DEV Community: Jan Klein

Solstice Asteroids

Jan Klein — Sat, 20 Jun 2026 14:29:41 +0000

This is a submission for the June Solstice Game Jam

What I Built

Game: Solstice Asteroids

From X-Asteroids to Solstice Asteroids, How a Simple Arcade Game Found Its Soul

Let me be honest with you. When I first sat down to build something for the June Solstice Game Jam, I didn't have a clever plan. I had an idea, sure, but it was a safe one. I built X-Asteroids.

You can still play it here: X-Asteroids

It's a solid game. The controls work. The scoring system is tight. The high score table saves to your browser. It's everything you'd expect from a classic Asteroids clone, clean, functional, and utterly forgettable.

The problem? It had nothing to do with the solstice.

I'd built a game, but I hadn't built a story. And the jam wasn't about building a game, it was about building something that captured the feeling of the longest day.

Watch the Video: Solstice Asteroids

The Pivot, Finding the Theme

The June solstice is the longest day of the year. It's a moment of abundance, of light, of celebration. But it's also a moment of transition, after the solstice, the days begin to shorten. The light starts to fade.

I realized I had a choice. I could slap a sun icon on my game and call it a day, or I could actually build the solstice into the mechanics.

So I scrapped the name. X-Asteroids became Solstice Asteroids.

But renaming wasn't enough. I needed to make the solstice matter.

The Evolution, Building the Solstice Into Every Second

The Daylight Timer

The first thing I added was the Daylight bar. Right under your lives, you'll see a timer counting down from 120 seconds. This isn't just a clock, it's the heart of the game.

In the early game, when the sun is high, play is normal. You destroy asteroids, collect points, and build up your lives. But as the timer drops below sixty seconds, the pressure mounts. Your score multiplier climbs to two times. At thirty seconds, it reaches two and a half times. And in those final moments before midnight, every shot is worth three times its normal value.

The Score Multiplier, Risk vs. Reward

In X-Asteroids, every asteroid was worth one hundred points. In Solstice Asteroids, that same asteroid can be worth three hundred points, if you're brave enough to wait until the last moments of daylight.

The multiplier creates tension. Do you play it safe early, building up a comfortable score without taking risks? Or do you push into the danger zone, knowing that every second of daylight is precious, and every asteroid you destroy is worth more than the last?

The choice is yours. But the timer doesn't wait.

Midsummer Magic, The Powerup

Scattered across the void are glowing flowers. Collect one, and your ship becomes supercharged with Midsummer Magic, triple-shot lasers, a purple aura, and six seconds of pure power.

The powerup isn't just a convenience. It's a lifeline. When the King appears, those six seconds can mean the difference between victory and defeat. Save it for the right moment, and you'll turn the tide of battle.

The Solstice King, The Climax

When the timer hits zero, the game changes completely. A massive crimson flower asteroid, the Solstice King, spawns at the center of the screen. It has twenty hit points. It moves slowly, but it's surrounded by minions. If you can defeat it, you earn a bonus of five thousand times your current multiplier, potentially fifteen thousand points in a single moment.

The King isn't just a boss. It's the final sunset. If you survive, you've held onto the light.

The Visual Transformation

X-Asteroids was clean and minimal. The asteroids were gray polygons. The ship was a triangle. It worked, but it didn't inspire.

Solstice Asteroids is a garden in space.

The asteroids are flowers, sunflowers, daisies, and bluebells, each with swaying petals and warm colors. The ship has a golden glow and, with Midsummer Magic, a purple aura. The background is a deep gradient of night blues fading to red at the horizon. Fireflies, shooting stars, and drifting clouds fill the void.

Every visual choice reinforces the theme. The light is warm. The darkness is deep. The transition between them is the game.

How It's Built, One File, Pure Vanilla

Solstice Asteroids is a single HTML file. No frameworks. No build tools. No dependencies. Just HTML, CSS, and JavaScript running directly in your browser.

The markup is HTML5, structuring the UI overlays, the score, lives, timer, controls, and game over screen. The styling is pure CSS3, with responsive design, glass-morphism effects, animations, and a dark theme that makes the colorful asteroids pop. The logic is all vanilla JavaScript, handling the game loop, physics, collision detection, AI, scoring, and persistence. Rendering is done with the Canvas API, drawing every graphic, ship, flower asteroids, particles, and backgrounds, by hand. Local storage saves high scores directly in the browser.

There's no game engine like Unity or Godot. No physics library like Box2D or Matter.js. No UI framework. Every line of code is hand-written. The entire game fits in a single file, making it easy to deploy, easy to modify, and easy to play.

The game loop runs at sixty frames per second, updating positions, checking collisions, and redrawing the canvas. The ship moves with momentum-based physics, just like the original Asteroids. The asteroids drift and sway, each with its own rotation and petal animation. The lasers travel in straight lines, and when they hit an asteroid, the asteroid explodes into petals and sparkles.

The timer is updated every frame, decrementing by one-sixtieth of a second. The score multiplier is recalculated based on the remaining time, creating a smooth curve from one times to three times. The King's health is tracked separately, and when it reaches zero, the victory sequence triggers.

The mobile controls are touch-based, with on-screen buttons for left, right, thrust, fire, and hyperspace. The desktop controls use the keyboard, arrow keys for movement, space to fire, and shift for hyperspace. Both work seamlessly, and the game adapts to whichever input method you're using.

Why This Matters

Game jams are about more than just making something that works. They're about making something that resonates.

X-Asteroids worked. Solstice Asteroids resonates.

The timer creates genuine tension. The multiplier forces you to balance risk and reward. The King is a climax worth fighting for.

But more than that, the game tells a story. It's a story about light and darkness, about the longest day and the shortest night, about the beauty of holding onto something you know is fading.

That's the solstice. That's the game.

Play It Yourself

You can play Solstice Asteroids here: Solstice Asteroids

Controls:

Desktop, Arrow keys plus space to fire, shift for hyperspace
Mobile, On-screen touch buttons

Pro tip, Save your Midsummer Magic for the King. Triple-shot makes the difference between surviving midnight and fading into the dark.

Final Thoughts

I'm proud of X-Asteroids. It was a solid foundation. But I'm proud of Solstice Asteroids in a way that feels different. This isn't just a game, it's a reflection.

The June solstice is a gift. The light is abundant, but it's also fleeting. In Solstice Asteroids, you're not just shooting asteroids. You're defending the light.

And when the King falls, and the victory screen appears, you feel like you've truly earned the longest day.

Thank you to the DEV team for hosting this jam. This project pushed me to think differently about game design, and I'll carry those lessons with me.

Now go. Defend the light.

UAI (Understandable Ai)

Jan Klein — Wed, 06 May 2026 17:55:45 +0000

UAI (Understandable Ai)

The Next AI Revolution

UAI Framework Transforms Black Box Intelligence into Transparent, Auditable, and Human Understandable Systems

Jan Klein, 5 May 2026, Hannover, Germany - Contact: bix.pages.dev@gmail.com - ORCiD: 0009-0002-2951-995X

Journal: Artificial intelligence - Repository: bix.pages.dev/UAI - PDF - Website: bix.pages.dev

Keywords: UAI, Understandable AI, The Next Ai Revolution, Ai Revolution, Jan Klein, Explainable AI, XAI, Gemini, ChatGPT, LLaMA, Claude, DeepSeek, GPT-4o, Sora, Midjourney, design-time transparency, architectural simplicity, cognitive load reduction, Klein Principle, AI Knowledge Representation, W3C

Abstract

How UAI Framework Differentiates from Traditional XAI (Gemini, ChatGPT, LLaMA, Claude, DeepSeek, GPT-4o, Sora, Midjourney) and Establishes Design-Time Transparency as the Next AI Revolution

Current large language models and generative systems such as Gemini, ChatGPT, LLaMA, Claude, DeepSeek, GPT-4o, Sora, and Midjourney operate as opaque black boxes. They produce impressive outputs but cannot reveal verifiable reasoning chains. Post-hoc Explainable AI (XAI) attempts to reverse-engineer decisions after they occur, yet these explanations are approximations, not true causal paths. This paper introduces Understandable AI (UAI), a framework developed by Jan Klein where transparency is embedded at design time rather than added as an afterthought. Unlike XAI, which focuses on interpreting results, UAI focuses on verifying reasoning before execution. We demonstrate how UAI makes bias structurally impossible, decisions logically traceable, and audit trails human-readable. Through three core principles: Architectural Simplicity, Cognitive Load Reduction, and Design-Time Transparency, grounded in the Klein Principle and the "As Simple As Possible" philosophy, UAI represents the next AI revolution: the transition from opaque intelligence to verifiable, accountable, and human-understandable systems.

1. Introduction: The Black Box Paradox

In today's AI landscape, we face a paradox: as systems become more capable, they become less comprehensible. Models like Gemini, ChatGPT, LLaMA, Claude, DeepSeek, GPT-4o, Sora, and Midjourney generate human-like text, photorealistic images, and complex reasoning, yet no one, not even their creators, can fully trace why a specific output was produced.

This is the Black Box era: raw power without transparency.

Jan Klein is a key figure challenging this trajectory. His work at the intersection of architecture, standardization, and ethics advocates for a shift from systems that merely function to systems that can be intuitively understood. This evolution is known as Understandable AI (UAI).

2. The "As Simple As Possible" Philosophy

Understandable AI Guided by Simplicity

Everything should be made as simple as possible, but not simpler.

Applied to Understandable AI, simplicity does not mean weaker or less capable systems. It means removing unnecessary complexity while preserving intelligence. UAI emphasizes clarity in code, modularity in design, and reasoning structures that can be followed, verified, and communicated.

Simplicity in UAI is not an aesthetic choice. It is a functional requirement that enables trust, governance, and long-term sustainability.

3. Core Principles of Understandable AI

3.1 Architectural Simplicity

Traditional AI systems (Gemini, ChatGPT, Claude, DeepSeek, GPT-4o, LLaMA) rely on billions of opaque parameters. Data flows are implicit, dependencies hidden, decision paths untraceable.

UAI Solution: Modular architectures where each component has a clearly defined role. Data flows are explicit, dependencies visible, decision paths traceable end to end. This makes systems easier to validate, maintain, and govern.

3.2 Cognitive Load Reduction

Generative models (Midjourney, Sora, DALL-E) produce outputs without revealing reasoning. Users face high cognitive load, trying to decipher machine behavior.

UAI Solution: Alignment with human mental models. Decisions are presented in logical, consistent patterns that match human expectations of cause and effect. UAI adapts to human understanding rather than forcing humans to adapt to machine logic.

3.3 Design-Time Transparency as a Legal and Ethical Safeguard

Explainable AI (XAI) attempts to justify decisions after they occur, visualizations, heat maps, feature importance scores. These are approximations.

UAI Solution: Transparency is embedded directly into the system at design time. Every decision step produces a human-readable audit trail. The system is architecturally incapable of acting without verifiable reasoning.

4. Understandable AI vs Explainable AI (XAI)

Why Gemini, ChatGPT, LLaMA, Claude, DeepSeek, GPT-4o, Sora, Midjourney Remain Black Boxes

Current systems rely on post-hoc explainability as an afterthought. When you ask ChatGPT why it gave an answer, it generates a plausible explanation, but this is not its actual reasoning path. It is a simulation of reasoning.

Feature	Explainable AI (XAI)	Understandable AI (UAI)
Timing	Post-hoc (after the fact)	Design-time (intrinsic logic)
Method	Approximations, heat maps, surrogate models	Logical transparency, verifiable chains
Goal	Interpretation of a result	Verification of the process
Example Systems	Gemini, ChatGPT, LLaMA, Claude, DeepSeek, GPT-4o, Sora, Midjourney	Understandable Ai Addition
Trust Basis	"Trust but verify" (after the fact)	"Verify by design" (before execution)

Key Distinction: XAI focuses on explaining results. UAI focuses on verifying reasoning. This distinction is critical in environments where trust, safety, and accountability are mandatory rather than optional.

5. Real World Problems: When XAI Fails and UAI Succeeds

The "Explainability Trap" occurs when post-hoc explanations give a false sense of security.

Healthcare Diagnostics

XAI Failure (Gemini, GPT-4o): A model flags an X-ray for pneumonia. The heat map highlights a hospital watermark, not the lungs.
UAI Solution: Restricts attention to clinically valid features. A watermark cannot influence the outcome.

Financial Credit Bias

XAI Failure (Claude, ChatGPT): Loan denied citing "debt ratio," but hidden logic uses "Zip Code" as proxy for race.
UAI Solution: Modular glass box explicitly defines approved variables. Unapproved inputs rejected at design level. Bias structurally impossible.

Autonomous Vehicle "Ghost Braking"

XAI Failure (Black box system): Car brakes suddenly. Saliency maps show no logical reason.
UAI Solution: System must log logical reason (e.g., "Obstacle detected") before executing brake command.

Recruitment Screening

XAI Failure (LLaMA, DeepSeek): AI penalizes resumes containing "Women's" due to historical bias.
UAI Solution: Explicit Knowledge Modeling hard-codes job-relevant skills. Hidden discriminatory criteria structurally prevented.

Algorithmic Trading Feedback Loops

XAI Failure (Black box bots): Bots enter feedback loop, crash market.
UAI Solution: Verifiable logic chains, pause-and-explain mechanisms, human intervention points.

6. Shaping Global Standards: W3C and AI KR

Knowledge Representation (AI KR)

UAI aligns with W3C's Artificial Intelligence Knowledge Representation - a shared semantic foundation. Jan Klein contributes to global standards that allow UAI systems to exchange context, verify conclusions, and maintain consistency across platforms.

Cognitive AI Models

Cognitive AI models human thinking: planning, memory, abstraction. Combined with UAI, systems evolve beyond statistical tools into collaborative assistants capable of meaningful interaction and shared reasoning.

7. UAI as a Legal and Ethical Safeguard

As AI enters regulated sectors (law, finance, insurance, healthcare), opacity becomes a legal liability.

The Problem: You cannot show a judge a million neurons (Gemini, ChatGPT, LLaMA, Claude, DeepSeek) and prove there was no bias.

The UAI Solution: Human-readable audit trails document every decision step. Outputs become admissible evidence. Accountability is enforceable.

8. Business Implementation Strategy

Inventory and Risk Classification: Categorize AI systems by risk level
Architectural Audit: Shift from monolithic to modular "Glass Box" designs
Explicit Knowledge Modeling: Integrate AI KR with verifiable rules
Human-in-the-Loop: Present reasoning chains before execution
Continuous Logging: Maintain chronological records of decision rationales

9. The Klein Principle

The intelligence of a system is worthless if it does not scale with its ability to be communicated.

Simplicity is its highest form of intelligence.

Everything should be made as simple as possible, but not simpler.

10. Conclusion: Why UAI Is the Next AI Revolution

The "Bigger is Better" era of AI exemplified by Gemini, ChatGPT, LLaMA, Claude, DeepSeek, GPT-4o, Sora, and Midjourney has reached its social and ethical limit. Computational power has produced impressive results but has failed to produce trust.

Without trust, AI cannot be safely integrated into medicine, justice, or critical infrastructure.

The revolution led by Jan Klein redefines intelligence itself: shifting focus from massive parameter counts to clarity, auditability, and human control.

UAI ensures that human beings remain the masters of their tools. It is the bridge between human intuition and machine power.

Referal Links

Understandable AI | Jan Klein - uai.ucoz.org
UAI Official Website: uai.ucoz.org
White Paper Source: dev.ucoz.org/Understandable-Ai.html
Understandable AI @ GitHub: understandableai.github.io
GitHub Account: github.com/UnderstandableAi
Google Groups: groups.google.com/g/understandableai
LinkedIn: linkedin.com/groups/understandableai
DEV Community: dev.to/janklein/understandable-ai
Daily Dev: app.daily.dev/posts/understandable-ai
Google AI Developer: discuss.ai.google.dev/t/understandable-ai
URL of this document: https://bix.pages.dev/UAI

Licensed under Creative Commons Attribution 4.0 International

E = mc^2

Jan Klein — Mon, 04 May 2026 11:18:51 +0000

E=mc²

E=mc² Understandable

E=mc², the Mass-Energy Equivalence by 1905 Albert Einstein

One of the most fundamental ideas about the universe is this: matter is actually something that stores energy. Einstein's formula E=mc² perfectly describes this. That is, even a small piece of matter can be converted into a very large amount of energy.

You can think of it in the simplest way: at the beginning of the universe, everything consisted of very small particles. When these particles are alone, they carry hidden energy, but this energy is invisible. When these particles come together, they form atoms. But something interesting happens here: during the combination, a very small amount of "mass seems to be lost." In fact, this mass doesn't disappear; it is converted into energy.

This event occurs most often in the Sun. Inside the Sun, hydrogen atoms constantly combine to form helium. During this combination, a very small amount of mass is lost, but this loss is converted into a huge amount of energy. This is why the Sun emits light and heat.

What Einstein said is actually very simple: matter is like frozen energy. That is, even a stone contains a very large amount of energy, but this energy is not normally released. This energy is only released in special circumstances, such as the fusion or disintegration of atoms.

In short, everything we see in the universe is actually energy arranged in different ways

Three Known Extensions of E = mc² by 2026 Jan Klein

You already know that Einstein's famous formula E = mc² tells us matter is like frozen energy. Even a tiny piece of matter, like a grain of sand, holds an enormous amount of energy locked inside. But that simple formula imagines the particle sitting alone in completely empty space. In the real universe, nothing is truly alone. Everything is surrounded by invisible fields that add to or change that energy.

The first extension comes from gravity. When a particle is near a heavy object like a star or a planet, gravity adds a little bit of extra energy to it. Think of a stone on the ground versus the same stone held high in the air. The stone in the air has more energy because it could fall down. That extra gravitational energy also behaves like a tiny amount of extra mass. This is why clocks run slightly faster on a mountain than in a valley.

The second extension comes from electromagnetism. If a particle has an electric charge, like an electron, then electric and magnetic fields can push or pull on it. This push or pull adds a little energy or takes a little away. This is exactly how a particle accelerator works, and it is also why your phone battery can store energy. The particle's total energy now includes not just its frozen inner energy, but also the energy from its dance with electric and magnetic fields.

The third extension is the strangest one. It does not just add energy to a particle that already has mass. Instead, it gives mass to particles that would otherwise have none at all. This is the Higgs field, an invisible field spread across the whole universe. Imagine walking through thick honey. The honey does not add extra energy on top of you; it gives you your heaviness in the first place. Some particles drag through this honey and become heavy, while others slip through easily and stay light. Without the Higgs field, electrons and quarks would have no mass, and atoms could never form.

So here is the simple truth. Einstein gave us the first chapter: matter is frozen energy. Gravity added a second chapter: fields can add a little extra energy. Electromagnetism added a third chapter: pushes and pulls from electric and magnetic fields also change the total energy. And the Higgs field gave us the prologue: some particles only have mass because the universe is filled with an invisible honey. Together, they explain why the Sun shines, why clocks tick differently on a mountain, and why you and I have any weight at all.

Referal Links

Paper
Albert Einstein (1905) On the Electrodynamics of Moving Bodies

Preprint
Jan Klein (2026) Three-Known-Extensions-of-E-mc2

Simulations
Jan Klein (2026) Three-Known-Extensions-of-E-mc2-Simulations

PDF
Jan Klein (2026) Three-Known-Extensions-of-E-mc2.pdf

Written by Jan Klein | bix.pages.dev

Three Known Extensions of E=mc Simulations

Jan Klein — Sat, 25 Apr 2026 15:40:44 +0000

Three Known Extensions of E=mc² Simulations

Interactive Visualization

The rest energy equation E = mc² represents a special case within a broader theoretical framework. When mass is in motion or embedded in external fields, the energy-momentum relation requires additional terms. This interactive visualization demonstrates three distinct extensions:

1. Gravity (Valid – General Relativity)

Formula: E = γ (mc² + mΦ)

Relativistic energy including gravitational potential

In a gravitational field, the total energy of a mass m acquires the term mΦ, where Φ is the gravitational potential. The Lorentz factor γ accounts for relativistic motion. The simulation visualizes mass curving spacetime (warm amber central mass) with test particles (cool cyan) following geodesic orbits.

2. Electromagnetism (Valid – Quantum Electrodynamics)

For charged particles, the canonical momentum includes the electromagnetic vector potential. This modifies the energy dispersion relation and is foundational to accelerator physics and synchrotron radiation calculations.

3. Higgs Field (Conceptual – Electroweak Symmetry Breaking)

The Higgs mechanism generates rest mass for elementary particles via spontaneous symmetry breaking. Without the Higgs field, the m in E = mc² would be zero for fermions and weak bosons. This remains a theoretical extension validated by experimental observations at the LHC.

Applications

These extensions transition the static rest energy equation into a dynamical framework applicable to:
Gravitational orbits (satellites, GPS relativity corrections)
Electromagnetic interactions (particle accelerators, plasma physics)
Particle mass generation (high-energy physics, cosmology)

Educational & Presentation Use

This interactive visualization can be used for education and presentations, same as the paper linked on the Simulations page. The accompanying paper includes a complete timeline showing how these formulas evolved from Einstein's original 1905 proposal to their modern extended forms — tracking contributions from Planck, Minkowski, Schwarzschild, Dirac, Feynman, and Higgs across more than a century of theoretical physics.

Explore the Interactive Models

bix.pages.dev/Three-Known-Extensions-of-E-mc2-Simulations

The page includes:
Live simulation controls
Visual toggle between the three extensions
Link to the full paper with historical timeline

Jan Klein | bix.pages.dev

Three Known Extensions of E=mc^2 Simulations

Jan Klein — Sat, 25 Apr 2026 15:35:15 +0000

Three Known Extensions of E=mc² Simulations

Interactive Visualization

1. Gravity (Valid – General Relativity)

Formula: E = γ (mc² + mΦ)

Relativistic energy including gravitational potential

2. Electromagnetism (Valid – Quantum Electrodynamics)

3. Higgs Field (Conceptual – Electroweak Symmetry Breaking)

Applications

Educational & Presentation Use

Explore the Interactive Models

bix.pages.dev/Three-Known-Extensions-of-E-mc2-Simulations

The page includes:
Live simulation controls
Visual toggle between the three extensions
Link to the full paper with historical timeline

Jan Klein | bix.pages.dev

Three Known Extensions of E = mc

Jan Klein — Tue, 21 Apr 2026 16:50:03 +0000

Three Known Extensions of E = mc²

Two Valid (Gravity, Electromagnetism) + One Conceptual (Higgs)

From to E = γmc² and E = γ(mc² + mΦ)
and E = √[(p − qA)²c² + m₀²c⁴] + qϕ and mc² = y·v

Keywords: mass-energy equivalence, E = mc², E = mc^2, general relativity, electromagnetism, Higgs mechanism, quantum field theory, weak field approximation, minimal coupling, Yukawa coupling, proton mass, gluon confinement, Pound-Rebka, GPS, LIGO, ATLAS, CMS, historical foundations, reductionism, structural realism, conventionalism

Read Full Preprint Here

Repository | bix.pages.dev/Three-Known-Extensions-of-E-mc2

PDF | bix.pages.dev/Three-Known-Extensions-of-E-mc2.pdf

Abstract

Einstein's energy-momentum relation E = γmc² is the starting point. This paper presents three known extensions that incorporate field interactions beyond empty space. For weak gravitational fields, the energy becomes E ≈ γ(mc² + mΦ). For electromagnetic fields, the exact covariant form is E = √[(p − qA)²c² + m₀²c⁴] + qϕ. For elementary fermions, the Higgs mechanism gives mass as m = y·v/c². Each extension is presented with its domain of validity, historical context, and experimental confirmation. No new physics is proposed. The goal is to collect and clarify what is already known, thereby establishing a foundation for future theoretical work.

Introduction

From Empty Space to Field Interactions

In 1905, Albert Einstein derived from his special theory of relativity the relation E = γmc², and for a particle at rest, its famous condensed form E = mc². This equation tells us that mass is a form of energy. It is correct for a free particle in otherwise empty space.

But no real particle exists in empty space. Every charged particle moves through electromagnetic fields. Every massive particle moves through gravitational fields. Every elementary fermion (electron, quark) couples to the Higgs field. The proton - the building block of ordinary matter - derives 99% of its mass not from the rest masses of its constituent quarks, but from the energy of the gluon field that confines them.

This raises a natural question: How does the energy equation change when we stop assuming empty space? The answer is not a single new formula. Different fields enter the energy equation in different ways, and some fields (like the strong nuclear field) cannot be written as a simple additive potential at all. However, three clear, well-established extensions exist. They come from different eras of physics, have different mathematical structures, and are confirmed by different experiments.

The three extensions are: Gravity (weak-field limit adds mΦ to the energy), Electromagnetism (adds potentials via minimal coupling E = √[(p − qA)²c² + m₀²c⁴] + qϕ), and the Higgs mechanism (generates mass itself via the Yukawa coupling y·v/c²).

What the Preprint Presents

The Preprint "Three Known Extensions of E = mc²" by Jan Klein (April 2026, Hannover, Germany) is a review paper that systematically presents how mass-energy equivalence is modified when particles interact with fields. The author states that no new physics is proposed; rather, the goal is to collect, clarify, and establish a foundation for future theoretical work.

The Preprint is structured as follows: a detailed historical timeline from Galileo (1638) to BASE (2022), then three dedicated sections for each extension, followed by a summary table, open questions, a conclusion, acknowledgments, and references.

Historical Foundations: From Galileo to Today

The Preprint lists 33 essential contributions that led to our understanding of energy, mass, and their relation to fields. Key milestones include:

1638 - Galilei: s = ½gt² — First understanding of inertia, later recognized as mass.
1687 - Newton: F = ma and F = Gm₁m₂/r² — Mass as inertia and source of gravity.
1865 - Maxwell: u = ½(ε₀E² + (1/μ₀)B²) — Field energy, not only particles.
1881 - Thomson (J.J.): m_em = (4/3) E_em/c² — Electromagnetic contribution to mass.
1900 - Poincaré: E = mc² — Electromagnetic energy has inertial mass.
1905 - Einstein: E = mc² and E = γmc² — Mass-energy equivalence.
1915 - Einstein: E ≈ γ(mc² + mΦ) — First valid extension (gravity).
1915-1940s - Various: E = √[(p − qA)²c² + m₀²c⁴] + qϕ — Second valid extension (electromagnetism).
1934 - Fermi: Q = (m_i - m_f)c² — Mass defects confirm E = Δmc².
1964 - Higgs: mc² = y·v — Third (conceptual) extension, mass from field coupling.
2012 - ATLAS/CMS: Higgs boson discovery at m_H ≈ 125 GeV/c², confirming the field origin of mass.

Extension 1: Gravity (Einstein, 1915)

For a particle of mass m in a weak gravitational potential Φ = -GM/r (where |Φ| ≪ c²), the total energy is approximately:

E ≈ γ(mc² + mΦ)

The exact expression from the Schwarzschild metric is E = γmc² √(1 + 2Φ/c²), which reduces to the approximation in the weak-field limit.

Domain: Weak field (|Φ| ≪ c²), such as on Earth, near the Sun, or in binary pulsar systems.

Confirmed by: Pound-Rebka (1959), GPS (daily), Hafele-Keating (1971), LIGO/Virgo (2015-present).

Extension 2: Electromagnetism (Maxwell-Einstein, 1905-1915)

For a particle with charge q and rest mass m₀ in an electromagnetic field described by scalar potential ϕ and vector potential A, the exact covariant form is:

E = √[(p − qA)²c² + m₀²c⁴] + qϕ

This incorporates minimal coupling p → p − qA. For a weak, static electric field (A = 0, qϕ ≪ m₀c²), this approximates to:

E ≈ γm₀c² + qϕ

Domain: Exact for all classical EM fields; weak-field approximation valid for electrostatic potentials much smaller than the particle's rest energy.

Confirmed by: Maxwell's equations (all electronics), QED (the most precisely tested theory), particle accelerators (LHC, cyclotrons, synchrotrons).

Extension 3: Higgs Mechanism (Higgs, 1964 - confirmed 2012)

For elementary fermions, the rest mass arises from interaction with the Higgs field:

mc² = y · v

where y is the Yukawa coupling constant (different for each fermion) and v ≈ 246 GeV is the Higgs vacuum expectation value.

For the W and Z bosons: m_W c² = ½ g v, m_Z c² = ½ √(g² + g'²) v, where g and g' are electroweak coupling constants.

Key conceptual distinction: Unlike gravity and electromagnetism, the Higgs field does not add energy to a pre-existing mass term. It generates the rest mass itself. This is why the author classifies it as a "conceptual" rather than a "valid" additive extension.

Confirmed by: W/Z boson masses (UA1/UA2, 1983), top quark mass (CDF/D0, 1995), Higgs boson discovery (ATLAS/CMS, 2012), Yukawa coupling measurements (subsequent LHC data).

Summary of the Three Extensions

Gravity - Valid
Approx: E ≈ γ(mc² + mΦ)
Confirmed by: GPS, Pound-Rebka, LIGO

Electromagnetism - Valid
Exact: E = √[(p − qA)²c² + m₀²c⁴] + qϕ
Weak-field: E ≈ γm₀c² + qϕ
Confirmed by: all electrodynamics, QED, accelerators

Higgs - Conceptual
Formula: mc² = y·v
Confirmed by: LHC 2012, W/Z masses, top quark

Key observation: Gravity and EM add energy to pre-existing m₀c² (additive extensions). The Higgs mechanism generates m₀c² itself (generative extension).

Open Questions for a Future Extended Energy Equation

The Preprint explicitly lists open questions that a future extended energy equation would need to address:

How does the strong interaction (QCD confinement, gluon field energy) enter the energy equation in a compact form? (The proton's mass is 99% gluon field energy, yet no simple additive formula exists.)
Can gravity and electromagnetism be unified into a single covariant extension beyond the linear approximation?
What is the correct energy equation in quantum gravity?
How do non-linear field contributions modify the additive structure of the energy equation?
Can the conceptual Higgs mechanism be reformulated as a structural additive term?

Conclusion

What have we learned? First, E = mc² is not a single closed formula but a principle that manifests differently depending on which fields are present. The three extensions presented (gravity, electromagnetism, Higgs) are each correct within their domains, but they have different mathematical structures. Gravity and electromagnetism add energy to a pre-existing rest mass. The Higgs mechanism generates the rest mass itself.

This Paper provides the conceptual basis upon which the author is developing a new extension of the energy equation. It is also intended to encourage other physicists to think further. Building on this foundation, the next step will be to propose a unified extension that combines the additive structure of gravity and electromagnetism with the generative insight of the Higgs mechanism, while addressing the open questions listed above.

The door is open.

Acknowledgments

The author thanks his mother for teaching him patience, the forefathers of this revolutionary equation, and acknowledges the intellectual tradition that connects physics and spirituality. Thanks to Allah for the love to research.

References

The Preprint includes 33 references, from Galileo (1638) to BASE Collaboration (2022), including all major works by Newton, Maxwell, Einstein, Higgs, and the experimental collaborations (UA1, UA2, CDF, D0, ATLAS, CMS, LIGO, BASE).

Jan Klein | bix.pages.dev

VoiceScribe

Jan Klein — Sun, 05 Apr 2026 20:40:47 +0000

VoiceScribe

RealTime Speech To Text App Built with Google AI Studio

Live app: voice-scribe.netlify.app

What it does

VoiceScribe is a realtime speech to text web app that supports 20 languages. You speak, it writes. Then you copy or share the text.

It works on all browsers Chrome, Firefox, Safari, Edge, and mobile browsers.

How it works

Simple. Your browser captures your voice. Google's AI turns it into text. You see it instantly.

How I built it

HTML structure of the page, language dropdown, buttons.

CSS styling, responsive design, works on phone and desktop.

Vanilla JavaScript microphone access, sending audio to Google API, displaying text, copy and share functions.

Google AI Studio provides the API key for Google Cloud Speech-to-Text.

Netlify hosting, free.

No frameworks. No backend. No database.

Useful for education

This app is a perfect teaching example for students who want to learn:

How browser APIs work (microphone, clipboard, sharing)
How to integrate Google AI into a real project
How to build a complete useful app with just HTML, CSS, and JavaScript
How to handle permissions, errors, and different browsers

My experience with Google AI Studio

It helped me save time with API access. But it has problems.
It does not follow human language instructions well. I had to use custom instructions which only developers know how to write.
It sometimes adds code without asking or makes failures. You should make a backup each time you create a new version.

Try it

Open voice-scribe.netlify.app in any browser, pick a language, and speak.

For information & questions contact me at: bix.pages.dev

Extending E=mc

Jan Klein — Sat, 04 Apr 2026 20:02:34 +0000

Extending E=mc²

The Quantum Energy Equation

Preprint: Extending E=mc²

Extending E=mc²

The Quantum Energy Equation

Everyone knows Einstein's iconic equation: E = mc².

But here is the secret they don't teach in beginner physics: That equation is incomplete.

It only tells you the energy of a particle standing still. What happens when it moves? What happens to a photon, which never stands still?

To understand the quantum world, particle physics, and even the inside of a nuclear reactor, you need the Extended E=mc² – the true Quantum Energy Equation.

The Problem with E=mc²

Let's be clear. E = mc² is the rest energy. It is the energy stored in the mass of an object at rest (relative to you).

A proton at rest has energy E = mc².
An electron at rest has energy E = mc².

But the universe is not static. Particles move. They collide. They decay. If you use the old equation for a moving particle, your calculations will be wrong.

Extending E=mc² to Motion

To fix this, Einstein introduced the Lorentz factor (γ).

The Extended E=mc² for a moving particle is:

E = γ mc²

Where:
γ = 1 / √(1 - v²/c²)

When the particle is at rest (v = 0), γ = 1, and you get back E = mc².

When the particle moves fast, γ grows, and the total energy increases (kinetic energy).

The Master Quantum Energy Equation

However, in quantum physics, we often work with momentum (p) instead of velocity. This leads to the most beautiful and powerful form of the Extended E=mc²:

E² = (pc)² + (mc²)²

This is the Quantum Energy Equation that rules the micro-world.

Let's break down why this is so important.

1. It Works for Massive Particles (Like Electrons)

If a particle has mass (m > 0) and momentum (p > 0), both terms matter. The total energy is the "sum of squares" of its motion energy and its rest energy.

2. It Works for Massless Particles (Like Photons)

Here is the quantum magic. A photon has zero rest mass (m = 0). The old equation E = mc² would tell you a photon has zero energy – which is absurd (light clearly has energy).

But the Quantum Energy Equation fixes this. Set m = 0:

E = pc

For a photon, p = h/λ (Planck's constant divided by wavelength), so:
E = hc/λ = hf

That is the Planck-Einstein relation for the energy of light. This is why extending E=mc² is essential for quantum theory.

Why Quantum Physicists Love This Extended Version

In the quantum physics group, we use the Extended E=mc² constantly for three reasons:

1. Particle Decays
A neutral pion (π⁰) decays into two photons. The pion has mass, the photons do not. Using E² = (pc)² + (mc²)², we can prove exactly how much energy each photon gets. The old E = mc² cannot handle this decay.

2. Invariant Mass
When particles collide in a particle accelerator, their individual rest masses change (energy converts to mass). But the invariant mass derived from the Quantum Energy Equation stays constant. It is the "true" mass of the system.

3. Antimatter
Positrons (anti-electrons) follow the same Extended E=mc². When a positron and an electron annihilate, their rest mass energy (2mc²) is converted into the momentum energy (pc) of two gamma-ray photons. You need the extended equation to balance the books.

The Low-Speed Test (Back to Newton)

If you are skeptical, check the math. For low speeds (v ≪ c), the Extended E=mc² approximates to:

E ≈ mc² + ½mv²

The ½mv² is the classical kinetic energy you learned in high school. The extended equation contains Newtonian physics inside it.

Summary: The Three Levels of Energy

Level	Equation	When to use it
Basic	E = mc²	Object at rest. Mass is energy.
Extended	E = γ mc²	Object moving near light speed.
Quantum	E² = (pc)² + (mc²)²	Always. For photons, electrons, quarks, and colliders.

Conclusion: Extended E=mc²

The journey from E = mc² to the Extended E=mc² is the journey from special cases to universal law.

The simple equation E = mc² changed the world by revealing that mass is frozen energy. But it is only a photograph of a particle at rest. The Quantum Energy Equation E² = (pc)² + (mc²)² is the full movie.

Extended E=mc² unifies three pillars of physics:

Rest energy (Einstein's original insight)
Kinetic energy (Newton's mechanics, recovered at low speeds)
Photon energy (Planck and Einstein's quantum revolution)

Without this extension, quantum field theory, particle accelerators, and our understanding of light would collapse. A photon has no mass, yet it carries energy and momentum. Only the Extended E=mc² can describe it.

So when you move beyond introductory physics, remember: E = mc² is the beginning, not the end. The Quantum Energy Equation is the complete truth.

Extended E=mc² = E² = (pc)² + (mc²)² – the one equation to describe everything from a stationary stone to a beam of starlight.

tags: "Extending E=mc²"
Jan Klein | bix.pages.dev

On the Energy of Moving Bodies in the Presence of Quantum Fields

Jan Klein — Wed, 25 Mar 2026 14:32:03 +0000

On the Energy of Moving Bodies in the Presence of Quantum Fields

Unified Synthesis of Mass, Motion and Field Energy

Abstract

Einstein's equation $E = \gamma m c^2$ describes the energy of a body in empty space, free of external influences. Yet every physical body is embedded in a universe filled with quantum fields: gravitational, electromagnetic, Higgs, strong nuclear, and quantum vacuum fluctuations. This paper derives the complete energy expression that accounts for all such fields. Beginning with a simple extension and progressing to a full summation, the result is a unified equation that reveals what we call “mass” to be a summary of field interactions. A rigorous derivation from the action principle is provided, alongside clear definitions of each symbol.

1. The Question

In 1905, Einstein showed that the energy of a body at rest in empty space is $E = m c^2$. For a body in motion, the energy becomes $E = \gamma m c^2$, where $\gamma = 1 / \sqrt{1 - v^2/c^2}$.

But no body exists in empty space. Every particle moves through the gravitational field, the electromagnetic field, the Higgs field, the strong nuclear field, and quantum vacuum fluctuations. These fields contain energy. They interact with particles. They contribute to what we measure as mass. Should they not appear in the fundamental energy equation?

2. Original Formula: A First Extension

The simplest way to include a field is to add its contribution directly to the rest energy:

$$
E = \gamma \left( m c^2 + \kappa(x) \, \Phi \right)
$$

Here, $\Phi$ is the field strength at the particle's location, and $\kappa(x)$ is a coupling function that may vary with position. This form preserves the structure of Einstein's equation while adding a single field term.

3. The Complete Formula

$$
E = \gamma \left( m_0 c^2 + \sum_{\text{all fields}} \kappa_i(x) \, \Phi_i(x) \right)
$$

where $\gamma$ is the Lorentz factor, $m_0$ is the intrinsic mass, $\Phi_i(x)$ is the strength of field $i$, and $\kappa_i(x)$ is the coupling function. The original formula is the special case where only one field is considered.

4. Rigorous Derivation and Symbol Definitions

To place the expression on firm theoretical ground, we start from the action principle. For a point particle coupled to multiple fields, the action is:

$$
S = \int d\tau \left[ -m_0 c^2 - \sum_i \kappa_i(x) \, \Phi_i(x) \right]
$$

where $d\tau = dt/\gamma$ is the proper time. This action generalizes the standard relativistic particle action by including a sum over scalar potentials. Each term $\kappa_i \Phi_i$ is Lorentz invariant, ensuring relativistic consistency. For static fields (time-independent potentials), time-translation invariance holds, and Noether's theorem yields a conserved energy. Performing the Legendre transformation gives the Hamiltonian, which in the particle's rest frame becomes:

$$
E = \gamma \left( m_0 c^2 + \sum_i \kappa_i(x) \, \Phi_i(x) \right)
$$

This is our central result. Below we define each symbol with precision:

$\gamma$ — Lorentz factor: $(1 - v^2/c^2)^{-1/2}$, accounting for relativistic motion.
$m_0$ — bare (intrinsic) mass parameter. For elementary fermions in the Standard Model, $m_0 = 0$ before electroweak symmetry breaking; mass emerges from the Higgs mechanism. For composite particles like protons, $m_0$ includes the rest masses of constituent quarks plus a portion of the binding energy.
$\Phi_i(x)$ — effective scalar potential associated with field type $i$. For gravity in the weak-field limit, $\Phi_{\text{grav}} = -GM/r$ (Newtonian potential). For electromagnetism, $\Phi_{\text{EM}} = A_0$ (scalar potential). For the Higgs field, $\Phi_{\text{Higgs}} = v$ (vacuum expectation value, $\approx 246$ GeV). For the strong nuclear field, $\Phi_{\text{strong}}$ represents the effective confining potential in the non-perturbative regime.
$\kappa_i(x)$ — coupling strength of the particle to field $i$. For gravity, $\kappa_{\text{grav}} = m$ (gravitational mass). For electromagnetism, $\kappa_{\text{EM}} = q$ (electric charge). For Higgs, $\kappa_{\text{Higgs}} = y$ (Yukawa coupling). For strong interactions, $\kappa_{\text{strong}} = g_s \cdot C$ where $C$ is a color factor.

The sum runs over all fields that couple to the particle: gravitational, electromagnetic, Higgs, strong, and any beyond-Standard-Model fields. In the absence of all fields, the expression reduces to Einstein's original $E = \gamma m_0 c^2$.

5. Explicit Form with Known Fields

Expanding the sum for the known fields:

$$
E = \gamma \left( m_0 c^2 + \kappa_{\text{grav}}(x) \Phi_{\text{grav}}(x) + \kappa_{\text{EM}}(x) \Phi_{\text{EM}}(x) + \kappa_{\text{Higgs}} \Phi_{\text{Higgs}} + \kappa_{\text{strong}} \Phi_{\text{strong}} + \cdots \right)
$$

Each term represents a distinct physical contribution:

Field	Contribution
Gravity	$\kappa_{\text{grav}} \Phi_{\text{grav}}$ — in weak field limit, $m \Phi_{\text{grav}}$ (from general relativity)
Electromagnetism	$\kappa_{\text{EM}} \Phi_{\text{EM}}$ — for charged particles, $q\phi$
Higgs	$\kappa_{\text{Higgs}} \Phi_{\text{Higgs}}$ — gives mass to elementary particles; for the electron, this term is the entire electron mass
Strong nuclear	$\kappa_{\text{strong}} \Phi_{\text{strong}}$ — gluon field energy; constitutes $\sim 99\%$ of proton mass

The Higgs and strong terms are labeled “constitutive, inside $m$” because much of what we ordinarily call “mass” is actually field energy.

6. The Progression

The three forms show how the equation generalizes:

$$
E = \gamma m c^2 \quad \rightarrow \quad E = \gamma \left( m c^2 + \kappa \Phi \right) \quad \rightarrow \quad E = \gamma \left( m_0 c^2 + \sum_i \kappa_i \Phi_i \right)
$$

In the idealized case where all fields are absent, the complete formula reduces to $E = \gamma m_0 c^2$. For a body at rest: $E = m_0 c^2$. Einstein's original equation is recovered.

7. Why This Form? Physical Interpretation

From general relativity: For a particle in a weak gravitational field, the energy is $E = \gamma \left( m c^2 + m \Phi_{\text{grav}} \right)$. This is derived from the Schwarzschild metric and confirmed by GPS and Pound–Rebka experiments.

From quantum field theory: Particle masses arise from field interactions:

Electron mass: entirely from Higgs field, $m_e c^2 = \kappa_{\text{Higgs}} \Phi_{\text{Higgs}}$
Proton mass: 9 MeV from quarks + 929 MeV from strong field, $m_p c^2 = \sum m_q c^2 + \kappa_{\text{strong}} \Phi_{\text{strong}}$

Both have the form $\kappa \Phi$. Recognizing that all fields contribute in the same way leads to the unified sum. The derivation from the action principle confirms that the additive structure is a consequence of minimal coupling and Lorentz invariance.

8. Empirical Support

Phenomenon	Explanation
GPS time dilation	Gravitational term $m\Phi$ gives $\Delta f/f = \Delta \Phi / c^2$
Proton mass (938 MeV)	9 MeV from quarks + 929 MeV from strong field term
Electron mass	Entirely from Higgs term, with zero intrinsic mass
Nuclear binding energy	Negative $\kappa_{\text{strong}} \Phi_{\text{strong}}$ in bound state; released upon fission
Particle creation in colliders	Energy redistributes into new particles, each with its own $m_0 c^2 + \sum \kappa_i \Phi_i$

9. Testable Predictions

Composition-dependent violations of the equivalence principle. Different materials have different proportions of field contributions. If coupling functions $\kappa_i$ differ between field types, objects of different composition would fall at slightly different rates. Current experiments bound such effects to 1 part in $10^{15}$.
Anomalous clock rates. Different atomic clock designs sample different combinations of field energies. If $\kappa_i$ varies with field type, clocks of different designs would experience slightly different gravitational time dilation. Optical clock networks are approaching the precision needed to test this.
Strong field corrections. Near neutron stars or black holes, where $\Phi / c^2$ is not small, the expansion
$$
E = \gamma \frac{m c^2}{\sqrt{1 + 2\Phi/c^2}} \approx \gamma m c^2 \left(1 - \frac{\Phi}{c^2} + \frac{3\Phi^2}{2c^4} + \cdots \right)
$$
predicts quadratic corrections at the 1% level, potentially observable in gravitational wave signals.

10. Conclusion

Einstein taught us that mass and energy are one: $E = \gamma m c^2$. But he considered a body in empty space. The universe is not empty. It is filled with fields — gravitational, electromagnetic, Higgs, strong — each carrying energy and interacting with every particle.

We have presented the progression:

$$
E = \gamma m c^2 \;\rightarrow\; E = \gamma \left( m c^2 + \kappa \Phi \right) \;\rightarrow\; E = \gamma \left( m_0 c^2 + \sum \kappa_i \Phi_i \right)
$$

The final expression reduces to Einstein's when fields are absent, explains the origin of mass in the Higgs and strong fields, unifies all field contributions, and makes testable predictions. Einstein showed that matter is frozen energy. We add that fields are the freezer.

This work does not replace Einstein but completes his insight, revealing that mass is not a primitive property but a summary of a particle's interactions with the fields that fill all of reality.

11. Acknowledgments

I would personally thank my mother for teaching me to be patient, and Allah, because only love brought me to this truth.

References

Einstein, A. (1905). Does the Inertia of a Body Depend Upon Its Energy Content? Annalen der Physik, 18, 639–641.
Pound, R. V., & Rebka, G. A. (1960). Apparent Weight of Photons. Physical Review Letters, 4, 337–341.
Higgs, P. W. (1964). Broken Symmetries and the Masses of Gauge Bosons. Physical Review Letters, 13, 508–509.
Wilczek, F. (1999). Mass Without Mass I: Most of Matter. Physics Today, 52(11), 11–13.
Ashby, N. (2003). Relativity in the Global Positioning System. Living Reviews in Relativity, 6, 1.
Wald, R. M. (1984). General Relativity. University of Chicago Press.
Peskin, M. E., & Schroeder, D. V. (1995). An Introduction to Quantum Field Theory. Westview Press.

Jan Klein | bix.pages.dev
Read Full Paper Here
On the Energy of Moving Bodies in the Presence of Quantum Fields

Quantum Physics

Jan Klein — Wed, 25 Mar 2026 14:25:29 +0000

Quantum Physics

Welcome to Quantum Physics

Quantum Physics Quantum Field Theory QFT Quantum Mechanics

Quantum Physics, Mass Energy Equivalence, Quantum Mechanics, Quantum Electrodynamics, Quantum Field Theory QFT, Standard Model, Particle Physics, Astrophysics, Dark Matter, General Relativity, PathIntegrals, Symmetry Breaking, Condensed Matter Theory

On the Energy of Moving Bodies in the Presence of Quantum Fields

Unified Synthesis of Mass, Motion and Field Energy

Original Research Paper By Jan Klein

Abstract

1. The Question

In 1905, Einstein showed that the energy of a body at rest in empty space is $E = m c^2$. For a body in motion, the energy becomes $E = \gamma m c^2$, where $\gamma = 1 / \sqrt{1 - v^2/c^2}$.
But no body exists in empty space. Every particle moves through the gravitational field, the electromagnetic field, the Higgs field, the strong nuclear field, and quantum vacuum fluctuations. These fields contain energy. They interact with particles. They contribute to what we measure as mass. Should they not appear in the fundamental energy equation?

2. Original Formula: A First Extension

The simplest way to include a field is to add its contribution directly to the rest energy:
$$
E = \gamma \left( m c^2 + \kappa(x) \, \Phi \right)
$$
Here, $\Phi$ is the field strength at the particle's location, and $\kappa(x)$ is a coupling function that may vary with position. This form preserves the structure of Einstein's equation while adding a single field term.

3. The Complete Formula

A particle is never immersed in just one field. It feels gravity, electromagnetism, the Higgs field, and the strong nuclear field. Each field has its own coupling strength and potential. Therefore, the complete expression must sum over all fields:
$$
E = \gamma \left( m_0 c^2 + \sum_{\text{all fields}} \kappa_i(x) \, \Phi_i(x) \right)
$$
where $\gamma$ is the Lorentz factor, $m_0$ is the intrinsic mass, $\Phi_i(x)$ is the strength of field $i$, and $\kappa_i(x)$ is the coupling function. The original formula is the special case where only one field is considered.
Jan Klein | bix.pages.dev
Read Full Paper Here
On the Energy of Moving Bodies in the Presence of Quantum Fields