In general media, explanations of gravity, free fall, and acceleration, make reference to two things
1/ a human jumping off a building in free fall does not feel acceleration, therefore, it must be the earths surface accelerating towards the human
2/ they then say, this is confirmed by dropping an accelerometer from a building, in free fall, it will show 0G which means it must be the earth accelerating towards it
First the topic of a human "feeling" acceleration. The reason I feel acceleration say in a fast car, is because the car seat is pushing different parts of my gelatinous body at different rates. My internal organs have a lag in being accelerated, the muscles in my neck take time to pull my head along , blood sloshes and pools as its accelerated in a different direction of where its supposed to go etc etc
But...if we could accelerate every single atom in my body at the same time and at the same rate, I think I would feel no acceleration at all and would survive ridiculous acceleration eg:1000G and feel nothing , maybe with the only limit being quantum affects above a certain level of acceleration?.
What if gravity accelerates every single atom of a free falling human at the same rate? Would that not explain why the human would not feel the acceleration in free fall?
Similarly, if every atom of an accelerometer was simultaneously accelerated by gravity, it would read 0G, no?
To me this makes more sense ie: being accelerated without "feeling" acceleration and in some ways differentiating acceleration due to gravity vs acceleration from a lift, rocket or a car
Also, I would then see the force (weight) I feel standing on the earth as nothing more than gravity accelerating me constantly at 1G against the floor while the atomic bonds of the atoms that make up the floor being far stronger than my weight pushing back with an equal force
The laws of GR predict that the object will fall towards the centre of the Earth, because that is its natural (freefall) trajectory in the curved spacetime around a dense mass.
The object in free fall feels no "proper" acceleration.
Now, put the Earth back to its usual size. An object on the surface of the Earth has the same natural trajectory. But, it cannot fall through the surface. A real force prevents it, causing upwards acceleration. Acceleration, however, does not imply motion.
Relative to the surface of the Earth, the object in free fall accelerates towards the Earth's surface. And the object on the surface is relatively at rest.
And that, in fact, is a valid global picture across the Earth's surface.
Relative to the falling object, the Earth's surface accelerates upwards towards it. That's true in Newtonian gravity as well.
However, that reference frame is only valid locally. That view of things cannot be extended across the globe. Because, the free fall rest frame is a local frame.
Yes, but then it would not be an acceleratometer.
You can also construct an accelerometer with a lamp and a light sensor, mounted at constant distance.
A proper acceleration leads to a Doppler frequency-shift, because after the finite time, a light pulse needs from the lamp to the sensor, the sensor is already moving faster than the lamp, when it sent out the light pluse.
If such an accelerometer is at rest relative to the surface of Earth, then the measured frequeny-shift is called "gravitational frequency-shift".
That's not quite the reason. The reason is that the car seat pushing on you causes stresses inside your body, because the force exerted by the car seat on your back is transmitted through the rest of your body, and the atoms in your body resist being pushed by the force. That means the overall configuration of your body is slightly changed from what it would be in free fall: the distances between the atoms are slightly different, and so the forces between the atoms are slightly different. You feel that as a force pushing on you.
Similarly, when you stand on the surface of the Earth, the Earth pushes on your feet, and that force gets transmitted through the rest of your body, and the atoms in your body resist being pushed by the force, and the overall configuration of your body is slightly changed from what it would be if you jumped off the roof of a building and were free-falling towards the ground. You feel that difference as weight.
Similar remarks apply to an accelerometer: it is a device that's designed to measure the very slight changes in configuration that are caused by it being pushed on by a force, and show them to you. The fact that an accelerometer moving solely under "gravity" reads zero is a manifestation of the fact that "gravity" is not a force--it doesn't push on anything. It's part of the geometry of spacetime.
It is actually more than that, and is not limited to your body.The reason I feel acceleration say in a fast car, is because the car seat is pushing different parts of my gelatinous body at different rates. My internal organs have a lag in being accelerated, the muscles in my neck take time to pull my head along , blood sloshes and pools as its accelerated in a different direction of where its supposed to go etc etcBut...if we could accelerate every single atom in my body at the same time and at the same rate, I think I would feel no acceleration at all and would survive ridiculous acceleration
Consider an electromagnetic field. In the case where an accelerometer reads 0, pulses of light move in straight lines and the electric field lines emanating from a co-moving charge are isotropic. In the case where an accelerometer reads non-zero, pulses of light curve and the electric field lines emanating from a co-moving charge are anisotropic.
So it is not about your squishiness or the uniformity of the acceleration. It is about the basic laws of physics themselves.
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