IB PHYSICS A.5 GALILEAN AND
SPECIAL RELATIVITY (HL ONLY)
Reference frames and Galilean relativity
A reference frame is a coordinate system for
describing the position and motion of objects.
Inertial frames: Newton’s laws hold true (object
remains at rest or constant velocity unless acted on).
Non-inertial frames: accelerating
require fictitious
forces to explain motion.
Newton’s laws are the same in all inertial reference
frames, known as Galilean relativity.
Galilean transformations describe how coordinates
change between frames moving at constant relative
velocity v:
x' = x - vt
t' = t
These lead to the velocity addition formula in classical
mechanics: u' = u - v
Assumes absolute time and linear velocity addition.
→
Inertial frames = constant velocity or rest
Non-inertial frames = accelerating
Einstein’s postulates and Lorentz transformations
→
Galilean relativity fails for light
experiments
(Michelson-Morley) showed speed of light is constant for
all observers.
Einstein proposed two postulates:
Principle of Relativity: The laws of physics are the
same in all inertial frames.
Constancy of c: The speed of light in vacuum is the
same for all observers, regardless of motion.
These lead to Lorentz transformations, which replace
Galilean transformations at relativistic speeds:
Lorentz transformations ensure that light speed
remains invariant.
Length contraction
Length contraction: Moving objects appear shorter
along the direction of motion.
where
frame).
is proper length (measured in object’s rest
Time dilation
Time Dilation: Moving clocks run
slower relative to stationary
observers.
where
is proper time (measured
in rest frame of the clock).
Time dilates, length contracts,
but only in the direction of
motion.
Always define which frame
is measuring what.
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Spacetime interval and relativity of simultaneity
Simultaneity is relative: two events simultaneous
in one frame may not be in another.
Spacetime interval:
This is invariant for all inertial frames.
Space-time diagrams and experimental evidence
Worldlines show motion in spacetime:
vertical worldline
object at rest.
slanted worldline
moving object.
45° worldline
light (v = c).
Angle of worldline relates to speed:
→
→
→
→
steeper
slower motion
45° = light
Two lightning strikes simultaneous in one
frame appear at different times in another
moving frame.
Muon decay provides experimental evidence for time
dilation & length contraction.
Muons from upper atmosphere reach Earth because:
Earth frame: their lifetime is dilated.
Muon frame: the distance to Earth is contracted.
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