Welcome back to the Unconventional Engineering Department! This week, Lao Gao released a video about the July 5th prophecy, featuring Yasue Kunio, a remarkable physicist. Yasue Kunio was a student of Tomonaga Shin'ichirō , a Nobel Prize winner in Physics. He has a wide range of interests, especially in researching topics related to aliens. He is also very fond of prophecies and mysteries.
Yasue Kunio: Physicist and Polymath
Yasue Kunio has made significant contributions to both classical and quantum physics. Notably, he developed what's known as the Yasue Equation, arguably the most important work of his life. Legend says he conceived this equation while driving, experiencing a moment of insight where the formula appeared before his eyes.
The Genesis of the Yasue Equation
Initially unsure of the equation's meaning, Yasue Kunio wrote it down. His strong physics intuition and mathematical ability allowed him to deduce its significance. He discovered the equation bridged the gap between classical and quantum physics. It essentially built a bridge connecting these two seemingly disparate fields.
Classical Physics vs. Quantum Physics
Let's explore the differences between classical and quantum physics to understand the importance of bridging the gap.
Classical Physics: Predictability and Determinism
In classical physics, consider an atom with electrons orbiting a nucleus. We can accurately determine the forces acting upon the electron (electromagnetic and gravitational) using four basic quantities: position (X), velocity (V), acceleration (a), and time (t).
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These allow us to calculate the orbit's radius (R).
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Having this information, we can predict the electron's future trajectory.
This predictability is a key characteristic. We can predict that trajectory. For example, consider an object in freefall. We can reasonably determine its trajectory given appropriate conditions.
Quantum Physics: Probability and Superposition
Quantum physics operates differently. Instead of a defined orbit, we have a probability cloud. The electron exists as a probability of being in a range of positions. This is known as superposition.
Consider Schrödinger's cat, which before opening the box, it is in a superposition of being both alive and dead.
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Observation: The act of opening the box, performing an observation, collapses the superposition.
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Wave Function Collapse: Suddenly, only one state becomes real (the cat is either alive or dead). This is called wave function collapse. All other possibilities become zero.
Before measurement, all states are possible. After measurement, only one is. Imagine a lottery before the draw; anyone could win. The moment the numbers are drawn, one winner is revealed, and everyone else's chances become zero. The electron can exist in many states but by observing it, it randomly appears in one.
The quantum mechanical model uses the concept of an electron cloud, where electrons exist in these superimposed states. Classical mechanics allows precise prediction, while quantum mechanics relies on probability to determine where something is likely to be.
Unpacking Yasue Kunio's 1981 Equation
Let's delve into Yasue Kunio's 1981 equation to understand his work.
The Hamiltonian Principle and the Calculus of Variations
His starting point was the Hamiltonian principle of least action from classical mechanics. Crucially, he introduced the calculus of variations. This is a vital part of the equation. He based subsequent derivations based on this concept. The equation uses the Lagrangian.
The Lagrangian: A Minimum Action Approach
In classical physics, Newton's second law (F=ma) is a useful tool. However, it becomes cumbersome when dealing with multiple variables. The "Three-Body Problem" makes calculations complex due to multiple variables.
Consider a double pendulum:
- Its angle and height constantly change, making Newtonian calculations difficult.
The Lagrangian principle uses minimum action. It only concerns itself with the net change, or shortest distance. It takes the path of least resistance. Instead of X, Y, and Z variables, the Lagrangian uses the angle between the two pendulums. Using the angular displacement, we can find the trajectory. Researchers now realize Newton's second law is a special case of the Lagrangian. The Lagrangian encompasses Newton's second law.
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The equation expresses kinetic and potential energy.
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Each particle has three degrees of freedom, corresponding to spatial coordinates (X, Y, Z).
The formula shows the relationship between Newton's second law and potential energy.
Applying the Equation to a Falling Object
Imagine a cat falling from a height. The equation describes the forces acting on it, equating force (mass times acceleration) to the change in potential energy gradient. The cat falls due to gravity (mass interacting with gravitational acceleration). This satisfies Newton's second law (F=ma).
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The building's height (H) allows for the calculation of potential energy (mgh).
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The ground is defined as the zero-potential level. This accounts for the negative sign in the potential energy gradient calculation.
The change in the cat's gravitational force equals the change in potential energy as it falls.
Introducing Random Perturbations: Brownian Motion
Yasue Kunio's equation incorporates random disturbance terms, inspired by Brownian motion.
Brownian motion refers to the movement of particles suspended in a fluid medium, caused by collision with molecules in the fluid. The equation suggests that a body's motion equals drift and a disturbance. These are like the phenomena seen in classical physics, plus random perturbations.
Bridging the Gap to Quantum Mechanics: The Schrödinger Equation
The researcher makes an important assumption. With mathematical expressions, they describe the previous and the following states of a body. These ideas are then incorporated into the Lagrangian equations, where they are rewritten into a stochastic variational formula. This creates a rudimentary model. Upon computing its derivative, it is possible to see the changes in velocity and the influence of probability.
Through Madelung transformation, the probability density P and the phase related to the S-wave flow are introduced to describe the wave function. Through deriving these concepts, they can derive the Schrödinger equation, the most important formula in quantum mechanics.
In the Schrödinger equation, electrons are treated as wave packets composed of energy. Schrödinger’s equation deals with the state of the wave and predicts the position of the waves.
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The left side describes the location at any moment.
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The first term on the right represents kinetic energy.
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The second term represents potential energy.
This breakdown explains Yasue Kunio's groundbreaking equation. Because Lao Gao discussed Yasue Kunio this week, I wanted to share some of the information with you.
That's it for today's video. See you next time from the Unconventional Engineering Department! Goodbye!