Relativity II The Relativity Postulate: The laws of physics are the same for all observers in all inertial reference frames. No one frame is preferred over any other.

Relativity II The Speed of Light Postulate: The speed of light in a vacuum has the same value ‘c’ in all directions and in all inertial reference frames.

Relativity II Simultaneity  If two observers are in relative motion they will not, in general, agree to whether two events are simultaneous. If one observer finds them to be simultaneous, the other will generally not.  Simultaneity is not an absolute concept, but rather a relative one, depending on the motion of the observer.

The rocket is moving at (5/8)c. Relativity II - Simultaneity

Relativity II Time The time interval between two events depends on how far apart they occur in both space AND time; that is, their spatial and temporal separation are entangled.

Relativity II - Time If observer is moving with the train… Train Example… D D

Relativity II - Time Train Example… Remember, the only thing truly the same for all observers is the speed of light, c. c = distancetime = 2 D Δt o Δt o Δto =Δto =Δto =Δto = 2 D c Where, Δt o is called the proper time – that is the time measured by someone in the reference frame of the event.

Relativity II - Time If observer is on the ground (or in a tree)… Train Example… L L

Relativity II - Time Train Example… Remember, the only thing truly the same for all observers is the speed of light, c. c = distancetime = 2 L Δt L = c Δt 12 And, if the train is moving at a speed v… L = ( v Δt ) 2 + D 2 12 L L x = v ( Δt ) D D 12

Relativity II - Time Train Example… Set the two equations equal… And remembering from the first case that c Δt = ( v Δt ) 2 + D Δto =Δto =Δto =Δto = 2 D c D = c Δt o 12 c Δt = ( v Δt ) 2 + ( c Δt o )

Relativity II - Time Train Example… ( c Δt ) 2 = ( v Δt ) 2 + ( c Δt o ) c 2 Δt 2 = v 2 Δt 2 + c 2 Δt o 2 c 2 Δt 2 - v 2 Δt 2 = c 2 Δt o 2 (c 2 - v 2 ) Δt 2 = c 2 Δt o 2 c 2 Δt o 2 (c 2 - v 2 ) Δt 2 =

Relativity II - Time c 2 Δt o 2 / c 2 (c 2 - v 2 ) / c 2 Δt 2 = Δt o 2 v 2 v 2 c 2 c 2 Δt 2 = 1 - ΔtoΔtoΔtoΔto Δt = vcvc Once again, the observer in the reference frame of the event is said to measure the proper time ( Δt o ). Train Example…

Relativity II - Time Example problem… You get into a spaceship and travel at 0.9c for 10 years. This gets you to the best restaurant in the entire universe. You have dinner and then get back in you ship for the return trip. You travel at 0.9c for the return trip and it takes another 10 years. How long does the round trip take according to measurements taken on earth?

Relativity II - Length L = L o vcvc L o. Where, L o is the length of an object as measured by someone in the reference frame that is moving with the object. The length of an object in the direction of motion changes as well…

Relativity II - Length Example problem… How long is a meter stick in our classroom as measured by an observer flying by at 1/2 the speed of light?