- #1
V0ODO0CH1LD
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I am going to explain what I am looking for, of course all the while hoping that what I am looking for actually exists, by talking about how I got comfortable with the idea of harmonic oscillators.
I never quite understood why the forces on a harmonic oscillator were of the form ## F=-kx ##, I just accepted that it was an empirical fact. People measured infinitely many springs and all kinds of oscillating "things" in laboratories and by some awesome coincidence they all turned out to obey this one law. Nature was compliant.
It wasn't until I read this one article that I realized that things were not so simple. The whole idea of ## F=-kx ## coming from taylor series approximations of the potential energy was fascinating! It is not a coincidence that all things that oscillate around their state of equilibrium behave the same. It's just that they can all be reduced to the same approximation.
So that is what I am looking for with gravity. And what I've been trying to look for in everything else since the harmonic oscillator insight. It's hard to believe that two things like gravity and electricity have force laws so similar. Did someone really run enough experiments that the data just screamed ## F=G\frac{m_1m_2}{r^2} ##? Or is there another perspective?
And in general; are most laws of physics achieved by the same "technique" as the harmonic oscillator force law? As in, it makes sense theoretically, let's see if nature rolls with it?
I never quite understood why the forces on a harmonic oscillator were of the form ## F=-kx ##, I just accepted that it was an empirical fact. People measured infinitely many springs and all kinds of oscillating "things" in laboratories and by some awesome coincidence they all turned out to obey this one law. Nature was compliant.
It wasn't until I read this one article that I realized that things were not so simple. The whole idea of ## F=-kx ## coming from taylor series approximations of the potential energy was fascinating! It is not a coincidence that all things that oscillate around their state of equilibrium behave the same. It's just that they can all be reduced to the same approximation.
So that is what I am looking for with gravity. And what I've been trying to look for in everything else since the harmonic oscillator insight. It's hard to believe that two things like gravity and electricity have force laws so similar. Did someone really run enough experiments that the data just screamed ## F=G\frac{m_1m_2}{r^2} ##? Or is there another perspective?
And in general; are most laws of physics achieved by the same "technique" as the harmonic oscillator force law? As in, it makes sense theoretically, let's see if nature rolls with it?