## Relative Clocks

Time runs slower in anything that is moving relative to you.

### animation

Time runs more slowly in anything that is moving relative to you. This effect is called time dilation. The faster the object is moving the slower time will pass in that object relative to your time.

Gravity also affects the flow of time and so we are considering a region of space far from the influence of strong gravity.

The proof for time dilation relies on the velocity of light being a constant. The following are a list of points to be mindful of when studying the animation.

• There are two identical clocks. One stationary relative to you and the other on the spacecraft.
• The two clocks mark off time using photons. Set the spacecraft speed to zero to see that the two clocks mark off time at the same rate.
• Each time a photon hits a mirror an event is created and the respective clock increments one unit of time.
• An event is anything with a precise time and location. Like a photon hitting a mirror.
• The spacecraft velocity has no effect on the photon speed relative to you. The direction of the photon changes, the speed does not.
• The photon, in the spacecraft, has further to travel between mirrors the faster the spacecraft travels.
• The spacecraft clock ticks slower because the photon speed is always c, while the distance travelled by the photon between mirrors increases with spacecraft velocity.

### animation controls

Below the animation are a number of clickable controls. Radio buttons for velocity control, and check boxes for adding useful visual aids.

• photon trail: Each photon leaves a trail. This makes it easy to measure how far the photons have travelled between events.
• velocity vector: Vectors are drawn to illustrate the direction of travel. The photon vector is always c in length, while the spacecraft vector length can be changed.
• length contraction: Length contraction is a relativitistic effect that contracts the length of the spacecraft. This will be dealt with later in the course.
• show events: The events created by the photon reflecting off the mirrors are highlighted. These events must be maintained irrespective of the spacecraft velocity.

### description

Time dilation is the slowing of time in anything that is moving relative to you. In the animation there are two clocks regulated by photons. In each clock when a photon hits a mirror the clock advances one tick. The continual oscillation of the photon marks of regular, uniform intervals of time. The slowing of time is applicable to this inanimate photon clock, and to animate objects as well. A person in the spacecraft would also age more slowly relative to you. Like the events created by the photon reflecting off the mirrors, the aging process is also a sequence of events at a microscopic level. The communication between atoms in an aging person is all achieved through the exchange of photons. Events can be said to be created at the creation of a photon and the absorption of a photon. The process is not unlike the photon clock. The conclusion is if the photon clock slows then the aging process slows.

In a relative universe someone in their spacecraft floating in space will feel stationary and the laws of physics for them should apply to every other spacecraft floating in space. However, there may be a relative velocity between spacecraft and so everyone in their spacecraft will say that every other clock, in every other spacecraft, is running slow. This seems to be a paradox. How can everyone say that every other clock is running slow? The paradox is resolved when the relativistic effects of loss of simultaneity and length contraction are applied.