Effects of relativity IB DP Physics Study Notes - 2025 Syllabus
Effects of relativity IB DP Physics Study Notes
Effects of relativity IB DP Physics Study Notes at IITian Academy focus on specific topic and type of questions asked in actual exam. Study Notes focus on IB Physics syllabus with Students should understand
that the space-time interval $\Delta s$ between two events is an invariant quantity as given by
$(\Delta s)^2=(c \Delta t)^2-(\Delta x)^2$
proper time interval and proper length
time dilation as given by $\Delta t=\gamma \Delta t_0$
length contraction as given by $L=\frac{L_0}{\gamma}$
the relativity of simultaneity
Standard level and higher level: There is no Standard level content
Additional higher level: 8 hours
- IB DP Physics 2025 SL- IB Style Practice Questions with Answer-Topic Wise-Paper 1
- IB DP Physics 2025 HL- IB Style Practice Questions with Answer-Topic Wise-Paper 1
- IB DP Physics 2025 SL- IB Style Practice Questions with Answer-Topic Wise-Paper 2
- IB DP Physics 2025 HL- IB Style Practice Questions with Answer-Topic Wise-Paper 2
Space-Time Interval
The space-time interval is a fundamental quantity in special relativity that remains invariant across all inertial reference frames.
It is given by the equation:
\[
(\Delta s)^2 = (c\Delta t)^2 – (\Delta x)^2
\]
where:
\( \Delta s \) is the space-time interval,
\( \Delta t \) is the time interval between two events in a given reference frame,
\( \Delta x \) is the spatial separation between the events,
\( c \) is the speed of light.
This equation shows that space and time are interconnected, forming a four-dimensional continuum rather than being separate, independent entities.
Unlike distances in classical mechanics, the space-time interval can be positive, negative, or zero, classifying events as time-like, space-like, or light-like respectively
Proper Time and Proper Length
Proper Time (\(\Delta t_0\)): The time measured in the frame where two events occur at the same location.
It is the shortest time interval between two events, unaffected by motion.
In a moving reference frame, time dilation occurs, making the observed time longer.
Proper Length (\( L_0 \)): The length of an object measured in its own rest frame.
When observed from a moving frame, the length appears **contracted** along the direction of motion.
Time Dilation
Time Dilation describes how a moving clock appears to run slower than a stationary one.
The relationship between proper time and observed time is given by:
\[
\Delta t = \gamma \Delta t_0
\]
where:
\( \gamma = \frac{1}{\sqrt{1 – \frac{v^2}{c^2}}} \) is the **Lorentz factor**,
\( \Delta t_0 \) is the **proper time** (measured in the object’s rest frame),
\( \Delta t \) is the time measured in another frame moving at velocity \( v \).
Length Contraction
Length Contraction states that objects in motion appear shorter along the direction of motion.
The contracted length is given by:
\[
L = \frac{L_0}{\gamma}
\]
where:
\( L_0 \) is the **proper length** (length in the object’s rest frame),
\( L \) is the observed length in a moving frame,
\( \gamma \) is the Lorentz factor.
Implication: The faster an object moves, the more it appears shortened in the direction of motion.
Relativity of Simultaneity
- In special relativity, simultaneity is relative—events that are simultaneous in one frame may not be simultaneous in another.
- This is a consequence of the finite speed of light and the Lorentz transformations.
- If two events occur at different locations, observers moving relative to those events will generally perceive them as happening at different times.
- Key insight: There is no absolute “universal time”—the order and timing of events depend on the observer’s motion.
These concepts—time dilation, length contraction, and the relativity of simultaneity—demonstrate how space and time behave differently at relativistic speeds, fundamentally changing our classical understanding of motion and simultaneity.
IB Physics Effects of relativity Exam Style Worked Out Questions
Question
A spacecraft, moving with speed $v$ relative to Earth, passes Earth on its way to a planet. As the spacecraft passes Earth, clocks on Earth and in the spacecraft show zero.
The planet is a distance $D$ from Earth, according to an observer on Earth.
What are the readings on the Earth clock and on the spacecraft clock when the spacecraft arrives at the planet?
▶️Answer/Explanation
Ans:A
Question
Two spaceships, $\mathrm{X}$ and $\mathrm{Y}$ move in opposite directions away from a space station. The speeds of the spaceships relative to the space station are $u$ and $v$.
space station
What is the speed of $\mathrm{Y}$ in the reference frame of $\mathrm{X}$ ?
A. $\frac{u-v}{1-\frac{v v}{c^2}}$
B. $\frac{u-v}{1+\frac{v v}{c^2}}$
C. $\frac{u+v}{1-\frac{u v}{c^2}}$
D. $\frac{u+v}{1+\frac{u v}{c^2}}$
▶️Answer/Explanation
Ans:D