Space Time Show is a set of self-contained physics demos. Some are relativity (clocks in gravity wells, aging twins, light crossing galaxies). Some are classical (a falling clock under Earth, Moon, Mars, Jupiter gravity). Each page is a minimal instrument. Everything runs locally in your browser. No external calls.

The core equations are standard physics. We show special relativity, general relativity, and basic Newtonian motion under constant gravity. We solve and display the clean form. When we fake or ignore something (air drag, tidal forces, fuel, cosmic expansion) we say so on the page.

Special relativity handles motion at high fraction of light speed. General relativity handles clocks in strong gravity. We use whichever dominates the effect we want you to see.

Black background. Cyan text. Soft glow. This keeps visual identity stable across all modules and keeps focus on time readouts. The style also works in dark rooms and OLED screens without frying pupils.

Two clocks run side by side: one on Earth, one on Miller’s Planet near the black hole Gargantua from Interstellar. You watch them advance live. On Miller’s surface, almost no time passes while Earth races ahead.

Deep gravity wells warp spacetime. Clocks closer to a massive object tick slower compared to clocks far away. The math is:

Here G is the gravitational constant, M is the mass of the black hole, r is orbital radius, and c is the speed of light. If r is very close to the event horizon of a supermassive black hole, the factor becomes extreme.

The movie uses a ratio around 61 320 : 1. That implies a stable orbit barely outside a horizon of a black hole with millions to hundreds of millions of solar masses. In practice tidal forces and radiation would likely kill you. The demo isolates the time dilation only. Structural survival, atmosphere, tides, and radiation are ignored.

That is the theatrical release date of Interstellar. We pin Earth time to a real historical timestamp so you can ask: Since that date on Earth, how much subjective time has passed for someone “standing” on Miller’s Planet?

Perspective. In Earth view you see Earth as normal and Miller time crawling. In Miller view you see Miller as normal and Earth racing. Relativity is always comparative.

You launch one photon now. You watch it leave the Solar System, reach nearby stars, reach Andromeda, reach deep structures, and finally the edge of what we can observe. The UI lights up milestones when the photon “arrives.”

We compress reality so that: In normal physics light takes 1 year to go 1 light-year. Here you see that same jump in one literal second. This lets you perceive interstellar and intergalactic distances as timed beats.

The nearest star (Proxima Centauri) is ~4.24 light-years away. The observable edge of the universe is ~46 billion light-years in comoving distance. Ratio is about 10,000,000,000 : 1. A linear bar would either clip or look empty. Log spacing lets local stars and far galaxies live in one frame.

Space itself stretches. While a photon is in flight, the source galaxy keeps receding as the metric expands. So by the time that photon reaches us, the place it left is now tens of billions of light-years away, not ~13.8. This is standard cosmology.

No. For clarity we freeze the background. We pretend Euclidean distance in static space. We do not include:

• metric expansion (accelerating expansion of the universe)
• gravitational bending of photon paths
• horizon limits where recession speed > c

This is intentional. The goal is to make “1 light-year per second” emotionally legible.

No. In vacuum light speed is constant, c. The apparent “slowness” you feel is distance, not reduced speed.

Two twins. One stays on Earth. One flies to a target star at relativistic speed, turns around, and returns. The page shows two live clocks: Earth twin time and traveler time. The gap between them is real physics, not fiction.

Proper time is the time measured by a clock along its path through spacetime. High-speed paths accumulate less proper time between two events than low-speed paths. So the traveler experiences less time, and returns physically younger. This is not “optical illusion.” Their biology actually experienced fewer seconds.

Speed fraction of light: β = v / c
Lorentz factor: Round trip distance (Earth frame): 2D
Earth-frame trip time: Ship-frame trip time (traveler’s aging): Age gap on reunion: This is what the UI displays.

It means three simplifications:

• Fuel: We assume infinite thrust. No mass ratio. No propellant math. The ship just attains the chosen speed.
• Turning physics: We force an instant flip at halfway. Real ships accelerate, decelerate, burn, coast. That acceleration matters, but we collapse it to a zero-duration frame change.
• Cosmic expansion: For distant galaxies, space itself stretches and distant targets recede faster than light in comoving coordinates. We ignore that and pretend flat, static space, so you can “reach” anything.

In other words, we strip engineering and cosmology and show only pure time dilation.

Relativity blocks v ≥ c. At v = c, γ becomes infinite. At v > c, the square root in γ would be of a negative number. That implies imaginary time. Physical clocks do not tick imaginary time. So the UI clamps speed to something like 0.995c but never 1.0c or higher.

The “paradox” is that each twin sees the other as moving. So why doesn’t each claim “you aged less”? The resolution is acceleration. The traveling twin changes inertial frames during turnaround. That frame change breaks symmetry. The stay-at-home twin does not. Result: traveler is younger on reunion.

You pick a height and a gravity field. Then you drop a clock. The page shows four things in real time:

• time since release
• current speed downward
• acceleration from gravity
• remaining height above ground

This is basic Newtonian motion under constant acceleration.

We assume:

• no air
• constant gravity g
• flat, fixed ground

The equations are: Drop ends when y(t) hits zero.

Height presets anchor the numbers to real places a learner has heard of. Gravity presets (Earth, Moon, Mars, Jupiter) show how the same drop plays out in different fields. Low gravity means slow fall and long hang time. High gravity means fast impact.

No. At extreme altitude on Earth, drag and heating dominate. Real objects stop speeding up so fast because air pushes back. The page tells you this in the warning panel. We ignore drag because the goal is to teach clean kinematics first.

No. This one is classical mechanics. Constant downward acceleration, like you learn before relativity. We include it because you should first grasp “a = g makes speed grow every second” before you tackle “time itself runs at different rates.”

Yes. GPS satellites run on relativity. Their onboard atomic clocks tick:

• faster because they sit higher in Earth's gravity well (weaker gravity → faster clock)
• slower because they are moving fast relative to you on the ground

Net offset is tens of microseconds per day. If uncorrected, GPS position drift would blow up to kilometers.

• Proper time: what your wristwatch measures along your path through spacetime. Your aging.
• Coordinate time: a bookkeeping time for some chosen frame, like “Earth stationary frame.”

Relativity says everyone agrees on local physical laws, but not everyone agrees on how much coordinate time passed between events.

Yes. Each page is a single HTML file with inline CSS and JS. You can study it, fork it, or adapt it for teaching. Preserve attribution and the privacy stance.

See the "Further reading" below. Take a look at our Wiki.