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'''The Status Quo of General Relativity in School Curricula'''  '''On the Status Quo of General Relativity in School Curricula''' 
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Is GR mentioned in the curriculum of this country?  Is general relativity mentioned in the curriculum of this country? 
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 country  curriculum on GR  remarks   Brazil (Rio de Janeiro)  Recognize the present models of the universe (stellar evolution, black holes, curved space and big bang)  Ensino Medio, age 15  Germany (Bremen)  Equivalence principle, experimental tests (precession of the perihelion of Mercury, light deflection near the sun, gravitational redshift)  advanced level, ages 1617  Germany (North RhineWestfalia)  Basic statements of GR: gravitational time dilation, equivalence principle, gravitation and time measurement (describe qualitatively); gravitation, time measurement and curvature of space (illustrate using models and graphics); impact on physical world view  advanced level, ages 1617  Germany (Saarland)  Reference to GR as theory of gravitation and to its significance for astrophysics and cosmology  age 16   Germany (Saxony)  Evidence for the impact of gravitation on light: reference to GR, gravitation and curved spacetime, experiments with atomic clocks, black holes in the universe  standard level, age 16    Selected aspects of GR: gravitation and curved spacetime, experiments with atomic clocks, black holes in the universe, big bang theory  advanced level, age 16   Norway  … give a qualitative description of general relativity  upper secondary school   Scotland  Knowledge that special relativity deals with motion in inertial (nonaccelerating) frames of reference and that general relativity deals with motion in noninertial (accelerating) frames of reference.  Statement of the equivalence principle (that it is not possible to distinguish between the effects on an observer of a uniform gravitational field and of a constant acceleration) and awareness of its consequences.  Consideration of spacetime as a representation of four dimensional space.  Knowledge that light or a freely moving object follows a geodesic (the shortest distance between two points) in spacetime.  Knowledge that GR leads to the interpretation that mass curves spacetime, and that gravity arises from the curvature of spacetime.  Representation of World lines for objects which are stationary, moving with constant velocity and accelerating.  Use of an appropriate relationship to solve problems relating to the Schwarzschild radius of a black hole.  Knowledge that time appears to be frozen at the event horizon of a black hole.  Advanced Higher Physics, ages 1718   Sweden  … an introduction to the general theory of relativity    Switzerland  Basic principles of general relativity. // Basic principles of general relativity, experimental tests. // The students know ideas and basic concepts of general relativity in a qualitative way. // The students are given a short, qualitative insight into general relativity. // The students can explain the concept of spatial curvature using a simple example. // The students can state the limited field of application of special relativity and fundamental principles of general relativity using a simple example. // The students can explain the concept of spatial curvature using a simple example.  From individual cantonal and school curricula    The equivalence principle, the gravitational field, the curvature of spacetime  Implementation of a school curriculum   Turkey  Big Bang, Cosmological models    USA  Concepts: Einstein's principle of equivalence, the concept of spacetime and that moving objects follow the shortest path between two points in spacetime, the concept of gravitational red shift, the concept of gravitational lensing.   Skills/Performance Expectations: Deduce that the principle of equivalence predicts bending of light rays in a gravitational field.  Deduce that the principle of equivalence predicts that time slows down near a massive body.  Explain gravitational attraction in terms of the warping of spacetime by matter.  Describe black holes, define and calculate the Schwarzschild radius and solve problems involving time dilation close to a black hole.  Solve problems involving frequency shifts between different points in a uniform gravitational field.  Solve problems using the gravitational time dilation formula.  Outline an experiment for the bending of EM waves by a massive object.  Outline an experiment that provides evidence for gravitational red shift.  A school curriculum, New Jersey (exceptional case)  
 country  curriculum on GR  remarks  Data as at   Brazil (Rio de Janeiro)  Recognize the present models of the universe (stellar evolution, black holes, curved space and big bang)  Ensino Medio, age 15 07/2017   Germany (Bremen)  Equivalence principle, experimental tests (precession of the perihelion of Mercury, light deflection near the sun, gravitational redshift)  advanced level, ages 1617 12/2017   Germany (North RhineWestfalia)  Basic statements of GR: gravitational time dilation, equivalence principle, gravitation and time measurement (describe qualitatively); gravitation, time measurement and curvature of space (illustrate using models and graphics); impact on physical world view  advanced level, ages 1617 12/2017   Germany (Saarland)  Reference to GR as theory of gravitation and to its significance for astrophysics and cosmology  age 16  12/2017   Germany (Saxony)  Evidence for the impact of gravitation on light: reference to GR, gravitation and curved spacetime, experiments with atomic clocks, black holes in the universe  standard level, age 16  12/2017    Selected aspects of GR: gravitation and curved spacetime, experiments with atomic clocks, black holes in the universe, big bang theory  advanced level, age 16  12/2017   Norway  … give a qualitative description of general relativity  upper secondary school  07/2017   Scotland  Knowledge that special relativity deals with motion in inertial (nonaccelerating) frames of reference and that general relativity deals with motion in noninertial (accelerating) frames of reference.  Statement of the equivalence principle (that it is not possible to distinguish between the effects on an observer of a uniform gravitational field and of a constant acceleration) and awareness of its consequences.  Consideration of spacetime as a representation of four dimensional space.  Knowledge that light or a freely moving object follows a geodesic (the shortest distance between two points) in spacetime.  Knowledge that GR leads to the interpretation that mass curves spacetime, and that gravity arises from the curvature of spacetime.  Representation of World lines for objects which are stationary, moving with constant velocity and accelerating.  Use of an appropriate relationship to solve problems relating to the Schwarzschild radius of a black hole.  Knowledge that time appears to be frozen at the event horizon of a black hole.  Advanced Higher Physics, ages 1718  02/2019   Sweden  … an introduction to the general theory of relativity   08/2017   Switzerland  Basic principles of general relativity. // Basic principles of general relativity, experimental tests. // The students know ideas and basic concepts of general relativity in a qualitative way. // The students are given a short, qualitative insight into general relativity. // The students can explain the concept of spatial curvature using a simple example. // The students can state the limited field of application of special relativity and fundamental principles of general relativity using a simple example. // The students can explain the concept of spatial curvature using a simple example.  From individual cantonal and school curricula  2018   Turkey  Big Bang, Cosmological models   09/2017  ##  USA  Concepts: Einstein's principle of equivalence, the concept of spacetime and that moving objects follow the shortest path between two points in spacetime, the concept of gravitational red shift, the concept of gravitational lensing.   Skills/Performance Expectations: Deduce that the principle of equivalence predicts bending of light rays in a gravitational field.  Deduce that the principle of equivalence predicts that time slows down near a massive body.  Explain gravitational attraction in terms of the warping of spacetime by matter.  Describe black holes, define and calculate the Schwarzschild radius and solve problems involving time dilation close to a black hole.  Solve problems involving frequency shifts between different points in a uniform gravitational field.  Solve problems using the gravitational time dilation formula.  Outline an experiment for the bending of EM waves by a massive object.  Outline an experiment that provides evidence for gravitational red shift.  A school curriculum, New Jersey (exceptional case)  
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## Switzerland ##   The equivalence principle, the gravitational field, the curvature of spacetime  Implementation of a school curriculum  
On the Status Quo of General Relativity in School Curricula
With contributions by Lisa Büssing, Stuart Farmer, Lorenzo Galante, Fadeel Joubran, Magdalena Kersting, Gerd Kortemeyer, Ute Kraus, Richard Meagher, Alina Neumann, Joao Pereira.
I) Overview
Is general relativity mentioned in the curriculum of this country?
Country 
yes 
no 
remarks 
Data as at 
Australia 

x 
federal curriculum: no, state curricula? 
02/2019 
Belgium (Flanders) 

x 
other regions? 
09/2017 
Brazil (Rio de Janeiro) 
x 

other regions? 
07/2017 
Czech Republic 

x 

09/2017 
Denmark 

x 

09/2017 
Finland 

x 

07/2017 
Germany 
x 

4 out of 16 states: yes, others: no 
12/2017 
Italy 

x 

02/2019 
Israel 

x 

02/2019 
Netherlands 

x 

09/2017 
Norway 
x 


07/2017 
Scotland 
x 


02/2019 
Sweden 
x 


08/2017 
Switzerland 
x 

in some cantons, in some schools 
2018 
Turkey 
x 


09/2017 
USA 
x 

federal curriculum: no, some school curricula: yes 
2017 
II) Content
country 
curriculum on GR 
remarks 
Data as at 
Brazil (Rio de Janeiro) 
Recognize the present models of the universe (stellar evolution, black holes, curved space and big bang) 
Ensino Medio, age 15 
07/2017 
Germany (Bremen) 
Equivalence principle, experimental tests (precession of the perihelion of Mercury, light deflection near the sun, gravitational redshift) 
advanced level, ages 1617 
12/2017 
Germany (North RhineWestfalia) 
Basic statements of GR: gravitational time dilation, equivalence principle, gravitation and time measurement (describe qualitatively); gravitation, time measurement and curvature of space (illustrate using models and graphics); impact on physical world view 
advanced level, ages 1617 
12/2017 
Germany (Saarland) 
Reference to GR as theory of gravitation and to its significance for astrophysics and cosmology 
age 16 
12/2017 
Germany (Saxony) 
Evidence for the impact of gravitation on light: reference to GR, gravitation and curved spacetime, experiments with atomic clocks, black holes in the universe 
standard level, age 16 
12/2017 

Selected aspects of GR: gravitation and curved spacetime, experiments with atomic clocks, black holes in the universe, big bang theory 
advanced level, age 16 
12/2017 
Norway 
… give a qualitative description of general relativity 
upper secondary school 
07/2017 
Scotland 
Knowledge that special relativity deals with motion in inertial (nonaccelerating) frames of reference and that general relativity deals with motion in noninertial (accelerating) frames of reference.  Statement of the equivalence principle (that it is not possible to distinguish between the effects on an observer of a uniform gravitational field and of a constant acceleration) and awareness of its consequences.  Consideration of spacetime as a representation of four dimensional space.  Knowledge that light or a freely moving object follows a geodesic (the shortest distance between two points) in spacetime.  Knowledge that GR leads to the interpretation that mass curves spacetime, and that gravity arises from the curvature of spacetime.  Representation of World lines for objects which are stationary, moving with constant velocity and accelerating.  Use of an appropriate relationship to solve problems relating to the Schwarzschild radius of a black hole.  Knowledge that time appears to be frozen at the event horizon of a black hole. 
Advanced Higher Physics, ages 1718 
02/2019 
Sweden 
… an introduction to the general theory of relativity 

08/2017 
Switzerland 
Basic principles of general relativity. // Basic principles of general relativity, experimental tests. // The students know ideas and basic concepts of general relativity in a qualitative way. // The students are given a short, qualitative insight into general relativity. // The students can explain the concept of spatial curvature using a simple example. // The students can state the limited field of application of special relativity and fundamental principles of general relativity using a simple example. // The students can explain the concept of spatial curvature using a simple example. 
From individual cantonal and school curricula 
2018 
Turkey 
Big Bang, Cosmological models 

09/2017 