Skills

Physics 5: Special Relativity and Modern Physics

14 weeks · 4 milestones

Space-time, photons, matter waves, atoms and nuclei. Course 5 of the Varsity Curriculum: Physics. Free sources only.

Part of: Physics · Proves for: UG

Milestone map

4 milestones

Special relativity

4 weeks (about 9 hrs/week)

Watch the 8.20 lecture videos and read Volume 3 chapter 5. Then solve the 8.20 problem sets. Self-check: MIT 8.20 problem sets with solutions.

Proof required

Link the public repo with the 8.20 problem sets written up (a typeset PDF, LaTeX source or notebook), and show the self-check: which answers matched and how you fixed the ones that did not.

What gets checked

Each problem names its frames of reference.
Space-time diagrams are drawn for timing questions.
Each set is marked against its solutions.

Common mistakes

Answers copied from the key with no working.
Wrong units or missing signs.

Powstik Guide

A public write-up of the 8.20 problem sets, with the self-check shown.

Steps

Study the linked course and chapters.
Solve the problems on your own first.
Check them against the self-check and rework the misses.
Typeset the write-up (LaTeX or a notebook) in a public repo.
Ask someone who knows physics to check it.

Template

README
Physics 5: Special Relativity and Modern Physics, unit 1: Special relativity
Problems:
Self-check result (matched / reworked):
What I got wrong first and why:

What gets sent back

No working shown.
The self-check result is missing.

Resources

Foundationstart here

Depthgo deeper

What a verifier looks for

Each problem names its frames of reference.
Space-time diagrams are drawn for timing questions.
Each set is marked against its solutions.
Is the physics right, not just the final number?

You'll sign in first, then come straight back here.

Photons, matter waves and the atom

4 weeks (about 9 hrs/week)

Read Volume 3 chapters 6–8. Then solve the odd-numbered problems of chapters 6–8. Self-check: University Physics Volume 3, Answer Keys, chapters 6–8.

Proof required

Link the public repo with the odd-numbered problems of chapters 6–8 written up (a typeset PDF, LaTeX source or notebook), and show the self-check: which answers matched and how you fixed the ones that did not.

What gets checked

Energies are in consistent units (joules or electronvolts).
Photon and wave pictures are used where each fits.
Answers are checked against the key, and misses are reworked.

Common mistakes

Answers copied from the key with no working.
Wrong units or missing signs.

Powstik Guide

A public write-up of the odd-numbered problems of chapters 6–8, with the self-check shown.

Steps

Study the linked course and chapters.
Solve the problems on your own first.
Check them against the self-check and rework the misses.
Typeset the write-up (LaTeX or a notebook) in a public repo.
Ask someone who knows physics to check it.

Template

README
Physics 5: Special Relativity and Modern Physics, unit 2: Photons, matter waves and the atom
Problems:
Self-check result (matched / reworked):
What I got wrong first and why:

What gets sent back

No working shown.
The self-check result is missing.

Resources

Foundationstart here

Depthgo deeper

What a verifier looks for

Energies are in consistent units (joules or electronvolts).
Photon and wave pictures are used where each fits.
Answers are checked against the key, and misses are reworked.
Is the physics right, not just the final number?

You'll sign in first, then come straight back here.

Nuclei and radioactive decay

4 weeks (about 9 hrs/week)

Read Volume 3 chapter 10 (theory only: no radioactive sources are used anywhere here). Then solve the odd-numbered problems of chapter 10. Self-check: University Physics Volume 3, Answer Key, chapter 10.

Proof required

Link the public repo with the odd-numbered problems of chapter 10 written up (a typeset PDF, LaTeX source or notebook), and show the self-check: which answers matched and how you fixed the ones that did not.

What gets checked

Half-life and decay constant are linked correctly (λ = ln 2 / t½).
Binding energies use mass differences correctly.
Answers are checked against the key, and misses are reworked.

Common mistakes

Answers copied from the key with no working.
Wrong units or missing signs.

Powstik Guide

A public write-up of the odd-numbered problems of chapter 10, with the self-check shown.

Steps

Study the linked course and chapters.
Solve the problems on your own first.
Check them against the self-check and rework the misses.
Typeset the write-up (LaTeX or a notebook) in a public repo.
Ask someone who knows physics to check it.

Template

README
Physics 5: Special Relativity and Modern Physics, unit 3: Nuclei and radioactive decay
Problems:
Self-check result (matched / reworked):
What I got wrong first and why:

What gets sent back

No working shown.
The self-check result is missing.

Resources

Foundationstart here

Depthgo deeper

What a verifier looks for

Half-life and decay constant are linked correctly (λ = ln 2 / t½).
Binding energies use mass differences correctly.
Answers are checked against the key, and misses are reworked.
Is the physics right, not just the final number?

You'll sign in first, then come straight back here.

Derive time dilation and test it on muons

4 weeks (about 9 hrs/week)

Make a derivation write-up of time dilation and length contraction from the Lorentz transformation, applied to cosmic-ray muons reaching the ground. Derive each result, then compute what fraction of muons made about 15 km up should reach the ground with and without relativity, using the muon lifetime (2.2 µs) and γ = E / (105.7 MeV) for a stated energy.

Proof required

Link the public repo with the derivation write-up, the result with its uncertainty, and a README that says what you did and what limits the result.

What gets checked

Every step of the derivation follows from the one before.
The fractions use sourced inputs, and a range of heights (10–20 km) and energies gives the spread.
The two predictions are compared and the difference explained.

Common mistakes

A result with no uncertainty.
Code or data that cannot be rerun from the repo.

Powstik Guide

A derivation write-up of time dilation and length contraction from the Lorentz transformation, applied to cosmic-ray muons reaching the ground, in a public repo.

Steps

Write down what you expect before you start.
Derive each result, then compute what fraction of muons made about 15 km up should reach the ground with and without relativity, using the muon lifetime (2.2 µs) and γ = E / (105.7 MeV) for a stated energy.
Work out the uncertainty from your own data.
Compare with the accepted value and explain any gap.
Write the README and ask someone who knows physics to check it.

Template

README
Physics 5: Special Relativity and Modern Physics — Derive time dilation and test it on muons
What I expected:
Method:
Result (value ± uncertainty):
Accepted value and comparison:
What limits the result:

What gets sent back

No uncertainty, or one that is guessed.
Code that does not run.

Resources

Foundationstart here

What a verifier looks for

Every step of the derivation follows from the one before.
The fractions use sourced inputs, and a range of heights (10–20 km) and energies gives the spread.
The two predictions are compared and the difference explained.
The uncertainty is worked out from the data or runs (spread of repeats, instrument limits, fit errors or a range of inputs), not guessed, and it is shown on the result.
Is the physics right, and could someone rerun it from the repo?

You'll sign in first, then come straight back here.

Part of

Physics 5: Special Relativity and Modern Physics →

Related outcomes

Milestone map

4 milestones

Special relativity

4 weeks (about 9 hrs/week)

Watch the 8.20 lecture videos and read Volume 3 chapter 5. Then solve the 8.20 problem sets. Self-check: MIT 8.20 problem sets with solutions.

Proof required

Link the public repo with the 8.20 problem sets written up (a typeset PDF, LaTeX source or notebook), and show the self-check: which answers matched and how you fixed the ones that did not.

What gets checked

Each problem names its frames of reference.
Space-time diagrams are drawn for timing questions.
Each set is marked against its solutions.

Common mistakes

Answers copied from the key with no working.
Wrong units or missing signs.

Powstik Guide

A public write-up of the 8.20 problem sets, with the self-check shown.

Steps

Study the linked course and chapters.
Solve the problems on your own first.
Check them against the self-check and rework the misses.
Typeset the write-up (LaTeX or a notebook) in a public repo.
Ask someone who knows physics to check it.

Template

README
Physics 5: Special Relativity and Modern Physics, unit 1: Special relativity
Problems:
Self-check result (matched / reworked):
What I got wrong first and why:

What gets sent back

No working shown.
The self-check result is missing.

Resources

Foundationstart here

Depthgo deeper

What a verifier looks for

Each problem names its frames of reference.
Space-time diagrams are drawn for timing questions.
Each set is marked against its solutions.
Is the physics right, not just the final number?

You'll sign in first, then come straight back here.

Photons, matter waves and the atom

4 weeks (about 9 hrs/week)

Read Volume 3 chapters 6–8. Then solve the odd-numbered problems of chapters 6–8. Self-check: University Physics Volume 3, Answer Keys, chapters 6–8.

Proof required

What gets checked

Energies are in consistent units (joules or electronvolts).
Photon and wave pictures are used where each fits.
Answers are checked against the key, and misses are reworked.

Common mistakes

Answers copied from the key with no working.
Wrong units or missing signs.

Powstik Guide

A public write-up of the odd-numbered problems of chapters 6–8, with the self-check shown.

Steps

Study the linked course and chapters.
Solve the problems on your own first.
Check them against the self-check and rework the misses.
Typeset the write-up (LaTeX or a notebook) in a public repo.
Ask someone who knows physics to check it.

Template

README
Physics 5: Special Relativity and Modern Physics, unit 2: Photons, matter waves and the atom
Problems:
Self-check result (matched / reworked):
What I got wrong first and why:

What gets sent back

No working shown.
The self-check result is missing.

Resources

Foundationstart here

Depthgo deeper

What a verifier looks for

Energies are in consistent units (joules or electronvolts).
Photon and wave pictures are used where each fits.
Answers are checked against the key, and misses are reworked.
Is the physics right, not just the final number?

You'll sign in first, then come straight back here.

Nuclei and radioactive decay

4 weeks (about 9 hrs/week)

Proof required

What gets checked

Half-life and decay constant are linked correctly (λ = ln 2 / t½).
Binding energies use mass differences correctly.
Answers are checked against the key, and misses are reworked.

Common mistakes

Answers copied from the key with no working.
Wrong units or missing signs.

Powstik Guide

A public write-up of the odd-numbered problems of chapter 10, with the self-check shown.

Steps

Study the linked course and chapters.
Solve the problems on your own first.
Check them against the self-check and rework the misses.
Typeset the write-up (LaTeX or a notebook) in a public repo.
Ask someone who knows physics to check it.

Template

README
Physics 5: Special Relativity and Modern Physics, unit 3: Nuclei and radioactive decay
Problems:
Self-check result (matched / reworked):
What I got wrong first and why:

What gets sent back

No working shown.
The self-check result is missing.

Resources

Foundationstart here

Depthgo deeper

What a verifier looks for

Half-life and decay constant are linked correctly (λ = ln 2 / t½).
Binding energies use mass differences correctly.
Answers are checked against the key, and misses are reworked.
Is the physics right, not just the final number?

You'll sign in first, then come straight back here.

Derive time dilation and test it on muons

4 weeks (about 9 hrs/week)

Proof required

Link the public repo with the derivation write-up, the result with its uncertainty, and a README that says what you did and what limits the result.

What gets checked

Every step of the derivation follows from the one before.
The fractions use sourced inputs, and a range of heights (10–20 km) and energies gives the spread.
The two predictions are compared and the difference explained.

Common mistakes

A result with no uncertainty.
Code or data that cannot be rerun from the repo.

Powstik Guide

A derivation write-up of time dilation and length contraction from the Lorentz transformation, applied to cosmic-ray muons reaching the ground, in a public repo.

Steps

Write down what you expect before you start.
Derive each result, then compute what fraction of muons made about 15 km up should reach the ground with and without relativity, using the muon lifetime (2.2 µs) and γ = E / (105.7 MeV) for a stated energy.
Work out the uncertainty from your own data.
Compare with the accepted value and explain any gap.
Write the README and ask someone who knows physics to check it.

Template

README
Physics 5: Special Relativity and Modern Physics — Derive time dilation and test it on muons
What I expected:
Method:
Result (value ± uncertainty):
Accepted value and comparison:
What limits the result:

What gets sent back

No uncertainty, or one that is guessed.
Code that does not run.

Resources

Foundationstart here

What a verifier looks for

Every step of the derivation follows from the one before.
The fractions use sourced inputs, and a range of heights (10–20 km) and energies gives the spread.
The two predictions are compared and the difference explained.
The uncertainty is worked out from the data or runs (spread of repeats, instrument limits, fit errors or a range of inputs), not guessed, and it is shown on the result.
Is the physics right, and could someone rerun it from the repo?

You'll sign in first, then come straight back here.