Overview

SPACE, TIME, A LITTLE SALT
AND THE AUDACITY
OF ALBERT EINSTEIN

The Theory of Relativity is one of the most important ideas in modern physics, developed by Albert Einstein in the early 20th century. It explains how space, time, and gravity work — especially when objects move very fast or when gravity is extremely strong.

Einstein's theory explains that space and time are connected through spacetime, that time is relative depending on motion and gravity, and that mass and energy are related. Both special and general relativity have been tested many times. Relativity is not theoretical.

Disclaimer: All of this is simplified for easier reading and understanding, and is as accurate as possible in this form. — The Author

The First Postulate Inertial Frames

YOU'RE ALREADY
MOVING —
YOU JUST DON'T
KNOW IT

Special relativity (1905) describes how space and time work for objects moving at constant speeds — no gravity involved. It rests on two postulates:

• The laws of physics are the same for all inertial frames (non-accelerating).
• The speed of light in a vacuum is always $c \approx 3.0 \times 10^8$ m/s — no matter how fast the observer is moving.

Thought Experiment

THE SEALED TRAIN

Imagine you are on a sealed train — no windows, no gaps — travelling at a constant speed. You do not know you are moving. You roll a ball on the floor. It drops to the ground and rolls exactly as it would on solid ground.

From inside, you have no way of knowing how fast the train is moving. Physics behaves identically at any constant speed. The laws of physics are the same in all inertial frames.

This means two observers moving at different constant speeds will each measure the same speed of light — not different values, as classical physics would predict. Einstein's insight was that this forces space and time to be flexible instead.

THE BALL EXPERIMENT

Imagine a ruler and two observers: one standing still, the other moving to the right. A football is thrown to the left. Both measure its speed using their own ruler and clock. The stationary observer measures 50 m/s; the moving observer measures 150 m/s. In classical (Newtonian) physics, both are valid — motion is always relative, and each observer considers themselves "at rest."

Logically then, a stationary observer should measure light at $c$, and a moving observer at $c + 50$ m/s. But Einstein said this is wrong. The speed of light in a vacuum is always the same, regardless of the observer's motion.

THE LIGHT CLOCK

To explore the consequences, imagine a light clock — a beam of light bouncing between two mirrors. Seen from inside a moving train and from a stationary observer on the ground, the same clock behaves differently.

For the rider, the photon travels straight up and down. For the ground observer, because the clock moves sideways, the photon follows a longer diagonal path — while still moving at exactly the speed of light.

As a result, the ground observer concludes that less time has passed on the moving clock. A moving clock runs more slowly. This is time dilation.

Example 01

THE IMMORTAL MUON

Muons are created when cosmic rays — high-energy particles from space — strike nuclei in the upper atmosphere. At rest, a muon's average lifetime is about 2.2 microseconds; far too short to travel the ~18 km to sea level before decaying.

Logically, muons should never reach the ground. Yet many are observed at sea level, confirmed by experiments on Mount Washington. Using the time dilation formula, their lifetime as seen from Earth can be about ten times longer than their proper lifetime — enough to travel several kilometres and reach the sensors.

Example 02

THE VERY YOUNG SIBLING

The twin paradox: one twin stays on Earth while the other travels at high speed to a distant star and returns. From Earth's frame, the traveling twin's clock runs slow — the traveler returns younger.

From the traveler's view, Earth seems to move, so Earth's clocks appear slow too. Paradox?

The resolution: the traveling twin changes inertial frames at the turnaround — they experience acceleration. The Earth-bound twin does not. When the traveler switches frames, Earth's time coordinate "jumps" forward in the new frame. Over the whole journey, this frame-switching creates a larger total elapsed time for Earth. When they reunite, the traveling twin is much younger.

The Core Idea

GRAVITY ISN'T
A FORCE,
IT'S A VIBE

Imagine a single spherically symmetrical object — non-rotating and electrically neutral — alone in an empty universe. Release a ring of stationary particles around it (far away). The particles gradually speed up towards the object until they reach it.

Release more and more streams until you have a uniform flow all accelerating toward the object. Now, instead of particles, think of it as spacetime itself flowing like a river into the object, carrying anything in its path. That is how gravity actually works.

Free Fall & Geodesics

THE STRAIGHTEST POSSIBLE
CROOKED PATH

Free fall — like an orbiting planet or a dropped object — is actually the object moving along the "straightest possible path" (a geodesic) in curved spacetime. There is no force pulling it. The path itself is curved by nearby mass.

Every object is already moving through time. Spacetime warping converts that temporal motion into spatial motion — pulling things toward massive objects.

We cannot create a perfectly correct visual for general relativity for one key reason: it includes a fourth dimension. Instead of a spatial dimension, Einstein's theory includes time as the fourth dimension. We can make useful 3D approximations — but they are always approximations.

To look at gravitational time dilation, we look at the Schwarzschild Solution — the spacetime geometry around a single, spherical, non-rotating, uncharged mass. We do not need a big new equation; the time dilation factor is already inside it.

$$ds^2 = -\!\left(1 - \frac{2GM}{c^2 r}\right)c^2\,dt^2 + \left(1 - \frac{2GM}{c^2 r}\right)^{-1}dr^2 + r^2\,d\Omega^2$$ $$r_s = \frac{2GM}{c^2}$$

The highlighted term $\left(1 - \frac{2GM}{c^2 r}\right)$ appears in the metric's time component. Take its square root to get the gravitational time dilation factor:

$$\text{Grav. TD Factor} = \sqrt{1 - \frac{2GM}{c^2 r}}$$

1905 Special Relativity

EINSTEIN BEGINS
THE JOURNEY

In 1905, Einstein published the special theory of relativity, a theory that would change the world. At the time, it was highly controversial because it contradicted Newtonian laws, and many people thought that was impossible. People were right; almost no one would use this theory at the time. But Einstein, knowing that his theory was correct, realised that Newtonian gravity couldn't be true because it would violate special relativity, so it had to be revised. He concluded that instead of acting immediately, gravitational waves must propagate through space at the speed of light. Einstein used Maxwell's equations of electromagnetism together with mechanics to ensure that Newtonian gravity obeyed the same principle. Einstein performed thought experiments to figure out how gravity actually works. He noticed that he could not derive the solution from his current theory. So he had to work on a completely new theory, one that is more refined and in-depth than the current theory.

Fig. H1 — Einstein's 1905 annus mirabilis papers.

1908–1912 Geometry of Gravity

MASS CURVES
SPACETIME

Soon after Einstein realised this, Hermann Minkowski coincidentally developed a four-dimensional formulation of special relativity in which space and time were intertwined. Einstein used this spacetime to develop his theory. Einstein had realised the possibility that a mass would curve the spacetime around it, causing objects to follow a 'straight' path in that curved geometry, causing it to move towards the mass. So, Einstein started doing thought experiments in outer space. He imagined a photon travelling in a stationary rocket from one end to the other, and it travelled straight. Then he applied a constant acceleration of 9.8 m/s² and then shot the photon. Einstein realised that the photon would move very slightly downwards from the perspective of someone inside the ship. Then, using the equivalence principle, he concluded that the photon would move the same distance on Earth as well. He concluded that this happened due to the light travelling in a 'straight' path along a curved spacetime. This led him to conclude that masses pull on spacetime, which causes objects travelling through the spacetime to curve towards the masses.

Fig. H3 — Minkowski diagram.

1916 World War I

A LETTER FROM
THE TRENCHES

Even though Einstein had the formulas derived and his theory done, he still couldn't find an exact solution to his equations. But the papers Einstein wrote managed to travel to the war zone during World War I, where they reached Karl Schwarzschild. Schwarzschild was delighted to take a break from the war, and he said, in his note to Einstein, "The war treated me kind enough, despite the heavy gunfire, to allow me to get away from it all and take this walk in the land of your ideas." He worked on Einstein's equations by hyper-simplifying the universe to where there is only one mass in the universe, one that is electrically neutral and spherically symmetric. In a matter of weeks, he developed the formula to solve for any curve in spacetime, given that you know the mass and distance to the object; this was the Schwarzschild solution. This solution consequently created the Schwarzschild radius, or the radius an object must be compressed to for it to become a black hole.

"The war treated me kind enough, despite the heavy gunfire, to allow me to get away from it all and take this walk in the land of your ideas." — Karl Schwarzschild, letter to Einstein, 1916

Fig. H5 — Karl Schwarzschild, who solved Einstein's equations from the front.

1925–1930 Quantum Mechanics

THE WHITE DWARF
BARRIER

Now Pauli's exclusion principle states that no two fermions, such as electrons, can occupy the same space. What does this mean? Well, since Heisenberg's Uncertainty Principle states that you cannot know both a particle's momentum and position with absolute certainty, and as each electron gets constrained in space, its uncertainty in momentum would have to increase, therefore causing it to vibrate and wiggle around faster and faster. Because the white dwarf was becoming so condensed, the atoms were vibrating so much that they prevented the star from collapsing any further. This is known as the Chandrasekhar limit, equivalent to about 1.44 solar masses.

Fig. H7 — Electron degeneracy pressure holding up a white dwarf.