> ...Being accelerated by such a pseudo-force won't register on an accelerometer...
Just checked the accelerometer on my phone. It reads around 9.8m/s/s pointing downwards.
Just checked the accelerometer on my phone. It reads around 9.8m/s/s pointing downwards.
An accelerometer works by comparing the difference between some mass that is acted upon by an external force and a related mass that is loosely connected to it (e.g. by a spring-like linkage. whose strain we can measure) as not to be acted upon by that force directly.
If you move the casing of an accelerometer, the sprung mass inside it lags behind, and thereby the acceleration can be measured via strain gauges or whatever.
Gravity defies accelerometers because, unsurprisingly, gravity acts on all of the the masses contained in an object equally.
(At least any gravitational field you are likely to encounter in ordinary experience is going be almost perfectly uniform across an everyday object.)
It is when you are in free-fall, that is when you're accelerating due to gravity. And that's exactly when the accelerometer doesn't tell you anything, because every part of the object is in the same free-fall; all of you is accelerating. The accelerometer is differential. It doesn't see a difference, so it doesn't see acceleration.
You now that free-fall is acceleration because orbiting satellites are in free fall and they follow circular paths. Objects will not move in a circle unless a force accelerates them toward the center. Like when you spin a mass on the end of as string, it goes in a circle due to the centripetal force exerted by the tension carried in the string.
When you're standing on the planet, your accelerometer is lying to you. Gravity is acting on the sprung mass inside the accelerometer, and it's also acting on the case which holds that mass. But the case is constrained from moving, whereas the sprung mass isn't. So a differential strain develops, which "looks and feels" like acceleration.
In summary, an accelerometer is an instrument which measures the acceleration due to a force which is applied just to its casing, and not to some critical piece of mass held inside. Gravity causes equal acceleration of the casing and that piece of mass, and so gravitational acceleration is immeasurable by that accelerometer.
Acceleration can be measured with regard to some frame of reference via distance and time calculations.
Either ways, the accelerometer is registering something. If gravity was purely a ‘pseudo force’ as GGP said, I should’ve expected a 0 reading.
Am I misunderstanding the point made about the accelerometer?
If you jump off a bridge, during your brief flight you could look at your accelerometer and see zero. The gravitational influence on you hasn't changed at all by jumping off a bridge- the only change was removing the upward force that stopped you from falling.
Why is the soil not in free-fall? Because it feels normal force of all the earth below.
And why is not the whole earth in free fall towards its core? Because it has an electrostatic force (a real one!) which keeps all the atoms and molecules from collapsing on itself. If it would collapse on itself, it would first become a neutron star and then a black hole.
To be clear, my confusion is about how this interpretation is consistent with the facts, not the facts themselves (I think).
So the field is going radially inwards towards the center of the massive object.
"Gravity" is the curvature of spacetime. An inertial "straight line" follows that curvature, like going "straight" on the Earth's surface draws a spatial curve. Remove what's supporting me (dirt, bridge) and I'll continue on my inertial straight line, which actually orbits and settles down to the center. Even "at rest" at the center/bottom of the gravity well is not zero inertia per se, it is a continuing inertial line orbiting with still-constant velocity at zero radius. Ergo gravity isn't a force; gravitational attraction is just masses' inertial lines being distorted by the infinite-reaching distortions of other masses. There is no "gravitational force" to unify with other forces. OMG.
I've been trying to get my head wrapped around gravity for years. You just tied the knot.
Next questions: why does mass distort spacetime? As E=mc^2, does/can energy distort spacetime? Mass & energy being just different units of the same thing, what's the nature of that thing without thinking in terms of divided mass/energy colloquial thought? And then questions on to weak & strong nuclear forces, and reconsideration of electromagnetic force.
Do you know of any diagrams that might illustrate this idea to a layperson?
The electrostatic forces and bonds between atoms are exactly what prevents these atoms from following inertial paths. The atoms act on each other, and collectively produce a force radially outwards from the center of Earth supporting its mass.
Earth isn't pulling itself apart because nothing is pulling in the first place. All the mass is pushing against itself, refusing to be packed tighter, despite the flow of spacetime around it drawing it together over time.
When we're standing on Earth, our particles are following the same flows of spacetime toward the core of Earth. From our inertial frame, the ground below us is moving toward us, because as noted Earth resists being compacted further. So we meet the surface, we both resist being compacted by the other, and we experience a stable force.
That said, your description does kind of explain it for me, unless I am misunderstanding, though at the moment I only get it as a "negative" argument: we are being accelerated upwards/outwards with respect to the field's reference frame, because otherwise we would be moving along our natural inertial path.
It is still a bit puzzling that if the ground disappears we appear to accelerate, whereas my current reading of what you wrote seems to imply that we would immediately return to our "inertial path".
What I'm really wondering is if all of this "acceleration relative to the field" business is a misleading abstraction, and "relative reference frames" fix it (and indeed that was my very primitive understanding of relativity). However, on balance it seems much more likely that I'm simply misunderstanding things.
Fair, and I'm not sure I follow that, either. I'm not sure how an entire field can really have a reference frame in the first place.
> though at the moment I only get it as a "negative" argument: we are being accelerated upwards/outwards with respect to the field's reference frame, because otherwise we would be moving along our natural inertial path.
That pretty succinctly captures my understanding.
> It is still a bit puzzling that if the ground disappears we appear to accelerate, whereas my current reading of what you wrote seems to imply that we would immediately return to our "inertial path".
Yes, that's the sticky bit! I think "appear" is load-bearing here, because what are you measuring relative to? The surface of the Earth is not an inertial reference frame (according to general relativity, it's accelerating!).
It might be easier to think about if we use centrifugal force -- the fictitious force you feel when being swung in a circle from some central point. From an inertial reference frame, you have some velocity in the tangential direction, and a rope (say) is pulling on you in the radial direction. This force accumulates with the existing velocity over time to produce a circular path.
From your perspective, however, you feel a force pushing you outwards, which is resisted by the rope you're attached to. You would feel that, if the rope was cut, you'd be "pulled" out into space (radially away). But this is because you're not aware of -- you don't sense -- the tangential velocity you possess, because it's canceled by the choice of a frame that's moving with you.
The change to an inertial frame introduces an extra velocity term, and this in turn allows us to replace the unattributable outward pull of the centrifugal force with a force merely attributed to the tension of the rope you're attached to. (In fact, this might be a good intuition for what an "inertial frame" even is: it's a frame in which all forces are equal and opposite to other forces. Gravity and the centrifugal force are unbalanced in this sense.)
The gravitational field (curvature of spacetime) plays the same role that the hidden velocity does. In an Earth surface frame, the feeling of being pulled "down" is attributed vaguely to the fact that there's a bunch of mass "down there". In an inertial frame, the feeling of being pulled "down" is attributed to the ground pushing "up" at you.
In both scenarios, we can find a frame involving an extra term that lets us redescribe the phenomenon we observe in terms of forces attributable to physical entities.
The "Fictitious forces" Wikipedia page has some pretty good schematic animations for the centrifugal force, FWIW.