Mr. Baldwin PHYSICS

5/23/2014Relativity

Aim: What does it mean to travel at light speed?

Do Now:

What happens when an object’s length (dimensions) as it approaches the speed of light?

Relativity TheoryRelativity TheoryThe days come and go like muffled veiled figures from a distant friendly party, but they say nothing, and if we do not use gifts they bring, they carry them as silently away.

Ralph Waldo Emerson

It’s only relative.It’s only relative.

• Einstein’s theory of relativity is actually fairly simple. It is based on two very simple ideas.– Principle of relativity– Principle of the constancy of lightspeed

To understand this theory one needs the mental flexibility to follow an argument wherever it might lead.

Constancy of Lightspeed: Strange but true.Constancy of Lightspeed: Strange but true.

• No matter how fast you move, a light beam always passes you at a speed c, relative to you.– Einstein concluded that every observer ought to observe

every light beam to move at speed c, regardless of the observer’s motion.

• The Principle of the Constancy of Lightspeed– The speed of light in empty space is the same for all

nonaccelerated observers, regardless of the motion of the light source or of the observer.

• The principle is valid only for nonaccelerated observers.

Newton’s Laws and Mass-Energy Equivalence

• Accepting Einstein’s postulates requires some major changes in how we think about space and time.

• For example, does Newton’s second law of motion still apply when objects are moving at large velocities?

F = ma = p / t• In order to maintain conservation of

momentum, Einstein redefined momentum asp = mv

• Mechanical energy also must take on a new meaning:KE = mc2 - mc2

• The quantity mc2 = E0 is called the rest energy.

• Accelerating an object increases its energy above its rest energy.

• Therefore its total energy would be E = mc2.

• The rest energy term E0 = mc2 indicates a startling equivalence between mass and energy.

• Einstein’s famous equation correctly predicts the amount of energy released in nuclear reactions.– Rest-mass energy is

transformed into kinetic energy in nuclear fission and fusion.

A Bunsen burner adds 1000 J of heat energy to a beaker of water. What is the

increase in the mass of the water?

a) 1000 kgb) 1110 kgc) 1.11 x 10-14

kgd) 1.11 x 10-18

kg

E mc 2

m Ec 2

1000 J

3108 m/s 2

1000 J9 1018 m2/s2

1.1110 14 kg

E 1000 J

c 3108 m/s

m ?

The Relativity of TimeThe Relativity of Time

• Time is the measure of events that goes through periodic or identical repetitions.

• A light clock: two parallel facing mirrors with a light beam placed between them.– Distance between them 150,000 km– Time from one mirror to the next and back is 1 sec

• The relativity of time is called time dilation– Time is relative to the observer– Objects that travel near the speed of light experiences an

increase in time as observed by an outside observer.

Time Travel: You Can’t Go Home AgainTime Travel: You Can’t Go Home Again

• The twin paradoxThe twin paradox: in the accelerated reference frame relativity theory does not apply. Twin that leaves and returns ages slower.

• A light year (l.y.) is the distance light travels in one year

• 1 l.y. = 9.45 x 1015 m

02

1

TTsc

Mr. Baldwin PHYSICS

2/26/09 RelativityAim: What happens to objects when they travel at light

speed?

Do Now: 1. What happens to the length of an object when it

travels near the speed of light?2. What happens to the mass of an object when it

travels at the speed of light?3. What happens to a clock on a spaceship

traveling at a fraction of light speed when viewed from Earth?

Time DilationTime Dilation

02

1

How will time change for a person travelling at half the speed of light (0.5c)?

TTsc

0 0 0

2 2 2

0 00

1 0.50.5 0.51 1

1.151 0.25 0.75

T T TTc c

c cT T T

The Relativity of SpaceThe Relativity of Space• Space: “what is measured by rulers”

– At high speeds space-time becomes distorted (non-relative) for observers

• Time & space are tangled up with each other!– Measurements parallel to the direction of motion

becomes contracted (shortened); while measurements perpendicular to the direction of motion remain unchanged.

• This distortion of space is called length contraction.

Length ContractionLength Contraction• Problem: Maia’s spaceship is 100

m long and 10 m high as measured by Maia. She passes Marshall at 60% of lightspeed (0.6C). As observed by Marshall, what are the dimensions of Maia’s space craft?

2

0 21 sL Lc

22 2

0

2

0.60 0.601 100 1 100 1

100 1 0.60 100 1 0.36 100 0.64 100 0.8 80

Hence, Mort's measurements would be 80 m x 10 m.

s c cL L Lc c c

m