Inertia of space, impression of force, directed acceleration of quantities of matter and implied quantities of motion form the background to Newton's third law. Action and Reaction is his catch all term for all sorts of activities and bodily contacts and interactions. How could all these situations be described as equal and opposite reactions?
There is a sense in which this law is incorrectly expressed . The many copious examples show the difficulty Newton had in expressing it.
The first example was the pushing of a finger on a stone, a small pressure. Te stone is seen to push back. What do we see? depending on how elastic the stone is we see an indentation in the finger and an indentation in the stone. This is clearly some kind of action reaction system, but are they equal? In addition this action reaction system is nestled ithin a larger force system. The finger pushes the stone, we zero in on the point of contact. Both remain stationary, but the surrounding points move sequentially into contact, This movement represents a deformation of the 2 bodies at and around the point of contact. this deformation allows movement relative to the 2 bodies local referenece frames while remaining stationary in an external reference frame. Each point tha t comes into contact remains in contact in a pressure situation in which the points exert equal and opposite force on each other, But then something happenes. The excess of quantity of motion behind these points compress on the points and begin a wave of motion throuhout the bodies. This wave transfer quantity of motion from one to the other, Suddenly no more deformation takes place , whole body motion begins. at the point of contact the points maintain an equilibrium of equal forces or pressures. But the quantity of motion behind this pressure surface feeds into the other body creating a movement towards a balance in the quantity of motion between the two bodies. Now should the finger stop pushing the stone continues with its quantity of motion now increased, and the surface of interaction relaxes back into its original shape.
Now in a free rolling collision the same situation exists but why would, in certain circumstances one object stop while the other continued? The only mechanism is Newton's posited opposite and equal reaction. Thus a ball colliding with a stationary ball, imposes a deformation through force equalisation which stops the moving balland transfers all its quantity of motion excess into the stationary ball. That ball then moves off without exerting any pressure on the first ball regaining its relaxed shape.
Thus , this third law is talking about this detailed analysisi of motion transfer , by an action which as we have posited includes a wave action, a reciprocity of action and a deformation and form with relaxation. There aree also pressures and points of contact and transfer, and more things going on than he can describe.
Action and Reaction is therefore a complex notion of force systems that transfer quantities of motion. The equal refere to only a small portion of the interaction, where the bodies are actually in contact. Thus a boundary becomes stabilised by equal forces, but only relatively . The rest of the parts of the body continue in their motion "causing" a transfer of motion. But this is instantaneous, because the motion destroys the equilibrium moving the second body on. The deformations move in reciprocity between relaxed and tensed or deformed states and back again, and this reciprocity is what Newton refers to as Equal.
The force situation is more complex than just a direct force, Torque forces ar clearly included in the deformation as are shear forces. Elastic deformation includes not only spring like forces , but also twisting and shearing forces. but it is torque forces i want to look at next.
Torque is defined as a twisting force, but this is in fact a shear force acting on both sides of the shear. It is often dealt with as a moment of turn. However a true torque is a continuous rotating force! such a force exists but it is unstable, because it is allied with a tangential force and a centripetal force and or a centrifugal force.. Tis torque force is confused with the composition of the tangential and centripetal force, but in fact this does not work. The tangential force has to continue to be applied tangentially to n orbit, that is the tangential force must continually change direction with the motion of the body, Such a force, that behaves in this way is a torque force.
Torque forces are some of the weaker forces in any system, and that is why they have been missed. Weak as they are, they can generate incredible velocities.As these velocities increase so do the tangential velocities, and it is the tangential velocities that disrupt the torqued system, leading to breakdown and damage. The rotating system must be able to withstand these tangential forces to maintain a torqued motion. This is often characterised as an acceleration toward the centre of curvature, but that is to counteract the tangential velocities. A torque acceleration is still needed to rotate the bodies.
http://en.wikipedia.org/wiki/Torque
http://www.sparknotes.com/testprep/books/sat2/physics/chapter10section4.rhtml
http://www.sparknotes.com/testprep/books/sat2/physics/chapter10section2.rhtml
http://en.wikipedia.org/wiki/Coriolis_effect
http://www.gyroscopes.org/glossary.asp
Now the analysisi has one proviso, which is that these forces, torques and accelerations have to be instantaneous. What does that mean? Well it does not mean in no time at all thats for sure! This is why the third law is important, because it explains what Newton tried to communicate by Action And Reaction. In Newtons Fluxion method he does not ever take a value at Zero. That would e a nonsense to him, and should be to us. He uses terms like nascent and evanescent to invoke the barest most essential form of any magnitude or quantity as an ad infinitum rocess is used, In some cases a limit is achieved that does not vanish in other cases no limit is achieved and the quantity diminishes and will ultimately vanish or ascend to an incomprehensible quantity , a magnitude. In these cases a judgement is required and an approximate answer is utilised. Newton is nothing if not sensible to these behaviours of ratios of quantities, which is why he is careful to frame his law as he does.
So the problem of gravitational acceleration is approached by some approximation, and the closeness to the observed value is the ratio of equality that Newton seeks to arrive at. However, the clear assumption is that this is a model using understood laws of motion to approximate what is not understood.
Thus by approaching it 2 ways, one as a pressure imposed by a circular boundary and the other as an attraction imposed by some rope of fixed length, the early scientists attempted to MODEL orbital behaviours or Actions. Thus the third law is derived in such an imprecise manner, that is a generalised manner to cover al sorts of actions and behaviours.
The Newtonian model is an attraction/pressure model and it is Cotes who equates the 2 as a single force. His equation is procedurall wrong even if it is ostensibly correct. In any case Cotes gave this equation in a preface to the Principia, and prefaces are allowed to posit philosophical views. We only assume that this was Newton's private thinking, or what he published in The System of the Worlds, for what is in the Principia is a careful rendition of the facts as known and the model as derived.
Within the model then, instantaneous action is covered by the third law. Such an action is not continuous, nor even constant, for why would it be? Then why is it we posit a constant gravitational force ? Because of the kind of thinking Cotes referred to: one force acting equally and mutually on 2 bodies in a dynamic system. While in calculation mode this is a useful rule of thumb, in the actual physics this is innaccurate, and in terms of the model it is innaccurate. The model posits uniformity which is not the same as constancy or oneness! If uniformity does not communicate to you try symmetry and identicality and congruency. The model posits that for a uniform motion and identical acceleration is symmetrically distributed around a circle, and that acceleration is applied within the instance of coincidence between the uniformly moving object and the circle, according to the third law, in which the object is bothe decelerated and accelerated equally in an elastic collision, only in that part of its motion that is perpendicular to the circle, that is along a diameter. This resultant acceleration is therefore instantaneous, that is ist occurs within an instance, and that instance is "governed" ie explained by the third law. This is the pressure model of orbital motion, in which we see that Newtons compounding Algebra may cogently be applied.
We have to recognise that Newtons use of a vector Algebra here was in line with his contemporaries, and so was vaiously understood by them, but all Newton posits is that the motion can be resolved into these parts in a uniform motion situation for that instant.
Now the second part of the model was the attraction model, and this is what i call the hidden Torque model. Nwton himself did many experiments with this model to try and understand it and he remained intrigued by it, and sufficiently persuaded of its importance to mention the spinning top version as a lonk between the local and the distant application of his principles. In other words he did not think there was a crystal sphere in space bouncing or rolling the planets round per se, but some kind of attractive Forces, note the plural, that acted like the tension in a string pulling his buckets round with spinning motion too.
What was holding all those particles together in a spinning top? What was DRAGGING them round? This centrifugal force is Torque, but we have identified it wrongly with the centripetal force, and that was due to Cotes et al.
The model for the centrifugal force is to be fair almost identical, but it is not identical. We lose the difference by dropping a part of the set up as insignificant.. In the centrifugal model the tensile force applied by the string is able to drag a body into orbit! This is clearly a torquing force! Once in orbit, it maintains the orbit by a similar explanation to the centripetal model. However, we can clearly observe the tensile force acting on the orbiting body both restraining it from flying off, but also turning it both around the orbit centre And around the objects own local centre, that is within its own frame of reference. The centripetal model is defective in this local rotation without an instantaneous torque being added to the mix in the instantaneous acceleration.
Thus the pressure model definitely needs the third law to retain its applicability, for by the third law we can add this instantaneous torque into the mix in the centripetal model. Again this is an non continuous non constant torque. Thus the model should posit a uniform torque field within the symmetrical distribution of contact with the circle, at this uniform velocity. So now , in the centripetal model. all these accelerations add up to zero. so compounding the accelerations tells us only that they balance out symmetrically, not that there is no acceleration. But the torques do not compound to zero. They compound to a local rotation around the centre of the moving object, the orbiting body.
These instantaneous accelerations and torques, necessarily will appear to be week because they act over so short a peried of time. We may use a Dirac function to model these types of interaction, and a Dirac function is a precise model of the third law.
When observed closely, the tensile torque force is seen to be a tensile vorticular wave action along the rope, resonant with the rotating source of the torque. Thus the gravitational attraction field is an analogous vorticular wave field in resonance with the rotating bodies under mutual action.Space is already torsed under a Newton model of pressure-attraction-torsion. Yes i add in the posited Torque force as Newtonian
Back to the centrifugal, attraction model. Newton was not unaware of the problem of attaching the rope to the moving body to apply the Torque force. While others discounted it Newton new that the attachment was like to that of a pulley, or a hook, providing either pressure uniformly on a back part of the moving body or on the front part of the bod or somehow both. By whatever means the tensile force transmitted quantity of motion instantaneously to every part of the body, but again not constantly and not continuously. The difficulty lies in these notions of constant and continuous. Constant means unchanging, continuous means not stopping or not breaking off or apart.
Continuous motions must continue to move, even if they cahnge direction, but the same cannot be said of forces if they are defined as tangential. If however we define a continuous force, then we may use it in such a manner, but in the Newtin Model, no such force is defined. A compound force is defined, but it is not made up of continuous parts, and so the compound force is not continuous. Continuous forces do exist, and i believe that Torque is one of those forces, but being strict to the model means we are only talking about instantaneous, and thus non continuous and non constant forces, governed by the third law.
So back to the centrifugal model, this instantaneous transmission of quantity of motion by the tensile rope clearly also generates local rotational motion, and thus instantaneous Torque. However we can see hat in this case the instantaneous torque is balanced, so as to not continually accelerate the local rotation. this is a factor of the attachment of the tensile rope. Consequently Newton did experiments with buckets containing rotating liquids. The idea was to try to get a degree of freedom which was only acted upon by the instantaneous accelerations, not the pressure from the bucket or the tensile rope. Whatever his conclusions were he never seems to have fully published, but we can see the development of these ideas in the topic of gyroscopy. Eric Laithwaite is probably the best non conventional researcher in this area, and sadly he has passed on, but left a powerful legacy.
The Third law of Newton allows for a Torque force to be added that is different to and a weakr element of the total force resolution f any orbital system. The notion of torque which is based on couples is not the same as the instantaneous forces discussed in the orbital context. This instantaneous torque force may be the coriolis force, i have not yet an opinion on that, but what it is not is the couple moment.
The Newtonian pressure attraction model contains this weak Torque force along with the weak acceleration of the pressure wall or attractor, but there are powerful tensile or tangential forces that are instantaneously being accessed to perform this orbiting motion, forces that are linked to those that hold bodies together or accelerate bodies in any fixed direction. My only example is the induction motor, which yes is usually explained in terms of moment couples, but this is in fact an accepted approximate explanation. We all know we have to switch the magnetic fields on and off and rely on angular momentum. We do not accept that a similar thing is occurring gravitationally! For this reason a weal torque force is necessary to destabilise the systems so that rotation may occur.
One of the biggest shifts in our fundamental distinctions that we have made is in relation to electrostatics and magnetism. What was once non magnetic is now diamagnetic, and what was once called an insulator we now call dielectric. Thus we now have a basis for an entirely electromagnetic theory of gravitational action, Something Newton pondered about for the rest of his life.
What model of space interaction does this give? It seems to me that a weak torque force exists around every regional pole in Shunya, with powerful radiating forces that push and/or pull bodies towards poles or away from poles. That is the nature of the force field, the resultant motion field, or it could be the other way round, that the motion field generates the force field, whatever it may be the resultant motion field allows for strong linear accelerations and high resultant velocities, strong rotational accelerations only proportional to the strength of the centralising accelerations. Thus an orbiting body rotates faster the closer it is to the pole to which it is being pressed and or pulled. and slower the further away it is.
What does this mean for unifyng electromagnetism and gravity? We could posit the strong radiating forces as electromagnetic, and the weal torquing force as gravitational, and we could do the same for the weak and strong nuclear forces.
What say you?
