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Generalized Form of Newton’s Third Law of motion and NASA’s EmDrive
Ajay Sharma
Fundamental Physics Society His Mercy Enclave, Post Box 107 GPO Shimla 171001 HP India
Email: ajoy.plus@gmail.com
Abstract
In Newton’s Principia the Third Law of Motion states: ‘to every action there is always opposed
an equal reaction.’ The law only refers to the ‘bodies’, not to any other factors. The law is
universally applicable to all elastic or nonelastic or all types bodies and surfaces without any
constraints at all. But practically the law does not take into account the significant factors e.g.
inherent characteristics, nature, compositions, flexibility, rigidity, magnitude, size, elasticity,
shape , distinctiveness of interacting bodies, mode of interactions, point of impact etc. The
bodies may be of steel, wood, rubber, cloth, wool, sponge, spring, typical plastic, porous
material, mud or kneaded flour or chewing gum specifically fabricated material etc. The
interacting bodies may be solid, liquid, gas or mixture of all. For all such bodies if the action is
same, then the reaction must be the same. In the Principia Newton had given just three
qualitative examples to illustrate the law. Thus, to take elusive and effective factors into account,
the Third Law of Motion is generalized as: ‘To every action there may be reaction, but may or
may not be always equal and opposite, depending upon the inherent characteristics of the
interacting bodies.’ Mathematically, Reaction =K action, the value of K may be equal to, less
than, or greater than unity depending upon experimental parameters. The value of coefficient of
proportionality K takes in account the inherent characteristics of the process. It is justified in
collisions and other experiments. The third law is true under ideal conditions only and Newton
has neglected numerous examples. NASA’s recent paper on EmDrive confirms that there is no
reaction for definite action, thus confirming the inadequacy of the third law. Chinese scientists
have claimed that they have already achieved similar results and further tests are being
conducted aboard China's Tiangong2 space station using EmDrive. These finding are consistent
with author’s generalized form of third law published earlier.
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1.0 The Principia’s Third Law of Motion
The original form of the Third Law of Motion is:
To every action there is always opposed an equal reaction; or the mutual actions of two
bodies upon each other are always equal, and directed to contrary parts. [1,2].
Action =  Reaction (1)
or Mutual action of one body =  Mutual reaction of other body (1)
There is no other factor in the law. The equation indicates the action and reaction are universally
equal without constraints for elastic or nonelastic or all type of bodies etc. The bodies can be of
solid, liquid, gas or mixture of all. The law is applicable for all bodies thus can be considered for
waves as well.
In Newton’s time it was beginning of science in systematic way. Thus
physical quantities, units, dimensions were not defined. Thus the terms action and reaction do
not possess units and dimensions, as Newton did not define action and reaction in terms of
specific physical quantities. However, in the qualitative explanation given after the definition to
the law, Newton expressed action and reaction in terms of push or pull (force) and motion
(velocity), in the Principia at page 20. Newton did not write eq. (1) in the Principia. Newton
wrote the Principia’s Second Law of Motion in proportionality form like Law of Gravitation, but
The Third Law is expressed in equality form, which implies that all other factors are
insignificant. The third law is true under ideal conditions only and Newton has neglected
numerous examples.
2.0 Newton’s Original Explanation of the Third Law of Motion in the Principia
“Whatever draws or presses another is as much drawn or pressed by that other. If you press a
stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a
rope, the horse (if I may so say) will be equally drawn back towards the stone: for the distended
rope, by the same endeavour to relax or unbend itself, will draw the horse as much towards the
stone as it does the stone towards the horse, and will obstruct the progress of the one as much as
it advances that of the other.
If a body impinges upon another and by its force change the motion of the other, that body also
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(because of the quality of, the mutual pressure) will undergo an equal change, in its own motion,
towards the contrary part. The changes made by these actions are equal, not in the velocities but
in the motions of bodies; that is to say, if the bodies are not hindered by any other impediments.
For, because the motions are equally changed, the changes of the velocities made towards
contrary parts are reciprocally proportional to the bodies. This law takes place also in
attractions, as will be proved in the next scholium.”
In the Principia , Newton did not write any equation to explain the Third Law of
Motion quantitatively. For example, one cannot measure force applied by horse on stone and
force with which horse is pulled by stone. Similar is the case when one body impinges on the
other. Further, there is no equation given by Newton to calculate change in motion of projectile
and target. So the illustration is qualitative, not quantitative in the Principia.
3.0 Newton did not consider the following experiments.
In the Principia Newton had only given three qualitative examples to justify the definition of the
third law of motion and neglected numerous other examples which can alter the definition. The
following simple experiments (along with many others) have not been considered by Newton at
all while formulating and elaborating the third law of motion. Thus these are discussed here.
(i) Consider a rubber ball of mass 0.1 kg each. Let ball is dropped from height of 1 meter, and
reaches the floor in time t. Then it will have weight/force 0.98N or energy (mgh), 0.98J , the
action. If the mass of ball (irrespective of characteristics, composition etc. ) is same and dropped
from same height 1m then its action i.e. force or weight 9.8N or energy 0.98J is same. It must
be noted that Newton had expressed action and reaction in terms of push or pull (force) , motion
(velocity) , just after definition of the law in the Principia.
After striking the floor (action) the rubber ball rebounds (reaction) identically i.e. reach the
same point (1m above ) in the same time t. Thus reaction is 0.98N. Obviously action and
reaction (may be expressed in terms of force or energy) are same, and Newton’s law holds good.
Action (0.98N) = Reaction (0.98N) (2)
This observation is completely consistent with Newton’s Third Law of Motion.
(ii) If all other parameters remain the same (rubber ball 0.1kg, height 1 meter ) as in first case
but now ball falls on the mattress ( rather than on floor). Now we find that the rubber ball
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rebounds to ½ meter from mattress, in previous case it rebounded to 1m and 2m. The action
(0.98N) is same in all the three cases. The inherent characteristics of floor and mattress are
entirely different causing different interactions between projectiles and targets. Thus the rubber
ball of same mass rebounded to the lesser height means possesses lesser reaction (force) than
previous case. Hence
Reaction = ½ Action (3)
or Reaction <Action
It is undoubtedly clear that the reaction depends upon the inherent characteristics of system,
which are not taken in account by the Principia’s third law.
(iii) Super elastic collisions: Consider a specially fabricated rubber ( or suitable material) ball
of mass 0.1 kg. Let this ball is also dropped from height of 1 meter, on the specially fabricated
floor. This ball will have action (Weight =0.98N or energy 0.98J).
After striking this specially fabricated floor the rubber ball rebound to greater height, say 2m in
time t then reaction would be double,
Reaction =2 Action (4)
or Reaction >Action
Thus in this case the reaction is twice the action. Had this specially fabricated ball rises to height
of 1m only, then reaction would have been equal to action. Hence there would have been no
scope for debate on quantitative validity of the law. But in super elastic collisions the interactions
of target and projectile are such that after the collision the kinetic energy is double. It is only
possible with specially fabricated projectile and target which have special characteristics.
Imagine a massive spring of high spring constant being compressed with an
extremely delicate device (i.e. once touched will release the spring). Now we can envision that a
collision between a slowly moving particle and this device, would release the spring and the final
kinetic energies of the massive spring and the particle will be larger than their initial one,
because the elastic potential energy was converted into kinetic energy. It would have been due to
inherent characteristics of the projectile and target which are never taken in account in the
Principia’s third law of motion, but correctly taken in account in generalized form of third law of
motion.
(iv) Further, if a typical sponge ball of mass 0.1kg (W=0.98N, energy =0.98J or action) is
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dropped from the height 1m on the soft surface. Then it does not rebound at all. Thus
Action = 0.98N (5)
Reaction =0 (6)
Again action and reaction are not equal. It is due to characteristics of system, which are not
taken in account by third law of motion. Action and reaction would have been equal if the
sponge ball would have risen to original height of 1m in time t.
(v) If the golden ball (sharp edged) of mass 0.1kg (W=0.98N or Energy =0.98J) is dropped on
the stretched paper, then it pierces through it. The reason is that the paper is unable to offer even
fraction of reaction compared to action. Thus due to this paper cannot stop ball and later tears it
and falls down. The similar is the reason a bullet pierces through the wall, tree of body.
Thus the Third Law of Motion is true under special or ideal conditions only. Had Newton
thought about these and similar other experiments he would have given the Third Law of Motion
in different way i.e. in generalized form.
Thus it is evident from various discussed examples, that different reactions for same mass (
same action) are different due to inherent characteristics, nature, compositions , flexibility,
rigidity etc. of projectiles and targets. The Principia’s third law neglects all these factors.
Hence third law has been generalized or extended so that the factors described in article are taken
in account.
(vi) The similar results are obtained in onedimensional elastic collisions [34]. Furthermore, in
collisions comparative size and point of impact, of target and projectile, roughness of surfaces
and resistive forces play significant roles. In collisions the mathematical equations indicate law is
true under ideal or special conditions only, not in general [6]. Thus law may be regarded as under
ideal conditions only. Like this collision of ball on the wall can also be considered.
Further Newton’s law is completely silent about electrical and magnetic interactions between
the various bodies, these are exception in some cases. The similar poles of magnets are drifted
away before striking whereas opposite poles stuck together and do not suffer any reaction. For
comprehensive understanding such experiments can be conducted in space under zero or reduced
gravity conditions.
(vii) Let a rocket weighing equal to 5,000kg is moving with speed 8,00m/s i.e. momentum
(forward ) 4x106 kg m/s. Third law implies that the backward momentum of exhaust ( gases,
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smoke etc ) must be equal to 4x106 kg m/s. But such measurements have never been reported,
as it is impossible to measure mass of exhaust at any instant. Thus in this case third law must be
regarded as qualitatively true only. The toy aeroplanes fly with electronic batteries do not emit
any exhaust required for validity of third law. If exhaust is necessary for rocket , then it would
have been absolute requirement for motion of bus , truck, train, ship , moving electronic
equipments etc. The trials can be made by reducing the resistive forces to bare minimum of the
system as well.
Table I. Comparison of action and reaction when body of mass (0.1kg or 0.98N or 0.98 J,
Action) of different characteristics striking at different surfaces when dropped from the
same height. The action is same for all bodies (0.1kg is 0.98N ) but reactions may be
different.
Sr.
No.
Projectile
Ball (0.1kg)
Striking
surface
Action
(body dropped)
Reaction
(body rises)
Deduction
1
Rubber
Floor
1m
1m
Action =Reaction
2
Rubber
Mattress
1m
½ m
Reaction = ½
Action
3
Specially
fabricated
Specially
fabricated
1m
2m
Reaction = 2Action
4
Sponge
Soft surface
1m
0
Action =0
5
Golden
Paper
1m
0
Reaction?
(paper torn)
Note. Action and reaction are equal only in first case, unequal in all other cases.
4.0 The reasons for inconsistent results
Newton did not give any equation to measure or calculate the magnitudes of action and
reaction. Newton’s explanation is only qualitative. Thus Newton provided conceptual, thematic
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and philosophical explanation of the law, not quantitative which is understandable for scientific
developments in 17th century. Newton’s law is unconditionally applicable to all interacting
bodies, action and reaction are always equal and opposite for all interacting bodies. In the Table
I, five examples are shown and only one is consistent with third law of motion. One may argue
that ball bounces to different heights due to reason they have different inherent properties. It is
true but the Principia’s third law of motion does not take in account the inherent
characteristics, nature, composition , flexibility etc. in account for projectile and target.
The Principia’s law does not take in account the inherent
characteristics, nature, composition, flexibility, rigidity, magnitude, size, distinctiveness of
interacting bodies etc. There is no term, which accounts for the above significant factors. The
bodies may be composed of steel, wood, rubber, cloth, wool, sponge, spring, elastic , plastic,
typical plastic, porous material, mud or kneaded flour or chewing gum, especially fabricated
etc. The bodies may be solids, liquids, gases, or mixture of all. These factors play important role
in action and reaction phenomena. In the Principia’s third law Newton blatantly neglected these
factors. These are very significant factors affecting the results and are taken in account via a
coefficient of proportionality (K) in the generalized law i.e. eq.(32). The value of K is
determined experimentally. Due to these factors different bodies experience different reaction
for same action. In the preface Newton did not mention name of any scientist who read the
manuscript. So Newton did not mention these factors at all and summed up the basic law just
giving three qualitative examples. Just possible that Edmund Halley (sponsor or publisher)
wanted the manuscript as soon as possible. Also other contemporary scientists like Robert Hook
and Leibniz were raising priority issues.
4.0 The various types of collisions and the Third Law of Motion.
Newton applied the Third Law of Motion to the collisions in third qualitative example in the
Principia. “If a body impinges upon another and by its force change the motion of the other, that
body also will undergo an equal change, in its own motion, towards the contrary part.”
The definition is universally applicable irrespective of characteristics of the projectile
and target. Collisions in which both momentum and kinetic energy of the system are conserved
are called elastic collisions [34]. The coefficient of restitution or coefficient of resilience is unity
(e = 1). Consider projectile and target of masses M1 and M2 moving along the same straight line
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with speeds u1 and u2 respectively. The bodies will collide only if u1 > u2. The final speeds of
projectile and target are v1 and v2.
v1 =
21
22121 2
MM
uMuMM
(7) v2 =
21
11212 2
MM
uMuMM
(8)
If the target is at rest (u2 = 0), then Eqs. (78) become
v1 =
21
121
MM
uMM
(9) v2 =
21
11
2
MM
uM
(10)
The initial velocity of u1 of the projectile is regarded as action, and its final velocity v1 as
reaction. The various subcases are discussed below.
(i) When M2 >> M1 i.e. target is very massive compared to the projectile. The target M2
remains at rest v2=0. For example, when projectile (ball) collide with huge target (wall). Thus
M1  M2 = M2, M2 + M1 = M2
In this case the final speeds of the projectile and target can be calculated from eqs.(910).
v1 (reaction) =
2
12
M
uM
= u1 (action) (11)
Final speed of projectile = Initial speed projectile.
Action (u1) = Reaction (v1) (12)
The velocity of target , v2=0
Thus projectile (ball) rebounds with original velocity and target (wall) remains at rest, the third
law is obeyed. The negative sign in v1 indicates that direction of projectile reverses after
collision. e =
21
12
uu
vv
=
1
1
u
u
=1 (13)
As the coefficient of restitution is unity, the collision is elastic.
Ideal calculations only: However these are ideal mathematical calculations as we have not
considered actual experimental characteristics at all i.e. magnitude, shapes, sizes of projectile and
target, point of impact, resistive force , compositions etc. The composition of various bodies
may be different [5] e.g. body B can be of cloth and body A of wood, body B can be water
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filled ball and body A of aluminum, body B may be an air filled football and body A of gold,
etc. The various experiments must be conducted before drawing final conclusions.
(ii) Mass of target is 1000 times larger than that of projectile. If we consider that the target
is 1000 times more massive than the projectile i.e. M2 = 1000M1, M1+M2 = 1001M2 , M1M2 =
999M2 then eq.(9) becomes
v1 = 0.998001998u1 (14 )
u1 = 1.002002v1
Initial velocity of projectile or action = 1.002002 final velocity of target or reaction
Action(u1)=1.002002Reaction(v1) (15)
Thus Newton’s third law of motion is not justified in this case. The collision is elastic as
e =
21
12
uu
vv
= [
1
11
1001
2
M
uM

1
11
1001
999
M
uM
]/[u10] = 1 (16)
(iii) Let us consider the case when the target is very2 small compared to projectile. (
M2<<M1 or even mass of target may be negligible compared to projectile). M2+M1 = M2. The
various velocities can be calculated. Now from eqs.(910)
v1=
M
uM 11
=u1 (17)
Reaction = Action
Thus the projectile does not rebound at all , which is contrary to original form of third law of
motion i.e. ‘to every action there is opposite and equal reaction.’
It implies that inherent characteristics, nature, magnitude, shape, size, point of impact of
projectile and target play significant roles in experiments. These are not taken in account by
original form of law, hence Principia’s law is generalized.
v2 =
1
1
11 2
2u
M
uM
(18)
The final velocity of target = 2 initial velocity of projectile.
This situation can be theoretically understood by visualizing a ball hanging in air in train track .
The moving train ( projectile) hits the ball, the ball moves with double velocity of train and train
keep on moving with original velocity. Further it is the maximum velocity which a target can
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obtain, thus this prediction is true under special conditions only. The velocity may be different in
case of super elastic collisions.
e =
21
12
uu
vv
=
1
11
2
u
uu
=u1 (19)
(vi) Let us consider the target is slightly heavier than projectile i.e. M2 =1.01M1
Thus, M1M2 = M11.01M1=  0.01M1, M1+M2= M1+1.01M1=1.01M1
In this case the final velocities of projectile and target are can be calculated from eqs.( 910 )
v1 =
11
111
01.1
01.1
MM
uMM
=
1
11
01.2
01.0
M
uM
= 0.004975u1 (20)
Final velocity of projectile =  0.004975 Initial velocity of projectile.
Action = 201.005 Reaction (21)
The negative sign in v1 indicates that direction of projectile after collision reverses. But
magnitudes of action and reaction are different, thus third law is not obeyed.
v2 =
11
11
01.1
2
MM
uM
=
1
11
01.2
2
M
uM
= 0.995024u1 (22)
The coefficient of restitution in this case is also unity i.e.
e =
21
12
uu
vv
= [
1
11
01.2
2
M
uM
+
1
11
01.2
01.0
M
uM
]/[u10] =1 (23)
(v) Let us consider the case when masses of projectile and target are equal i.e. M1=M2 =M.
The various velocities can be calculated (u2>0). Now from eqs.(78) we get
v1 =
21
22121 2
MM
uMuMM
=
MM
Mu
2
20
(24)
v1 ( reaction) = u2
v2 =
21
11212 2
MM
uMuMM
=
MM
Mu
1
20
(25)
v2 = u1 (initial velocity of projectile)
Thus projectile and target exchange their velocities, and continue to move in the same direction.
Let projectile is moving with velocity 10m/s and target 5m/s , only then they will collide (
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u1>u2) . After collision projectile does not rebound , thus suffers no reaction and there is no
motion in reverse direction, and moves with reduced velocity 5m/s. The third law of motion is
not obeyed as there is no reaction (the projectile does not retrace the path).
(vi) Let us consider the case when masses of projectile and target are equal i.e. M1=M2 =M.
Now consider the case when target is at rest (u2 =0), then we get,
v1 =
MM
0
=0 (26)
The projectile comes to rest after collision i.e. reaction =0
v2 =
M
uM
2
21
= u1 (27)
Final velocity of target = Initial velocity of projectile
Experimentally it can be easily observed if one marble properly hits other in typical collision ;
then one marble (projectile) comes to rest and target starts moving with velocity of projectile.
Table II . The theoretical comparison of action and reaction (initial and final velocities of
projectile) under ideal conditions, in elastic collisions (coefficient of restitution, e=1). The
Principia’s Third Law is obeyed in first case only.
Sr.
No
Projectile
(mass)
Target
(mass)
Initial
velocity
(action)
Final
velocity
(reaction)
Action = Reaction
Third
Law
Obeyed
1
M1
M2>>M1
u1
u1
Action =Reaction
Yes
2
M1
M2=1000M1
u1
0.998002 u1
Action =1.002 Reaction
No
3
M1
M2<<M1
u1
+u1
Reaction=0, No rebound
No
4
M1
M1 =M2
u1
v1 =0
Reaction =0, projectile at rest
4
M1
M2=1.01M1
u1
0.004975u1
Action = 201 Reaction
No
5
M1
M1=M2
u1
u2
Reaction=0, No rebound
No
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Note : The action and reaction are equal only in first case.
5.0 The various bodies struck on the various targets
Consider a gun or injecting /firing device is specially fabricated for throwing various bodies with
known force on the target (concrete wall, say). Let the gun is placed at 5 meters away from the
wall.
(i) The rubber ball is thrown to the wall after firing the gun and reaches the target at 5m in time
t. Let the force applied on the ball be Faction. The ball strikes the wall and rebounds to original
position travelling distance 5m in time t. Thus, the ball rebounds or retraces its path identically.
The Freaction and Faction are same.
Faction =  Freaction (28)
Thus Newton’s Third Law is obeyed.
(ii) Let especially a rubber ball is fabricated. The rubber ball is thrown on the wall after firing the
gun and reaches the target at 5m in time t. Thus, action be Faction. After striking, the ball
rebounds to original position in time t/2 s. Thus in this case reaction will be Freaction or 2 Faction .
Thus
Freaction = 2Faction (29)
or Faction ≠ Freaction
(iii) Consider a chewing gum ball of the same mass ( as in above two cases). The chewing gum
is thrown on the wall after firing the gun and reaches the target at 5m in time t. After striking the
wall the chewing gum sticks to wall and does not rebound. Thus
Freaction = 0 (30)
Hence in this Newton’s third law is not obeyed.
Faction ≠ Freaction
(vi) Now consider that the concrete wall is replaced by cardboard wall. The rubber ball is
thrown at the wall after firing the gun and reaches the target at 5m in time t. Let the force applied
on the wall be Faction. Now as the ball strikes at the cardboard wall, it breaks and rubber ball
crosses the broken cardboard wall. The ball does not rebound hence
Freaction = 0 (31)
Faction ≠ Freaction
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Thus third law of motion is not obeyed.
(v) Consider two magnets A and B of equal and significant pole strengths. Let both the magnets
are placed on the smooth table at distance of ½ m (say).
(a) Let the north pole of magnet B is pushed with force Faction towards south pole of magnet A
(stationary). As the opposite poles attract each other, so both the magnets are stuck to each
other. Thus magnet B does not retraces its path, as according to Newton to every action there
must be reaction (motion in opposite direction). But in this cases reaction is zero i.e.
Freaction = 0 and Faction ≠ Freaction
(b) Let the north pole of magnet B is pushed with force Faction towards north pole of magnet A.
The opposite poles of magnets repel each other. When magnets come in the magnetic field of
each other, they repel each other and move away. There is definite reaction without physical
contact.
Table III Comparison of action and reaction, for various bodies colliding various surfaces
Sr.
No.
Projectile
Target
Action
Reaction
Third Law of Motion
1
Rubber ball
Concrete wall
Faction
Faction
Action = Reaction
2
Rubber ball
(special)
Concrete wall
(specially fabricated)
Faction
½ Faction
Faction ≠ Freaction
3
Rubber wall
Cardboard wall
Faction
0
(wall
breaks )
Faction ≠ Freaction
4
Chewing gum
ball
Concrete wall
Faction
0
( ball
sticks)
Faction ≠ Freaction
5
Magnet B
Magnet A
(stationary)
Faction
0
(Magnets
Faction ≠ Freaction
14
stick)
Note: One thing is common in illustration in Table ITable III, that the Pricipia’s third law of otio
neglects the characteristics of body, which are experimentally significant.
6.0 Generalized form of the Third Law of Motion rebound
It is a basic principle of science that no conclusions can be drawn on the basis of a single or few
qualitative observations. If the results are repeated under all conditions for different parameters,
only then the law is accepted experimentally.
On the basis of the above observations The Principia’s Third Law of Motion is generalized:
‘To every action there may be reaction, but may or may not be always equal and opposite;
depending upon the inherent characteristics of the interacting bodies.’ or
“The mutual actions of two bodies may not always be equal and opposite, depending upon the
inherent characteristics of the interacting system.”.
Action
Reaction
or Reaction =  K Action (32)
K is the coefficient of proportionality and depends upon the inherent characteristics of
interacting bodies. The coefficient of proportionality takes into account the inherent
characteristics, nature, composition, flexibility, elasticity, rigidity, magnitude, plasticity,
distinctiveness of interacting bodies. The bodies may be of steel, wood, rubber, cloth, wool, clay,
kneaded flour, chewing gum , sponge, spring, etc. The bodies can be of solid, liquid, gas or
mixture of all. The law is applicable for all bodies thus can be considered for waves as well. The
coefficient of proportionality, K is consistent with existing coefficients in physics and can be
experimentally determined. Thus generalized form of third law is universally applicable, and the
Principia’s law is applicable for ideal or super special cases only.
7.0 The results of NASA’s Electromagnetic Drive
NASA's Eagleworks Laboratory reported significant results for the EmDrive
(the “EM” stands for “electromagnetic”), violating the third law of motion. The EmDrive works
without any fuel or propellants at all; by simply bouncing microwave photons back and forth
inside a coneshaped closed metal cavity. This appears to violate wellestablished laws of
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physics ( the engine moved forward without exhaust ) such as the third law of motion . NASA’s
Johnson Space Center reported the thrust data from forward, reverse, and null suggested that the
system was consistently performing at 1.2 ± 0.1 millinewton/kilowatt, which was very close to
the average impulsive performance measured in air [6]. The system is completely reaction less
i.e. value of K in eq.(32 ) tends to zero. The value of K depends upon inherent characteristics
of the system. The original inventor of EmDrive Roger Shawyer predicted that it will make
space travels cheaper and quicker, and can take spacecraft to mars just in 70 days.
Chinese scientists too have supported NASA’s results as they too have found similar
results earlier and they are conducting the same , Em Drive experiments in zero gravity situations
in the Tiangong 2 space station. Then scientists plan to project satellites in space with this
technique. However Chinese scientists have not released the experimental data and design of
their EM Derive yet, so no comparison is possible available observations of NASA. The success
of experiments will automatically establish the generalized form of third law of motion and
cheaper methods for space flights.
8.0 Statistical Mechanics where Newton’s Third Law is Broken
The limitations of the third law of motion can be understood in statistical mechanics also. Even
though it is one of the fundamental laws of physics, Newton's third law has been violated in
certain nonequilibrium (outofbalance) situations. Generally, the actionreaction symmetry can
be broken for mesoscopic particles, when their effective interactions are mediated by a
nonequilibrium environment. When two objects or particles violate the third law, they are said to
have nonreciprocal interactions. Violations can occur when the environment becomes involved
in the interaction between the two particles in some way, such as when an environment moves
with respect to the two particles. The different classes of nonreciprocal interactions relevant to
real experimental situations are investigated and statistical mechanics analysis has been
presented by Ivlev et al [7]. They have verified the principal theoretical predictions in
experimental tests performed with twodimensional binary complex plasmas. Thus inadequacy
of third law of motion can be illustrated in different ways.
9.0 Conclusions
The Pincipia’s third law of motion is universally applicable to all elastic or nonelastic or all
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types bodies. But practically the law does not take into account the significant factors e.g.
inherent characteristics, nature, compositions, flexibility, rigidity, magnitude, size, elasticity,
shape , distinctiveness of interacting bodies, mode of interactions, point of impact etc. The
bodies may be of steel, wood, rubber, cloth, wool, sponge, spring, typical plastic, porous
material, mud or kneaded flour or chewing gum specifically fabricated material etc. The
interacting bodies may be solid, liquid, gas or mixture of all. These factors affect the reaction,
hence the law is generalized to take these in account as
‘To every action there may be reaction, but may or may not be always equal and opposite;
depending upon the inherent characteristics of the interacting bodies.’
Now mathematically the generalized form is given by eq.(32) i.e. Reaction =  K Action, where
coefficient K accounts for elusive factors as mentioned above. The third law is true under ideal
conditions only and Newton has neglected numerous examples, which can be explained with the
generalized for of third law of motion.
Acknowledgements
The author is highly indebted to Prof. Robert Bradley, Dr. Steve Crothers and Anjana Sharma
for encouragement at various stages of the work.
References
[1] I. Newton, Mathematical Principles of Natural Philosophy (printed for Benjamin Motte,
Middle Temple Gate, London, 1727 ), pp.1920, translated by Andrew Motte from the Latin.
[2] I. Newton, Mathematical Principles of Natural Philosophy
http://books.google.co.in/books?id=Tm0FAAAAQAAJ&pg=PA1&redir_esc=y#v=onepage&q&
f=false accessed on 8th January 2017
[3] Elastic collision http://en.wikipedia.org/wiki/Elastic_collision accessed on 3rd January 3,
2017
[4 ] R. Resnick and D. Halliday, Physics Part I (Wiley Eastern limited, New Delhi, 2nd Ed. 1996
reprinted ), pp.21522
[5] Sharma, A Acta Ciencia Indica Vol. XXV P No.3 113 (1999)