Centrifugal Force = Prefered Frame of Reference?

[spikenigma]

Centrifugal Force = Prefered Frame of Reference?

ok, so there is an empty universe completely devoid of matter except for two space stations of the Stanford Torus type, Station A and Station B.

Station A decides to accellerate itself to a constant (i.e no further accelleration) roation speed of 1rpm relative to the other to produce a centrifugal force on it's hull and thus earthlike gravity within itself. Station B remains motionless relative to the other.

A year later, a person from another dimension arrives in the near-empty universe and radios Stations A and B. Both Captains insist the other station is the one which is rotating at a constant 1rpm, and (as I understand it) under general/special relativity this is true - there is no prefered frame of reference of any two frames which are not under acceleration.

The visitor to the near-empty universe steps onto Station A, he floats around inside it at 0g and concludes that it is not rotating. He then docks with Station B and walks along the ground inside it experiencing the artifical gravity at 1g and concludes that Station B is the one which is rotating

Thus the prefered frame of reference is station A?

[Gigaliel]

Centrifugal Force = Prefered Frame of Reference?

ok, so there is an empty universe completely devoid of matter except for two space stations of the Stanford Torus type, Station A and Station B.

Station A decides to accellerate itself to a constant (i.e no further accelleration) roation speed of 1rpm relative to the other to produce a centrifugal force on it's hull and thus earthlike gravity within itself. Station B remains motionless relative to the other.

A year later, a person from another dimension arrives in the near-empty universe and radios Stations A and B. Both Captains insist the other station is the one which is rotating at a constant 1rpm, and (as I understand it) under general/special relativity this is true - there is no prefered frame of reference of any two frames which are not under acceleration.

The visitor to the near-empty universe steps onto Station A, he floats around inside it at 0g and concludes that it is not rotating. He then docks with Station B and walks along the ground inside it experiencing the artifical gravity at 1g and concludes that Station B is the one which is rotating

Thus the prefered frame of reference is station A?

Uh, some basic physics would tell you the rotating torus is undergoing circular acceleration. Notice how any point on the ring is constantly changing its velocity's direction in order to travel in a circle. Ergo, that's the one that's accelerating. That's also why the simulate gravity and why everyone would be floating in the other torus.

[Darth Wong]

There is no preferred inertial frame of reference. However, Station A is accelerating relative to its own inertial frame of reference at any given time.

[spikenigma]

Uh, some basic physics would tell you the rotating torus is undergoing circular acceleration. Notice how any point on the ring is constantly changing its velocity's direction in order to travel in a circle. Ergo, that's the one that's accelerating. That's also why the simulate gravity and why everyone would be floating in the other torus.

Circular motion is accelerated even if the speed is constant, because the object's velocity vector is constantly changing direction.

http://en.wikipedia.org/wiki/Circular_motion

thanks. I think what I'm trying to get at is, I just don't understand what in the universe determines that it's the velocity vector of station B that is constantly changing direction and the velocity vector of station A that is not. To the occupants of station B (disregarding the earthlike gravity for a moment) station A is spinning around.

What mechanism with no further energy going into the system has determined that station B is the one that is undergoing circular acceleration and station A is not.

Further, looking at the system from a mile away, what objective standard in the state of the matter or change in the matter which makes up the stations allows one station to have the centrifugal force and one not to?

There is no preferred inertial frame of reference. However, Station A is accelerating relative to its own inertial frame of reference at any given time.

Station B you mean, the one that is turning at 1rpm?

I suppose it is like the famous experiment to try to prove the luminiferous ether (http://en.wikipedia.org/wiki/Michelson- ... experiment) , the spot the light hit moves because frame of reference the light was produced by has moved since it was produced.

But who's to say that the universe hasn't moved and the two points ( A - the light source and B- the detector ) have stayed in the exact same location and have not accelerated if there is no prefered frame of reference?

[Executor32]

Which one is the one that is actually turning? You first stated that Station A accelerated itself to rotate at 1 rpm, then at the end you stated that Station B was the one rotating.

[Terralthra]

thanks. I think what I'm trying to get at is, I just don't understand what in the universe determines that it's the velocity vector of station B that is constantly changing direction and the velocity vector of station A that is not. To the occupants of station B (disregarding the earthlike gravity for a moment) station A is spinning around.

No, it's not. If B is rotating at 1 RPM and A is not, the occupants of B see A doing a complete circle around them once a minute. They do NOT see A as spinning at all.

[Kuroneko]

I think what I'm trying to get at is, I just don't understand what in the universe determines that it's the velocity vector of station B that is constantly changing direction and the velocity vector of station A that is not. To the occupants of station B (disregarding the earthlike gravity for a moment) station A is spinning around.

As has been pointed out above, please note that there is a fundamental asymmetry between the two stations even when the forces involved are completely ignored: an observer on station A sees station B in rotation about its own (B's) axis, while an observer on station B does not see station A rotate about its own (A's) exis. Therefore, as there is no true symmetry in this scenario, we should not be overly surprised that one of the stations experiences fictitious forces but the other does not.

Further, looking at the system from a mile away, what objective standard in the state of the matter or change in the matter which makes up the stations allows one station to have the centrifugal force and one not to?

I'm not sure what you're asking. If you believe that the situation is symmetric, you're mistaken. On the other hand, if you're asking why centrifugal force is seen by B and not A rather than A and not B, that is a strange question that probably doesn't have any deep, meaningful answer.

Given the context of your scenario, there are two possible answers to this. One way is to simply tie everything to experiment and leave it at that. In other words, what determines which station is accelerated is the behavior of a free particle (say, yourself) inside the stations. I suspect that you'd be dissatisfied with that sort of approach, which is really something like "inertial frames are those in which Newton's laws hold [to first order, etc.]; all else requires fictitious forces."

That's really a kind of definition of what it means to be 'inertial' in the first place, but it is also the most scientifically sound answer: the only things we talk about are the results of experiments.

A second kind of answer, which is possible in special relativity because there is an absolute fixed background, Minkowksi spacetime, in which station A can fully communicate with any other point in space, while someone on station B observes a horizon that hampers communication with all but a finite region of space. But this is really in the same spirit as the previous answer, except that is substitutes global observations in place of local ones: inertial frames in STR are those without any horizons anywhere.

I suppose it is like the famous experiment to try to prove the luminiferous ether (http://en.wikipedia.org/wiki/Michelson- ... experiment) , the spot the light hit moves because frame of reference the light was produced by has moved since it was produced.

That particular phrasing is very misleading, suggesting an interpretation that is completely wrong. But regardless...

But who's to say that the universe hasn't moved and the two points ( A - the light source and B- the detector ) have stayed in the exact same location ...

What does that mean? Scientifically speaking, that distinction is incoherent, because even if there is some fundamental difference between the two cases (a question best left for those concerned with metaphysics), there would still not be any observational difference between them.

[SpacedTeddyBear]

There is a preference toward inertial reference frames over the non-inertial, simply because Newtonian mechanics and SR comes only apply to inertial motion. One can easily tell which is in a non-inertial reference frame by hanging a pendulum from the ceiling.

There is no preference toward reference frames so long as they are inertial.

[Kuroneko]

It may be worth noting that this sort of preference towards the inertial is dependent on which formulation of STR we're talking about. Dynamics (and gravitation, for that matter, but that's not STR) can be stated entirely in terms of geometrical properties of spacetime, e.g., the "straight lines" of Newton's first law being replaced with "geodesics", "acceleration" of Newton's second law with "curvature of the world-line", etc. Stated in those terms, there is no real preference toward the inertial frames--both the inertial and the non-inertial follow exactly the same laws.

[SpacedTeddyBear]

It may be worth noting that this sort of preference towards the inertial is dependent on which formulation of STR we're talking about. Dynamics (and gravitation, for that matter, but that's not STR) can be stated entirely in terms of geometrical properties of spacetime, e.g., the "straight lines" of Newton's first law being replaced with "geodesics", "acceleration" of Newton's second law with "curvature of the world-line", etc. Stated in those terms, there is no real preference toward the inertial frames--both the inertial and the non-inertial follow exactly the same laws.

So if this observation between these two stations were made in a gravitational field, there will be no "preference" for either frames?

[Kuroneko]

There's a bit of miscommunication, it appears. In physics, a type of reference frames being "preferred" means that the physical laws in those frames have some special character not present in other frames. For example, in Newtonian mechanics, inertial frames have no centrifugal or Coriolis forces, whereas rotating frames do. Thus, non-inertial frames have "fictitious" forces that need to be accounted for in the equations of motion.

I'm merely pointing out that in STR (gravity need not apply), it is possible to formulate the laws of physics in such a way as to have all reference frames exactly the the same equations of motion. It doesn't mean that someone in the rotating station won't experience what feels like gravity, but it does mean that we won't have any "preferred" frames because the theory no longer makes any explicit distrinction.

[SpacedTeddyBear]

There's a bit of miscommunication, it appears. In physics, a type of reference frames being "preferred" means that the physical laws in those frames have some special character not present in other frames. For example, in Newtonian mechanics, inertial frames have no centrifugal or Coriolis forces, whereas rotating frames do. Thus, non-inertial frames have "fictitious" forces that need to be accounted for in the equations of motion.

I'm merely pointing out that in STR (gravity need not apply), it is possible to formulate the laws of physics in such a way as to have all reference frames exactly the the same equations of motion. It doesn't mean that someone in the rotating station won't experience what feels like gravity, but it does mean that we won't have any "preferred" frames because the theory no longer makes any explicit distrinction.

OK that makes sense. My physics covers undergrad knowledge of the first paragraph; It stops short of geodesics though.....

[spikenigma]

perhaps I'm just thick, I still don't understand how the two statements:

* both the occupants of Station A and Station B can rightfully say the other is rotating
* Station A is experiencing the centrifugal force associated with rotation Station B is experiencing no centrifugal force ascociated with no rotation

can both be correct

anyway, I'll leave it here and perhaps read up on it later to get my head around it, thanks for your time

[Terralthra]

perhaps I'm just thick, I still don't understand how the two statements:

* both the occupants of Station A and Station B can rightfully say the other is rotating
* Station A is experiencing the centrifugal force associated with rotation Station B is experiencing no centrifugal force ascociated with no rotation

can both be correct

anyway, I'll leave it here and perhaps read up on it later to get my head around it, thanks for your time

That's because as I explained, statement one is not correct. You are visualizing the situation badly.

Assuming A is spinning:

The occupants of B see station A rotating at 1 rotation per minute.

The occupants of A see station B (and the entire universe) circling them once per minute.

This is not symmetric.

[spikenigma]

That's because as I explained, statement one is not correct. You are visualizing the situation badly.

Assuming A is spinning:

The occupants of B see station A rotating at 1 rotation per minute.

The occupants of A see station B (and the entire universe) circling them once per minute.

This is not symmetric.

it is symetric, I'll animate a gif and provide an illustration

I'll say that just in case I haven't made myself clear, perhaps think of the shape of two stargates facing each other and one is rotating around it's middle whilst still facing the other

* Station A to us is rotating clockwise; so to its occupants, Station B is rotating anticlockwise whilst they are stationery
* To the occupants of station B, they believe that Station A is rotating anticlockwise whilst they are stationery

gif and illustrations to follow as soon as I get the chance

[Terralthra]

Ah, I understand what you mean. You mean that the rotation of Station A is along a line which also intersects the center of station B. Yes, from that perspective, each would appear to the other as rotating. The key point is that a visitor who arrives from another dimension is not on either station when he or she arrives, and unless space-time in this universe is inexplicably warped, he or she would easily be able to tell which of the two stations is spinning relative to him.

Rotation is not velocity. Angular momentum is a constant acceleration about an axis. If you were to say A is accelerating 1 m/s/s in a direction, and B remains stationary, observer foo could not tell which one is actually moving, sure, but rotation doesn't work like that.

[Kuroneko]

Oh, you're making the axes identical. We can still break the symmetry by allowing multiple observers at different distances from the common axis; this is in effect just like having an external observer decide for us. But notice that we cannot ordinarily be sure whether the external observer himself is not in orbit about the common axis unless we do some sort of experiment to decide that: there is an implicit assumption that such an external observer is himself inertial.

Now, I realize that by asking what "determines" which one the stations experiences centrifugal force, you'd not be satisfied with the sort of definitional answer that's usually given: in whichever one the particles behave as if there is centrifugal force. On the level of experiments, we don't need anything more than that, so the only thing I'll add is that we can also do this with light as well as massive particles. For example, a two simultaneous but opposite pulses of light traveling along the circumference of the station will arrive at their common point of origin at the same time iff the station is inertial.

The only alternative is to take spacetime itself as somehow "metaphysically prior", in which case we can appeal to it instead. There is no purely scientific difference between this interpretation and the one above it, because we can know the structure of spacetime only by doing experiments, but philosophically, I suppose one can make the distinction. So now in addition to you also have the alternative "the geometry of spacetime determines which is the one that accelerates." If you like, I can give the details.

[Terralthra]

Oh, you're making the axes identical. We can still break the symmetry by allowing multiple observers at different distances from the common axis; this is in effect just like having an external observer decide for us. But notice that we cannot ordinarily be sure whether the external observer himself is not in orbit about the common axis unless we do some sort of experiment to decide that: there is an implicit assumption that such an external observer is himself inertial.

Now, I realize that by asking what "determines" which one the stations experiences centrifugal force, you'd not be satisfied with the sort of definitional answer that's usually given: in whichever one the particles behave as if there is centrifugal force. On the level of experiments, we don't need anything more than that, so the only thing I'll add is that we can also do this with light as well as massive particles. For example, a two simultaneous but opposite pulses of light traveling along the circumference of the station will arrive at their common point of origin at the same time iff the station is inertial.

The only alternative is to take spacetime itself as somehow "metaphysically prior", in which case we can appeal to it instead. There is no purely scientific difference between this interpretation and the one above it, because we can know the structure of spacetime only by doing experiments, but philosophically, I suppose one can make the distinction. So now in addition to you also have the alternative "the geometry of spacetime determines which is the one that accelerates." If you like, I can give the details.

I considered the orbiting external observer idea, but discarded it. He would undoubtedly know he or she was in orbit, because he or she would feel the same centripetal/centrifugal forces that anyone on the interior of the rotating object feels.

[Twoyboy]

There's a bit of miscommunication, it appears. In physics, a type of reference frames being "preferred" means that the physical laws in those frames have some special character not present in other frames. For example, in Newtonian mechanics, inertial frames have no centrifugal or Coriolis forces, whereas rotating frames do. Thus, non-inertial frames have "fictitious" forces that need to be accounted for in the equations of motion.

Please tell me if I'm out of line with this thread hijack, but this ties into my understanding of the above statement.

If the forces are fictitious, does this mean they aren't capable of doing work? Specifically, someone I knew once calculated the speed at which a car with flat tyres would have to travel to "inflate" the tyres via centrifugal force. Would I be correct in saying this is not possible, because the force only exists using the rotating reference frame?

[Kuroneko]

I considered the orbiting external observer idea, but discarded it. He would undoubtedly know he or she was in orbit, because he or she would feel the same centripetal/centrifugal forces that anyone on the interior of the rotating object feels.

That's certainly the only sort of answer we would ever actually need in Newtonian mechanics, but I thought that the premise of this thread is to see if we can characterize what it means for a frame to be "inertial" in ways other than, but equivalent to, the presence of fictitious forces. Otherwise, spikenigma's question makes no sense: observers at either station know whether or not they're rotating by the presence or absence of centrifugal force, end of story.

[Steel]

There's a bit of miscommunication, it appears. In physics, a type of reference frames being "preferred" means that the physical laws in those frames have some special character not present in other frames. For example, in Newtonian mechanics, inertial frames have no centrifugal or Coriolis forces, whereas rotating frames do. Thus, non-inertial frames have "fictitious" forces that need to be accounted for in the equations of motion.

Please tell me if I'm out of line with this thread hijack, but this ties into my understanding of the above statement.

If the forces are fictitious, does this mean they aren't capable of doing work? Specifically, someone I knew once calculated the speed at which a car with flat tyres would have to travel to "inflate" the tyres via centrifugal force. Would I be correct in saying this is not possible, because the force only exists using the rotating reference frame?

No. You could theoretically gotthe tyres to inflate by doing that.

The forces are referred to as ficticious as they arent there in a standard intertial frame. Think about whats going on here.

Imagine the frame as a camera thats sitting there, and you have to determine whats going on by just what you see in the camera. If there are two objects that are just sitting there relative to the camera, and the camera isnt spinning, then you say there is no force being exerted on them. If you then set the camera rotating about its axis, the objects appear to be then moving round in circles, which requires them to have a force acting on them, this force is then a "ficticious" force as it isnt there in the standard inertial frame.

[Kuroneko]

Twoyboy: Sorry; I didn't see your post earlier (didn't check thread after posting reply to Terralthra). Your question has already been answered, but in case you're curious as to how it quantitatively comes out, here's some further information.

Suppose we have motion in two dimensions with polar coordinates (r,θ), and that there is a potential V = -mω²r²/2. With a kinetic energy T = mv²/2, v² = (dr/dt)²+r²(dθ/dt)², the Lagrangian L = T - V gives the following equation of motion:
(d/dt)[∂L/∂(dr/dt)] = ∂L/∂r, which is
m[d²r/dt²] = mr(dθ/dt)² + mω²r.
The second term is clearly the centrifugal force, so we can call V as the potential energy of the centrifugal force. Thus, not only can the centrifugal force do work, but being dependent only on position, it also does so conservatively (unlike Coriolis force, which nonetheless has a meaningful potential).

From the point of view of any inertial frame, the centrifugal potential is just as fictitious as the force, but don't let that bother you. Kinetic energy is frame-dependent as well. As for the tires, yes, it's possible to at least slightly increase their pressure by spinning them. I'm hesitant to estimate the magnitude of the effect without doing a rather involved calculation; that sort of thing would depend various viscous/frictional forces of the air in the tire. If there are no such forces, the tire pressure won't change a bit, although if there are, I suppose one can argue that waiting "long enough" is sufficient to remove such concerns.