A 4D MODEL OF MATTER
JOHN (IOANNIS) PAPADIMITROPOYLOS
MECHANICAL ENGINEER
THE SPECIAL THEORY OF RELATIVITY RE-EXAMINED
This analysis assumes you are aware of the special theory of relativity. I will try to explain the concepts of the theory in a different way from what is found in the literature, as this is instrumental to the explanation and development of the 4D model. In and of itself, this perspective on the theory of relativity can prove useful in reaching an intuitive understanding of a fourth dimension.
We can imagine two systems moving through space-time at the same measure of velocity c, but at a different direction. By projecting the “moving” system unto the system of reference we can deduce the equations for the distortion of space and time with simple math.
system x’,t’ moving at u in relation to system x,t
PARTICLE MASS
Taking this principle further we can imagine that a point mass, at rest relative to us, means that its c velocity vector is parallel to our system of reference. We can imagine, in addition, that, since all the laws of mechanics are reversible it is simultaneously moving forwards AND backwards in time.
When we do classical mechanics, we are forward looking in time and therefore only take the forward vector into account, but for accounting the total energy we would have to add both vectors as below…
DYNAMICS
Now that we have our model, all we have to do is check if the laws of mechanics hold. Let’s assume a force F is exerted on our point mass. This will deflect the c vector as it will be perpendicular to it, when the mass is at rest and as the angle changes with the speed, so will the effectiveness of said force.
Let c the speed of light, u the velocity of the object in the 3D inertial frame of reference
ακ the centrifugal acceleration (the object is moving at the speed of light in 4D)
Δtobj/Δtobs the ratio between the time elapsed for the object and observer frame resp.*
Fk the active centrifugal component of Force F
α the acceleration in the inertial frame of reference (observed acceleration)
Then by applying Newtonian mechanics in the 4D we can easily solve for the acceleration of the particle.
* This is the most difficult part in understanding this analysis
THE BASIC MODEL
Imagine a car at a time t-dt, t, and t+dt this is the immediate past, present and immediate future. Acceleration and deceleration changes the immediate past and the immediate future. Thus we can imagine this as a static situation and remove the present and consider the immediate future and the immediate past that creates a present. Taking this notion and applying it to matter we can again imagine that observable mass is really two point masses, one in the future and one in the past, oscillating or orbiting around the present.
We can imagine this as static or dynamic (oscillating or orbiting) and from this we will try to explain the four forces of physics from the basic attractive force between the past and the future masses.
Looking at the schematic and the analysis we’ve done so far speed is defined (from the observers perspective) as Px/r, where speed is a ratio of the speed of light, but from the objects perspective it is Px/Pt and the speed becomes infinite (at the speed of light) because there is no time component.
Again we can apply Newtonian mechanics derived from the macrocosm and estimate the radius of such a particle, let K be the gravitational constant of this “basic force”, estimated equal to the strong nuclear, then from the equation for two orbiting bodies we see that the radius comes out very close to the upper bound radius for the up quark.
STRONG NUCLEAR FORCE –
GEOMETRY ATTRACTION-REPULSION
For the strong nuclear force we have only to imagine the two masses and another point mass at a distance l that is of the same order of magnitude as the radius r of the particle. Then torques are created that translate as attractive force in the 3D world of our experience. The geometry and the distance will play a role and this force could be repulsive as well, as is observed in practice.
ELECTRIC CHARGE ATTRACTION
Electrically charged particles can be understood through the direction of the orbit (spin) and the introduction of a small imbalance (one particle mass has more mass) as seen in the schematic. This also explains matter and anti-matter and conversion as the spins neutralize each other causing the particles to implode unto themselves. If we then think about the imbalanced force that would be created and gyroscopic procession we can understand how attractive and repulsive forces can be generated.
Gyroscopic procession, force is shifted by 90 degrees.
ELECTROMAGNETISM
Remember, in this model, attraction is a torque that tends to bring the “future” masses together, while repulsion is when the “past” masses are drawn together. This way we can explain the electromagnetic attraction in two parallel wires by projecting the orbit/oscillation on the direction of “movement” of the electrical charge. This causes a 90 degree phase shift which explains why charges moving in parallel attract and vice versa. It also predicts the weak nuclear force which is of course measured.
ELECTROWEAK
The same principle as the electric force the imbalance causes gyroscopic phenomenon that result in an attractive force.
SELF FORCE (Abraham-Lorentz)
Since we have imagined that electromagnetism is caused by a small imbalance in these two masses, we can easily explain the Self Force encountered during the application of jerk (super acceleration) on charged particles. We always have to keep in mind that acceleration in our 3D existence is rotation of the particle.
As such, reversing this, an acceleration of the rotation of the particle is jerk. Since the two masses have different inertia, they will be out of line during the application of jerk, and exert a force upon themselves that tends to rotate/accelerate the particle. We can also explain the phenomenon of pre-acceleration as the “past” mass exerts force on the future.
GRAVITY
Gravity is a second order phenomenon which is why it is so weak compared to the other forces of physics. Gravity has to do with the curvature/distortion of the orbit itself rather than the revolution of the particle on the x,t plane. The reason for this is that simply, at great distances the forces are parallel and this becomes the dominant phenomenon.
Take into account that force requires time (Δt) to act so as each mass moves from t=0, it deviates from the “straight” (as projected on the xt plane) orbit. This could explain the stream of charged particles at the edge of black holes and the interplay between gravity and electromagnetism, because as the particle is deformed there is the possibility for self-force phenomena to take place.
The other thing it explains is the non-locality of time as all the “watches” are deformed in this way.
A 4D MODEL OF MATTER 