I've been down a bit of a YouTube / AI wormhole recently, prompted by a post on Facebook about gravity. It's a long story but I follow some of the Flat Earth pages for a laugh. They usually don't believe in gravity.
Anyway - naively, I thought of gravity as a force, the idea that all objects with mass attract each other. Isaac Newton came up with a formula to describe this:
F = G(m₁m₂)/r².
.. where F is the gravitational force, G is the gravitational constant, a fundamental feature of the universe, each mass is described by m₁ and m₂ and r² is the square of the distance.
This can be used to calculate the apparent gravitational force between objects very accurately in most situations, but - it actually describes something that's fundamentally wrong. Newton's formula describes what gravity does in most situations as a model, but it misunderstands why.
I expect some of you will know this stuff already but physics was never a strong point for me at school and I find it fascinating. Anyway - in reality gravity is not a force at all. What really happens is that objects with mass distort spacetime around them. Einstein realised this. So when the Moon orbits the Earth, there's no force acting on it - it's just following a natural path through the spacetime distorted (curved) by Earth's mass. The Moon is actually following a straight line, through warped space. Isn't that wild?
Similarly, when you drop something from your hand, it's not being "attracted" by the Earth - it's just continuing to move in space from the momentum it already had, but through a natural path, determined by the shape of spacetime around the planet.
Two significant experiments proved this.
Firstly - Mercury's orbit around the sun is slightly different in its behaviour than the Newtonian laws would imply. It was observed, even before Einstein's time, that the perihelion (closest point to the Sun) of its orbit was shifting gradually (ie preceding) , which was expected - but a bit more than it should have. It actually shifts by about 575 arcseconds per century, mainly due to the gravitational influences of other planets - but this only accounted for 532 arcseconds.
When you do the math based on Einstein's idea, to account for the curvature of spacetime predicted by General Relativity - the precession comes to the correct figure.
Secondly - a solar eclipse in 1919 showed that starlight was bending as it passed the Sun - the apparent positions of stars adjacent to the eclipsed Sun in the night sky changed very slightly compared to their usual positions with the Sun out of the way. Because photons are massless, the Newtonian notion of gravity has no explanation for this.
I know it's an overused phrase but it is truly mind-boggling stuff. The idea that space is bendable and that objects with or without mass find themselves following tracks of apparent nothingness is fascinating.
Had a think about this notion of light bending due to gravity. It follows that when you observe something at a distance there must be a microscopic influence due to the mass of the Earth curving its path.
I asked an AI to do the maths.
So firstly, due to the curvature of the Earth (nothing to do with its gravity) and assuming no obstacles, the furthest away I'd be able to see someone over the horizon is about 9.56km. In other words if someone the same height as myself (eyes 179cm from the ground) were standing 9.56km away and I had very powerful binoculars, I'd be able to see the top of their head from the eyes up just over the horizon.
So, ignoring refraction or atmospheric effects, what difference does the curvature of light due to Earth's gravity make? I thought it would be absolutely microscopic. And it is indeed very small. It turns out that that the other person's eyes in my binocular image would appear 0.027mm higher than if light travelled in an exact straight line.
That's obviously tiny and would be overwhelmed by hand movement, not to mention the limitations of the optics. It's very much a conceptual experiment. But the difference is a significant fraction of a millimetre. For comparison, it's 100,000 times larger than the width of a water molecule.
What's the circumference of the imaginary circle described by this curved path of light over the surface of the Earth? About 6 light years.
I used Claude.AI for this and confirmed it with ChatGPT which came up with 0.0266 mm for the discrepancy due to gravity - the same, to within three decimal places.
I've been down a bit of a YouTube / AI rabbit hole this last couple of days, trying to understand entangled particles in some superficial way. It's mind-bending stuff.