For me, a hurdle to get over was trying to understand in the context of my experience of the world. Like, popsci has this whole “is X a wave or a particle? Scientists still don’t know…” schtick. And our understanding at some level is, “here’s the math to describe this system.”
Getting away from always mapping that onto the world we experience is, IMHO, really important. Not that it should be understood solely as math, by any means! But you really need to throw away intuition gained from the macroscopic world we interact with.
My favorite example was looking at reflection coefficients and seeing that an “infinite wall” is the same as an “infinite cliff” — you’ll reflect off of both. Which makes zero sense if you imagine driving a bumper car into a wall (bounce back) vs. over an infinite cliff! But it does me make sense in its own way, and after building up intuition, so do other “weird” and counterintuitive things.
Waves are underrated in pop-sci context. Even classical waves you can make with household items like strings can have counterintuitive and cool behaviors!
Absolutely. As a kid I liked to see how many nodes I could get into ‘simple’ system of rotating a jump rope tied to something fixed at one end. I can’t say my understanding of harmonics is great now, but I can at least relate it to personal experience.
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.
For me, a hurdle to get over was trying to understand in the context of my experience of the world. Like, popsci has this whole “is X a wave or a particle? Scientists still don’t know…” schtick. And our understanding at some level is, “here’s the math to describe this system.”
Getting away from always mapping that onto the world we experience is, IMHO, really important. Not that it should be understood solely as math, by any means! But you really need to throw away intuition gained from the macroscopic world we interact with.
My favorite example was looking at reflection coefficients and seeing that an “infinite wall” is the same as an “infinite cliff” — you’ll reflect off of both. Which makes zero sense if you imagine driving a bumper car into a wall (bounce back) vs. over an infinite cliff! But it does me make sense in its own way, and after building up intuition, so do other “weird” and counterintuitive things.
Waves are underrated in pop-sci context. Even classical waves you can make with household items like strings can have counterintuitive and cool behaviors!
Absolutely. As a kid I liked to see how many nodes I could get into ‘simple’ system of rotating a jump rope tied to something fixed at one end. I can’t say my understanding of harmonics is great now, but I can at least relate it to personal experience.
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.