modern test 2

speed of light is measured at c

BY EVERY OBSERVER

basis of time dilation

velocity © has to stay constant so time hasw to change

th moving clock runs slow =

an outside stationary observer sees time pass more slowly for a moving object

guy on the train

proper time , views light going up and down

observer on the tracfk views its as a longer path/diagonal

longer time

proper length

observer on the trakcs

guy on the spaceship time is proper

earth has proper time

farther away from earth, clock ticks faster

earth pre deterine time

if photon had clock

no ticks

Since a single clock in Clock A's frame cannot be at both event locations at once,

Clock A's frame must use multiple synchronized clocks spaced apart to measure the start and end of that interval.

proper time

observers own refernece frame

one clock

no spatial dsitnacfe

dialted time

same or other ref frame

multiple clocks

spatial distacne

given 1 time not the other5

time dialtino

alpha and beta are 2 seperate places

proper length

in whoevers ref frame where obj r at test

contracted

observer who sees the onj moving

gamma

It tells you how much two observers will disagree on measurements of time and space based on their relative speed.NOT INVARIANT DEPENDS ON WHOS REFERENCE FRMAE UR USING, aka whos v ur using

twin paradox

start w earth frame, v=x/t

finding rockets time

time/gamma

earth link clock accfording to rocket when it gets to planet P

t = t (our) gamma

x = x (our) gamma

time on earth according to rocket coming back

time slipage plus earth time

privilleged frame

absolute rest

absolt tiem

gedmeotry of

SPACETIME

time and spacfe

MEASURD!!! differnelty, clocks dcont acc change3 the way they tick

so your saying since measuring megth is t4echnically measuring 1 length to another

that one length to another is not the same across all reference frames therefore its length is different dpe4ended on reference fram

divide spacfe by c

distance in seconds

multiplyby c

time units into length

time in earths pov

mulyiply gamma to how much time spent on planet

add outbotnd ( kinematics ) to inbound ( gamma )

same ref frame

divide/multiply gamma

turn arouhd n= change of simutlanelity

xhange in how ur seeing the clocks , earths clock appears to jump

While you are coasting smoothly toward Canopus, the situation remains symmetric: you see Earth's clocks running slower than yours

This is because your two frames disagree on what events occur simultaneously across space.

turn doesnt create agte differnenecfe

it simply aligns your reference frame with Earth's so both of you can stand side-by-side and agree on the final result.

coordinatees, spacfetime invariant

s² = v² - t²

find invariant

pythag