And if they are not the same, then what information do you need to determine which one is affecting you?
Per Einstein, there is no inherent way to tell the difference between gravity and acceleration. Centrifugal “Force” is a form of acceleration.
Is gravity also a form of acceleration?
But centrifugal force varies with distance from the center, and so does gravity. If you’re on an orbiting space ship, there will be a very slight tidal force which would tend to cause your feet and your head to want to be in slightly different orbits.
There is a famous thought experiment describing a person in a closed box, like an elevator car. If they drop an object and it falls downward with an acceleration of 1g, two things could be true:
[ul][li]The elevator car is at rest on the Earth’s surface (or on some other body with a natural gravity of 1g, or[/li][li]The elevator car is accelerating through space at 1g.[/li][/ul]
There is a flaw, though. If you drop a ball near the side of the elevator car, it won’t fall exactly straight (i.e. perfectly parallel to the car’s sides) if you are on Earth. Rather, it will fall toward Earth’s center of gravity, on a slight inward angle relative to the car. Thid wouldn’t happen if the car was moving with a uniform acceleration of 1g. The deviation will be slight, but postulating a large enough elevator car and precise enough instruments…
Anyhoo, centrifugal force isn’t really a force as such. Rather, it’s your own momentum being blocked, which feels like a force. Your weight wants to keep going in a straight line (as any object flung off a spinning base wants to) but this damn bulkhead keeps getting in the way.
Clear as mud?
The effect of gravity between two bodies is acceleration.
You might find this guy’s whacky idea interesting.
Technically speaking, centrifugal force does not exist. That is, there is no “outward force” that is directed at a vector outwards from the center of a spinning system. What is actually happening is a combination of infinitesmals of force, every one tangental to the circular direction of spin. The vector sum of these infinitesmals at any instant is perceived as being a single force going outward in a single vector from the center.
Is inertia another term for centrifugal force?
Umm… blocked inertia is centrifugal force.
Then did Einstein mean blocked inertia in the passage cited by Ring?
This doesn’t help. If the ball falls at an angle due to the elevator wall, it is just as reasonable to assume that you are being accelerated in a direction that is not perfectly aligned with the elevator walls.
Believe me, if you are building a rotating space habitat, you will soon find that there is a lot of difference between gravity and centrifugal force; in a small ship, or wheel, or habitat coriolis forces will be so strong that your inner ears will be affected, and you may well be unable to adapt;
and thrown or falling objects will fall in a curving trajectory, making many activities difficult.
This is not so apparent in a large rotating habitat.
SF worldbuilding at
http://www.orionsarm.com/main.html
You can distinguish between the cases by dropping two balls. If their paths converge, you are in a gravitational field. If they diverge, you are spinning. If the paths are parallel you are accelerating (or you are too far from the center of mass/axis of rotation to measure the convergence/divergence of the paths).
An object rotating about the origin with a constant velocity has an acceleration that is center directed. The magnitude of the acceleration is proportional to the distance from the center and to the angular velocity. Since you are accelerating toward the center, you experience a force away from the center.origin
Gravity is green. Centrifugal force is blue.
Remember G for gravity and G for green. I don’t have a trick for remembering centrifugal force.
Maybe these further quotes from Albert will clear it up.
What Einstein is saying is that in a non-rotating frame centrifugal force is nothing more than the reaction force which arises from causing an inertial mass to follow a non geodesic path. However in the rotating frame it’s a real force albeit one that does not have an apparent source.
To expand a bit on Ring’s last quotation, it was very common in Einstein’s own presentations of GR to start from the thought experiment of a rotating system of coordinates.
Suppose you’re rotating. What does special relativity tell you about how you see of the space round about. Well, objects moving perpendicular to your line of sight are contracted, so you’d regard the circumference of circles about you as smaller than if you were stationary. But the radius remains the same. Space has become curved. Rotating and non-rotating observers thus disagree about the geometry of the space round about them. And since curved space is manifest as gravity, they disagree about the “forces” they see operating around them.
In the 1916 Annalen der Physik paper where he first lays out the full completed theory, he uses this argument at the start to motivate the fact that the theory will involve non-Euclidean geometry (it’s section 3; see the translation in The Principle of Relativity, Dover, 1952, p115-8), though as far as I can see he never mentions the connection to centrifugal forces. That is spelt out in the equivalent passage at the start of the discussion of GR in The Meaning of Relativity (Methuen, 1922; Chapman and Hall, 1967, p59):
To judge by a quotation from it in Pais’ Subtle is the Lord … (Oxford, 1982, p243), there’s an even more explicit statement in an earlier 1914 paper:
In one of his Mr. Tompkins books, George Gamow developed the throught experiment in the form of observers on a roundabout in quite some detail on a non-technical level. Would be an excellent place to look for a good explanation.