Basic and Original Research
Geometry : Multi Foci Closed Curves
Two types of closed curves, circles and ellipses, are characterized by continuous and differentiable radius of curvature, mechanically traced with one and two fixed points (foci), respectively. A novel concept introduces multi-focal curves, with more than two non-collinear foci, forming triellipses, quadraellipses, and beyond. These curves’ equations, along with the concept of relative focal distance, find applications in nuclear physics and quantum mechanics. With 2n subsections, they exhibit complex energy wave patterns, offering insights into electron clouds and quantum phenomena, thus possessing more than three degrees of freedom. Valuable in various fields including nuclear science and space exploration, they’re utilized in spatial planning by some European geometricians.
Relativity
Special Relativity Concept and Flaw in the theory
Einstein’s first postulate of special relativity, which assigns an extra magnitude to the resting posture, by allotting -v to the stationary frame, has been pointed out as misleading. This misunderstanding led to violations of kinetic energy conservation laws, particularly in one dimensional, two-dimensional motion scenarios and three dimensional motions.
Empirical Approach in daily experiences
Two trains, A and B , each with mass m and velocity v m/s, are moving towards each other. When they collide, the ground observer calculates their energies by adding 1/2 mv^2and 1/2 mv^2 summing up to mv^2, as in frontal collisions. However, train-bound observers calculate relative velocities. To determine relative velocity, they transfer their train’s real magnitude v m/s to the opposite train’s magnitude v m/s, leaving themselves motionless and allowing the opposing train to move with combined magnitude 2v m/s. Thus, A feels B at 2v m/s while being motionless. The sum of their kinetic energies, 1/2 m〖(2v)〗^2 or 2mv^2, is double that obtained with ground velocities, seemingly violating energy conservation laws. However, with complex relative velocities, train-bound observers transfer an imaginary magnitude to B, adding it to B’s real magnitude, resulting in a complex velocity(v+iv) . This produces kinetic energy 1/2 m(|v+iv|)^2 exactly mv^2 the the same as that obtained with ground velocities, avoiding violation of energy conservation laws. When you transfer your magnitude to the opposite train, the process is not real but rather imaginary. This is because you neither push nor pull the magnitude itself; instead, you simply feel as though you were giving it to opposite train. Hence, the transfer process is perceived as imaginary.
Base of Special Relativity is Shaky:
Originally, Newton demonstrated two opposite states within his first law, namely the law of inertia, where change in these states without force is impossible. Neither rest can be changed into motion nor motion into rest. Einstein thought that such a thing would be possible in deep space where there is neither reference nor force. To demonstrate both states together, he imagined two frames: one at rest and the other moving at constant velocity. From these frames, Einstein concludes that no observer can determine if they are at rest while their counterpart is in motion, or vice versa. He asserts that relative motion or rest is the true reality, dependent on the observer’s perspective.
Therefore, both are moving relative to each other. Only their directions will be different. If one is moving with velocity v, then the other will be moving with velocity-v. To justify this assumption, he took support from Newton’s second law, where F=ma or F=m(v-u), with u=v, resulting in F=0 for inertial frames at rest or moving with equal and opposite velocities. Einstein further hypothesized that both frames will share a single magnitude between them. And he imagined all this because of the phenomenon of the trains: where a moving train crosses one stationary, the observer inside the moving train feels as though the stationary train is moving, and while aboard his moving train, he feels it is motionless, and vice versa for the stationary-train-bound observer. This phenomenon demonstrates a smooth transition between states without the application of force. However, the stationary frame never gets physically displaced, which is the condition for motion. So, these three points seriously violate the laws of physics and also hammer simple logics.
Three questions emerge:
Can basic observations yield a force capable of transitioning a stationary object into motion?
Can a reference frame experience genuine motion without undergoing displacement while remaining stationary?
Is it possible for a solitary force (common single magnitude) acting upon one object to propel another object in the opposite direction with its full strength simultaneously?
The questions outlined above directly concern the violation of kinetic energy conservation laws, Newton’s first law, the law of inertia, the law of causality, and entropy. According to the theory discussed, the mass relation violates Newton’s first law, conservation laws, and entropy. In the formula presented, where only mass and velocity are considered, their simultaneous increase raises ambiguity regarding what exactly decreases. While it’s understandable that vector increase relative to vector constant is valid, the notion that scalar mass also increases relative to the same constant vector is absurd. Vectors remain finite, yet the scalar mass approaches infinity. This contradiction challenges fundamental physical principles and warrants further examination.
Author’s View Point
The author, with meticulous attention, refined the foundational concepts and unearthed remarkably enthusiastic results. In a feat of intellectual prowess, they unraveled the enigmatic puzzle surrounding the everyday phenomenon of trains—a conundrum familiar to commuters worldwide. Through rigorous real-time analysis of the universe, a new theory emerged, solidifying their contribution to the annals of scientific discovery.
A philosophical Shift in Special Relativity
From our philosophical standpoint, we perceive the elusive condition as a composite blend of kinematics and optics, maintaining the phenomenological behavior of bodies existing in opposing states without the influence of external forces. Thus, a creative methodology reinforces Newton’s fundamental principle, affirming that motion cannot transition into rest without force, and vice versa. We designate rest and motion as “iv” and “v” respectively. Rest is characterized by a moving frame perceiving its motion reflected by a stationary frame. Our approach primarily revolves around what we term as complex relative motion—an analytical emulation of Newton’s first law. Given that they are unaffected by external forces, only complex velocities facilitate seamless transitions between states.
Seamless Transition of States is the Replica of Newton’s Law of Inertia:
Without an outside force, Q is traveling at a constant speed v while P is at rest. Q is moving, and when it looks to P, it sees its own motion reflected in P. Because P appears to be going in the opposite direction, it is at – iv ⃗. Thus, P remains in its original location, and Q continues to move in the same direction. Since P has an imaginary vector, iv ⃗, which doesn’t travel real distance but we may take it as a visual pathway (Rashed, 2007) and Q is traveling rectilinearly, the total of the vectors is |v ⃗- iv ⃗ | or v√(2.) and the system magnitude is |v + iv|or v√2. The vector sum’s value and the system’s magnitude are clearly equal. In the absence of external forces, this consistency shows that each frame is still preserving it in its previous state. Since the first law is more fundamental and self-contained, it does not require the application of Newton’s second law in relation to the concept of mutual observations in the absence of surroundings. It seems that no observation has the ability to generate a force strong enough to move a stationary state.
Additionally, under the paradigm, iv stands for resting posture and v for motion. As so, it is the first mathematical expression of Newton’s law. Newton’s first law thus supports the smooth transition from a state of rest to motion and vice versa, but only in complex forms. When velocities are real, they attract forces.
Complex relative motion is a synthesis of real and imaginary motions with direction reversibility.
Jk Transformation Inverse Laws x=(x^’+ivt^’)/( √(1-〖(iv)〗^2/c^2 )) (11) t=(t^’+(ivt^’)/c^2 )/( √(1-〖(iv)〗^2/c^2 )) only inverse laws are different from the Lorentz inverse laws.
New mass relation is m(v)=(m_0 √(c^4-v^4 ))/((c^2-v^2 ) ) , it shows two opposing processes within a single process and checks infinite growth of mass at c, at c matter transforms into gamma ray photons. Opposing processes give birth to antimatters.
New conclusions are 〖 L〗^’=L √(c^4-c^4 )/((c^2-v^2 ) ), moving length lengthens and it contracts at rest. Its justification lies in the persistence of vision.
Similarly, t^’=t (c^2-v^2)/√(c^4-v^4 ) moving time runs fast and it dilates at rest. The rationale resides within the resounding roar of thunder and the brilliant flash of lightning.
The aforementioned three formulas are currently under review by a reputable journal for a month, therefore, I am unable to provide a detailed discussion at this time about them.