# A. Relativity

**A. Relativity**

**A. Relativity**

**Core**

**Core**

**A.1 – The beginnings of relativity**

**A.1 – The beginnings of relativity**

**Nature of science:**

Paradigm shift: The fundamental fact that the speed of light is constant for all inertial observers has far-reaching consequences about our understanding of space and time. Ideas about space and time that went unchallenged for more than 2,000 years were shown to be false. The extension of the principle of relativity to accelerated frames of reference leads to the revolutionary idea of general relativity that the mass and energy that spacetime contains determine the geometry of spacetime.

**Understandings:**

Reference frames

Galilean relativity and Newton’s postulates concerning time and space

Maxwell and the constancy of the speed of light

Forces on a charge or current

**Applications and skills:**

Using the Galilean transformation equations

Determining whether a force on a charge or current is electric or magnetic in a given frame of reference

Determining the nature of the fields observed by different observers

**A.2 – Lorentz transformations**

**A.2 – Lorentz transformations**

**Nature of science:**

Pure science: Einstein based his theory of relativity on two postulates and deduced the rest by mathematical analysis. The first postulate integrates all of the laws of physics including the laws of electromagnetism, not only Newton’s laws of mechanics.

**Understandings:**

The two postulates of special relativity

Clock synchronization

The Lorentz transformations

Velocity addition

Invariant quantities (spacetime interval, proper time, proper length and rest mass)

Time dilation

Length contraction

The muon decay experiment

**Applications and skills:**

Using the Lorentz transformations to describe how different measurements of space and time by two observers can be converted into the measurements observed in either frame of reference

Using the Lorentz transformation equations to determine the position and time coordinates of various events

Using the Lorentz transformation equations to show that if two events are simultaneous for one observer but happen at different points in space, then the events are not simultaneous for an observer in a different reference frame

Solving problems involving velocity addition

Deriving the time dilation and length contraction equations using the Lorentz equations

Solving problems involving time dilation and length contraction

Solving problems involving the muon decay experiment

**A.3 – Spacetime diagrams**

**A.3 – Spacetime diagrams**

**Nature of science:**

Visualization of models: The visualization of the description of events in terms of spacetime diagrams is an enormous advance in understanding the concept of spacetime.

**Understandings:**

Spacetime diagrams

Worldlines

The twin paradox

**Applications and skills:**

Representing events on a spacetime diagram as points

Representing the positions of a moving particle on a spacetime diagram by a curve (the worldline)

Representing more than one inertial reference frame on the same spacetime diagram

Determining the angle between a worldline for specific speed and the time axis on a spacetime diagram

Solving problems on simultaneity and kinematics using spacetime diagrams

Representing time dilation and length contraction on spacetime diagrams

Describing the twin paradox

Resolving of the twin paradox through spacetime diagrams

**Additional higher level**

**Additional higher level**

**A.4 – Relativistic mechanics**

**A.4 – Relativistic mechanics**

**Nature of science:**

Paradigm shift: Einstein realized that the law of conservation of momentum could not be maintained as a law of physics. He therefore deduced that in order for momentum to be conserved under all conditions, the definition of momentum had to change and along with it the definitions of other mechanics quantities such as kinetic energy and total energy of a particle. This was a major paradigm shift.

**Understandings:**

Total energy and rest energy

Relativistic momentum

Particle acceleration

Electric charge as an invariant quantity

MeV c –2 as the unit of mass and MeV c –1 as the unit of momentum

**Applications and skills:**

Describing the laws of conservation of momentum and conservation of energy within special relativity

Determining the potential difference necessary to accelerate a particle to a given speed or energy

Solving problems involving relativistic energy and momentum conservation in collisions and particle decays

**A.5 – General relativity**

**A.5 – General relativity**

**Nature of science:**

Creative and critical thinking: Einstein’s great achievement, the general theory of relativity, is based on intuition, creative thinking and imagination, namely to connect the geometry of spacetime (through its curvature) to the mass and energy content of spacetime. For years it was thought that nothing could escape a black hole and this is true but only for classical black holes. When quantum theory is taken into account a black hole radiates like a black body. This unexpected result revealed other equally unexpected connections between black holes and thermodynamics.

**Understandings:**

The equivalence principle

The bending of light

Gravitational redshift and the Pound–Rebka–Snider experiment

Schwarzschild black holes

Event horizons

Time dilation near a black hole

Applications of general relativity to the universe as a whole

**Applications and skills:**

Using the equivalence principle to deduce and explain light bending near massive objects

Using the equivalence principle to deduce and explain gravitational time dilation

Calculating gravitational frequency shifts

Describing an experiment in which gravitational redshift is observed and measured

Calculating the Schwarzschild radius of a black hole

Applying the formula for gravitational time dilation near the event horizon of a black hole

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