A. Relativity

A. Relativity

Core

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

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

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

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

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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