The cause of inertia

Abstract. This paper presents the cause for inertia. We present a theoretical model of the mechanism of inertia and propose an experiment to test the new theory. Inertia is emerging at macroscopic level from the variable inertia of the microscopic particles which compose an object. The rectilinear uniform motion is just false impression caused by sinusoidal rectilinear motion. The mechanism of inertia reveals that inertia is quantized.


The principle of inertia suggests two main points. First, it implies that an object cannot act upon itself to start moving uniformly or to stop from uniform motion. Secondly, it suggests that in absence of an external force acting on it an object moving rectilinearly can move only uniformly. In this paper, we argue against those conclusions, exposing that the object itself is the main cause of inertia. In the next section we present an experiment together with a theoretical model which describes the continuous motion of an object in absence of external forces. Since inertia is continuous motion in lack of external forces, we reason that our experiment describes in fact the mechanism of inertia. We show that inertia is an undulatory rectilinear motion of an object which is maintained by the object itself. The cause of inertia was veiled by the assumption included in its definition saying that an object moves uniformly after it is not acted upon by an external force anymore. We explain then that macroscopically we view motion as uniform due to the undulatory motion of the atomic particles which compose the object.

The Mechanism of Inertia

In order to investigate inertia we describe in Figure 1 a system consisting of two devices connected back-to-back along their common side OO’, with O being the origin of the reference system. We assume that the devices are mechanically or electromagnetically connected together being possible to easily disconnect the devices as need it during the experiment.

Each device consists of a plate of mass M and two weights of mass, m, that are attached on the plate and that can rotate around the connecting pivoting points on an arm of length r and of negligible mass. The weights of the first device (i.e. device 1) rotate in opposing direction of the weights of the second device (i.e. device 2). Within a device the weights rotate in opposing directions, one clockwise and another counterclockwise. We assume that all weights start rotating in the same time and with the same constant speed, v, and that they move synchronously. As they rotate, the weights will pull the devices with equal centrifugal forces, F.

Figure 2 shows the state of the system as the weights pass through the points located at 450 from their starting position shown in Figure 1. The entire system is in equilibrium remaining at rest because the centrifugal forces cancel each other out.

Figure 1

Figure 2

If we split de system along the OO’ axis, disconnecting the devices from each other at the moment when the weights pass through their starting position, then the system will lose its equilibrium. The components of the centrifugal forces on the y-axis, Fy, will not cancel each other anymore, exerting a traction force on each device. Note that the components of the centrifugal forces on x-axis, Fx, cancel each other out in each device. As a result of the Fy forces, the devices will move away in opposite directions on the y-axis. For device 1, the acceleration caused by the Fy forces is given by equation (1):



where ω is the angular velocity given by ω = v/r.

The equation of the speed vy with which device 1 moves along y-axis can be easily calculated as follows:



where C1 is a constant which can be calculated knowing that at the start time, t = 0, the device is at rest, vy = 0. Therefore C1 is given by:



Rewriting C1 in equation (2), the speed of device 1 becomes:



If we define the constant kmvr = 2mv/(2m + M), then equation (4) becomes:



The coordinate of device 1 as it moves along y-axis is given by:



Where C2 = 0 since y = 0 at t = 0. Thus:



The equation of speed is relevant for our analysis. It shows that an object moves continuously under its own action, accelerating and decelerating by itself until it stops and then it continues with this cycle forever as shown in Figure 3. The object moves on a straight-line. In short, we say that the object has a sinusoidal rectilinear motion.

Figure 3

The period of the motion depends on the angular velocity of the rotating subparts of the object according to the formulas known from classical physics: T=2π/ω. At high frequencies the motion would appear as uniform, an observer seeing only the envelope not noticing the stops of the object. Another factor which would make the motion appear as uniform is the constant kmvr which gives the amplitude of the speed variations. When kmvr is very small an observer would not be able to see speed changes, but he will see only a constant speed. Note that if we know the angular velocity and the constant kmvr, then all parameters of the motion – speed, acceleration, coordinates – can be calculated from equations (1), (5) and (6).

The formulas for the sinusoidal rectilinear motion could have been deduced by using an experiment with one single device set near a wall on a frictionless surface like shown in Figure 4.

Figure 4

The experiments described in Figure 1 and Figure 4 have been developed in Algodoo, a physics simulator, the simulation confirming the sinusoidal rectilinear motion deduced in this paper.

The case of the motion with multiple rotating objects in three-dimensional space is similar to the analysis done for the rotation of two weights in the two-dimensional space, since the components of the centrifugal forces on the x-axis and z-axis cancel each other out, the component on the y-axis remaining again the only relevant force. We also assume that other internal forces, such elastic forces, can create repetitive rectilinear motion, but their speed would change according to other formulas. We will not present in this paper the analysis of models using elastic forces or threedimensional coordinates, but focus on interpreting the results of the two-dimensional analysis of the sinusoidal rectilinear motion.

Consequences of Sinusoidal Rectiliniar Motion

There are several direct observations which result from the analysis of the experiment described in this paper.

1. Emergence of uniform inertia

The motion of device 1 appears to violate Newton’s laws of motion, but we must note that the object does not move uniformly as stated in the first law of motion. The sinusoidal rectilinear motion describes the mechanism of sinusoidal inertia, showing how objects keep moving continuously on a straight path in absence of external forces but using only internal forces. The rectilinear uniform motion emerges from the sinusoidal rectilinear motion for specific values of the angular velocity and of the constant kmvr. For formality only, we denominate Newtonian inertia as uniform inertia and the sinusoidal inertia as variable inertia. The macroscopic uniform inertia emerges from the microscopic variable inertia of the atomic particles. We note that uniform inertia can emerge at macroscopic level from macroscopic variable inertia as well.

2. Quantization of inertia

The graph of the speed displayed in Figure 3 shows that inertia of an object in sinusoidal rectilinear motion is quantized. Consequently, its kinetic energy is quantized as well.

3. Effects of sinusoidal inertia

Similar to uniform inertia, the sinusoidal inertia is not felt inside the moving objects. In addition, an object can start in and stop from sinusoidal rectilinear motion without an impact on the object or its components. Furthermore, knowing initial conditions, angular velocity and kmvr, the speed of a system in sinusoidal rectilinear motion can be calculated at any time from inside the system by measuring the position of the rotating weights.

4. Conversion from sinusoidal rectilinear motion to rest and uniform rectilinear motion

Let us assume that while device 1 is in sinusoidal motion after the split from device 2, we release the weights from the arms at the moment when they pass through their starting position. Since the device is just a plate without walls, the weights will fly away from the device as displayed in Figure 5.

Figure 5

When the weights are released, device 1 is at rest in the reference system. Since no other external or internal forces will act on it, the device will remain at rest while the two weights will fly out continuing to move uniformly with speed v.

This may appear to violate Newton’s third law of motion because the device remains at rest after it throws out mass without moving in the opposite direction. But for an external observer, his perception is dependent on either he sees (measures) the motion of device 1 as sinusoidal or uniform prior the release of the weights.

This method of procedure can have practical applications for ground and space transportation for stopping a ship from high-speed to full stop without destroying it.

5. Wave-particle duality

Variable inertia provides a mechanism explaining how particles move as waves without the need of a particular medium. That has been a question of physics since the discovery of light’s wave behavior. Particles in sinusoidal rectilinear motion do not “wave”, but they have a sinusoidal kinetic energy which pose challenges in measuring.

The interference patterns observed with light and electrons may be caused by particles’ interaction with the particles of the measuring sensors and not by interference as in the case of mechanical waves.

Similarly, the interference pattern and the anomalies of the dual-slit experiment have now better grounds for studies in order to eliminate the ambiguities of current explanations.


In this paper we presented a theory for the cause of inertia. We introduced the concept of variable inertia as the ability of an object to move continuously in sinusoidal rectilinear motion. We demonstrated mathematically that the object is able to maintain such motion without an external force but only through the use of internal forces, such as the centrifugal forces. Inertia, as known by classical physics, emerges from the variable inertia of the microscopic particles which compose an object. The concept of variable inertia brings a new view on motion and physics in general. The impact on few concepts of physics has been briefly presented, but we foresee that, in the light of the new information on inertia, a revision is required of several other concepts of physics.


  1. Raymond A. Serway, Chris Vuille, College Physics, Brooks/Cole, 9th ed., Vol.1, p. 88, 2012

Note: The PDF version of this article can be downloaded from here: The cause of inertia.

The following video shows the simulation done in Algodoo for the device described in Figure 4.

Breaking Newton’s laws of motion

Newton’s first law of motion says that in an inertial frame of reference a “body remains at rest or in rectilinear uniform motion unless an external force acts upon it“. This law is a definition of inertia which is seen as a body’s capacity to stay at rest or move in uniform motion on straight line.

As we argued in the first article, The cause of inertia, there is also a sinusoidal motion on straight line which a body maintains unless an external force upon it. This situation is not included in Newton’s first law of motion, which talks about uniform motion only. We proposed then that the cause of the macroscopic inertia is emergent from the variable microscopic inertia of the particles which compose a body.

We considered then that such motion does not obey Newton’s laws of motion.

In order to provide further evidence for our argument we designed a much simpler experiment to show that a body changes its state from rest to uniform motion without external forces acting upon it. We start with one ball and a box at rest in empty space as shown in the following picture.

The ball is pushed towards the box which has an opening which closes automatically after the ball goes thru it inside the box. We assume that the ball and box have equal masses (1 kg) and that after is pushed the ball will move uniformly with 1 m/s. We ignore gravity and assume that the collisions between the ball and the inside walls of the box are perfectly elastic. In consequence, the ball will start bouncing between the walls of the box which will start moving as shown in the following simulation.

We notice that the box keeps changing its state from rest to uniform motion without any external force acting upon it, but only due to the collisions with the internal ball.

We consider that this body (the box together with the ball) violates Newton’s first and third laws of motion.

Yes, we know that the center of mass for this example moves uniformly and obeys mathematically Newton’s first laws of motion, but we believe that this is irrelevant for the physical world. Why?

In the physical world observers do not have information about the central of mass of the bodies they measure. For example, astronomers do not know if a remote star, galaxy or planet has any internal cores which move, rotate or bounce inside it. Similarly, in the microscopic world we consider electrons, photons and other particles as point masses without any internal dynamics or structure. Moreover, when we see a star at rest we do not have any information about its origin or past collisions which could have impacted its internal dynamics.

An external observer, looking at objects on sky or Earth, sees and analyzes their motion without dissecting them or knowing their history at their origin. For example, if we consider that the box in our example has front walls, then an external observer will see an object that moves suddenly from rest to uniform motion without any external force acting upon it, like shown in the following simulation.

Moreover, if we open the front wall of the box and let the ball move out of box like in the simulation below, then the external observer sees a body at rest which expels mass without moving backwards to conserve momentum. We could have also let the box move when the ball was at rest. These examples show an action without reaction which is a violation of Newton’s third law of motion.

Newton’s laws of motion cannot be declared universal since we do not know the internal structure or the history of collisions of the bodies in the universe or at microscopic level.