Yes, change in relative positions causes the break. But differences in velocities caused the change in relative positions. And differences in acceleration caused the differences in velocities.
Normally, you can approximate that a planet’s gravitational field is constant with the region containing a person, so it will cause a uniform acceleration, that will change the person’s velocity uniformly, which will not cause any relative change in position.
However, the strength of the gravitational field really varies inversely with the square of the distance to the center of the planet, so if the person’s head is further from the the planet than their feet, their feet will be accelerated more than their head. This is known as gravitational shear. For small objects in weak fields, this effect is small enough not to be noticed.
Okay, thanks, that makes sense. So being in free fall in a gravitational field isn’t really comparable to crashing into something, because the difference in acceleration across my body in free fall is very small (though I suppose could be high for a small, ultra-dense planet).
So, in free fall, the (slight) weaking gravitational field as you get farther from the planet should put your body in (minor) tension, since, if you stand as normal, your feet accelerate faster, pulling your head along. If you put the frame of reference at your feet, how would you account for your head appearing to move away from you, since the planet is pulling it in the direction of your feet?
If you put the frame of reference at your feet, how would you account for your head appearing to move away from you, since the planet is pulling it in the direction of your feet?
Your feet are in an accelerating reference frame, being pulled towards the planet faster than your head. One way to look at it is that the acceleration of your feet cancels out a gravitational field stronger than that experienced by your head.
But I’ve ruled that explanation out from this perspective. My feet are defined to be at rest, and everything else is moving relative to them. Relativity says I can do that.
Relavtivity says that there are no observable consequences from imposing a uniform gravitational field on the entire universe. So, imagine that we turn on a uniform gravitational field that exactly cancels the gravitational field of the planet at your feet. Then you can use an inertial (non accelerating) frame centered at your feet. The planet, due to the uniform field, accelerates towards you. Your head experiences the gravitational pull of the planet, plus the uniform field. At the location of your head the uniform field is slightly stronger than is needed to cancel the planet’s gravity, so your head feels a slight pull in the opposite direction, away from your feet.
An important principle here is that you have to apply the same transformation that lets you say your feet are at rest to the rest of the universe.
Yes, change in relative positions causes the break. But differences in velocities caused the change in relative positions. And differences in acceleration caused the differences in velocities.
Normally, you can approximate that a planet’s gravitational field is constant with the region containing a person, so it will cause a uniform acceleration, that will change the person’s velocity uniformly, which will not cause any relative change in position.
However, the strength of the gravitational field really varies inversely with the square of the distance to the center of the planet, so if the person’s head is further from the the planet than their feet, their feet will be accelerated more than their head. This is known as gravitational shear. For small objects in weak fields, this effect is small enough not to be noticed.
Okay, thanks, that makes sense. So being in free fall in a gravitational field isn’t really comparable to crashing into something, because the difference in acceleration across my body in free fall is very small (though I suppose could be high for a small, ultra-dense planet).
So, in free fall, the (slight) weaking gravitational field as you get farther from the planet should put your body in (minor) tension, since, if you stand as normal, your feet accelerate faster, pulling your head along. If you put the frame of reference at your feet, how would you account for your head appearing to move away from you, since the planet is pulling it in the direction of your feet?
Spaghettification.
Your feet are in an accelerating reference frame, being pulled towards the planet faster than your head. One way to look at it is that the acceleration of your feet cancels out a gravitational field stronger than that experienced by your head.
But I’ve ruled that explanation out from this perspective. My feet are defined to be at rest, and everything else is moving relative to them. Relativity says I can do that.
Relavtivity says that there are no observable consequences from imposing a uniform gravitational field on the entire universe. So, imagine that we turn on a uniform gravitational field that exactly cancels the gravitational field of the planet at your feet. Then you can use an inertial (non accelerating) frame centered at your feet. The planet, due to the uniform field, accelerates towards you. Your head experiences the gravitational pull of the planet, plus the uniform field. At the location of your head the uniform field is slightly stronger than is needed to cancel the planet’s gravity, so your head feels a slight pull in the opposite direction, away from your feet.
An important principle here is that you have to apply the same transformation that lets you say your feet are at rest to the rest of the universe.