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The Theory Lab
Set the numbers for a warp drive, a wormhole or a starship, and see which laws of physics allow it and which rule it out.
Science fiction depends on a few big ideas: faster-than-light travel, shortcuts through space, and time travel. Some of them are forbidden by physics. Others are allowed in principle but need things nobody has found. The Theory Lab lets you set the numbers yourself and see exactly where an idea runs into trouble. Each page shows your inputs, the results, the mathematics behind them, and a list of checks against what we know.
How ideas are judged
Every check gets one of four verdicts:
| Verdict | Meaning |
|---|---|
| Works with known physics | Possible with physics that has been tested, and in some cases with technology we already have. |
| Allowed, but far beyond our technology | No law forbids it, but the engineering, energy or materials are far out of reach. |
| Needs physics we haven't found | Only works if something exotic exists, such as matter with negative energy. |
| Breaks an established law | It contradicts something tested many times, such as conservation of energy or the speed of light. |
The topics
Warp drive: the Alcubierre metric (1994)
In 1994 the physicist Miguel Alcubierre found a solution to Einstein's equations in which a region of space contracts in front of a ship and expands behind it. The ship sits still inside a "bubble" while the bubble itself moves, and the bubble can in principle move faster than light. The catch is that the bubble wall needs negative energy density, a kind of exotic matter that has never been found in the required form or amount. Early estimates needed more energy than exists in the observable universe. Later refinements reduced that enormously, but none removed the need for negative energy. Change the bubble's speed and size to see how the requirements grow.
Wormhole: Morris–Thorne traversable wormholes (1988)
A wormhole is a tunnel connecting two distant places. In 1988 Michael Morris and Kip Thorne worked out what a wormhole would need for a person to travel through it and survive. The throat has to be held open, again by exotic negative energy. Choose the size of the throat to see the tidal forces on a traveller and the amount of exotic matter needed.
Wormhole time machine: Morris, Thorne & Yurtsever (1988)
Move one mouth of a wormhole at high speed and back, and the two mouths end up at different times. Stepping through would then take you into the past. Stephen Hawking proposed in 1992 that nature prevents this, an idea he called the chronology protection conjecture. The lab shows how such a time machine would be set up and why physicists suspect it destroys itself.
The twin paradox: special relativity
One twin travels to a star at close to the speed of light and comes back; the other stays home. The traveller returns younger. This isn't a paradox at all. It's measured routinely, with atomic clocks flown on aircraft and with fast-moving particles. It's real travel into the future. Choose a destination and speed to see how much younger the traveller would be.
Time near a black hole: the Kerr metric
Gravity slows time as well. GPS satellites have to correct for it: their clocks run about 38 microseconds a day fast compared with clocks on the ground, from the combined effect of gravity and speed. Near a black hole the effect is extreme. This page uses the exact solution for a spinning black hole (Roy Kerr, 1963) to show how much slower time passes as you orbit closer.
Design a starship: the relativistic rocket equation
How much fuel does it take to reach another star? Choose the engine's exhaust speed, the acceleration and the distance, and the relativistic rocket equation gives the trip time on Earth and on board, the fuel needed and the energy involved. The checks then show what that means in practice: antimatter fuel, crushing accelerations, or a generation ship whose crew's descendants arrive.
Power a civilisation: E = mc², the Kardashev scale and waste heat
From today's world energy use up to harnessing a whole star or galaxy: how much mass you'd convert, how efficient each source can be (feeding a spinning black hole can release up to 42% of matter's mass-energy), and how much radiator area you'd need to get rid of the waste heat.
Beat the light barrier
Choose where you want to go and how fast, and the lab compares the options: a relativistic rocket, a warp bubble or a wormhole, and the price each one carries.
Your own equation
Type in any formula. It's displayed as typeset mathematics and calculated with real units. Physical constants fill themselves in, and every other symbol gets a slider. Then it's judged the same way as everything else. Do the units balance? Does the answer break a known limit, such as the speed of light, absolute zero, 100% efficiency or the Planck scale? Does it pack so much into so small a space that it would collapse into a black hole? Your equations are saved on your own device.
Each link above opens that page of the Theory Lab directly. Your settings are kept in the page address, so you can share a particular design with someone else.