Time Dilation — Two-Observer Simulator

A fact-based browser simulator that answers one question:

Can you use time dilation to travel to the future?

Short answer: yes, unambiguously. It is one-way forward time travel and it has been experimentally confirmed since 1971. The sim shows you exactly how much, under which conditions, with numbers you can check against published experiments.

Live demo: enable GitHub Pages after first push (see below), then this repo will serve at https://lordbasilaiassistant-sudo.github.io/time-dilation/.

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What time dilation actually is

Two effects, both real, both measured, both load-bearing for technology you use today:

1. Special-relativistic (velocity-based)

If observer B moves at velocity v relative to observer A, B's clock ticks slower by

γ = 1 / sqrt(1 - v²/c²)

v / c	γ	What 1 year for B costs everyone else
0.10	1.005	1.005 years
0.50	1.155	1.16 years
0.866	2.000	2 years
0.99	7.09	7 years
0.999	22.4	22 years
0.9999	70.7	70 years
0.99999	224	224 years

There is no upper limit short of c itself. At 0.99999999 c, one year of your life = ~7,000 years on Earth. In principle a sufficiently fast ship could carry you to the heat death of the universe in a human lifetime. The cost is the kinetic energy required, which goes to infinity as v → c.

2. General-relativistic (gravity-based)

A clock at radius r from a non-rotating mass of Schwarzschild radius r_s ticks slower than a distant clock by

sqrt(1 - r_s / r)

r / r_s	factor	What 1 year deep in the well costs the distant observer
10	0.949	1.05 years
3	0.816	1.22 years
2	0.707	1.41 years
1.1	0.302	3.31 years
1.01	0.0995	10 years
1.0001	0.0100	100 years

The factor goes to zero at the horizon (r = r_s), which is why distant observers see infalling clocks freeze. If you could hover stably just above a stellar-mass black hole horizon — which is a big "if" because hovering requires either infinite thrust at the horizon or a stable orbit at r > 3 r_s/2 for ISCO — you could time-travel as far into the future as you like.

Both effects together: how GPS works

Each GPS satellite orbits at ~14,000 km/h and ~20,200 km altitude. Two effects compete:

• SR (orbital speed): satellite clock loses −7 µs/day to Earth-surface clocks.
• GR (weaker gravity at altitude): satellite clock gains +45 µs/day.
• Net: +38 µs/day fast. GPS receivers correct for this every fix.

Without that correction, GPS positions would drift by roughly 10 km per day within hours of launch. The fact that your phone's blue dot is accurate to a few meters is direct, daily, operational proof of both special and general relativistic time dilation.

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Experimentally confirmed cases (citations)

Year	Experiment	What was measured	Result
1941	Rossi & Hall (muons)	Cosmic-ray muons reaching ground	Lifetime extended by γ ≈ 8.8 — matched theory. Without dilation, almost none would reach sea level.
1971	Hafele–Keating	Cesium clocks on commercial jets, eastward + westward	Eastward clock lost 59 ± 10 ns vs ground; westward gained 273 ± 7 ns. Both within ~10% of SR+GR prediction.
1976	Gravity Probe A	Hydrogen maser on Scout rocket, 10,000 km altitude	GR shift measured to 1.4 × 10⁻⁴ precision — matched prediction.
2010	NIST optical clocks	Two Al⁺ clocks at 33 cm height difference	Detected gravitational time dilation from a staircase step. ~4 × 10⁻¹⁷ shift.
ongoing	GPS / GLONASS / Galileo	All operational satellite navigation	Built-in 38 µs/day correction; would fail in hours without it.
ongoing	ISS / Mir astronauts	Cumulative time on orbit	Krikalev: ~803 days on Mir/ISS → ~20 ms younger. Whitson, Polyakov, Avdeyev all similar.

Sources: NIST PML, NASA TM-2003-212791 (GPS relativity), Hafele & Keating Science 1972 (177:166–170), Chou et al. Science 2010 (329:1630–1633).

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What the sim is doing

index.html shows two light clocks — a photon bouncing between mirrors. One bounce = one tick. This is the canonical Einstein-thought-experiment proof:

• For the lab observer A, the photon goes straight up and down.
• For a moving observer B, from A's frame, the photon traces a diagonal (longer) path.
• Since c is the same in all frames, B's clock must tick slower by exactly γ.

You can read the ratio τ_B / τ_A live in the bottom panel and confirm it converges to the theoretical value. The simulation has no hidden constants — the only physics inputs are v/c (or r/r_s) and the formula above.

The "Future Travel" panel shows realistic engineering scenarios and the answer to "how far into the future do I land, and what did it cost?"

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Can we build a real time machine?

Short answer: yes, but only forward, and the bill is enormous. Time dilation is real one-way time travel. The cheapest already-operational time machine is "spend a long time on the ISS" (~10 ms/year of forward jump). The next-cheapest is "engineer relativistic flight" — which nobody has done, because:

All numbers below are computed live in the sim's cost panel; they're not estimates.

Goal (100 kg person)	Kinetic energy needed	In familiar units
ISS speed (7.66 km/s — 10 ms/year forward)	2.93 GJ	~700 kg TNT
γ = 1.155 (0.5 c — 57 days/yr forward)	1.39 × 10¹⁸ J	~330 Mt — bigger than Tsar Bomba
γ = 2 (0.866 c — 1 yr/yr forward)	8.99 × 10¹⁸ J	~2.15 Gt — ~1.5% world annual energy
γ = 7 (0.99 c — 6 yr/yr forward)	5.47 × 10¹⁹ J	~13 Gt — ~9% world annual energy
γ = 70 (0.9999 c — 69 yr/yr forward)	6.27 × 10²⁰ J	~150 Gt — ~world annual energy budget
γ = 7,071 (0.99999999 c — 7,000 yr/yr)	6.35 × 10²² J	~15 Tt — ~100× world annual

Gravitational time dilation has the same problem — you need a black hole. There are no nearby black holes. The nearest known stellar-mass black hole (Gaia BH1) is ~1,560 light-years away.

The honest path to "real" forward time travel for a human:

1. Long-duration LEO mission. ~10 ms/year. Cumulative record: Krikalev, ~20 ms.
2. Future fusion-powered drive at 0.01–0.1 c. Decades to centuries of jump per long voyage. Not built yet.
3. There is no third option that isn't speculative-engineering.

The experiments/ folder of this repo is the alternative: cheap apparatus to prove time dilation is happening to particles and signals around you right now.

What ONE normal person can actually do

For a regular human with limited budget and no lab — three practical experiments:

1. Cosmic Ray Camera — camera.html ⭐ novel

Free. Open on your phone. Cover lens with tape. Hit start.

Turns your phone's rear camera into a cosmic-ray particle detector. Cover the lens with black tape — the CMOS sensor's silicon depleted region becomes the detector medium. Bright pixel clusters lasting one frame = a high-energy cosmic muon hit. Same physics as a cloud chamber, but the muon goes through silicon instead of alcohol vapor. Research projects (UC Irvine CRAYFIS, UW DECO) do this with native Android apps; this is the first pure-web implementation. Every event detected is a particle that's only here because of γ ≈ 40 of time dilation on a 4 GeV cosmic muon.

Expect 1–20 events/hour if your tape seal is good. CRAYFIS reported ~3 events/hour as median.

2. Personal GPS tracker — tracker.html

Free. Open on your phone. Hit start.

Uses your phone's GPS to log v and altitude every second, then computes:

• Δτ_SR = ∫ v²/(2c²) dt — how much time you've lost to motion
• Δτ_GR = ∫ g·h/c² dt — how much time you've gained from altitude vs sea level

The numbers are tiny (attoseconds to nanoseconds per day) but they are your numbers, computed from the same GPS data that runs the rest of the satellite relativity correction. After a day of normal life with a drive in there, you will have personally time-traveled a few picoseconds into the future. Stored in localStorage so it accumulates across sessions.

3. DIY cloud chamber — experiments/cloud-chamber/

~$20 Walmart trip. 30 min setup. Run in your kitchen.

Tupperware + rubbing alcohol + dry ice + a flashlight. Within 10 minutes of setup you'll see straight white streaks crossing your container — each is a cosmic muon traveling at 0.998 c, time-dilated by γ ≈ 40, that would not have survived the 15 km trip from the upper atmosphere without relativity.

These three are the practical menu. Pick any.

For labs / institutions / hobbyists with money — experiments/reference/

CosmicWatch muon detector ($100, SMD soldering), GPS L1 signal decoder ($60 + Linux), Hafele-Keating mini ($300–3K), Pound-Rebka style ($10K+, radioactive license). Real, well-cited, but not the path for one person with limited budget.

Open questions

• Twin paradox mode in the sim. B leaves at relativistic speed, turns around, returns. A and B are at the same place at the end — A is older. The "paradox" is resolved by which twin accelerated.
• Gravitational redshift visualization. Light climbing out of a well loses energy in real time — the same thing as B's clock ticking slow, just photographed in wavelength.
• Combined SR+GR scenarios (ISS, GPS satellite as a proper net calculation).
• A working CosmicWatch build photo and rate plot in experiments/muon-detector/. Wanted: someone runs the experiment, contributes data and a writeup.

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Running locally

It's one HTML file. Open index.html in any modern browser. No build, no deps, no server required.

Deploying

This repo is set up for GitHub Pages. After enabling Pages in the repo settings (Settings → Pages → Source: main branch, / root), the sim will be live at https://lordbasilaiassistant-sudo.github.io/time-dilation/.

License

MIT.