the same time with arbitrary precision.
The velocity of a wave is a function of its frequency and wavelength. But imagine a highly localized wave, essentially just a peak. What’s its frequency? Well, we find that it doesn’t have one frequency! If you decompose the wave, you find its mathematically a superposition of multiple sine or cosine functions with different frequencies and therefore velocities. So the more localized the wave is, i.e the more you know its position, the less and less you know about its frequency and therefore velocity.
This stuff blew my mind when it was first explained to me.
The reason you need to slow down is because you’re starting on Earth, which means you’re moving fast enough parallel to the sun’s surface that for every foot you fall downwards toward the sun, the sun’s surface curves away by 1 foot. This results in the nearly circular orbit around the sun we exist in.
If you start speeding up, the orbit becomes more elliptical, except your aphelion starts raising away from the sun because now you’re moving fast enough that you’ve moved more than 1 foot sideways in the time you’ve fallen 1 foot downwards.
Slowing down has the opposite effect. If you get your speed down to 0, you’ll fall straight down toward the sun as normal with gravity. But you don’t need to go all the way down to 0 velocity to enter the sun, you just need to slow down until your elliptical orbit brushes up against the sun’s surface. If you then want to speed back up to avoid falling into the sun, you need to do it parallel to the sun’s surface. At this point, speeding up toward the sun will actually make you fall into the sun faster.
So basically the problem isn’t that you’re moving too fast to fall into the sun. By virtue of Earth’s orbit, you’re moving too fast in a direction away from hitting the sun’s surface.