4.3 The Locking of Energy

Of all equations in human civilization, none carries more totemic significance than $E=m{c}^2$.

It appears on T-shirts, in comics, and has even become synonymous with genius. Albert Einstein told us that energy ($E$) and mass ($m$) are interchangeable. More chillingly, because the conversion coefficient $c^2$ (the square of the speed of light) is an enormous number ($9\times 10^{16}$), this means that extremely tiny masses contain devastating energy.

But why?

Why would a quiet stone hide fire like the Sun? Why the square of the speed of light? This sounds like mysterious alchemy.

But in our “scattering of time” framework, this equation is no longer mysterious. It is no longer an alchemical formula about “conversion,” but a statement about geometric identity.

Curled Bandwidth

Let us examine one last time that right triangle ruling the universe (Pythagorean theorem): $v_{ext}^2+v_{int}^2=c^2$.

We have already established in Axiom A1 that every entity in the universe is essentially a state vector of constant length $c$ in Hilbert Space. The length of this vector represents the entire “existence budget” the universe grants this entity—that is, its total energy ($E$).

When an object is at rest in space ($v_{ext}=0$), something marvelous happens:

1. External velocity is zero: It is not moving in space.

2. Internal velocity is maximized: According to the Pythagorean theorem, its internal evolution rate $v_{int}$ must be completely equal to the total rate $c$.

We have already defined in section 4.1 that mass ($m$) is this internal evolution rate ($m\propto v_{int}$).

Now, look at this geometric picture:

• Total Energy ($E$) is the total length of that arrow.

• Mass ($m$) is the projection length of this arrow on the “internal time axis.”

• When the object is at rest, this arrow points completely vertically upward (pure internal time direction).

• Therefore, the length of $E$ completely equals the length of $m$.

This is $E=m$.

So where does that famous $c^2$ come from? It is merely a historical artifact of unit conversion. This is like measuring length in “inches” but weight in “ounces,” finally discovering that these two numbers always differ by a fixed ratio. If we use “natural units” like theoretical physicists do (set $c=1$), then $E=m{c}^2$ becomes that extremely concise, extremely naked truth:

$$E=m$$

This reveals the ultimate secret of mass: Mass is not an independent entity; it is locked energy.

More accurately, mass is linear bandwidth curled into a loop.

Imagine a beam of light. It races forward at speed $c$, its energy manifest in its “kinetic energy,” expressed as pure external displacement.

Now, imagine this beam of light encounters some topological obstacle, forced to bite its own tail, beginning to spin in place. It no longer moves forward but becomes a tiny, high-speed rotating light ring.

To external observers, this light “stops.” It no longer has external velocity ($v_{ext}=0$). But its internal rotation speed is still $c$. The energy it originally used to traverse space is now entirely used to maintain this internal dead loop.

This “dead loop” is what we call a particle. This “energy spinning in place” is what we call mass.

Releasing the Devil

Understanding that “mass is curled time flow,” we can understand the principle of nuclear weapons.

Atomic bomb explosions do not “create” energy; they merely untie the knot.

When uranium nuclei split, what actually happens is: part of the evolution vector originally locked in internal dimensions ($v_{int}$) is suddenly freed from confinement. That originally frantically rotating internal velocity is redirected, returning to straight-sprinting external velocity ($v_{ext}$).

This is a geometric re-projection.

Those bandwidths originally spinning wildly in Hilbert Space are suddenly projected into external space, becoming gamma rays and high-speed particles flying at light speed.

Why are nuclear explosions so violent?

Because as we said in Chapter 1, the universe’s total bandwidth $c$ is an enormous value. Inside every tiny proton, a raging torrent running at light speed is imprisoned. When we untie this confinement, even releasing just a small part (the mass defect), the effect is catastrophic.

So, $E=m{c}^2$ actually tells us: Even the tiniest dust is woven from imprisoned light storms.

Conclusion of Part II: From Continuous to Discrete

Thus far, we have completed the reconstruction of macroscopic physics. We used the “Great Trade-off” (Pythagorean theorem) to explain Special Relativity. We see:

• Time is not an absolute river; it is a consumable resource.

• Space is not an empty stage; it is where time goes after exhaustion.

• Mass is not dead stone; it is a violently rotating knot of time.

Einstein’s universe is grand, elegant, and continuous. In this picture, Hilbert Space evolution seems like smooth fluid. We arbitrarily allocate total bandwidth $c$ between $v_{ext}$ and $v_{int}$, as smoothly as pouring water.

But this smoothness is only an illusion.

When we zoom in, and zoom in further, until penetrating deep into those heavy materials, trying to see how that “imprisoned time” actually knots, the smooth geometry shatters.

We discover that the universe is not an infinitely divisible fluid. At extremely small scales (Planck scale), the universe reveals its pixels. That original beam of time-light is not a continuous wave, but countless jumping bits.

Without understanding this discreteness, we cannot understand why time knots, why there are specific particles, why there are quantum mechanics ghosts.

It is time to put down Einstein’s telescope and pick up Bohr’s microscope. Let us enter Part III—The Knot of Time, to explore that real world composed of pixels.

（Next, we will enter Chapter 6 “The Pixels at the Bottom” of Part III “The Knot of Time,” revealing the discrete computational ontology beneath continuous spacetime.）