# Unit Planner: Relativity Unit: Relativity

Start date:

End date:

Diploma assessment

When will the content be assessed?

Paper 1
Paper 2
Paper 3 x
Investigation

Text book reference

Hamper - online resources

#### Inquiry: Establishing the purpose of the unit

Transfer Goals
List here one to three big, overarching, long-term goals for this unit. Transfer goals are the major goals that ask students to “transfer”, or apply, their knowledge, skills, and concepts at the end of the unit under new/different circumstances, and on their own without scaffolding from the teacher.

• To introduce the concept of relativity and to know the importance of the speed of light
• To understand the effects of time dilation and length contraction
• To be able to use Lorentz transformations and to use relativistic formulae

Content
List here the key content that students will know by the end of the unit

Relativity

• Galilean relativity and Newton’s postulates concerning time and space
• Maxwell and the constancy of the speed of light

Lorentz transformations

• The two postulates of special relativity
• The muon decay experiment
• Invariant quantities (spacetime interval, proper time, proper length and rest mass)

Spacetime diagrams

• Spacetime diagrams

Relativistic mechanics

• Total energy and rest energy
• MeV c^–2 as the unit of mass and MeV c^–1 as the unit of momentum

General relativity

• The equivalence principle
• The bending of light
• Gravitational redshift and the Pound–Rebka–Snider experiment
• Schwarzschild black holes

Skills
List here the key skills that students will develop by the end of the unit.

Relativity

• Use the Galilean transformation equations
• Determine whether a force on a charge or current is electric or magnetic in a given frame of reference

Lorentz transformations

• Use 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
• Use the Lorentz transformation equations to determine the position and time coordinates of various events
• Use 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
• Derive the time dilation and length contraction equations using the Lorentz equations

Spacetime diagrams

• Represent events on a spacetime diagram as points
• Represent the positions of a moving particle on a spacetime diagram by a curve (the worldline)
• Represent more than one inertial reference frame on the same spacetime diagram
• Represent time dilation and length contraction on spacetime diagrams

Relativistic mechanics

• Describe the laws of conservation of momentum and conservation of energy within special relativity
• Solve problems involving relativistic energy and momentum conservation in collisions and particle decays

General relativity

• Use the equivalence principle to deduce and explain light bending near massive objects
• Use the equivalence principle to deduce and explain gravitational time dilation
• Calculate gravitational frequency shifts
• Apply the formula for gravitational time dilation near the event horizon of a black hole

Concepts
List here the key concepts that students will understand by the end of the unit

Relativity

• Reference frames
• Forces on a charge or current

Lorentz transformations

• Clock synchronization
• The Lorentz transformations
• Time dilation
• Length contraction

Spacetime diagrams

• Worldlines

Relativistic mechanics

• Relativistic momentum
• Particle acceleration
• Electric charge as an invariant quantity
• Photons

General relativity

• Event horizons
• Time dilation near a black hole
• Applications of general relativity to the universe as a whole

Applications
Examples of real world practical applications of knowledge.

• Determine the nature of the fields observed by different observers
• Use 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
• Use the Lorentz transformation equations to determine the position and time coordinates of various events
• Use 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
• Solve problems involving velocity addition
• Solve problems involving time dilation and length contraction
• Solve problems involving the muon decay experiment
• Determine the angle between a worldline for specific speed and the time axis on a spacetime diagram
• Resolve the twin paradox through spacetime diagrams
• Determine the potential difference necessary to accelerate a particle to a given speed or energy
• Describe an experiment in which gravitational redshift is observed and measured
• Calculate the Schwarzschild radius of a black hole

#### Action: teaching and learning through Inquiry

Approaches to teaching
Tick boxes to indicate pedagogical approaches used.

Lecture x
Simulation x
Small group work (pairs) x
Hands on practical
Video x
Student centred inquiry x

TOK
Examples of how TOK can be introduced in this unit

• The idea that the size of a quantity such as velocity has different values depending on the frame of reference of the observer is an interesting one. If its true for physical measurement is it true for e.g. historical events?
• The Michelson Morley experiment is a rare example of an experiment with a result that showed that a relationship did not exist.
• Are events actually happening at a different time or do they just look like they are?
• The way the whole theory is based on two postulates is interesting. If the postulates are true then so is everything else. Students often think that time dilation and length contraction can't be true but agree that the postulates are correct.
• The light clock is a thought experiment. Does it matter that this can't be done in reality?
• Lots of videos on youtube showing what things might look like as we approach the speed of light. Students often ask "what would things look like if we went past the speed of light?" Well you can't so you might as well ask what would cheese smell like if I was a mouse?
• Now we have shown that KE is in fact an increase in mass why do we still talk about energy? Should new theories wipe out the old ones?
• A simple statement has far-reaching consequences.
• The original measurements of the bending of light by the sun by Arthur Eddlington was at the time sited as the first proof of general relativity, however the uncertainty in the measurements was very large and some thought affected by a desire to prove the theory correct. When asked what his reaction would have been if the experiment had not proved general relativity correct Einstein replied "The theory is correct anyway".

NOS
Examples of how NOS can be introduced in this unit.

• Again it's all a bit strange but if the postulates are true then length must contract in the direction of relative motion.
• It seems like magic when you find out that bodies that travel at the speed of light must have zero mass but its not. Same when you use the velocity transform equation and find that the velocity of light is the same as measured by all inertial observers but it would be wouldn't it? Sort of spoils the magic.
• Why do we still teach about Newtons universal law of gravity when it's wrong?

Assessments
Tests, exams and marked labs

Resources
Video clips, simulations demonstrations etc.

#### Reflections

What went well
List the portions of the unit (content, assessment, planning) that were successful

What didn’t work well
List the portions of the unit (content, assessment, planning) that were not as successful as hoped

Notes/changes/suggestions:
List any notes, suggestions, or considerations for the future teaching of this unit.

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