IB Physics Hub: The Relativity Series
A complete guide to the IBDP curriculum on Special Relativity, taught by Dr. Rao.
1. Welcome to Special Relativity:
Welcome to this series on the IBDP physics curriculum! This course contains FOUR core videos covering the entire relativity chapter. After the lessons, we'll dive into solving different problems based on these concepts. To begin with lets start with Galilean Transformations, which speaks about frames of references and how events in one frame can be related in another moving frame using these transformations.
1. Reference Frames: The foundation of Observations:
A reference frame is a perspective from which we observe and measure motion using a coordinate system. It's crucial because the observed motion of an object can change dramatically depending on the observer's frame.
Types of Reference Frames
a. Inertial Frame: A frame where objects move at a constant velocity or stay at rest. In these frames, Newton's Laws of Motion hold perfectly without the need for pseudo-forces. Example: A train moving at a constant speed in a straight line or A skydiver who has reached terminal velocity.
b. Non-Inertial Frame: A frame that is accelerating or rotating. In these frames, Newton's laws require adjustments with "pseudo-forces" to explain motion. Example: A plane taking off or a bus applying its brakes. You feel pushed forward or backward due to this "pseudo-force."
When you observe these events from a different frame that is either moving or at rest, how do you measure its speed or its position. The solution to it is given by the Galilean Transformations
These transformations are used in classical physics to switch between two inertial reference frames moving at a constant speed relative to each other. They work well at low velocities.
Coordinate Transformation Equations:
Velocity Addition
Velocities are simply additive. If a train moves at 12 m/s and a ball rolls at 2 m/s in the same direction, an observer on the ground sees the ball moving at 14 m/s (12 + 2).
Failure of Galilean Transformations
These transformations fail at speeds close to the speed of light and do not work for electromagnetism. For a stationary observer, a charge produces only an electric field, but for a moving observer, it produces both an electric and a magnetic field. Galilean transformations couldn't resolve this. Hence Lorentz Transformations are used , which is depicted in the next video.
Einstein's theory revolutionized physics by proposing two fundamental postulates for inertial frames.
1. The Principle of Relativity: All laws of physics (including mechanics and electromagnetism) are the same in all inertial frames.
2. The Constancy of the Speed of Light: The speed of light in a vacuum, c, is the same for all observers in inertial frames, regardless of the motion of the light source.
2. Relativistic Effects:
At relativistic speeds, we observe strange but real consequences.
1. Time Dilation: Time in a moving frame appears to run slower when observed from a stationary frame. "Moving clocks run slow."
2. Length Contraction: An object's length appears shorter in the direction of its motion when measured by a stationary observer.
3. Simultaneity: Events that are simultaneous in one reference frame may not be simultaneous in another frame that is moving relative to the first.
You can view in more details about all these effects in the below video:
3. Space-Time Interval:
While measurements of space (length) and time can change between observers, one quantity remains the same for everyone: the space-time interval (Δs²).
This value is invariant, meaning all inertial observers will calculate the exact same space-time interval between two events, even if their individual measurements of Δx and Δt are different. The following video gives you details about how space - time interval remains same with few examples.
4. Numericals in Relativity:
In this section, we apply the concepts learned so far to solve more advanced problems. The video below contains detailed explanations, with timestamps and problem types listed here for easy navigation. You can pause the video at each problem or directly jump to the respective timestamp to review that particular solution. These problems will help reinforce and strengthen your understanding of the concepts covered earlier.
Timestamps and Problems:
2:34 – Length Contraction: Problem 1 – Finding the angle of a rod due to length contraction
10:00 – Relativistic Velocity Addition: Problem 2 – Velocity of a photon in a water tunnel moving with speed v
13:48 – Fractional Uncertainty Calculation: Problem 3 – Fractional uncertainty of the volume of a sphere due to length contraction
18:00 – Length Contraction + Time Dilation: Problem 4 – Finding the speed of a spaceship
21:00 – Relativistic Velocity Addition + Length Contraction: Problem 5 – Finding the time to complete a journey.
