1. Chapter 12 Relativity Today Introduction (some things to think about)
Principle of Relativity
Intro to Relativity
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2. A man runs at 5 mph in a train car as shown.
The train is moving at 20 mph.
What is the speed of the man relative to someone standing on the ground?
5 mph
20 mph
15 mph
25 mph
30 mph
Is it exactly 25 mph?
But why?
Intro to Relativity

3. A flashlight on a train is turned on. Light moves forward at speed “c”
The train is moving at 20 mph.
What is the speed of the light relative to someone standing on the ground? c
c+5 mph
c+20 mph
c-20 mph
How could this be?
Intro to Relativity

4. A dog sits a distance 2 from back of train car.
The train is moving at 5 meters / second.
Back of car passes woman.
Distance from woman to dog 2 seconds later is…
2 meters
5 meters
7 meters
12 meters
20 meters
Intro to Relativity

5. Greek character “beta”
If “c” is the speed of light in a vacuum,
the International Space Station travels at a speed of about…
1.3 c
.3 c
.0003 c c c
c = 3.0 x 108 meters/second
ISS Speed = 8000 meters/second
¯ = v/c = 2.7 x 10-5
Greek character “beta”
Intro to Relativity

6. The electrons in the accelerator beam used by Prof
The electrons in the accelerator beam used by Prof. Franklin move at a speed of about…
0.001 c
.03 c
.95 c
.99 c c
Intro to Relativity

7. The Principle of Relativity was first stated in about…
212 BC
1632
1905
1915
2009
Principle of Relativity (Galileo)
 Special Relativity Theory (Einstein)
 General Relativity Theory (Einstein)
Intro to Relativity

8. Galileo’s Principle of Relativity
As stated by Hartle in “GRAVITY, an introduction to Einstein’s General Relativity:
“Identical experiments carried out in different inertial frames give identical results.”
Galilean Relativity

9. Galileo’s Principle of Relativity
As stated by Einstein in his 5th paper (1905):
“The laws according to which the states of physical systems change are independent of which one of the two coordinate systems (assumed to be in uniform parallel-translational motion relative to each other) is used to describe these changes (the principle of relativity).”
Galilean Relativity

10. Galileo’s Principle of Relativity
As stated by Galileo in Dialogue Concerning the Two Chief World Systems (1632):
SALVATIUS: Shut yourself up with some friend in the main cabin below decks on some large ship, and have with you there some flies, butterflies, and other small flying animals. Have a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it. With the ship standing still, observe carefully how the little animals fly with equal speed to all sides of the cabin…
Galilean Relativity

11. ...have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that.
You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still.
Galilean Relativity

12. Relativity is a topic of physics concerned with the concept that some physical quantities can only be defined relative to a frame of reference :
Which quantities are only relative?
How to they transform from one reference frame to another? (Galilean/Newtonian Transformation, Lorentz Transformation)
What quantities do not depend on a reference frame?
(Invariants)
How do these observations help scientists determine Laws of Physics in a single fixed reference frame?
Galilean Relativity

13. Principle of Relativity (1632 Galileo)
Key Terminology
Principle of Relativity (1632 Galileo)
used by Newton and Einstein
Equivalence Principle (1907 Einstein)
Acceleration and Gravity are related for General Relativity
Galilean / Newtonian Relativity (1632 / 1687)
uses “ordinary” frame transforms
Special Relativity (1904 Lorentz / 1905 Einstein)
Uses Lorentz frame transforms to preserve speed of light
General Relativity (1915 Einstein)
Deals with acceleration, gravity, and the equivalence principle
Galilean Relativity

14. Transformations is tell us how to go from one reference frame to another :y x x` y` y x
Galilean Relativity

15. Transformations tell us how to go from one reference frame to another :x` y` y x x y
x`= x – Vframe t
y` = y
z` = z
t` = t
Galilean /Newtonian
Transformation of
Space-Time Coordinates
Galilean Relativity

16. “Events” are things that happen at a specific point in space and time Space Time Coordinates: (x,y,z,t)The coordinates of an event is NOT an invariant.
Galilean Relativity

17. Length of an object =? (use space-time coords)
Find (x1,y1,z1,t1) of one end
Find (x2,y2,z2,t1) of other end
For moving objects, make sure it’s same t
Compute
(x2,y2,z2,t1)
y2-y1
(x1,y1,z1,t1)
x2-x1
Galilean Relativity

18. Length of an object =? (use space-time coords)
(x2,y2,z2,t1) dy
(x1,y1,z1,t1) or dx
Notation means difference in x-coordinate, etc.
Galilean Relativity

19. Is length an invariant in Newtonian Space-Time?
Endpoints of ruler at two space coordinates, same time coordinate.
(x2,y2,z2,t1) dy
(x1,y1,z1,t1) dx
Yes, same answer in both frames
Galilean Relativity

20. Is the time between two events an invariant in Newtonian Space-Time?
Yes, same answer in both frames
Special Case:
Simultaneity: If two events happen at the same
time in one frame, they happen at the same
time in all frames.
What other quantities are invariants
in Newtonian Space-Time?
Galilean Relativity