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The laws of motion have been well defined ever since Newton wrote his book on physics almost 400 years ago. Very little was left to describe after that. However, Newton never proposed a physical model for what was going on. His physics is entirely mathematical. No underlying mechanics is explained. He left this intentionally for others to explore.

Taking up Newton’s challenge, we will now investigate various phenomena related to motion and relate them back to our model. To do this, we will address the electron as our fundamental particle of inertial mass. Our macro world analogy for the electron will be the steel ball. Since we have as one of our premises that what’s going on at the subatomic is a direct reflection of what’s going on at the macro level, our steel ball analogy should be a very good fit for the electron.

With this in mind, let’s investigate the laws of motion in light of our model where everything has to be explained in terms of particles with 3 dimensions, size, motion and texture:

Pressures, tensions and impulses

Starting with our steel ball, we note that it does not move if we put it carefully on a plane tabletop. To make it move, we have to apply force to it, and the force has to be applied unevenly. If evenly applied, there’s pressure or tension in the ball, but no motion. Any energy passed onto the ball is immediately lost when force is evenly released after first having been evenly applied. However, when applied unevenly, force applied results in both linear motion and a change in energy.

From observations, we reach two conclusions:

  • Force has to be unevenly applied for an object to absorb energy.
  • Motion caused in this manner is always in the direction of force.

This can be explained in terms of our theory as follows:

  1. An impulse applied to a steel ball will result in a pressure wave, progressing through the ball.
  2. When the pressure wave reaches the far end of the steel ball, the ball expands by a tiny bit.
  3. The pressure wave returns to restore the shape of the ball.
  4. The shape is restored, but not its size.
  5. The new centre of mass is a tiny bit to the far end of the ball.
  6. To restore its shape, the ball moves in the direction of the new centre of mass.
  7. Without any new impulse, the ball continues in its new state, slightly larger and moving in the direction of the impulse that set it going.

This explanation is based on the idea that all particles will by their nature return to their original shape. We offer no explanation for this tendency. However, we can point out that the optimal ratio between surface area and volume is a sphere. There is therefore a good mathematical explanation for our axiom.

Time and inertia

Bringing this argument down to the electron, we note that the complete process of adding energy to the electron involves a pressure wave that has to first traverse its surface from one end to the other, and then return back to the point of the original impulse in order to restore its shape.

Assuming that the pressure wave moves at the speed of light, we note that it takes one half unit time to make the forward journey. The return journey takes another half unit time. This means that it always takes one unit time to complete an energy transfer onto or off of an electron. Our unit time is in other words something more than mere convention. It is tied directly to energy transfers in the real world. Measured time and physical time is one and the same thing.

Inertia can also be explained. It is the time-delay between impulse and completed energy transfer. This time-delay is very small for an electron, and very little energy is required. However, for a steel ball the process has to involve all its constituent particles in order to complete. This requires more time. More energy is also required because there are more particles over which to distribute the energy. Inertia becomes more noticeable. In the case of large trucks, ships and air-crafts, inertia becomes very noticeable.

Inertia is generally thought of as exclusively confined to inertial matter because photons and neutrinos never change their speed. However, photons and neutrinos can and do change their direction, and we have already concluded that this happens reluctantly. Large photons veer off to the side on their meandering trajectory through glass. This is for the same reason that steel balls do so when rolling down a curvy slide. We can therefore conclude that inertia is not strictly confined to inertial matter. Rather, inertial matter exhibit this phenomenon more fully due to its ability to move freely and unhindered by the aether. Since a change in direction can happen without any energy being added or subtracted, we note that inertia is not only a matter of energy transfers. There is something else going on as well.

Pilot waves as memory

Returning to the steel ball that we have just set in motion with an impulse, we see that it is again in a rest state. It is slightly larger as it moves at a steady speed in the direction of the impulse. It has more energy. To speed it up further, another impulse has to be given in the same direction as the first one. To slow it down, stop it, or reverse the direction of motion, an impulse must be given in the other direction. But how does the ball know whether the next impulse is adding to or subtracting from its energy? Where is the memory of the prior impulse stored?

The answer to this is that the local reference frame, in combination with pilot waves, constitute memory. Every particle in the ball has a pilot wave associated with it which directly reflects the direction of motion. When an impulse is in the direction of the associated pilot waves, it adds to the energy. When an impulse is in the opposite direction, it subtracts. If sufficiently forceful, the impulse stops the ball, or reverses its direction.

If the second impulse is of identical force and of opposite direction to the first one, we get the following sequence of events:

  1. The impulse result in a pressure wave, progressing through the ball in the opposite direction of motion.
  2. When the pressure wave reaches the far end of the steel ball, the ball expands by a tiny bit.
  3. The pressure wave returns to restore the shape of the ball.
  4. The shape is restored, but not its size. The associated pilot waves have compressed the ball.
  5. The new centre of mass is a tiny bit to the far end of the ball, opposite to the direction of motion.
  6. To restore its shape, the ball moves in the direction of the new centre of mass. This motion cancels out the motion caused by the first impulse.
  7. Without any new impulse, the ball continues in its new state, at rest and restored to its original size.

If the second impulse is less than the first one, the ball slows down without stopping. If greater than the first impulse, the ball reverses direction. The mechanism is the same in all cases. The differences in outcomes depend on the degree to which the impulses influence the ball and associated pilot waves.

Pilot Waves and the Arrow of Time

Pilot waves constitute memory. They dictate the direction in which energy is transferred. At any given moment, pilot waves define the state of a system, and dictate the further development of that system in a predictable manner. There is a forward direction implied in this, and it’s this forward direction that we know as the arrow of time.

One way to visualize this is to imagine a single particle with an associated pilot wave. The leading end of this pilot wave represents the particle’s immediate future, because that’s where its energy is headed. The trailing end of the pilot wave represents the particle’s immediate past, because that’s where its energy came from. With everything, including our consciousness, being driven forward by energy flow, we end up perceiving time as something perpetually moving forward.

Photon loosing energy as it moves through the aether
The arrow of time

Pilot Waves as Time

Entropy has been suggested as time because it has direction. Drop a glass on the floor, and it’s evident which way time flows, namely from order to disorder. However, this way of looking at time doesn’t work for processes where there’s no entropy.

Processes with no energy loss can be filmed and run backwards. It looks correct either way. But this is only because we are as yet unable to capture pilot waves on film. Once we do, we will see that no process is without direction, and that this has nothing to do with entropy. Even if there’s no energy loss, we have the pilot waves to tell us which frame of film comes before or after a given frame.

The only particles that have no pilot waves associated with them are zero-point particles in the aether itself. It can therefore be argued that the aether has no time of its own. It transmits and directs time, but time itself is local to each particle.

Each particle interacts with other particles in a time frame that is local to itself. However, particles coordinate their pilot waves with each other. They produce wave fronts and resonant structures. Time is thus coordinated through all systems, yielding a real but non-physical notion of universal time. Atomic time, in the form of single particles and their pilot waves, combine to produce universal time in much the same way that these particles combine into grand structures and systems that include our bodies and the universe at large.

Newton’s cradle

We can now proceed to explain Newton’s cradle in terms of our theory:

Newton's cradle
Newton’s cradle

In this set-up, we have seven steel balls suspended by strings from a steel frame. The balls are in contact with each other, but just barely.

If we swing the left ball up to the left and let it go, it swings down. When it knocks into the second ball, the rightmost ball swings up before coming down again. When the rightmost ball knocks into its neighbour, the leftmost ball swings up. The five balls between the outer left and outer right balls don’t move.

If we move the two leftmost balls up to repeat the experiment, but with two balls instead of one, we see that the two rightmost balls move up in response to the collision. The three balls in the middle remain stationary. Doing the experiment with three balls ends up with only the middle one remaining stationary.

In all three cases, we have a situation in which the balls acts as if they were a single pendulum. However, there is a tiny delay between the moment of impact and the response at the other side of the set-up. The bigger and heavier the balls, the more noticeable is this delay.

From our theory, this time-delay is inertia. Energy is propagated through the set-up, and this takes time.

As for the transfer of motion from one ball to the other, we have the following explanation:

The incoming ball is a tiny bit bigger than the other balls. It has more energy. When it hits its immediate neighbour, the effect is twofold:

  • The ball in motion receives an impulse from the stationary ball. This impulse is in the opposite direction of its motion. From our theory, we have that it becomes smaller, with a shift of its centre of mass opposite to its motion.
  • The stationary ball receives an equal and opposite impulse from the ball in motion. It becomes slightly larger, with a shift of its centre of mass in the direction of the impulse received.

The differences in sizes are too small to be measured. However, this happens so quickly that it has the effect of stopping the moving ball and starting the stationary ball. We have the following picture, grossly exaggerated for the purpose of illustration:

Left ball hitting the right ball
Left ball hitting the right ball

Before impact, the left ball is in motion. It has the full size of both shades of grey. The right ball is stationary. It is only the size of the light grey shade. After impact, the right ball has the full size, while the left ball is reduced to the size of its light grey area. The left ball has its centre of mass moved sufficiently to the left to make it stop. The right ball has its centre of mass moved sufficiently to the right to take on all the energy and motion of the left ball.

This transfer of size progresses through the train of balls like a pressure wave until the final one is reached. This final one progresses in the direction of impact, swings up to the right before coming back down to repeat the process from the opposite direction.

For two or three balls, the same logic applies. However, there is in these cases a train of energetic balls that send a train of shock waves through the set-up. When this train reaches the other end, two or three balls are set moving, depending on how many were swung in from the other side.

It should be noted that Newton’s cradle is an idealized system in which every ball is equal to every other ball. This set-up allows for perfect energy transfers. All the energy of an incoming ball is yielded to the next. In all other cases, less than all energy is yielded. In cases where there is a great difference in mass between elastic objects, hardly any energy is transferred between them.

Massive objects will continue to move, despite crashing into a multitude of smaller objects. Small objects will bounce off big ones, with hardly any change to their energy as they do so. This explains why a bullet can be shot through air with very little loss of energy, despite displacing volumes of air that add up to many times the weight of the bullet itself.

This too is due to inertia. Small elastic objects are simply too quick. They bounce off of bigger objects before much of any energy has been transferred. Conversely, large elastic objects are too slow to yield much of any energy to smaller objects that they knock into.

Angular acceleration

Our examples so far have pertained to impulses. We have seen that changes in motion have been accompanied by changes in energy. However, not all changes in motion correspond to changes in energy. An example of this is angular acceleration.

Unlike linear acceleration, angular acceleration requires no supply of energy. Why this is so is not self evident, because both types of acceleration include applied pressure or tension over time. However, by consulting our initial analysis of how pressure and tensions act to transfer energy onto an object, we find the explanation for the difference.

In the case of angular acceleration, force is applied evenly. This is in contrast to linear acceleration, where force is applied unevenly. From prior analysis, we know that transfer of energy requires uneven application of force. Therefore, no energy can be transferred through angular acceleration. We get tension or pressure, but no change in energy.

This can be illustrated as follows, again grossly exaggerated for the purpose of illustration:

Angular acceleration
Angular acceleration
  1. A steel ball moves from left to right with no force applied to it, until an anchor connected to a frictionless pivot, is attached to it.
  2. This induces an evenly distributed tension throughout the ball.
  3. Unless released from the pivot, and with no friction anywhere, the ball spins around the pivot point in a permanently tense state.

Angular acceleration requires a continuous redirection of associated pilot waves. This requires no energy, only tension. Hence the permanently tense state with no transfer of energy. Note that this too takes time. This too is inertia.

If we subsequently cut the wire, the tension is released as evenly as it was induced. Again, there’s no transfer of energy. The body continues in a straight line perpendicular to the prior anchor point:

Continued forward motion after cutting the wire
Continued forward motion after cutting the wire

Note that the dual bulging during rotation is equivalent to what Earth experiences under the influence of gravity from the Sun and the Moon. The joint forces of the Sun and the Moon induce angular momentum that manifests itself as two tidal bulges, one on each side of our planet. This is no coincidence. This dual bulging in response to angular acceleration happens at all levels, from the cosmic, and right down to the subatomic.

Free-falling objects

Free-falling objects represent another example of acceleration with no accompanying change in energy. This can best be understood in terms of an example:

Let us first consider a steel ball at rest on a floor of wet sand. To suspend it from a beam directly above this floor, we push the ball up. This process involves uneven pressure and therefore some distortion to the ball. Energy is transferred from us to the ball.

When we attach the ball by wire to the beam, we get a situation as follows, again grossly exaggerated for the purpose of illustration:

Suspended steel ball before and after the wire is cut
Suspended steel ball before and after the wire is cut

There is tension in the ball as it hangs from the beam. However, the tension is equally distributed. No energy is being transferred. Things are merely distorted.

The energy we added to the ball as we lifted it up is illustrated as a dark grey area. This energy equals the potential difference between the situation on the floor and the situation when the ball hangs above the floor. In the real world, of course, there’s no segregation between this potential energy and the rest of the ball. Energy does not come in different flavours. All energy is size. When we talk about the difference between potential and kinetic energy it is purely for calculation purposes. The fact that we can calculate the exact amount of energy that can and will be transferred to the wet sand once we cut the wire does not mean that reality operates with different types of energies.

When the wire is cut, there’s no longer any tension in the ball. The release happens evenly. There’s no transfer of energy. The ball is not in any way distorted as it falls, so no energy can be passed onto or off of it in the process.

Energy in the ball remains constant until it hits the floor. The entirety of the energy we pushed into the ball in order to attach it to the beam is then released as a displacement of the wet sand.

It should be noted that this logic applies to all field forces, be it electrical, gravitational or magnetic. In cases where acceleration happens without distortion, no energy is added or removed. What exactly causes this type of acceleration will be explained later in this book.

Speed limit of inertial matter

Sustained forward acceleration by impulse requires a sustained force. The object under acceleration must be continuously distorted in such a way that its centre of mass is continuously moved forward relative to its former self. It grows over time. However, it will never grow by much. It will hit quite a different problem long before it becomes significantly bigger than its original self.

As an object speeds up, the forward pressure wave of an energy impulse slows down. When an object is close to the speed of light, the forward impulse is reduced to almost a standstill. This is because the pressure wave moves with the aether. The forward motion of the object must be subtracted from the speed of the aether to arrive at the speed of the pressure wave. This is the same calculation that we do in order to calculate the speed of the aether inside the object.

At speeds very close to the speed of light, the time required to transport energy onto the object under acceleration goes to infinity. No matter how hard we push, the object never reaches light speed, because the final energy transfer required will never complete. This can be calculated as follows:

Time required to push energy onto a particle
Time required to push energy onto a particle

The time required to push energy onto a particle is the sum of the time required to produce the forward pressure wave and the time required to produce the returning pressure wave. Only when this whole process is completed do we have a complete transfer of energy.

This process involves the speed of the aether relative to the particle, which is calculated by subtracting the speed of the particle for the forward pressure wave, and adding the speed of the particle to the return pressure wave. The time required for the forward pressure wave to complete will tend towards infinity as the speed of the particle gets closer to light speed.

This applies to all particles of inertial matter, including the electron. Observed from outside, the unit time of a speeding electron is more sluggish than our local time. Furthermore, time inside the electron is equally slow.

Scaling this up to a spaceship moving close to the speed of light relative to its outside reference frame, we will notice a dramatic slow down of all activities inside the spaceship as we look in. However, astronauts on the inside see no change in anything. When they check their clocks and rulers, everything is as it has always been. One unit time is still the time it takes a photon to move around the circumference of an electron. What they cannot in any way detect inside their spaceship is the fact that the aether has slowed down. It is only when they look out into the surrounding space that they see that something dramatic has happened. Everything outside their local reference frame moves about at a frantic pace.

Relative motion and light

The clocks onboard the spaceship move slower than outside. All energy transfers happen at a slower rate. Time itself has slowed down. However, it’s not only the speed of things that are different inside and outside the spaceship. The astronauts onboard the spaceship notice that light from all directions is bluer than normal, except for light coming into their spaceship directly from behind.

Outside observers, on the other hand, see all light emanating from the spaceship as redder than normal, with the only exception being light coming directly from the front of the spaceship.

Using our heat analogy mentioned earlier, we can say that the aether inside the spaceship is cold relative to the aether outside. A photon coming into the spaceship from the front comes in hot. It has to slow down in order to conform to the much colder aether inside.

This applies to all photons coming into the spaceship from outside, with the sole exception being photons coming in from behind. Photons coming in from that direction require no slowing down to adapt to the cold aether. This is because the speed of the aether outside the spaceship is exactly equal to the speed of the spaceship plus the speed of the aether inside the spaceship. When a photon comes in from behind, we have to subtract the speed of the spaceship to get its new speed inside the spaceship. This new speed, is exactly the same speed as the aether inside, so no slowing down is required.

Conversely, viewed from outside, it is only photons coming out of the spaceship to the front that require no speeding up. In all other directions, photons have to speed up in order to conform to the hotter aether on the outside. Photons coming out of the spaceship comes out cold relative to the outside aether.

Now, we have to propose a rule in order to progress with our analysis. We’re not yet in a position to explain this rule so we have to consider it one of our axioms for now. This rule goes as follows:

  • When photons have to slow down, they become correspondingly bluer.
  • When photons have to speed up, they become correspondingly redder.

This means that our astronauts see light entering their spaceship from the front as bluer than normal. Turning towards the back of their ship, they see outside light progressively less blue until all blue-shift disappears straight out to the back.

Conversely, outside observers see no red-shift in light coming out from the front of the spaceship. However, light coming out of it is increasingly red-shifted as we shift our vantage point towards the back of the spaceship.

We can conclude that relative motions cause red-shifts and blue-shifts. This conforms to Einstein’s conclusion, but not in the same way. Our interpretation is based on motion relative to an outside reference frame that can be viewed as static. Einstein doesn’t do this. Using Einstein’s solution, we get red-shift as something exclusively associated with receding objects. This is different from our solution, which yields red-shift for any object moving faster than the observer relative to a common outside reference frame. Red-shifts are in our case signs of relative speeds. All speeding objects become red-shifted as long as they’re not moving right at the observer.

This has some interesting cosmological consequences. The relative abundance of red-shift we observe in the universe may not be a sign of expansion. It may simply mean that we live on a planet that is at relative rest compared to our external reference frame. Most other objects around us are moving faster than us. Only those moving slower come with blue-shifted light.

< Inertial matter ———— | ———— Electron orbits >

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