http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 1
Galilean relativity
• Homework assignment #1 is now posted on the course website. Be sure you put your name and course on each page. Staple the pages together, before submitting.
• First problem solving session will be Tuesday 1-3pm in G140 in Duane Physics.
• Homework is due next Fri. Sept. 6 at 1pm in wood box inside phys. helproom (G2B90).
• Web site www.colorado.edu/physics/phys2170/ contains lots of info, e.g. the course calendar has reading assignments and lecture notes.
Announcements:
Today we will cover Galilean relativity and the special relativity postulates.
Galileo Galilei (1564—1642):
Reading for Friday TZ&D 1.5-1.8
http://www.colorado.edu/physics/phys2170/
Announcements cont. • Physics Colloquium today is by Debbie Jin in G1B20
in Physics – cookies at 3:45pm in G031 title is “Ultracold Polar Molecules”.
• If you did research last summer, then you might consider giving a presentation at the Four Corners Section of the American Physical Society Meeting to be held on the University of Denver campus on Friday Oct. 18 and Sat. Oct. 19. Good opportunity, it’s close, and it builds your resume when you apply for REU positions for next summer. – can do poster or give a 10 minute talk.
• http://www.aps4CS2013.info/
Physics 2170 – Fall 2013 2
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 3
Compare two reference frames (in one-dimension)
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Frame S has origin here.
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Frame S′ has origin here, at x = 3 m according to reference frame S. The frame is shifted down so you can read both of them.
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 4
Compare two reference frames (in one-dimension)
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Observer in S measures ball at x = 2m.
Observer in S′ measures ball at x′ = −1 m.
Two different observers measure two different results for the location of the ball
And they are both correct!
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 5
Inertial reference frames
Imagine a train car moving with constant velocity with respect to the ground. The train runs smoothly, so that you can’t tell it’s moving by feeling the bumps on the track.
V
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 6
Inertial reference frames
Now, you’re playing pool on the train. The balls roll in straight lines on the table (assuming you put no English on them). In other words, the usual Newtonian law of inertia still holds. The frame as a whole is not accelerating.
V
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 7
As I’m lining up my shot, the train slows and approaches the station. I have not touched the cue ball. What does it do?
A. Rolls to the front of the train B. Rolls to the back of the train C. Remains motionless D. Grows legs and runs around the pool table
V
Clicker question 1 Set frequency to AD
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 8
As I’m lining up my shot, the train slows and approaches the station. I have not touched the cue ball. What does it do?
A. Rolls to the front of the train B. Rolls to the back of the train C. Remains motionless D. Grows legs and runs around the pool table
V
This frame is no longer inertial. It is a non-inertial frame.
Clicker question 1 Set frequency to AD
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 9
Comparing inertial frames
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v
Here are two inertial reference frames, moving with respect to one another.
According to S, S′ is moving to the right, with v = 1 m/s.
S
S’
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 10
Comparing inertial frames
Here are two inertial reference frames, moving with respect to one another.
According to S′, S is moving to the left, with v = −1 m/s.
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v
Both S′ and S are correct. It’s a question of reference frames
S
S’
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 11
Q. What is an inertial reference frame? A. Objects in inertial frames obey the law of inertia A. Inertial frames travel at constant velocity (can be 0)
Q. Which of the following is not an inertial reference frame? A. A car traveling at 100 mph down a straight road B. A car traveling at 20 mph around a corner C. A car in the process of crashing into a concrete barricade
E. None of the above
Equivalent statements
Clicker question 2 Set frequency to AD
D. More than one of the above
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 12
Q. What is an inertial reference frame? A. Objects in inertial frames obey the law of inertia A. Inertial frames travel at constant velocity (can be 0)
Q. Which of the following is not an inertial reference frame? A. A car traveling at 100 mph down a straight road B. A car traveling at 20 mph around a corner C. A car in the process of crashing into a concrete barricade D. More than one of the above E. None of the above
In A objects at rest stay at rest and reference frame velocity is constant
Equivalent statements
In B and C objects at rest will move because reference frame velocity is not constant: centripetal acceleration in B and linear acceleration in C.
Clicker question 2 Set frequency to AD
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 13
Comparing inertial frames
Think about two frames that coincide at t=0.
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v
Answer: Two local observers are there to measure the facts.
How do we know??
S’
S
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 14
Comparing inertial frames
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v
At time t = 0, the two frames coincide. A ball is at rest in frame S. Its position is • x = 2 m in S • x′ = 2 m in S′
How do we know?? Two more local observers: • One in S • One in S′
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 15
Comparing inertial frames
Frame S′ is moving to the right (relative to S) at v = 1 m/s. At time t = 3 sec, the position of the ball is
• x = 2 m in S • x′ = −1 m in S’
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v
How do we know?? YUP!
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 16
Definition of event • Where something is depends on when you
check on it (and on the movement of your own reference frame).
• Definition: an event is a measurement of where something is and when it is there.
Events are measurements in 4D space-time made by local observers on the scene.
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 17
Comparing inertial frames
Q. At time 0, the ball was at x = x′. At time t later, the ball is still at x in S. Where is it in S′?
A) x′ = x B) x′ = x + vt C) x′ = x − vt
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v
Clicker question 3 Set frequency to AD
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 18
Comparing inertial frames
Q. At time 0, the ball was at x = x′. At time t later, the ball is still at x in S. Where is it in S′?
A) x′ = x B) x′ = x + vt C) x′ = x − vt
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v
Clicker question 3 Set frequency to AD
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 19
Galilean transformations If S′ is moving with speed v in the positive x direction relative to S, then an object’s coordinates in S′ are
Note: in Galilean relativity, time is measured the same in both reference frames. And derivatives with respect to time in both reference frames are the same.
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 20
More Galilean relativity
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v
Same thing, but now the ball is moving in S, too, with a velocity of –2 m/s.
Q. Is the ball faster or slower, as measured in Frame S′?
A) faster B) slower C) same speed
Clicker question 4 Set frequency to DA
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 21
More Galilean relativity
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v
Same thing, but now the ball is moving in S, too, with a velocity of –2 m/s.
Q. Is the ball faster or slower, as measured in Frame S′?
A) faster B) slower C) same speed
Clicker question 4 Set frequency to DA
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 22
Galilean velocity transformation If an object has velocity u in frame S, then its position, x, changes with time, t. And if frame S′ is moving with velocity v relative to frame S, then the position of object in S′ is:
Velocity of object in S′ is therefore:
This is the classical velocity-addition formula which is simply vector addition
Two observers in different reference frames can give a different description of the same physical fact, in this case the velocity and position of the ball. And they’re both right!
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 23
From Newton’s 2nd law ( ) this means the object accelerates in frame S.
Dynamics
Now let’s apply a force to the object in frame S.
€
ʹ′ a =d ʹ′ u d ʹ′ t
=ddt(u − v) =
dudt
= a
We still have an object moving with velocity u in inertial frame S and an inertial frame S′ which moves at a constant velocity v with respect to frame S.
What is the acceleration in frame S′?
So, although the positions and velocities can be different in different inertial frames, the acceleration and forces are the same
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 24
Galilean relativity
In Galilean relativity, the laws of mechanics (F=ma and everything else in Physics 1110) are the same in any inertial frame of reference.
What about the physics of electromagnetism? Does E&M depend on which inertial frame you are in?
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 25
Q. A magnetic field points into the board. A wire loop moves into the field with velocity v. An electron in the wire feels a Lorentz force . What happens in the wire? A. nothing B. a current flows clockwise C. a current flows counterclockwise
v
Clicker question 5 Set frequency to DA
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 26
Q. A magnetic field points into the board. A wire loop moves into the field with velocity v. An electron in the wire feels a Lorentz force . What happens in the wire? A. nothing B. a current flows clockwise C. a current flows counterclockwise
v
Clicker question 5 Set frequency to DA
Remember the right hand rule and that current is the direction a positive charge would move
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 27
Q. Now the loop is stationary and the magnetic field moves into the loop. What happens in the wire? A. nothing B. a current flows clockwise C. a current flows counterclockwise
v
Clicker question 6 Set frequency to DA
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 28
Q. Now the loop is stationary and the magnetic field moves into the loop. What happens in the wire? A. nothing B. a current flows clockwise C. a current flows counterclockwise
v
Clicker question 6 Set frequency to DA
Faraday’s law states:
The magnetic flux through the loop is changing which induces an electric field and thereby drives a current.
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 29
OK, so which is correct? • In the reference frame of the magnetic field, an
observer thinks the electron feels a magnetic force. • In the reference frame of the electron, an observer
thinks the electron feels an (induced) electric force. • And they’re both right!
Einstein’s first postulate for special relativity is:
Postulate 1: All the laws of physics are the same in all inertial reference frames.
Not just mechanics but all physics laws
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 30
From Maxwell’s equations, light is an electromagnetic wave with speed:
Conventional wisdom: Waves must have a medium to travel in – sound in air, tsunami in water, density wave in galaxy, etc.
Therefore it was believed light traveled in stationary ether where the speed was 299792458 m/s.
If the ether exists, it is an incompressible, invisible, and non-viscous medium which permeates the universe (like The Force).
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 31
Boat travels back and forth across river with width
How long does it take to complete each trip?
Up & down river:
Across river:
Boat travels at speed on a river with current at velocity Boat travels up and down a river a distance of
You get different results depending on the route taken!
Basic Idea of Measuring Ether
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 32
Michelson-Morley experiment in 1887 to see ether effect
Measure speed of light in 2 perpendicular directions
Floated in mercury so could rotate to see effect. Also took data at different times of year.
Earth goes around sun at 30 km/s – must be going through ether
Should see ether flow as small as 1 km/s and saw nothing! Read Chap. 1.5 for details
http://www.colorado.edu/physics/phys2170/ Physics 2170 – Fall 2013 33
Present View: There is no ether
Electromagnetic waves are special. A time-changing electric field induces a magnetic field, and vice-versa. A medium (“ether”) is not necessary.