A. Relativity

Core

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:

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

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

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:

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

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:

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

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:

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

Last updated 2 years ago