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calculus_jy
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can someone tell me how to distinguish fictitious and real force, together with the correlation of fictitious acceleartion and real acceleration, my research seems to fail on this subject
In Newtonian physics and Special relativity, real forces are measured by inertial observers. A fictitious force is something that an accelerating observer would assume ought to exist in order to make Newton's second law true relative to his accelerating frame. An example is centrifugal force for a rotating observer. But, in Newtonian physics and Special relativity, Newton's second law is not true in an accelerating frame, so that is why the force is called "fictitious".calculus_jy said:can someone tell me how to distinguish fictitious and real force, together with the correlation of fictitious acceleartion and real acceleration, my research seems to fail on this subject
Is that really correct? It seems to me that it would make sense to define a "real" force as a non-zero value of [itex]m\cdot d^2x^\mu/dt^2[/itex] in a co-moving local inertial frame (it's a measure of the deviation from geodesic motion), and a "fictitious" force in an arbitrary frame as what we have to add to get Newton's second law (some four-vector version of it) to hold in those coordinates too. The first part of that definitely makes sense. I'm not sure about the second.DrGreg said:In General Relativity all forces are real -- relative to any observer -- and there are no fictitious forces.
DaleSpam said:Again, I like the GR approach. Real acceleration/force is an acceleration that can be measured by an accelerometer. A fictitious force/acceleration is one which cannot be measured by an accelerometer.
If you prefer the Newtonian approach you simply make an exception to the above by considering gravity as the only real force which cannot be measured by an accelerometer.
The accelerometer on a turntable registers an acceleration toward the center of the turntable. There is no reading for the outward fictitious centrifugal force. An accelerometer on an orbiting body registers zero acceleration. There is no reading for the inward fictitious gravitational force or for the outward fictitious centrifugal force.kev said:So as far as GR is concerned, centrifugal force on a turntable that produces a reading on an accelerometer IS a real force while centrifugal force acting on an orbiting body is a fictitious force?
I think you mean centripetal force. But yes, the centripetal force on a turntable is measurable by an accelerometer and is therefore real, while the centripetal force on a satellite is not measurable by an accelerometer and is therefore fictitious.kev said:So as far as GR is concerned, centrifugal force on a turntable that produces a reading on an accelerometer IS a real force while centrifugal force acting on an orbiting body is a fictitious force?
Perhaps it can be summed up by an analogy of travel in a car:DrGreg said:I don't claim to be a GR expert so my understanding could be wrong too. But my view is that, in GR, relative to a given frame, a force is anything that causes coordinate acceleration i.e. [itex]d^2 \textbf{x}/dt^2[/itex] measured in the frame's [itex](t, \textbf{x})[/itex] coordinates. (Or, to be more precise, causes a change in coordinate momentum.) Thus, for an object rotating on a disk, an inertial observer would say there is a centripetal force causing the object to accelerate, and no centrifugal force, whereas an accelerating observer who is stationary on the disk would say the object is not accelerating, the net force on the object is zero consisting of equal and opposite centripetal and centrifugal forces.
For a satellite in orbit, in the satellite's own free-falling frame there are no forces acting on it -- it is moving inertially (along a geodesic). For someone hovering "stationary" above the planet at the altitude of the satellite (and therefore non-inertial), the satellite is accelerating towards the planet due to a force called "gravity".
(Nevertheless, just to confuse things and play devil's advocate, there is a case to be made for attributing proper acceleration (measured by an accelerometer and equal to acceleration in the co-moving inertial frame) to a "real" force (which I guess you could call the "proper force") and any other acceleration to a "fictitious" force. Under this interpretation, gravity is a fictitious force.)
I stand to be corrected by any GR experts reading this.
DrGreg said:I don't claim to be a GR expert so my understanding could be wrong too. But my view is that, in GR, relative to a given frame, a force is anything that causes coordinate acceleration i.e. [itex]d^2 \textbf{x}/dt^2[/itex] measured in the frame's [itex](t, \textbf{x})[/itex] coordinates. (Or, to be more precise, causes a change in coordinate momentum.) Thus, for an object rotating on a disk, an inertial observer would say there is a centripetal force causing the object to accelerate, and no centrifugal force, whereas an accelerating observer who is stationary on the disk would say the object is not accelerating, the net force on the object is zero consisting of equal and opposite centripetal and centrifugal forces.
For a satellite in orbit, in the satellite's own free-falling frame there are no forces acting on it -- it is moving inertially (along a geodesic). For someone hovering "stationary" above the planet at the altitude of the satellite (and therefore non-inertial), the satellite is accelerating towards the planet due to a force called "gravity".
(Nevertheless, just to confuse things and play devil's advocate, there is a case to be made for attributing proper acceleration (measured by an accelerometer and equal to acceleration in the co-moving inertial frame) to a "real" force (which I guess you could call the "proper force") and any other acceleration to a "fictitious" force. Under this interpretation, gravity is a fictitious force.)
I stand to be corrected by any GR experts reading this.
An accelerometer essentially has a comoving inertial observer: The accelerometer's test masses. The accelerometer uses these test masses to ascertain the acceleration of the accelerometer case. That the test mass moves to the right with respect to the accelerometer case means the accelerometer case is accelerating to the left, and this is exactly what the accelerometer reports. You have the behavior of the accelerometer exactly wrong, particularly here:kev said:Some examples:
Car turning to the left while going forward.
Real centripetal force acting from right to left. (Not measured by an accelerometer) (Is accelerating from right to left according to a comoving inertial observer)
Fictititious reaction centrifugal force acting from left to right. (Is measured by an accelerometer)
The accelerometer measures the real normal force, not the fictitious gravitational force. In particular, an accelerometer resting on a table will report a 1g upward acceleration. An accelerometer does not measure the fictitious gravitational force. Attach an accelerometer to an orbiting satellite, as per your next example:Weight resting on a table.
Real force exerted by the table on the weight, acting upwards. (Not measured by an accelerometer) (Is accelerating upwards according to a comoving inertial observer)
Fictititious force (gravity) acting downwards. (Is measured by an accelerometer)
The centrifugal force only exists in the mind of an observer located at the center of the Earth and rotating with the satellite. Why this observer, rather than an observer on the surface of the Moon or in orbit around Jupiter? Moreover, this cancellation of gravitational and centrifugal force is only true for a satellite in a circular orbit in a two-body system. Centrifugal force does not cancel gravitational force for multi-body systems (e.g., a satellite whose orbit is perturbed by lunar and solar gravity), elliptical orbits or for vehicles in what some call "orthogonal orbits" (your next example):Satellite in orbit.
Fictitious centripetal force (gravity) acting towards the centre of orbital circle.
Fictitious centrifugal reaction force acting outwards.
Here your Devil's advocacy falls apart, and you know it. What fictitious reaction force acting upwards?Radially free falling object.
Fictitious gravity force acting downwards.
Fictitious reaction force acting upwards?
In this case there is also no acceleration according to a comoving inertial observer and the fictitious forces cancel out so there is no measurement on an accelerometer.
Accelerometers measure the acceleration due to the net real force. This example is a red herring as the net force is zero.Person pushing against an unmoving wall.
Real force exerted by person on the wall. (Tension in muscles.) (Not measured by accelerometer)
Real reaction force exerted by the wall on the person. (Tension in the wall) (Not measured by an accelerometer)
DrGreg said:I agree with DH's post #11.
Yeskev said:That hopefully makes more sense
That is certainly the view of inertial observers, and in SR and Galilean Relativity (=Newtonian mechanics) it is the only "real" view, all other views are "fictitious". But my understanding is that GR is more democratic than that, and celebrates the diversity of all observers equally. So what is fictitious to an inertial observer may be real to a non-inertial observer. (As always, I stand to be corrected by a GR expert who knows the official line on this.)kev said:When there is a non-inertial comoving observer, the real force is acting on the object and on the observer so there is no acceleration relative to the non-inertial observer. The fictitious forces (such as centrifugal force or gravity) are imaginary forces that are invented to explain the lack of acceleration relative to the non-inertial observer, but really no explanation is required beyond the fact that the non-inertial observer is also subject to the same real force and acceleration that is acting on the object he observering.
A fictitious force is a perceived force that appears to act on an object, but is actually a result of the object's motion and reference frame. It is not a real force that can be measured or detected. A real force, on the other hand, is a physical force that can be measured and has a direct effect on an object's motion.
One way to distinguish between a fictitious force and a real force is to consider the reference frame in which the force is observed. If the force is only present in a non-inertial reference frame (one that is accelerating or rotating), then it is likely a fictitious force. Real forces, on the other hand, are present in all reference frames.
An example of a fictitious force is the centrifugal force. When an object is rotating, it appears to experience an outward force, but this is actually a result of the object's inertia and its motion in a rotating reference frame. This force is not a real force, as it cannot be measured in an inertial reference frame.
Acceleration can affect the perception of fictitious forces because it can create non-inertial reference frames. In these frames, fictitious forces may appear to act on objects, but they are not real forces. For example, when a car accelerates, passengers may feel a "backward" force, but this is actually a result of their inertia and the car's acceleration, not a real force.
In most practical applications, fictitious forces can be ignored because they do not have a significant effect on an object's motion. However, in certain situations, such as when dealing with precise measurements or high speeds, these forces must be taken into account to accurately describe an object's motion.