Faster-Than-Light Shadow Simulator
Free faster-than-light shadow simulator: swing a torch beam or move a finger in front of a lamp and watch the spot or shadow on the Moon or a far screen move faster than the speed of light, with the real light-travel delay, and see why no message can ride on it.
Aim a torch at a far-away screen and swing it. Every bit of light moves at exactly the speed of light, but the spot where the beam lands can move faster, because it is not a thing: it is a different set of photons at every moment. Pick how far away the screen is and how fast you swing.
Move the pointer (or your finger) over the picture and the torch follows it. Flick it quickly and watch the spot.
Hold a finger in front of a lamp and its shadow lands on a distant wall, magnified. Move the finger a little and the shadow moves a lot: by the ratio of the two distances. Put the wall far enough away and a gentle wave of the hand sweeps the shadow past the speed of light.
If the spot can outrun light, could you use it to send a message faster than light? No, and the picture below shows why. Drag the slider to change how fast the spot moves between A and B.
Why nothing is sent
- Nothing travels along the spot. The photon that lights B was sent from the torch at its own moment; the photon at A is a different one. No photon, and no energy, goes from A to B.
- A cannot influence B. Blocking the spot at A (a card on the screen) changes nothing at B: B's light is already on its way from the torch, and the card cannot reach it. Only something done at the torch changes what lands at B, and that effect travels at c.
- The spot's own “start” is not the cause of its “arrival”. Both are effects of the same earlier act at the torch. To two observers a long way apart, the order of A and B can even differ; that is fine, because neither causes the other.
- The message still travels at c. If you swing the torch in a pattern (a signal) the receiver sees it only when the light from the torch reaches them.
Work out the sweep rate, finger speed or shadow speed for your own numbers. Type with units: 384,400 km, 1 AU, 2.5 million ly, 90 deg/s, 2 rpm, 0.78 m/s.
How fast must you swing to beat light?
“Sweep rate” is the angular speed at which the spot, straight ahead, moves at exactly c: ω = c / distance. “Finger speed” is for a finger held 1 metre from the lamp: v = c × (1 m) / distance.
A shadow can move faster than light
Nothing that carries energy, matter or information can travel through space faster than light. But some things that are not objects can have any speed at all. The classic example is the spot of a torch beam on a far screen: swing the torch and the spot is a fresh set of photons at every instant. Light from the torch reaches the screen at c, always. Where it lands is a matter of geometry, and geometry is not limited. The same goes for the shadow of a finger on a wall, the point where scissor blades cross, or a wave of lights switched on one after another.
The arithmetic
Swing a torch through an angle at ω radians per second towards a screen at distance D. Straight ahead the spot moves at v = ωD, and it passes the speed of light when ω = c / D. For the Moon (384,400 km) that is 0.78 radians per second, about 45 degrees per second: a flick of the wrist. For the Sun it is 0.115 degrees per second. For the Andromeda galaxy it is about one turn in 15 million years; for a sweeping laser pointer, a lazy wave is plenty. For a shadow, similar triangles give vshadow = vfinger × D / d (d is the finger's distance from the lamp), so a finger 1 metre from the lamp needs to move at only 0.78 m/s for its shadow to cross the Moon at the speed of light.
Light takes time, and the simulation shows it
The picture is not a cartoon of a straight beam: every ray is drawn where it really is, by tracking when it left the torch. A swung beam therefore curves like a garden-hose jet, and the spot on the screen shows the true arrival times. When the sweep reverses, the spot appears or vanishes in pairs, which is another sign it is not a single object. The speed shown uses the exact formula, v = sec²φ · φ′ / (1 + D φ′ sec φ tan φ), which includes the extra time later rays need to travel (the plain “ωD” rule is its on-axis, small-angle form). The animation is slowed down so the light takes a few seconds to cross the gap; the numbers are for the real distance you choose.
Does this break relativity?
No. Special relativity forbids signals and causal influences from outrunning light. A moving spot or shadow carries neither: the spot at B is not produced by the spot at A, but by an earlier act at the torch. You can see this on the “Can it carry a message?” tab: no light-speed (or slower) path joins A and B, so nobody at A can use the spot to tell anyone at B anything. What you can send is a pattern by swinging the torch, and that arrives at the screen at c.
What the page simulates, and what it does not
The screen is a flat wall straight across from the lamp, the beam is a thin ray fan with a small width, and light travels in a straight line in empty space. Not modelled: the Moon's curved surface (it changes the numbers a little but not the idea), the atmosphere, the beam spreading with distance (a real beam is far wider than a spot by the time it reaches the Moon, so a real torch spot there is faint), and the finite size of the lamp. The finger's shadow edge is treated as sharp. It is a teaching model.
Things people ask
- Has anyone done it? Yes, in effect: lighthouse and pulsar beams sweep across distant clouds of gas faster than light, and the “light echoes” seen around supernovae can appear to move superluminally. None of it carries a signal along the pattern.
- Could I really do it with a laser pointer and the Moon? Pointing is easy; the spot is the problem. A laser's beam is hundreds of kilometres wide by the time it reaches the Moon and the spot is very faint, so you would need a big telescope to see it, but its position would still move at ωD.
- Is a shadow made of anything? It is the absence of light in a region. A moving shadow is simply different regions going dark at different moments.
- Why does the speed go up toward the edge of the screen? The beam meets the screen at a steeper slant, so a small turn of the torch slides the spot farther. That is the sec²φ in the formula.
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