A massive object like the Earth has a significant amout of gravity. Gravity pulls you towards the center. Your feet are cloaser to the center than your head and since gravity weakens with distance² your feet are pulled stronger than your head. Now this is where tidal forces originate. You dont really feel any stretching because the difference in the gravitational force between your feet and head are tiny as the distance from the center is much larger. However if the object is very small and extremely dense like a black hole it allows you to go much cloaser.
When you are really close to that small and dense object your body length will be on the same order of magnitude as your average distance from the center. So your feet get a significantly larger pull than your head stretching your body. This stretching force eventually will overcome the strength of the bonds between your atoms. So you’ll turn into s string of atoms more or less hence the name, spagettification.
A less classical exploration is that gravity isnt pulling its space stretching. So space is curved by mass and when you have a lot of mass in a tiny volume the space around it curves extremely. On Earth this curvature is roughly constant through your body but not around a black hole where this curvature changes a lot. Your feet gets more acceleration than your head which results in stress build up and this force will rip you apart.
So this spagettification thing is only extreme tidal forces and tidal forces is something classical physics has a good handle on. But you can also think about it in terms of space-time curvature.
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