**assumptions**

The trapped momentum theory is based on the assumption, each particle has the same constant momentum and this could be observed, if a particle can move completely undisturbed. Fractions of this constant motions are only possible, if the particles are trapped and are oscillating between borders. The shape of the trap determines the frequency of oscillation The momentum of the trap is also oscillating, but it could standstill or move in a fraction of the trapped momentum.

The basic assumption is, that the model is compatible with the world of quantum matter. Additional assumptions are:

- Momentum particles have motion vector with constant length
- Momentum particle have a connection mechanism, which is a trap for other momentum particles.
- The traps are three dimensional and flexible.
- A trapped particle is oscillating between the trap borders, the motion vector length stays constant.
- Changes of the shape of a trap are changing the orientation of the vector of trapped particles, but the vector length stays constant but alters the direction.
- The momentum of a cluster is the vector sum of the trapped particles.

**trapped momentum**

Two free moving particles are hitting each other [A].

They could be connected to nearly undisturbed moving a chain [B] or a cluster [C], while oscillating between the borders of the trap. This oscillation is additional to an existing spinning of the particle of momentum.

The specific feature of this solution is, that **every particle is still moving by the speed of light**, but the different forms of the traps forces the particles to different frequencies of oscillations and the whole cluster moves doesn't move or move in a fraction of the speed of light.

There is a **relation between topology and kinetic energy**. The size of the sphere determines the trap borders and the frequency of the trapped particle. The trap is an interaction of the two particles which are tightened together.

Trapped and free moving particles are the same. The trapping borders belong to the structure of the particles.

The velocity of the particle is constant. Trapped or not trapped is an information. The shape has information. Depending on the shape of the trap, the particle is static oscillating or has a disturbed motion because of its oscillation.

Such a structure is very easy to construct. If this starts spinning, everything gets twisted.

The motion of the trapped particle depends on its relation to the connected cluster of other trapped particles.

There is a qualitative difference between the trapped oscillating and the free straight motion. Relativistic effects belong to trapped particles, while there is no such thing for the free motion. But to achieve a non relativistic state, a cluster has to be completely disintegrated.

**real world**

The basic idea is, that something is caught in a trap and oscillating. If the size of the trap changes, the oscillation changes.

The trap has to be at least 2 dimensional, because it can change it size. But a 3 dimensional object is more likely, because it needs a great surface for the interaction with other objects.

The trapped object have each dimension, but the motion of the trapped object ha to be a straight 2 dimensional path in order to gain a proportional relation between the change of the shape of the trap and the change of oscillation.

There are a lot of solutions possible. For example, a ball or a string caught in a balloon.

**wave particles and twisted strings**

The momentum of each Wave particles is constant. The trap is a connected string and the length determines the frequency of the connected particles. Two wave particles with equal sizes will standstill but oscillate. If the sizes differ, the trapped particles will move.

The momentum of each twisted string is constant. The twisted string has a glue crossing, which has the function of a trapping mechanism. The sphere created by the spinning branches is the trap for other twisted strings.

Only twisted strings with nearly the same size can be bound together.

Maybe the twisted strings is also a particle of momentum, but it is also possible that only a whole cluster acts like an particle of momentum.

**balance of momentum**

The particles of momenta are described as vectors. Crossing vectors are trapped particles of momenta.

The two trapped particles are catching another free moving particle, now there is a cluster of three. This is necessary to demonstrate the effect of distortion and the relation to motion.

Each vector of a cluster has to go through the center. The position of the center on the vector indicates the oscillation of the trapped momentum. If the center is near the arrow, the frequency of the trapped particle is high and vice versa.

The trapped particles are oscillating and the vectors are flipping. To analyze the momentum of the cluster, all particles are moving to the centre, because it is easier to determine the vector sum and the relation to the shape of the cluster.

The **center crossing** of a vector indicates its frequency of the trap oscillation. The center divides a vector in two parts, the momentum towards the motion of the cluster and towards the shape of the cluster. If a vector increases its frequency, the motion part also increase while the shape part shrinks. There is a **direct relation between motion and shape**.

The inner circle visualizes the **shape of momentum**, which indicates the motion of the cluster. In this case, the vector sum is zero and the cluster doesn't move. There are a vast number of shapes of momenta possible, which also have a vector sum of zero.

The outer circle is the **distortion shape**. In the case of a vector sum of zero it is a standstill shape of an object, which is either gained by an equal pressure or there isn't any distortion at all. But a distortion shape isn't the real shape, it indicates the momentum the shape is producing, but the shape could be every possible figure.

If there is only one size of traps, the trapped momenta cancel each other. But if there are different trap sizes, the balanced momentum will start to oscillate around its center.

**distortion and motion**

The standstill shape [A] gets a push, the shape is disturbed, the vector sum isn't zero anymore and the cluster is moving [B]. To stop the motion, the distortion could be reverted and the cluster gains its original shape, or the cluster gets an opposite distortion of the same extent and the cluster will have a new shape of standstill.

The force to move an object and to stop it are usually proportional, if the are no binding fall apart or new ones will created. This is derived from the equality of each of the trapped momenta. That means, each distortion creates motion and each motion is a distortion.

A hint, that such distortion shapes exists in the real world, is the relativistic doppler effect.

Graphic B, license: GFDL, author: Karl Bednarik

The more the square is accelerated, the more its disturbed standstill shape is transformed to its real undisturbed shape [A]. Its is just a model with four particles. A cluster with thousands of particles should have a distortion shape like the frequency distortion by the relativistic Doppler effect [B]. The pink vector indicates the velocity of 0,6 speed of light.

If a particle escapes from its trap, it is moving undisturbed and it should be like any other free moving particle. But the twisted string keeps its trap size. If a cluster is accelerated, the trap size changes and thus the size of the sphere of the twisted string changes. After escaping the trap, the sphere diameter and the corresponding tail oscillation indicates the size of the disturbed trap.

Because matter itself is disturbed, emitted photons are disturbed and keep this information.

**kinetic motion**

A cluster of trapped particles of motion is not moving, but because of the asynchrony of the oscillation the cluster is shaking on the spot.

**[A]** A cluster of trapped momentum particles has a balance of momentum, the trapped vector sum is zero. Now the cluster gets a push.

**[B]** The pushed trap of momentum shrinks, the frequency of the enclosed momentum increases and the vector sum of the momentum is greater than zero. The whole cluster absorbed the momentum of the push, changed its shape and is moving.

**[C1]** The moving cluster is hitting an obstacle. The particle hitting the obstacle is pushing back the disturbed trap, the balance of momentum and the shape of the cluster are restored and the cluster stops. The hitting causes a distortion of the obstacle, the momentum has moved from the cluster to the obstacle.

**[C2]** The moving cluster is hitting an obstacle. The whole cluster is disturbed and all momentum particles try to find a new balanced shape. The cluster is changing its shape, a new balance of momentum is reached and the cluster stops. The obstacle isn't affected by the collision, the momentum deformed the shape of the cluster permanently and is gone.

**[C3]** The moving cluster is hitting an obstacle. The particle hitting the obstacle destroys a trap and the cluster is falling apart. Because there is at least one trap destroyed, one or more photon will be emitted. This hypothetical small cluster has completely vanished and emitted three photons.

A normal exchange of momentum in the real world is a combination of [C1] and [C2]: A part of the momentum is moving from one of the colliding objects to the other and the other part of the momentum is deforming the shape of the objects.

For each momentum of the whole Cluster there is more than one shape possible. If a cluster has a balance of momentum and stand still, that doesn't mean it has the same shape or state. If a cluster receives a momentum, the shape determines, if the momentum can be absorbed or the momentum will break a trap and the cluster will fall apart.

**gravity**

Shapes of momenta of a stillstand [A] and some moving [B-D] objects in a gravity field

**conservation of linear momentum**

The theory of trapped momentum has no conservation of linear momentum. The higher the number of trapped particles of momentum is, the more the whole cluster will conserve the linear momentum. The opposite is, that small clusters won't conserve the linear momentum.

© 2019