The sad reason for that is that it’s a conversation killer. I would love to go back and forth for hours on things like the uncanny similarity between universal gravitation and Coulomb’s law. But, when I speak to someone with a similar background to mine it’s all…work-work-work-how-is-it-applied??, and when I speak to someone without that background it’s all yawns.
It’s a shame because in either case I think science is the most interesting topic. It’s just as edifying to dive casually into the philosophy as it is to dive rigourously into the maths. I learn more per unit time from either type of conversation than from studying papers. And, it’s a passion, but one whose expression is stymied either by explaining it in terms of football fields per dolphin or by making it marketable. Interaction with other minds is the most valuable type of learning.
I feel like I may come off as a bit of an elitist writing this, but the problem really is the opposite: I wish more people would get involved!
Well that’s lovely, thank you 😊
So Newton’s law of universal gravitation is:
F= G×M×m/r^2
which is simple enough to be able to say it in a sentence: "the force of gravity F on two masses M and m is proportional to their masses and square of the distance between them, r " so the heavier and closer planets/suns/black holes are, the greater the gravitationnel pull.
Coulomb’s law is:
F= k×Q×q/r^2
which is pretty much exactly the same as you have probably noticed: "the force of electrical attraction F on two charged particles Q and q is proportional to their charges and the square of the distance between them, r "
So the exact same rule applies to planets and atoms. Their behaviour can be explained in the same way. It’s called an “inverse square law”, it’s got a name because they happen everywhere. And it’s just, like… Why? Why does the universe work that way? You’re not really encouraged to ask that sort of question as a science student, because it “goes nowhere” and doesn’t lead to actionable results. But I think it quite spooky. There are loads of weird results like that in science and maths (see quantum theory for abundant examples!) but it’s unusual to be able to sit and think about it. There is, for the inverse square law, a pretty elegant mathematical explanation for why they’re so common, but it doesn’t quite scratch the itch for me, it just raises more questions
Edit sorry for text wall. This is probably why I shouldn’t do this!
I dunno, it’s an inverse square. Are we going to get excited each time something has a linear relationship to another thing? What makes the inverse square so special?
In my field of work (molecular biology) anything with a linear relationship gets exciting! I got an R^2 of .9968 last week that had me jumping for joy.
Bertrand’s theorem states that stable orbits are only possible for one single inverse distance relation (in classical mechanics): inverse square
If the law is not inverse square (or harmonic oscillator), there will be no long lasting orbits, no galaxy clusters, no galaxies, no star systems, no planet and moon pairs.
If the electrostatic force wasn’t inverse square, electromagnetic force would look much different. No gauss law would be possible.
There’s a lot of things which are required to be exactly as we observe them to be for our surroundings to work out as we observe them to be. If they weren’t we wouldn’t be here to observe, or, at the very least, we’d be quite different.
Also as to other universes: Who says that any random universe with other laws ties together objects based on their mass. For all we know their attractive force could be relative to photon emissions and elves keep the orbit stable by strategically shining torches at the sky (ok that’s not that likely evolutionary speaking but we’re talking physics).
That’s why it’s interesting that inverse square is in electrostatic and gravitational forces only. Weak and strong force don’t follow inverse square.
And we don’t see the highly complex organization inside the nucleus that we see outside it (otherwise we’d have stable orbits inside the nucleus as well)
The sad reason for that is that it’s a conversation killer. I would love to go back and forth for hours on things like the uncanny similarity between universal gravitation and Coulomb’s law. But, when I speak to someone with a similar background to mine it’s all…work-work-work-how-is-it-applied??, and when I speak to someone without that background it’s all yawns. It’s a shame because in either case I think science is the most interesting topic. It’s just as edifying to dive casually into the philosophy as it is to dive rigourously into the maths. I learn more per unit time from either type of conversation than from studying papers. And, it’s a passion, but one whose expression is stymied either by explaining it in terms of football fields per dolphin or by making it marketable. Interaction with other minds is the most valuable type of learning.
I feel like I may come off as a bit of an elitist writing this, but the problem really is the opposite: I wish more people would get involved!
I’m a person without that background and I’ll talk about it. What’s the uncanny similarity you mentioned?
Well that’s lovely, thank you 😊 So Newton’s law of universal gravitation is:
F= G×M×m/r^2
which is simple enough to be able to say it in a sentence: "the force of gravity F on two masses M and m is proportional to their masses and square of the distance between them, r " so the heavier and closer planets/suns/black holes are, the greater the gravitationnel pull.
Coulomb’s law is:
F= k×Q×q/r^2
which is pretty much exactly the same as you have probably noticed: "the force of electrical attraction F on two charged particles Q and q is proportional to their charges and the square of the distance between them, r "
So the exact same rule applies to planets and atoms. Their behaviour can be explained in the same way. It’s called an “inverse square law”, it’s got a name because they happen everywhere. And it’s just, like… Why? Why does the universe work that way? You’re not really encouraged to ask that sort of question as a science student, because it “goes nowhere” and doesn’t lead to actionable results. But I think it quite spooky. There are loads of weird results like that in science and maths (see quantum theory for abundant examples!) but it’s unusual to be able to sit and think about it. There is, for the inverse square law, a pretty elegant mathematical explanation for why they’re so common, but it doesn’t quite scratch the itch for me, it just raises more questions
Edit sorry for text wall. This is probably why I shouldn’t do this!
I dunno, it’s an inverse square. Are we going to get excited each time something has a linear relationship to another thing? What makes the inverse square so special?
In my field of work (molecular biology) anything with a linear relationship gets exciting! I got an R^2 of .9968 last week that had me jumping for joy.
Bertrand’s theorem states that stable orbits are only possible for one single inverse distance relation (in classical mechanics): inverse square
If the law is not inverse square (or harmonic oscillator), there will be no long lasting orbits, no galaxy clusters, no galaxies, no star systems, no planet and moon pairs.
If the electrostatic force wasn’t inverse square, electromagnetic force would look much different. No gauss law would be possible.
Inverse square relationship is really neat
There’s a lot of things which are required to be exactly as we observe them to be for our surroundings to work out as we observe them to be. If they weren’t we wouldn’t be here to observe, or, at the very least, we’d be quite different.
Also as to other universes: Who says that any random universe with other laws ties together objects based on their mass. For all we know their attractive force could be relative to photon emissions and elves keep the orbit stable by strategically shining torches at the sky (ok that’s not that likely evolutionary speaking but we’re talking physics).
That’s why it’s interesting that inverse square is in electrostatic and gravitational forces only. Weak and strong force don’t follow inverse square. And we don’t see the highly complex organization inside the nucleus that we see outside it (otherwise we’d have stable orbits inside the nucleus as well)