Deriving Einstein's most famous equation： Why does energy mass x speed of light squared？

Chapter 1: Introduction

• The equation equals MC squared is famous but few people know its meaning or origin

• Deriving the equation and understanding its meaning

• Insight into Einstein's theory of special relativity

Chapter 2: Mechanics and Frames of Reference

• Mechanics describes how bodies change position in space over time

• Observing the motion of a stone dropped from a moving train

• Stone appears to descend in a straight line from the train's frame of reference

• Stone appears to fall in a parabolic curve from the platform's frame of reference

• Using a system of coordinates to describe motion relative to a frame of reference

Chapter 3: Principle of Inertia and Inertial Frames of Reference

• The fundamental law of mechanics: A body continues in rest or uniform motion unless acted upon by an external force

• Principle of inertia

• An inertial frame of reference is a non-accelerating frame of reference

• Einstein's theory of special relativity focuses on inertial frames of reference

Chapter 4: Principle of Relativity

• Introduced by Galileo in his dialogue concerning the 2 chief world systems

Chapter 2: Particular Moving Clock

• Einstein's experiment with the speed of light

  • Spaceship traveling at 200,000 km/s relative to the road

  • Beam of light travels past at 300,000 km/s relative to the road

  • Speed of light relative to the spaceship is 100,000 km/s

  • Experiment shows light traveling 300,000 km/s relative to spaceship and road

  • Conclusion: Sense of space and time is not the same for a person standing still and a person moving

• Measuring the duration of time

  • Simple clock with parallel mirrors separated by one meter

  • Light signal reflects off mirrors, making a tick every time it moves up and a tock every time it comes down

  • Two clocks with same length are synchronized

  • Light always travels at the same speed

• Comparison of stationary and moving clocks

  • Stationary clock takes time T Naught for one tick-tock

  • Moving clock on a train takes longer path due to train's motion

  • Observer sees light taking a zigzag path in the moving clock

  • Path taken by light in moving clock is longer than in stationary clock

Chapter 1: Introduction

• The train is moving with velocity V relative to the platform

• The time taken for light to travel from bottom mirror to top mirror is big t

Chapter 2: Pythagoras' Theorem

• Using Pythagoras' theorem to find a relationship between the sides of a right angle triangle

• CT squared = 1 squared + vt squared

• Rearranging for t, the time taken for a tick of the moving clock

• t = 2 / square root of (c squared - v squared)

Chapter 3: Time Dilation

• Expressing t in terms of t naught, the time taken for the tick tock of the stationary clock

• t = t naught / square root of (1 - v squared / c squared)

• Gamma (γ) is the factor that tells us the difference between t and t naught

• If v = 0, then gamma = 1 and t = t naught

• If v > 0, then gamma > 1 and t > t naught

• All moving clocks run slower by the same amount to preserve the principle of relativity

• Time dilation is the difference in elapsed time between stationary and moving frames of reference

Chapter 4: Time Dilation at the Speed of Light

• As v approaches c, gamma approaches infinity and t tends to infinity

• The tick tock of the moving clock would get slower and eventually freeze

• Time dilation becomes more significant for very fast moving objects

Chapter 3: Energy Of Object

• Usane Bolt example

  • Calculating time dilation factor

  • t is essentially the same as t naught

• Time dilation with muons

  • Muons created in upper atmosphere decay quickly

  • Time dilation allows muons to travel further and be detected on the ground

• Linking time dilation to Einstein's equation

  • Defining energy in classical physics

  • Using Newton's second law and momentum

  • Expression for relativistic momentum

  • Derivative of momentum

  • Derivative of momentum in integral for kinetic energy

  • Changing variables in integral

Chapter 5: Energy Of Object

• Energy of an object at rest is its mass times the speed of light squared

• Equation for energy of a moving object: e = gammamzsquared

• The equation is the most general expression for the energy of an object moving with any velocity below the speed of light

• Speed of light represents an upper limit to the velocity an object can possess

• Plotting the kinetic energy function for a relativistic object shows that the kinetic energy tends to infinity when the velocity tends to the speed of light

• Speed of light represents a fundamental limit to the velocity of any object

• Not all objects have mass, for example, photons are massless particles that travel at the speed of light

• Substituting m = 0 and V = C into the equation E = gammamcsquared gives the energy of a photon

Chapter 1: Introduction

• Energy of a master's particle is not determined by velocity

• Question: Can massless particles have different energies if they all travel at the same velocity?

Chapter 2: Energy in terms of momentum

• Expressing total energy in terms of momentum

• Relating kinetic energy and momentum in classical physics

• Relativistic energy equation: e = γmz²

• Squaring both sides of the equation

• Combining terms and simplifying equation

• Energy squared equals momentum squared plus mass squared

• Advantage of this expression for describing all particles

Chapter 3: Energy of massless particles

• Energy of massless particle: e = PC

• Massless particles carry momentum

• Magnitude of momentum is energy divided by speed of light

• Relation between energy of massless photon and momentum

• Equation proposed by Louis De Bruyne and its impact on quantum mechanics

Chapter 4: Energy-momentum relation in particle physics

• Energy-momentum relation is fundamental in particle physics

• Conservation of energy and momentum in isolated systems

• Different observers assign different values for energy and momentum

• Mass of an object is a fundamental invariant

• Using energy-momentum relation to determine mass of particles

• Experimental discovery of Higgs Boson and determination of its mass

Conclusion

• Albert Einstein's wise words

Chapter 6: Conclusion

• The important thing is to not stop questioning.

• Curiosity has its own reason for existence.

• One cannot help but be in awe when contemplating the mysteries of eternity, life, and the marvelous structure of reality.

• It is enough if one tries merely to comprehend a little of this mystery each day.

• The video aims to help viewers comprehend a little of the mystery of relativity.

Thank you for watching.