physics 1

invariance of spacetime interval

time cannot be seperated from space

looking between events A and B as recorded by 2 diff observers in relative motion

compare space and time speratoin

interval remains the same

even if diff observerd are measuring diff sinta and times

lorentz geometry - time interval

relfets how obj move close 2 light speed

dist between sparks = 0

both sparks occur at rocket’s tip

rocket speed solo

speed = d/t

disagree on dist and time

agree on spacetime interval between events

proper time

spacetime interval for pair of events, events both happen at ur location

speed of light is constant

allows pacetime intervals to remain invariant and making predictions consistent across all frames

time and space must e treated on equal fotting inr elaitivty

the minus sign makes it difference

space and time dpeend on observer

spacetime is the emphasis. disagree on coordiknates but agree on disrance

no relative accelartion (passenger in a ship)

passenger floats

free float

objects feel the same path thru spacetime therefore float realtive to one another even if earth gravit is acting upon them

einstin theory

gravity disappears in freely falling frame , bc everything accelartes tg

ball thrown across

arc bc floor pushes on you

observing free float

gravity disappears, moving in a straight line

curved path is an illusion casued by

floor pushing on us, not a mysterious fg force

gravity is not a force

result of observing motion in a frame that is not in free floar

pencil fall

latticework of clock

where it happened (space)

when it happened (time)

sychronize clocks - lattice clockwork - no single human can be anywhere

1. Choose one clock as the reference clock.

2. At time zero, it emits a reference flash of light.

3. A clock 5 meters away is preset to read 5 meters of time.

4. When the flash arrives, that clock starts running.

Because light takes 5 meters of time to travel 5 meters of distance, all clocks end up synchronized.

latticle free float

test particles move in a stright line

constant speed

identical behaviors

free float frame is

test particles have same accelartion

no fg

newtons first law

inside a freely falling elevator e

principle of relativity

if ur ina closed free floatt frame, u dk whether ur moving or at rest

ship cabin below deck

ship moves smoothly, everything in that jawm looks exactly the same as if itw as at rest

motion

only menaginful relative to something else , refenrece

shows why spacetime intervals remain invraiant

every obj untuoched by a force

moves w zero accelartion

spacetime interval ar the only same tihng in inertial frames

velcoty

accelation

nagentic fields all dikff

relativty of simultenity

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

train paradox

• Lightning strikes the front and back of a moving train.

• A ground observer, standing exactly halfway between the char marks on the track, receives both flashes at the same time → concludes the strikes were simultaneous.

• A train observer, standing exactly halfway between the char marks on the train, receives the front flash first → concludes the front strike happened earlier.

2 events occur at diff places

they cannot be simultaneous in both frames

lorentz contraction

moving objects are shorter in the direction of motion

rod - moving and at rest

long megth and short length

relaivy effects must b measured

not visually observed bc light tew fast

dimensions perpenducalt to rod (lnegth, widnth)

dont change, called transverse demisions / shrinkage

longitudal dimensions

contract

front to back dimesnion, lies along relative motion

yes one liftime is enough traveling in earth

line of sychronized clocks

relasitvistc motion

using only one rocket clock and one Earth‑frame line of clocks.

mixing frames w units

• Distance was measured in the Earth frame

  • Time was measured in the rocket frame

In the rocket frame, the traveler does not move — the rocket is at rest.

n the Earth frame, the rocket moves at a sub‑light speed consistent with relativity.

The discrepancy in times (10 years Earth time vs. 6 years rocket time) i

time dilation

speed

computed using dist and time from the same reference frame

time dilations

allows long journey to be shortfor travler

time runs slower in earth

traveling close to the speed of light, earth sees ur onboard time slow down

99 light yrs is not the same for you

shorter, few yrs

twin paradox

straight path = shorter distance

parth w a turn = longer distance

opp

striaght path = long proper time (agemaxxing)

path w turn : less proper time

earth = age more

lorentz contraction

99 light yrs in 20 yrs is possible bc of diff time frames

99 light yrs is shorter than i the rocket frame

light clock

proves time dialtion

light clock leasures time using

round trip path

proper time

time measued by a clock loving along a paht

earth twin

maximum ticks

str8 path

light travels shortest , more tikets more agining

kinked path

light travles longer, fewer ticks, less aging

speed of light

every obsever despite their speed moeasues c spe

speed of light

space and time lust adjust themselves , producing time dilation, length contraciton twin pardox etc