Intro to Relativity

Chapter 12 Relativity

TodayIntroduction

(some things to think about)

Principle of Relativity

Intro to Relativity

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?

A) 5 mphB) 20 mphC) 15 mphD) 25 mphE) 30 mph

But why?

Is it exactly 25 mph?

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?

A) cB) c+5 mphC) c+20 mphD) c-20 mph

Intro to Relativity

How could this be?

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…A) 2 metersB) 5 metersC) 7 metersD) 12 metersE) 20 meters Intro to Relativity m

ss

mmx

Vtxx

12

252

Intro to Relativity

If “c” is the speed of light in a vacuum,the International Space Station travels at a speed of about…

A) 1.3 cB) .3 cC) .0003 cD) .00003 cE) .00000000003c

c = 3.0 x 108 meters/secondISS Speed = 8000 meters/second¯ = v/c = 2.7 x 10-5Greek character

“beta”

Intro to Relativity

The electrons in the accelerator beam used by Prof. Franklin move at a speed of about…

A) 0.001 cB) .03 cC) .95 cD) .99 cE) .999999995 c

Intro to Relativity

The Principle of Relativity was first stated in about…

A) 212 BCB) 1632C) 1905D) 1915E) 2009

Principle of Relativity (Galileo) Special Relativity Theory (Einstein) General Relativity Theory (Einstein)

Galilean Relativity

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

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

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

...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

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

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

Transformations is tell us how to go from one reference frame to another :

x

x`

y`y

x

y

Galilean Relativity

Transformations tell us how to go from one reference frame to another :

x

x`

y`y

x`= x – Vframe t

y` = yz` = zt` = t

Galilean /NewtonianTransformation ofSpace-Time Coordinates

x

y

Galilean Relativity

“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

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-x1

y2-y1(x1,y1,z1,t1)

(x2,y2,z2,t1)

2 2

2 1 2 1L x x y y

Galilean Relativity

Length of an object =? (use space-time coords)

dx

dy(x1,y1,z1,t1)

(x2,y2,z2,t1)

2 2

2 1 2 1L x x y y

2 2 2 2dL dx dy dz or

Notation means difference in x-coordinate, etc.

L0=p

((x2 ¡ Vt1) ¡ (x2 ¡ Vt1))2 + (y2 ¡ y1)2

Galilean Relativity

Is length an invariant in Newtonian Space-Time?

dx

dy(x1,y1,z1,t1)

(x2,y2,z2,t1)

2 2

2 1 2 1L x x y y

L L Yes, same answer in both frames

2 2

2 1 2 1L x x y y

Endpoints of ruler at two space coordinates, same time coordinate.

Galilean Relativity

Is the time between two events an invariant in Newtonian Space-Time?

2 1 2 1t t t t Yes, same answer in both frames

What other quantities are invariants in Newtonian Space-Time?

Special Case:Simultaneity: If two events happen at the sametime in one frame, they happen at the sametime in all frames.