A.5.2 Special relativity part 2 and 3xt

four things that are no longer universal truths under special relativity

time, length, distance, simultaneity

things that are universal truths in special relativity

speed of light

space time interval

the distance in space-time that is the same in all reference frames, it is invariant

what does it mean that spacetime interval is an invariant quality

quantity that is the same in all reference frames

space-time graphs

ct versus distance,

distance to distance, the gradient = velocity

steeper gradient slower teh object

world line

on a space-time graph. something occurring representing the position of a body at different times

the steeper the gradient the slower it is moving

at speed of light gradient is 1, can not be lower

positive gradient, moving towards the right

a world line object at rest

it is not getting further away from us, object at rest

worldline for constant velocity

q is an object at a constant velocity, shallower gradient not possible, faster than the speed of light

different y and x-axis for different frames of reference

we have to tilt the y and x-axis so that the gradient is the new speed of light

how to proof that you can not go faster than the speed of light from the space-time diagram

the gradient is steeper from moving from planet A to B, so taking the line parallel towards the axes to CT to find the time to travel from A to B proves that the time for B is less than A. This prove s it is wrong since you are traveling from A to B not B to A

simultaneity

events that are simultaneous in one frame of reference are not simultaneous in another

how to read space time graph

to find the time of the event, line drawn parallel to x until it meets ct and ct’. same for both observers

to find the position measured in S, taking a parallel line to ct-axis until it meets x axis.

to find the position of S’, take the parallel line of ct’ down to x axis

how do magnetic and electromagnetic forces expereinced chnage with reference frames

form an outside reference plane a charged particle moving next to for example a current-carrying wire, experiences a magnetic field, however, forthe particle it doenst know its moving thsu not creating the magnetic force and experiences electrostatic force

how can we synchronize two clocks

by starting them at the same time and then moving apart or synchronize all of the clocks at a master clock and then slowly move every other clock into place on the spacetime lattice.