Place events and explore their causal relationships through light cones—see which events can influence each other
Causality — the principle that cause precedes effect — is fundamental to physics. Special relativity doesn't violate causality; it reveals its geometric structure in spacetime. The speed of light isn't just a speed limit; it's the boundary between cause and effect.
Every event in spacetime has a light cone: the set of all events that can be reached by, or can reach, that event via light signals.
All events that can be causally influenced by the event. If you do something now at this location, only events within your future light cone can be affected. This region expands at the speed of light.
All events that could have causally influenced this event. Anything outside your past light cone could not have affected what's happening here and now. It's causally disconnected from your present.
Events outside both light cones are spacelike separated. They cannot influence each other with any signal traveling at or below c. These events have no definite time ordering — different observers disagree on which happened first.
The spacetime interval s² = (Δct)² - Δx² - Δy² - Δz² determines the causal relationship:
More separation in time than space. A massive particle can travel between these events. One event can cause the other. All observers agree on their time ordering.
Example: You at age 20 and you at age 30. These are the same location (you) at different times. The separation is purely timelike.
Equal separation in time and space. Only light can travel between these events. They lie on each other's light cones. All observers agree they're lightlike.
Example: A star exploding and you seeing the flash. The photons traveled on your past light cone to reach your eyes.
More separation in space than time. No signal at ≤ c can connect these events. They cannot influence each other. Different observers disagree on their time ordering.
Example: Two events happening "now" on opposite sides of the galaxy. In your frame, they're simultaneous. In another frame, one happens before the other.
Suppose you could send a signal faster than light, connecting two spacelike-separated events A and B. In your frame, A happens before B, and you send a message from A to B. Seems harmless.
But there exists another reference frame moving relative to you where B happens before A. In that frame, your signal traveled backward in time! An observer in that frame could send a reply "back" to you, and you'd receive it before you sent the original message.
This creates a closed timelike curve — a loop in time. You could receive a message telling you not to send the original message, creating a paradox. This is why FTL communication violates causality: it allows signaling into your own past.
While simultaneity is relative, causality is absolute. All observers agree on:
You and I might disagree on the coordinates (x,t) of events, but we agree on the spacetime interval s² and thus on causal relationships. The causal structure of spacetime is invariant.
Timelike Events: Create two events with large time separation and small space separation. Their light cones overlap. Try sending a signal at various speeds — even slow signals can connect them. They can be causally related.
Spacelike Events: Create two events with large space separation and small time separation. Their light cones don't overlap. Try sending a signal — unless you set v > c, you can't connect them. They're causally disconnected.
Light Speed Boundary: Place two events exactly on each other's light cone (try the "Lightlike Separation" scenario). A signal at exactly c can connect them. Any slower, and it can't. Light speed is the boundary of causality.
FTL Attempt: Try the "Causality Violation" scenario. Place spacelike-separated events and try to send an FTL signal. The visualization should highlight why this is problematic — different frames disagree on time ordering, allowing messages to your own past.
Multiple Events: Add several events and examine how light cones from different events intersect. Events within overlapping future and past light cones can potentially be causally related through a chain of signals.
Newton's gravity acted instantaneously — the Sun pulling on Earth across 150 million km with no delay. This violates causality. Einstein's general relativity fixes this: gravitational effects propagate at c. If the Sun vanished, Earth would orbit normally for 8 minutes until the "gravity signal" arrived.
Entangled particles seem to affect each other instantly, even across vast distances. But you cannot use entanglement to send information FTL. The correlations only appear when you compare measurements classically (at ≤ c). Causality is preserved.
A black hole's event horizon is a light cone boundary in curved spacetime. Events inside the horizon are in the future light cone of everything falling in, but in the past light cone of nothing outside. Information cannot escape because no signal at ≤ c can travel outward. This is a causal structure fact, not just a "strong gravity" fact.
Before relativity, physicists assumed absolute simultaneity. Events either happened before, after, or simultaneously — period. There was no concept of "spacelike separated." Every pair of events had a definite time ordering.
Einstein's 1905 paper shattered this. He showed that simultaneity depends on reference frame, but causality doesn't. The causal structure of spacetime is more fundamental than any notion of absolute time. This was philosophically revolutionary.
Modern physics goes further: in quantum field theory, particles are excitations of fields that respect causal structure. The commutator of field operators vanishes for spacelike separations, ensuring no FTL influence. In quantum gravity theories, spacetime itself might emerge from more fundamental structures, but causal structure remains primary.
Without causality, physics doesn't work. If effects could precede causes, or if we could send messages to our own past, the universe would be paradoxical. Time travel stories explore these paradoxes for entertainment, but nature forbids them.
The speed limit c isn't arbitrary — it's the speed of causality itself. It's built into the fabric of spacetime. Light just happens to travel at this speed because photons are massless. But even if photons didn't exist, c would still be the maximum speed for information, energy, and causal influence.
Every experiment ever done has confirmed this causal structure. We've never observed a violation. Special relativity isn't just a theory about fast-moving objects; it's a theory about the geometry of cause and effect.