The Principle of Least Action 🎯

[Xonas Pitfall]

The principle of least action reveals that the path minimizing action in physics leads to Newton's Second Law, linking mechanics and energy principles. By considering the potential's derivative as force and height's second derivative as acceleration, F = ma emerges, making least action integral to many different phenomena. The principle, simplified by Euler and Lagrange, enables problem-solving by substituting forces and vectors with energy terms in a Lagrangian, reducing complexity and making it accessible even in multiple dimensions or non-standard coordinates. Though often termed "least action," it's more precisely a "stationary action" principle, setting derivatives to zero to find stable points, not necessarily minima.

• Path of Least Effort: Objects naturally follow a path that requires the "least action" - meaning they move in a way that minimizes their energy use over time.
• Unified Approach to Motion: Using the principle of least action, you can solve mechanics problems by working with energies (kinetic and potential), which are simpler to calculate than forces, especially in complex situations like rotating systems or multiple dimensions.

A list of the main mysteries in quantum mechanics:

1. Wave-Particle Duality
   - Question: How can particles like electrons and photons behave as both particles and waves?
   - Weirdness: Sometimes particles act like tiny, solid objects; other times, they spread out like waves. This duality is visible in experiments like the double-slit experiment, where particles create interference patterns typical of waves.

2. Superposition
   - Question: How can particles exist in multiple states or locations at the same time?
   - Weirdness: Particles don’t commit to a single state or position until we measure them. Before measurement, they exist in a “superposition” of all possible states, as demonstrated in Schrödinger’s famous “cat” thought experiment.

3. Entanglement
   - Question: How can particles be instantly connected, no matter the distance?
   - Weirdness: When particles become entangled, their properties remain linked, even across vast distances. Measuring one instantly affects the other. Einstein famously called this “spooky action at a distance.”

4. Quantum Tunneling
   - Question: How can particles pass through barriers they shouldn't be able to cross?
   - Weirdness: Unlike a tennis ball that would bounce off a wall, particles can “tunnel” through barriers. This allows them to appear on the other side without having the energy needed to cross it directly.

5. The Uncertainty Principle
   - Question: Why can’t we know both the exact position and momentum of a particle at the same time?
   - Weirdness: The Heisenberg Uncertainty Principle states that measuring one property (like position) makes the other property (momentum) less certain. This is a fundamental limit, not due to measurement error, but built into the nature of particles.

6. Measurement Problem
   - Question: Why does observing a particle seem to “collapse” it into a single state?
   - Weirdness: Before we observe, particles exist in a superposition of all possibilities. Measurement forces them into a definite state, raising questions about whether observation creates reality.

7. Probability and Indeterminism
   - Question: Why does quantum mechanics only predict probabilities, not certainties?
   - Weirdness: Unlike classical physics, quantum mechanics can only tell us the likelihood of outcomes, not exact ones. This indeterminism means particles behave randomly, governed by probability rather than certainty.

8. Quantum Decoherence
   - Question: Why don’t we see quantum effects like superposition in everyday life?
   - Weirdness: Decoherence suggests that interactions with the environment cause quantum states to lose their “quantumness,” collapsing superpositions into definite states in larger systems, making quantum effects invisible at the macroscopic level.

9. Vacuum Fluctuations and Zero-Point Energy
   - Question: Why isn’t “empty” space truly empty?
   - Weirdness: Even in a vacuum, particles and energy pop in and out of existence. This zero-point energy is the lowest possible energy a system can have, and it’s why even “empty” space isn’t truly empty.

10. Many-Worlds Interpretation
   - Question: Do all possible outcomes of quantum events actually happen in different “worlds”?
   - Weirdness: The Many-Worlds interpretation proposes that all possible outcomes of quantum events happen in separate, branching universes. This would mean every quantum decision creates a new parallel universe.

11. Delayed-Choice Experiments
   - Question: Can future measurements affect a particle’s past behavior?
   - Weirdness: In delayed-choice experiments, particles seem to “decide” their past behavior based on measurements taken later, suggesting a strange connection between past and future events.

12. Nonlocality
   - Question: How can distant particles influence each other instantly, seemingly faster than light?
   - Weirdness: Entanglement and nonlocality suggest that space doesn’t separate particles as we think, allowing them to interact instantaneously across large distances without delay, defying relativity’s limit on the speed of information transfer.

13. The Observer Effect
   - Question: Does consciousness play a role in determining reality?
   - Weirdness: Some interpretations of quantum mechanics suggest that the presence of an observer affects the state of a particle, leading to philosophical debates about whether consciousness creates or influences reality.

14. Quantum Zeno Effect 
   - Question: How can repeatedly observing a particle prevent it from changing?
   - Weirdness: Constantly measuring a quantum system can “freeze” its state, preventing it from evolving. This is like watching a pot so closely that it never boils.

Wave-Particle Duality: In quantum physics, particles like electrons can act both as particles and as waves. The principle of least action suggests that particles "choose" paths that minimize action. But in quantum mechanics, particles actually take all possible paths simultaneously, with each path contributing to the particle's overall behavior. This approach, developed by Richard Feynman and known as the "path integral formulation," builds on the principle of least action, allowing particles to "explore" all paths, with each path adding to the particle's probability distribution.

Action in Quantum Mechanics: Instead of finding the one "best" path, quantum mechanics calculates the probability of different paths, with each path’s likelihood depending on its action. Paths that nearly satisfy the least action principle contribute the most to the particle’s behavior, but even paths far from this principle contribute slightly. This concept explains the interference patterns seen in experiments like the double-slit experiment, where particles "choose" paths that interfere with each other.

Stationary Action and Quantum States: In classical mechanics, action is minimized or kept stationary. In quantum mechanics, this stationary action principle becomes foundational in the Schrödinger equation, which governs how quantum states evolve over time. Essentially, the Schrödinger equation is a quantum form of the principle of least action, determining probabilities for particle locations and states rather than exact paths.

Quantum Tunneling and Probability: The principle of least action also helps explain phenomena like quantum tunneling, where particles cross energy barriers that they couldn't surmount classically. By allowing particles to take improbable paths with non-zero action contributions, the principle allows for such "forbidden" behaviors in the quantum world, matching observed phenomena in atomic physics.

Edited October 29 by Xonas Pitfall

[Xonas Pitfall]

This principle brings to mind something Leo mentioned in his solipsism video - why would the universe, or this supposedly infinite object we call "God," need to go through the trouble of creating endless complexities? It’s already everything; it encompasses all possible realities, all potential perspectives. Instead of constantly reinventing itself through endless variations, it could simply *be* — it could choose to create and imagine just one perfectly crafted frame. This single frame would exist for one primary viewer, a single observer, or "watcher" that could be thoroughly convinced of the illusion. That observer is you. In this way, the universe achieves a kind of ultimate efficiency. It doesn’t need to generate countless perspectives or endless layers of reality; it only needs to convince one perspective, one consciousness. This is the principle of least action in a sense — it’s the path of least resistance, the most ingenious and efficient design possible, reducing the universe's "effort" to a single, complete experience for one observer.

[Xonas Pitfall]

ᘛ⁐̤ᕐᐷ . . .🧀 !

[Xonas Pitfall]

Someone, please, pinch me and make sure I binge all these channels and documentaries when I’m high… ❗

Edited October 29 by Xonas Pitfall

[Princess Arabia]

Humans are the only ones that want to find the path of most resistance.

BTW @Xonas PitfallCould you do a thread on Sacred Geometry one day. Would love to hear your ideas on it.

[Xonas Pitfall]

@Princess Arabia Of course! How come the interest?  But, thanks so much for the inspiration!  Hopefully, I won’t be too human and take too many paths of most resistance when sharing it... 💖

[Princess Arabia]

1 hour ago, Xonas Pitfall said:

@Princess Arabia Of course! How come the interest?  But, thanks so much for the inspiration!  Hopefully, I won’t be too human and take too many paths of most resistance when sharing it... 💖

Hehe. These topics aren't discussed much and i see most of your posts, goes in this direction. I don't know enough about it to discuss or start a thread about, but my instincts tell me you do based on the kinds of posts you make. I think Sacred Geometry is fascinating, but I haven't delved deep enough into it to say much about it.

When I look into the woods, though, I can see the patterns. The entanglement of the trees. 

Edited October 30 by Princess Arabia