Special Relativity Space and Time

Spacetime Motion in space is related to motion in time. Special theory of relativity: describes how time is affected by motion in space at constant velocity, and how mass and energy are related. Einstein said that both space and time exist only within the universe. Space and time are two parts of one whole called spacetime. If you stand still, you are only travelling through time If you move a bit, some of your travel is through space and most is through time. If you travel at the speed of light, you travel through space but not through time.

Time dilation: stretching of time that occurs significantly for speeds approaching the speed of light. Motion is relative Necessary to specify the position from which motion is being observed. Read p206 Speed of light is constant: km/s in empty space Light from an approaching source reaches the observer at the same speed as light from a receding source.

The first postulate of special relativity All the laws of nature are the same in all uniformly moving frames of reference. No experiment can be devised to state the state of uniform motion. The second postulate of special relativity The speed of light in empty space will always have the same value regardless of the motion of the source or the motion of the observer. The speed of light unifies space and time.

Time dilation Einstein proposed that time depends on the motion between the observer and the event being observed. Read p211 Read p 214 The Twin Trip Space and time travel Read p220 Atomic_Physics.asf

Time dilation  t=  t 0 /  1- (v 2 /c 2 )  t: time interval between two events, measured by an observer who is in motion with respect to the events  t 0 : is the time interval between two events, as measured by an observer who is at rest with respect to the events v: is the speed of the moving object c: the speed of light

Length contraction When viewed by an outside observer, moving objects appear to contract along the direction of motion. The amount of contraction is related to the amount of time dilation. As relative speed gets closer to the speed of light, the measured lengths of objects contract closer and closer to zero. Space contracts in only one direction, the direction of motion.

L= L o  1-(v 2 /c 2 ) v: speed of the object relative to the observer. c: the speed of light L: length of moving object as measured by the observer. L o : the measured length of the object at rest. If the object moves at c, the object will contract its length to zero.

The increase of mass with speed When an object moves at a very high speed relative to an observer, its mass is measured as greater than the value when it is not moving. Nothing made of matter can be accelerated to the speed of light. Physicist working with high speed subatomic particles (99% the speed of light) find the increase of mass with speed an everyday fact of life.

Mass-energy equivalence Anything that has mass has energy. Anything that has energy has mass E=mc 2 NOVA | Einstein's Big Idea | E = mc2 Explained | PBS The correspondence principle If the equations of special relativity are valid, they must correspond to those of the mechanics of Newton (classical mechanics) when speeds much less than the speed of light are considered

Special Relativity Space and Time