Special Relativity

Objectives State Einstein’s postulates Recognize the consequences of Einstein’s postulates Calculate the effects of time dilation, length contraction and mass increases Describe the twin paradox Calculate mass-energy equivalence

Einstein’s Postulates The laws of physics are the same in all inertial frames of reference. The speed of light is the same for any uniformly moving observer.

Consequences Each person’s “now” is unique to themselves. “Before” and “after” are relative for distant events. Time is measured to slow down for objects in motion. Objects are measured to contract if they are moving. All massive objects get heavier the faster they travel. Only massless particles (photons) can travel at the speed of light.

Time Dilation Time is relative to the motion of the observer. When a clock moves at a speed it will appear to tick more slowly to a nonmoving observer.

The Twin Paradox If one twin leaves on a space flight his time will run slower than the twin who remains on Earth. When he returns, his twin will be older than he is.

LengthLength Contraction The length of a moving body will appear to contract in the direction of motion to a nonmoving observer.

A FAVORITE PUZZLE We have a 25 m long pole and a 20 m long barn, both as measured at rest relative to the pole and the barn. We will assume the back wall of the barn is very very strong. If the pole is moving towards the barn at 70% of the speed of light, its length will be contracted to about 18 m. Thus it clearly fits in the barn, and we can slam the door shut (and run!). But if we are riding along with the pole, its length is not contracted and is 25 m long. But the barn is contracted and is now about 14 m long. Clearly the pole does not fit in the barn. Does the pole fit into the barn or not?

Mass Increase The mass of a moving object increases with speed.

Mass-Energy Equivalence

Interesting Facts about Special Relativity Because of the speed that it reached on its journey to the moon, the Apollo 11 rocket was about 254 millionths of an inch shorter in flight than when it was standing on the launch pad. Someone orbiting the Earth on the space station for a year would age a full hundredth of a second less than the people on Earth.

Interesting Facts about Interstellar Travel A ton of antimatter could send a ship to the stars but scientists can only make it an atom at a time. Right now antimatter costs in the region of a trillion dollars an ounce. The Saturn 5 rocket that put men on the moon could have sent an Apollo craft to the stars. The one-way trip would have taken at least 50,000 years.