Winter 2018-2019

Department of Physics

Office: Disque 811

Phone: (215)895-2710

Email: vogeley@drexel.edu

Office hours: Wednesday 2:00-3:30pm

Teaching Assistant: Joseph Fabritius

Department of Physics

Office: Disque 808

Email: joseph.m.fabritius@drexel.edu

Phone: (215)895-2786

Office hours: Wednesday 3:30-5:00pm (in Disque 808)

Announcements

Course Meetings

Syllabus

Course Description and Philosophy

Grading

Course rules of conduct

Reading Assignments

Lecture Notes

Homework Assignments

Homework Hints

Homework Solutions

Exams

Midterm Solutions

Course Schedule

Welcome to the home page for Physics 233, Introduction to Relativity. Watch this space for important announcements and useful hints.

Send me email to ask questions about homework assignments and the course readings so that I can give you timely feedback and send any relevant homework hints to everyone else in the class. To ensure that you receive email sent to the class, you must read email sent to your official Drexel email address.

All lecture notes and homework solutions will be distributed as PDF files from this web page. No paper copies will be handed out.

If you will be unable to attend class, please notify me ahead of time or contact me as soon as possible.

**Office hours:** Wednesday 2:00-3:30 (Prof. Vogeley), 3:30-5:00
(TA Joseph Fabritius)

Relativity is sometimes thought of as "far out" science applicable only to extreme astrophysical circumstances. In fact, understanding of both Special and General Relativity is necessary for operation of several systems that we have come to rely on. Operation of satellites in orbit around the Earth requires that we compute the effects of both Special and General relativity. Systems like GPS would utterly fail without doing so (which means that most of our advanced weapons guidance systems would fail). I'll show you a "Handbook on Relativistic Time Transfer" that proves this point.

Topics that will be covered in this course include

- Spacetime metrics (unification of space and time)
- Physics in inertial frames of reference
- Transforming between inertial frames (Lorentz transformation)
- Length contraction and time dilation
- Relativity of simultaneity
- Time travel
- Causality
- Unification of momentum and energy
- Transformation of mass and energy
- Curved space: General Relativity

The most important goal of this course is that you further develop your ability to think clearly and quantitatively about the physical world. It is unlikely that your daily life and work will require you to instantly recall the equations that we will use. However, well-developed physical insight will serve you well in whatever endeavor you choose. Einstein was fond of the ``gedankenexperiment'' - the thought experiment - as a means of gaining insight on a problem. I hope that this course will likewise stretch your imagination.

Homework: 30%

Midterm Exam: 25%

Final Exam: 35%

Class Participation: 10%

The Class Participation component will be partially based on attendance. Extra credit will be given to new theories of spacetime and gravity that result in published papers in the Physical Review.

Electronic distractions: Silence your cell phone or leave it home. Only phone calls (to me) from the Nobel Prize committee will be tolerated. Laptop computers may be used only for taking notes. Web surfing, texting, reading/sending email is prohibited during class. I will ask you to leave the class if you violate this rule.

Plagiarism: Use your own very large brain (you're a physicist!) and
don't even think about cheating. See homework rules below. The usual University rules apply. By
stepping into the classroom, you agree to abide by Drexel's policy on
Academic Integrity

TEXTBOOK NEWS: The book is out of print. But the entire book may be
downloaded as PDF from here:

Spacetime
Physics Download

Please read the assignments *before* class and prepare to ask questions.

See the Course Schedule below for the weekly reading assignments.

Good biographies about Einstein:

*Subtle is the Lord* by Abraham Pais
(best for the science)
and
*Einstein: His Life and Universe* by Walter Isaacson (most recent
comprehensive biography).

Hagerty Library will have *Spacetime Physics* and the biographies
on reserve. You must use the 2nd edition to get the sections and problems right (I don't have the 1st, so please don't ask me how they correspond).

Solutions to the homework will be posted on the web page on the due date; that is why late homework will not be accepted. Please strive to present your answers in a neat, workmanlike fashion; the clarity of your solutions will count toward your grade.

Science is a collaborative enterprise and you are encouraged to
discuss the homework problems. Brainstorming is fun! (Even Einstein
received help.) * But you and you alone are responsible for the work
that you turn in.* In other words, you may talk about the problems
with your classmates, but you must write out your own solutions.
Serious breaches of this policy will result in homework scores being
dividing by the number of ``participants.'' Show your work. Answers
without justification will receive no credit.

**Homework 1:**

Chapter 1: problems 4a,b,c, 5, 8, 11, 12

Due in class Thursday, January 17.

**Homework 2:**

Chapter 2: problems 4, 9, 10, 11, 13

Due in class Thursday, January 24.

**Homework 3:**

Chapter 3: problems 2, 4 (explain your answer to each!), 12 (a, b only), 14 (a, b only), 17

Due in class Thursday, January 31.

**Homework 4:**

Chapter L: 6 (part a only), 7, 8

Due in class Thursday, February 7

**Homework 5:**
Chapter 4: 4-1 (Just one problem! Explanations, please. The answers are in the book.)

Due in class Thursday, February 21

**Homework 6:**
Chapter 5: 5-2, 5-4, 5-6

Due in class Thursday, February 28

**Homework 7:**
Chapter 6: 6-1, 6-3, 6-4

Due in class Thursday, March 7.

**Homework 8:**

Chapter 7: 7-2, 7-8 (ignore the bit about "mass handles")

Chapter 8: 8-8

Extra credit 8-40

Due in class Thursday, March 14.

Hints will be posted here as I think of useful info or in response to your questions.

**Homework hints 1:**

In problem 4, note that the distances are
given in light-seconds, so it's straightforward to measure both
distance and time in seconds.

Do Problem 5 using units of years and light-years. Think carefully, what is the speed of light in units of light-years/year?

In Problem 8, write down an equation that relates the time for a signal to travel across the computer to its size and the speed of signal transmission (what's the fastest speed that can be?). Note that completing a calculation requires a roundtrip to/from the processor.

In problem 11-b the point is to
*ignore* Special Relativity for the moment and consider what happens
if the time interval for an observer moving with the muons were the
same as an observer in the Earth frame. In the rest of the problem,
"rocket frame" means moving with the muons.

12-a likewise asks that you momentarily suspend your knowledge of Special Relativity.

In 12-b, try to use the equivalance of the spacetime intervals to get
an equation for the time dilation effect. Write down the full equation
for the equivalence of the square of the spacetime intervals in the
moving particle and lab frames. Substitute in or set to zero those
values that you know. Simplify that equation as much as possible. The
distance actually travelled in the lab frame is simply the velocity of
the particles times the time interval in the lab frame.

**Homework hints 2:**

Problem 4: Carefully read Section 7 of Lecture Notes 2 ("Rods and
Clocks") to understand how one should synchronize clocks (there are
other ways, but they must be consistent with this method).

Problem 10: Remember that F=ma, thus a=F/m. And recall that the distance travelled under constant acceleration a is x=(1/2)at**2. Assume a mass of 10 grams for the ball bearing in part (b).

**Homework hints 3:**

Problem 12 (part b): Note that the plane must overcome a crosswind, so
its velocity must have a component that is perpendicular to the
intended direction of travel. Then use the Pythagorean Theorem.

Problem 14: Think about what is actually moving. Is any physical object or information being transmitted faster than the speed of light? In part (a), use trigonometry to determine how far the intersection point moves in x as the rod moves in x, then write the equation for the x velocity of that intersection as a function of the y velocity of the rod and the angle of intersection. Note that the velocity had better be zero if the rod is vertical (theta=90 deg).

Problem 17: Note that in parts a, b, and c we pretend that the observer has no depth perception.

**Homework hints 4:**

Chapter L, ALL PROBLEMS: Assume that the rocket moves in the x direction. Remember that distances transverse to the direction
of motion do not change. And note carefully that time dilation always
occurs, regardless of which direction something is moving.

The Final will be 2 hours long, on Tuesday, March 19, 1:00-3:00pm in Disque 103. The Final will include material from the entire course, but with emphasis on the second half of the course. Please note that material from Week 10 is not covered in any homework, but will be covered in the final.

The exams will be open book and open note.
But you'll find that
an open *mind* will be most helpful.
Calculators may be used for simple arithmetic operations.
* The use of calculators for execution of ``memorized'' formulae is
specifically not allowed.* Ask me if you are uncertain about this policy.

Week |
Class Dates |
Reading |
Homework |
Exams |

1 | January 8, 10 | ch. 1 | HW1 | |

2 | January 15, 17 | ch. 2 | HW2 | |

3 | January 22, 24 | ch. 3 | HW3 | |

4 | January 29, 31 | ch. LT | HW4 | |

5 | February 5, 7 | ch. 4 | ||

6 | February 12, 14 | ch. 5 | HW5 | Midterm (Feb. 12) |

7 | February 19, 21 | ch. 6 | HW6 | |

8 | February 26, 28 | ch. 7 | HW7 | |

9 | March 5, 7 | ch. 8 | HW8 | |

10 | March 12, 14 | ch. 9 | ||

11 | No Class | Final Exam, TBA |

Last update: March 14, 2019