Fictitious Forces
The centrifugal force of a merry-go-round is supposedly fictitious because it vanishes when you jump off. This seems to me like the “if a tree falls in the wood and no one hears it does it make a sound?” thought. What exactly is meant by fictitious? Also what exactly are we considering a force to be? From my tutorial this Monday I got the idea that some philosophers started saying that all forces are “fictitious” and so causation is an illusion. Maybe I misheard/misunderstood? If I didn’t I’m interested in their argument. Were we going to talk about this later in the course?
Am I right in thinking the force is still real, and it’s fictitiousness stems uniquely from the fact that under certain circumstances you can’t perceive it? Perhaps I’m just being misled by the phrasing and making a difficulty out of what was basically a throwaway expression to simply illustrate the idea? If so it’s just because I’m not taking anything for granted when talking about things like quantum mechanics.
ALSO: Fictitious forces impart the same acceleration to objects regardless of the inertial mass of the object (cf: galileo and gravity). Yet these forces are all proportional to inertial mass. In the lectures we saw that gravitational mass is equal to inertial mass so: G(Mearth mball)/R^2 =mball * a <=> G(Mearth)/(R^2 ) =a Fgravity=G Mearth/R^2
So here it looks like the force of gravity is proportional to the inertial mass of the earth and not that of the ball, which is why the acceleration of any object is the same. Is this all that the above is saying? (I’d still like to see if anyone can solidify my understanding of what is meant by force and fictitious). As an aside, is the ball not effectively part of the inertial mass of the planet?
Guthrie, again (sorry if I’m being a bore)
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That’s a lot of questions Guthrie. I will try to answer most of them. Someone else can tell me if I’m wrong with any of the physics.
A force is an ‘external influence on an object that causes it to accelerate relative to an inertial reference frame’ (from Tipler and Mosca first year physics text (or at least it used to be). The external influence could be a massive object, such as earth. A force can be calculated as the product of the mass and acceleration of an object subjected to the force, according to Newton’s second law.
A fictitious force is an external influence on an inertial object that causes it to accelerate relative to a non-inertial reference frame (such as a rotating merry go round). The force disappears if the reference frame is inertial (ie stops rotating) and this is why it is called fictitious.
As I understand it, the existence of any force (real or fictitious) requires an object to be present to be influenced the force, otherwise the force does not exist. However, obviously the rotating merry go round itself still exists without the object – just like a tree does not require an observer to be present for it to exist (I think Berkley was wrong on this one, but I’m a realist. Maybe this argument gets more complicated in QM with regard to whether an electron exists in a particular location if you are not measuring its location – nevertheless the electron still exists somewhere - I’m sure we’ll get to that in later lectures).
One could question whether any type of ‘force’ really exists, or is it just the apparent behaviour of the object that exists? If a ball falls towards earth because space-time is curved, is there a force involved? In the lectures we were told that everything is freefalling along a geodesic in curved space-time. Is a force causing this freefall? Bodies will continue to freefall in the absence of any force. “In general relativity, the effects of gravitation are ascribed to spacetime curvature instead of a force.” (http://en.wikipedia.org/wiki/Gravitation)..)
There is a ‘force’ that stops us from falling to the centre of the earth if we are on the ground (electrostatic repulsive force between atoms). However, there is no gravitational “force” in General relativity, as I understand (or don’t understand) it. What appears to be a gravitational force is simply an object freefalling along the geodesic of curved space-time. Maybe even the apparent repulsive force between atoms may be better described simply as the reluctance of electrons to share electron orbitals? It could be called a force, but whether ‘force’ is actually something that exists, who knows?
So, getting back to the fictitious force, based on Newton’s second law (F = ma), the fictitious force of a merry go round depends on the acceleration caused by the rotation of the merry go round and the mass of the objects on the merry go round. If the acceleration stops, the force stops. (Incidentally, the earth’s rotation exerts a fictitious centrifugal force on objects on its surface, which slightly reduces the force of earth’s gravity).
Now, moving on to gravitational ‘force’ (using Newtonian terminology). You’re correct in saying the force of gravity on the ball (ie in the inertial frame of earth, not the inertial frame of the ball) is proportional to the inertial mass of earth and not the ball. Likewise, the force of gravity on the earth caused by the ball (seeing as the ball causes the earth to move towards it – ie, in Einsteinian terminology, the ball must curve space-time a tiny bit) is proportional to the inertial mass of ball and not the earth (which is why, if you throw a ball, the ball doesn’t move the earth very far). The total gravitational force between the ball and earth depends on both masses, as you say (F = GMm/r^2).
Regarding your last questions, the mass of the earth could include the ball (and everything else that has mass and is ‘connected’ to the Earth by gravity, such as the atmosphere), but only if you are considering the force of all that mass on something outside that mass (such as the moon). If you’re considering the gravitational force on the ball, then you can only consider the mass inside an imaginary sphere around the centre of earth, with the radius of the sphere being less than the distance between the centre of the earth and the centre of the ball. In other words, consider all the mass of each sphere to be at its respective centre and ensure the two spheres do not overlap.
As a consequence of this, I guess you should really consider other gravitational forces on the ball, such as the atmosphere above it, aeroplanes, birds and the moon. I don’t think these practicalities have any relevance to the Einstein though.
Hope that helps
David Clarke
Thanks. Good topic and really good answer, David.
You’re right: there is no force of gravity in General Relativity. There is gravity, but it’s not a force. This is a problem because some theories of particle physics assume that gravity IS a force. That’s a discrepancy that people don’t talk about much, but it’s going to have to be resolved eventually.
As for electrons, again you’re right that their behaviour in occupying different energy levels or “shells” can be explained by the Pauli Exclusion Principle, which doesn’t require a force … but in that case there is ALSO an actual force, according to current theories. Electromagnetic/weak interactions and nuclear interactions are currently thought to be due to real forces.
Jason
