Simulations

Instructions
A simulation will only respond to keyboard control when it is "in focus". If not you can click on the simulation area once to bring it to focus.

Simultaneity

Event blue and event red happen at the same time relative to the black spaceship. From the green spaceship's perspective, however, event blue happens before event red. Events that are considered "simultaneous" to one observer are not simultaneous from another reference frame. Note that length contraction is not taken into account in this simulation.

Time Dilation

The spaceships use photons bouncing up and down to measure time. Since the photon must travel at the speed of light, the faster the ship moves, the longer it takes for the photon to reach the other side of the ship (because it has to travel a zig-zag path), leading to the slowing down of time (time dilation).

The ship at the bottom tries to have its clock ticks at the same rate as the ship at rest to avoid time dilation. However, in doing so its photon has to travel faster than the ripples which spread at the speed of light, violating relativity.

Ladder and Garage Paradox

You have a ladder twice as long as the garage, how can you fit it inside the garage? How about move it at relativistic speed, then by length contraction it will get shorter and fit (at least momentarily) inside the garage!

What happens if you think from the moving ladder's point of view? In the ladder's reference frame, it is the garage that is moving, causing the garage to get even shorter, so the ladder would definitely not fit.So who is right?

You can find out by switching between two points of views in the simulation below by pressing "v". The short answer is that both views are correct, the garage will see the ladder fits (as long as it is moving sufficiently fast), but the ladder will see itself never once trapped inside the garage. It can be traced back to the fact that "inside" is itself a relative concept, dependent on the concept of simultaneity. For the ladder to be "inside", there must be a period during which both doors are SIMULTANEOUSLY closed, but two observers could disagree on the order in which events happen. To the garage, the left door closes before the right door opens, therefore trapping the ladder. To the ladder the order is reversed, the right door opens before the left door closes so it is never "inside" the garage.

In the simulation, if you see (time left door closed)<(time right door opened), then the ladder is momentarily trapped. This is satisfied from the garage's point of view at high velocity, but is never satisfied in the ladder's point of view. The times are measured by three clocks on each object in the front, center and back. In the object's rest frame, all three clocks are synchronized, but from another reference frame, the clocks are out of sync. This is why the two objects could disagree on which door opens/closes first.