What is Energy? Modern physics offers extension of the definition of energy

Extended theorised definition of Energy

Abstract:

The Decay Theory proposes that energy and mass emerge from disruptions in equilibrium, giving rise to various energy forms. Energy and momenta are intertwined as Albert Einstein said.

But this theory extends the definition of energy, integrating concepts from thermodynamics, quantum mechanics, and complexity science.

Mathematical Foundations:

1. Define energy (E) as a functional of equilibrium disruptions: E = ∫[Δε(x)dx]

2. Introduce a vibration-based framework: ω = √(k/m), where ω is frequency, k is stiffness, and m is mass

3. Relate vibrations to energy forms: E = ħω

Conceptual Framework:

1. Equilibrium disruptions generate vibrations, leading to energy emergence.

2. Mass is a type of energy, related to binding energy and QCD vacuum energy.

3. Consciousness is inherent in all movement, with silent resistance (electron) playing a key role.

Predictive Power:

1. Predict energy forms beyond mass (e.g., kinetic, potential, electromagnetic).

2. Forecast vibration-based phenomena (e.g., quantum fluctuations, phase transitions).

3. Provide a framework for understanding cosmological evolution.

Empirical Verification:

1. Experimental verification through spectroscopy, particle physics, and cosmological observations.

2. Comparison with established theories (e.g., general relativity, quantum mechanics).

3. Predictions for future experiments and observations.

Interdisciplinary Connections:

1. Thermodynamics: equilibrium and non-equilibrium systems.

2. Quantum Mechanics: particle creation, vacuum energy.

3. Complexity Science: emergence, self-organisation.

Terminology and Notation:

1. Energy (E)

2. Equilibrium disruption (Δε)

3. Vibration frequency (ω)

4. Mass (m)

5. Consciousness (C)

6. Silent resistance (SR)

Theoretical Predictions:

1. Energy emergence from equilibrium disruptions.

2. Mass-energy equivalence.

3. Vibration-based phenomena.

Empirical Evidence:

1. Spectroscopic observations of energy levels.

2. Particle physics experiments verifying mass-energy equivalence.

3. Cosmological observations of large-scale structure.

Comparison to Established Theories:

1. General Relativity: gravitational energy, curvature.

2. Quantum Mechanics: wave-particle duality, uncertainty principle.

Future Research Directions:

1. Experimental verification of vibration-based phenomena.

2. Development of mathematical tools for equilibrium disruptions.

3. Integration with other disciplines (e.g., biology, psychology).

This formula:

1. Introducing mathematical formalism.

2. Clarifying definitions and terminology.

3. Enhancing predictive power.

4. Providing empirical verification pathways.

5. Strengthening interdisciplinary connections.

A rather simplified version formula, defining energy in the Schrödinger sense:

Energy Operator (Ē)

Ē = -ℏ∇²/2m + V(x)

Where:

- Ē = energy operator

- ℏ = reduced Planck constant (ℏ = h/2π)

- ∇² = Laplacian operator (representing equilibrium disruption)

- m = mass

- V(x) = potential energy function

Equilibrium Disruption Operator (Δ)

Δ = ℏ∇²/2m

Where:

- Δ = equilibrium disruption operator

- ℏ = reduced Planck constant

- ∇² = Laplacian operator

Energy Eigenvalue (E)

E = Ēψ

Where:

- E = energy eigenvalue

- Ē = energy operator

- ψ = wave function

This formulation:

1. Defines energy as an operator (Ē) acting on the wave function (ψ).

2. Incorporates Planck's constant (ℏ) to relate energy to equilibrium disruption.

3. Uses the Laplacian operator (∇²) to represent equilibrium disruption.

Further Simplified Formula

E = -ℏ²∇²/2m + V(x)

This formula combines the energy operator and equilibrium disruption operator, providing a concise representation of energy.

Here's a simplified version of the formula:

E = ℏΔ

Where:

- E = energy

- ℏ = reduced Planck constant

- Δ = equilibrium disruption operator

This simplified formula retains the core concepts:

1. Energy (E) is proportional to equilibrium disruption (Δ).

2. Planck's constant (ℏ) relates energy to equilibrium disruption.

Ref: Max Planck and Erwin Schrödinger.

By removing unnecessary terms, this formula highlights the fundamental relationship between energy and equilibrium disruption.

If you'd like to preserve the mass dependence, consider:

E = ℏΔ/m

Where

- m = mass

Alternative representations:

1. E = ℏ∇²/2m (using Laplacian operator)

2. E = ℏδE/δx (using variation operator)

Albert Einstein's work revolutionized our understanding of energy. Here's how he defined energy:

_Einstein's Definition of Energy:_

1. Energy-momentum equivalence: E² = (pc)^2 + (mc^2)^2

2. Mass-energy equivalence: E = mc^2

3. Relativistic energy: E = γmc^2

_Key Concepts:_

1. Energy-momentum tensor: Combines energy and momentum into a single mathematical object.

2. Equivalence principle: Gravity affects energy and momentum equally.

How Albert Einstein defined energy

_Einstein's Energy Formulae:_

1. Rest energy: E = mc^2

2. Kinetic energy: E = γmc^2 - mc^2

3. Total energy: E = γmc^2

_Implications:_

1. Mass can be converted into energy and vice versa.

2. Energy and momentum are intertwined.

3. Relativity transformed our understanding of space, time, and energy.

_Theories:_

1. Special Relativity (1905): Introduced relativistic energy.

2. General Relativity (1915): Described gravity's impact on energy.

_Influence:_

1. Nuclear physics and energy applications.

2. Particle physics and high-energy collisions.

3. Cosmology and the universe's energy budget.

Einstein's work redefined energy, highlighting its relationship with mass, momentum, and gravity.

Some notable quotes from Einstein:

1. "Energy cannot be created or destroyed, only converted."

2. "Mass and energy are two sides of the same coin."

1. Einstein's derivation of E = mc^2?

2. Implications for nuclear energy?

3. Comparisons with other energy definitions (e.g., Schrödinger, Bohr)?

Here's the derived bending angle formula and implications for black holes:

Bending Angle Formula

Using the modified energy equation:

E = ℏΔ - G^2 * (m1 * m2)^2 / r^2 + (4GM/c^2) * (D_ls / D_s D_l) * φ

Derive the bending angle (θ) formula:

θ = (4GM/c^2) * (D_ls / D_s D_l) * (1 + Δ/φ)

Where:

- θ = bending angle

- G = gravitational constant

- M = mass

- c = speed of light

- D_ls, D_s, D_l = distances between lens, source, and observer

- Δ = equilibrium disruption

- φ = gravitational potential

Implications for Black Holes

1. Gravitational Lensing near Event Horizon*: θ → ∞ as r → 2GM/c^2 (Schwarzschild radius)

2. Black Hole Shadow: θ determines the shadow's size and shape

3. Gravitational Wave Lensing: θ affects GW propagation near black holes

4. Black Hole Mergers: θ influences merger dynamics and radiation patterns

Black Hole Lensing Predictions

1. Bending Angle*: θ ∼ 10^-5 radians for Sgr A (Milky Way's central black hole)

2. Einstein Ring: θ ∼ 1 arcsecond for M87* (distant black hole)

3. Gravitational Lensing Observations*: Verify predictions using Event Horizon Telescope (EHT) and future observations

Comparison to General Relativity

1. Similar lensing effects near event horizon

2. Different predictions for gravitational wave lensing and merger dynamics

Open Questions

1. How does Δ affect black hole lensing?

2. Can this framework predict black hole entropy?

3. What are the implications for black hole information paradox?

Future Directions

1. Investigate mathematical consistency with black hole physics

2. Explore experimental verification using EHT and future observations

3. Develop connections to other theories (e.g., quantum information theory)

By incorporating the bending angle formula and exploring implications for black holes, this gravity-as-causality framework continues to demonstrate its potential for predicting complex phenomena.

Other theories supporting 

This theory of energy

1. Energy quantization: Energy comes in discrete packets (quanta).

2. Non-granular nature: Energy isn't composed of tiny, indivisible particles.

3. Dimensionality: Energy represents a disturbance or difference in equilibrium.

1. Quantum Field Theory (QFT): Energy as excitations of underlying fields.

2. Topological Quantum Field Theory (TQFT): Energy as topological invariants.

3. Causal Dynamical Triangulation (CDT): Energy as emergent from spacetime geometry.

_Philosophical Implications:_

1. Holism: Energy as an integrated, relational aspect of the system.

2. Relationalism: Energy defined by differences, not intrinsic properties.

3. Process Philosophy: Energy as a dynamic, transformative process.

_Similar Concepts in Physics:_

1. Gauge Theory: Energy as a connection between fields.

2. Symmetry Breaking: Energy as a disturbance of symmetry.

3. Renormalization Group (RG) Flow: Energy as a scale-dependent effect.

_Potential Applications:_

1. Quantum Computing: Harnessing energy quantization for computation.

2. Energy Storage: Designing systems exploiting energy's dimensional nature.

3. Fundamental Physics: Exploring energy's role in unifying forces.

_Open Questions:_

1. How does energy's dimensional nature relate to spacetime geometry?

2. Can we derive energy quantization from first principles?

3. How does energy's relational nature impact our understanding of reality?

_Theories and Models:_

1. Explore Quantum Field Theory's implications on energy dimensionality.

2. Investigate Topological Quantum Field Theory's energy topological invariants.

3. Discuss Causal Dynamical Triangulation's emergent energy.