# Perceived acceleration in an artificially modulated gravitational field

It's intuitive that while accelerating in a locally constant gravitational field, there is no perception of acceleration, since the body accelerates uniformly.

What if a body were in a rapidly changing gravitational field? Say oscillating between +/- 5g? Would you still be unconscious of the rapid acceleration changes, if the changes were uniform?

• What exactly do you mean by "an artificially modulated gravitational field"? If you mean that (hypothetically speaking) you do something wrong that makes the bouncer at a bar throw you against the wall, then off the ceiling, then the down to the floor, and finally out into the street, yes, you would feel that. If on the other hand you mean some magical box that turns the Earth's gravitational field on and off, shifts it left and right, in that case, we don't know how to do that, and we probably never will. Oct 27 '14 at 23:24
• Either some hypothetical device like that, or, say a rapid slingshot trajectory around a dense body. Imagine being in a space suit and taking a drastic hyperbolic slingshot around the outside of a black hole, or other massive body. Oct 27 '14 at 23:37
• @David Hammen - in Newtonian physics where there is no limit on velocity, we could just imagine a massive body which very rapidly oscillates in its distance from you (perhaps a massive infinite plane, which in Newtonian physics creates a perfectly uniform gravitational field, though not so in general relativity). In general relativity you could have a body moving back and forth at a very large fraction of the speed of light, but this might generate sufficiently powerful gravitational waves for you to feel the tidal forces, I'm not sure. Oct 27 '14 at 23:38
• @Hypnosifl - And how exactly do you accomplish that, sans a Kardashev level III civilization (which is pure science fiction)? Oct 28 '14 at 0:15
• @David Hammen - I assumed it was a thought experiment for the purposes of better understanding physical principles, not an experimental proposal. And if you're dealing with a thought experiment, the fact that it may be practically impossible is irrelevant so long as the premise doesn't violate any fundamental physical laws. Oct 28 '14 at 0:48

It's intuitive that while accelerating in a locally constant gravitational field, there is no perception of acceleration, since the body accelerates uniformly.

The reason you can't perceive it is not that it's uniform, the reason is that there's nothing to compare with. If there's something to compare with, then you can see the difference. For instance, we can sense the difference in acceleration between a falling rock and the earth's surface.

What if a body were in a rapidly changing gravitational field? Say oscillating between +/- 5g? Would you still be unconscious of the rapid acceleration changes, if the changes were uniform?

Yes.

• I thought that it's not perceptible because the body itself is accelerating because of the gravitational well, rather than acted on by an external body. i.e. accelerating in a vacuum at 1g by stepping out of a U2 spy plane feels like weightlessness, but accelerating by being shoved at 1g across the utah salt flats in a car 'feels' like you're accelerating because your body is being compressed by the seat. Oct 27 '14 at 23:20
• @Justin - you "feel" acceleration when the accelerating force is only applied to one section of your body, like in a car where the force on your body is exerted by the seat on your back. The reason the front of your body accelerates along with it is that there is some compression in the material of your body, initially caused by the fact that your back begins to accelerate before your front does. This compression creates a spring-like force resisting the compression, pushing the front of your body--if the car's acceleration is constant an equilibrium will be reached Oct 27 '14 at 23:30
• (cont.) where the compression is just the right amount to accelerate the front of your body by the same amount that your back is being accelerated by the force from the seat. If all parts of your body were being accelerated equally by an external force, then even if it were varying in time there would be no reason for your body to become compressed or stretched so you wouldn't feel anything. Oct 27 '14 at 23:35
• Mach's principle! Oct 28 '14 at 0:08
• @ArtBrown - General relativity violates Mach's principle. Oct 28 '14 at 0:16

I'll go with an Equivalence Principle argument. For a model system, consider a test particle in a highly elliptical orbit around a neutron star; the particle will pass through regions of greatly different field strength.

But it feels no force as it "falls" around the star. Per the Equivalence Principle, at each point there is a locally inertial coordinate system (the freely falling frame) in which the laws of motion are the same as for special relativity, with no gravity (and hence no force).

Update: I want to poke at a couple things:

1) Your intuition that there is no perception of acceleration while falling in a locally constant gravitational field is actually your internalization of the Equivalence Principle, which implies that, in a gravitational field, all matter falls with the same acceleration. Since Galileo, people have been testing this proposition on various substances, and have never detected a difference (once other effects, such as air resistance, have been accounted for).

Instead of a "test particle" in my model system, suppose I substituted a block of crystalline copper, assumed small enough that tidal forces are undetectable. Crystalline copper comprises a matrix of ion cores immersed in a sea of conduction electrons. If electrons fell at a different rate than the nucleons of the ion cores, the conduction electrons would get pushed to one side of the block, and a voltage difference across the block would be created. That doesn't happen (to the best of our knowledge).

2) Similarly, arguing that acceleration cannot be perceived because there's nothing to compare with is only valid because of the Equivalence Principle. If different components of our bodies accelerated differently, there would in fact be differences to compare, and you could (at least in principle) perceive them as differential stresses.

• As I understand it the equivalence principle doesn't actually rule out the possibility that a free-falling observer could feel tidal forces though, see my answer to this question. Oct 28 '14 at 5:05
• @Hypnosifl, I think the thing about tidal forces is you need (at least) two particles separated in space-time, and the tidal forces decrease with the separation. (That's why I specified a "test particle".) You're right that the proverbial astronaut falling into a black hole will be spaghetti-fied. Oct 28 '14 at 5:11