A Special Theory of Relativity

Velocity = d/t

An equation’s meaning lies in its derivation. It is established empirical truth that, so far as mathematics is concerned, a result is greater than the sum of its parts. Variables are placeholders for empty operations. You cannot understand a theory without first understanding its constituents. And you wonder if there is supposed to be an overarching theory of everything, if mathematics can map a person like variables map equations, can a person attribute their actions to the integrands of a complex formula? Can we derive pain, summate loss? Light, inertia, motion, gravity, time — what if these things abide by the same laws that break our hearts?

The Lorentz Transformation: λ = 1/√(v²/c²)

You haven’t come to the carnival for the rides. They make you feel a little sick. You came to be with her, to watch the universe spin around you in ecstatic motion. She wanted to ride the Ferris wheel and the carousel and the pendulum pirate ship, but you were content to simply stand in the middle of it all. You are a still point at the heart of an orbit, and together, you watch the world spin around a new force of gravity.

But she wanted to ride the rides. So she pulled you into orbit with her. She sets you in motion, and inertia keeps you moving. You go faster, until the world is a blur of turbo bulbs and tinny foxtrots. You go faster, but go nowhere.

Relativistic mass = m₀ / √(1-v²/c²)

One of the consequences of Einstein’s Special Theory of Relativity is that mass increases with speed. The faster an object moves, the heavier it seems to get. This is not the same as centripetal force, the thing that keeps your head bolted to the wall on spinning carnie rides, your hand cemented with hers. Centripetal force only feels heavy. With Special Relativity, you are heavy. You can’t go fast. You can’t run away.

v = The Speed of Light = 186,000 m/s

Einstein said these increases in mass only become apparent when you’re traveling close to the speed of light. You’re not moving that fast, surely? The photons have traveled millions of miles and millions of years only to be stopped by her presence. The photons hit her hair, her clothes, her blue eyes, and ricochet into the world. Their absence is the shadow filling the space beside her. A shadow you can become, perhaps, in light of a lack of photons. A still thing moving where the speed of light could not go. But you still share some secret sympathies with the light of distant stars. She stopped you, too. She made you look. She made you look at her small smile and her bright eyes, the way the corner of her mouth crinkles when she laughs. You see her, and you suddenly believe that silly old expression that we are all starstuff. Every atom in her body was once part of a star, but unlike the stars, her light doesn’t have to travel so far to make you pause in wonder.

How much faster is light than sound? Fast enough for her to see you, long before she hears your words.

Kinetic Energy = (1/2)mv²

Relativistic mass isn’t felt by you. It’s only apparent to an external observer. It’s apparent to her, in a reference frame you do not occupy. The faster an object moves the more energy is needed to keep it moving. The closer you are, the harder it is to speak. That’s Newtonian Mechanics for you. Maybe you can’t see this, but she can. From this, she will infer that because mass is a resistance to acceleration, that you are resisting being accelerated, your mass has increased. You fat, dumb, slow thing. Just say it. Say the words.

E-mc² = (1/2)mv², for small v/c

To compensate for the apparent mass increase due to very high speeds, Einstein remembered that the kinetic energy of a body is equal to the increase in its mass as a consequence of its relative motion. But it’s all potential energy for the moment, something bottled up in your chest, like a swallowed scream. You’re rooted to the spot, and you can’t say it. Perhaps relative motion is an imagined thing, too. You’re running away. You’re not moving at all. And she looks at you like she wishes you would make up your mind.

E=E₀ – mc²

You can see that relativistic energy consists of two parts. The first part is kinetic and depends on speed. The second part is due to the mass increase and does not depend on speed. The energy is present: potential energy diffusing between you, between the stillness and the motion. What happens if you say the words? The potential will become kinetic. Mass will turn to energy. Kaboom.

E = mc²

Mass and energy are really the same thing, at the end of the day. We are bodies in perpetual motion, potential diffusing into kinetic. Moving fast, and yet going nowhere. Frozen in relative time. Stuck with words left unsaid and voyaging the space of ages between two passing seconds.

And when she says no, she binds eternity in a moment.

You never knew forever could happen so quickly.