American physicist Edward Witten explains why it wasn’t until Einstein's work that we fully understand the reason behind the inverse square law, and why it's specifically a square rather than some arbitrary decimal 1 / distance² vs. 1 / distance¹·⁷⁴⁸²²⋅⋅⋅

Pretty sure Gauss showed that it was a consequence of living in a universe with 3 space dimensions about a century before Einstein.

Nah. I think they already intuitively understood this. As soon as they noticed the observational data fit an exponent of ~2 they knew what was up.

Nah, this idea of something spreading through space was there before. It appears in too many other contexts (light or sound intensity for example).

Witten’s answer is incorrect. First, Newton’s theory of gravity can be reformulated as a nonrelativistic field theory where the inverse square law is a consequence of the Newtonian gravitational potential satisfying Poisson’s equation. This doesn’t require general relativity (Einstein’s theory of gravity), so the latter is a red herring. Second, the form of Einstein’s field equations that imply the inverse square law for gravity to leading order is experimentally constrained as much as Newton’s theory or its nonrelativistic field theoretic reformulation. Einstein’s theory thus doesn’t explain the inverse square law any better or further than Newton’s theory does when reformulated as a nonrelativistic field theory.

What are you talking about? The reason behind the inverse square law has been known since the time of Newton. It's simple math.

When I first read the inverse square, I think in 9th grade, I instinctively imagined it as being rooted in area of sphere. I had not been introduced to Einstein work. It’s pretty instinctive. Isn’t it ?

One of the strangest things about physics is that some equations are geometry revealing itself.

What? The inverse square law was a geometrical fact before Einsteins field theory ever existed?

Really? The Principia is drenched in geometry.

Dr Witten, a Fields medalist in 1990, was a history major in college. How he became a top mathematical physicist is fascinating but not well reported. Hope he will write a memoir to reveal his research thought process to inspire the next generations…

How so? This is high school math known since Newton and probably even before that. The same signal, or whatever, is spread out to a greater area, the area of the wave front sphere, which is proportional to the distance squared. ->

Any abstraction can be undermined by a new, fresh, recalibrated abstraction; meaning the confident certitudes of these people (fundamentalist physicists) is just so silly; black can't be white until someone shows that it can. Aristotelian categories are provisional, except when your mental flexibility has ossified.

Is there a similar (group theoretic or string) argument spacetime has D=4 instead of D=26 bosonic string theory and D=10 supersymmetric string theory? (Stability, Anomaly cancellation/chiral gauge theory,...) And why 3+1 instead of 2+2 or 4+0?

I think Lagrange had formulated something similar around 4 decades before Einstein, where Newtonian gravity was presented as a field theory similar to Gauss's law. (Though not with the General Relativity corrections.)

MOND is like scribbling mustaches on the Mona Lisa.

This is why I love physics. To see deeper into the mathematical structure of the universe. Ed Witten is a national treasure.

wait, for it to drop as the 2nd power, doesn't that require space to be Euclidean?

FWIW Newton didn't "postulate" it, he made precisely agreeing *measurements* that gravity was inverse square using a variety of phenomena--falling bodies, the Moon's orbit, the planets' orbits, Jovian moons, etc. Then he generalized it to all cases via the 4th Rule of Reasoning.

Err. What? I think the greeks came up with that one from the equation of a describing the area of a spherical surface.

wow. never seen physiognomy like that. instant aesthetic vortex. ffs

He didn't really explain, it, even when pressed. He just said it had to be an inverse square.

One of the things that really blew me away when I worked through the @oustudy's Understanding Space and Time course (S354) is that stable orbits are only possible with an inverse square law. With any other exponent, stable orbits don't exist...

"(Doah! The reason it is 'square' is because the substrate ground is geometric.)" tweet, tweet, tweedle tweet #physics

Bad! The inverse square law was already widely established - in many different fields (optics, sound, electrostatics, etc) - and that's why the 'surface field model' in relativity was specifically chosen to connect with that truth. A modeling choice, not an explanation

This is one of those deep physics ideas that sounds simple on the surface... but gets wild the basically pointing out that before Einstein, we knew the inverse-square law worked but we didn't fully understand why nature picked that exact 'square" rule instead of some weird number like 1.7 or 2.3.

Newton understood this in the Principia, especially when he calculated the potential inside a uniform spherical shell. Nah, Witten's wrong. As for the geometrization of gravity - as a grad student I saw an interesting talk about geom. of Newtonian space vs. Einstein space-time. GR has time and space curved, whereas Newtonian gravity is only space curved.

Idiots parroting the idiotic

On the same token, ElectroMagnetism is also a field theory, and so when Maxwell and Heaviside have shown that the EM field verifies the wave equation, they have explained the inverse-square law ... for electromagnetism.

Why need Einstein? It’s just Gauss’s Divergence Theorem. The power is 1 less than the dimension of space. In 2D it would be 1/r, in 1D it would be constant.

Einstein is mere scalar. Muppets Last Last Post Rules of The Game

I am so thrilled to waste my time watching a so-called journalist who stutters on camera.

La inversa del cuadrado tiene que ver con la caída de una radiación o la influencia de un campo cuando se propaga radialmente desde un centro en áreas esféricas que crecen precisamente con el cuadrado del radio. No veo que esto tenga nada que ver con Einstein.

Asaph Hall's model was such one where instead of inverse square law, he proposed 1/r^(2+a), a=0.00000016 in order to catch Mercury's anomalous precession of perihelion. But it did not fit with other planets. I saw it first in Penrose, I guess.