Download The Principle of Relativity Outline

Principle of Relativity
The Principle of Relativity
Relativity and Astrophysics
Lecture 04
Terry Herter
Outline

Continuation of worked problems from textbook


The Postulates of Relativity
Simultaneity of events
Lorentz Contraction
Invariance of Spacetime Interval

Reading



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Spacetime Physics: Chapter 3
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Principle of Relativity
Test Particles
Problem 2-10a
10 kg
A test particle is a tool to probe
spacetime with out affecting it

Its mass should be small enough
so that its presence does not affect
the motion of other nearby
particles
Example: 10 kg object may not be
a good test particle (depending
upon desired accuracy)


Acceleration due to gravity only
depends on mass!

Particles of the same mass but
different material, shapes, and
sizes in the same location all fall
towards Earth with the same
acceleration! (Galileo)
Allow us to define inertial reference
frame – otherwise aluminum would
behave differently than wood.
Important property of nature.



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10 cm
Force of gravity is:
F  ma 
GMm
r2
The acceleration is then:
6.673 10 11 m 3 /kg/s 2
10 kg
0.12 m 2
8
2
 6.673 10 m/sec
a
Assuming movement is small so that the
force doesn’t change appreciably, the
distance moved in 3 min (180 sec) is
1 2
at
2
1
m
180 sec2
 6.673 10 8
2
sec 2
 0.00108 m
s
 1.08 mm
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Problem: SP 2-13

Deflection of light by the Sun


A falling elevator is an inertial frame therefore a beam of light
shot across it will travel in a straight line. However, with
respect to the Earth the flash of light is falling because the
elevator is falling. Therefore light is deflected by a
gravitational field.
This effect is very small on the Earth but can be measure for
the Sun because gravity is much stronger than on Earth and
the travel time is larger.
Light from
a star
Earth
Sun
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Angular deflection, ,
greatly exaggerated
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2
Principle of Relativity
Problem: SP 2-13 (cont’d)
A) The “effective time of fall” for a photon is

te 

Dsun
1.4 109 m

 4.67 sec
c
3  108 m / sec
Time for photon to
cross Sun’s diameter
The velocity of the fall is the maximum acceleration acting
for this effective time.
vtran  asunte  275 m / sec 2  4.67 sec
Transverse velocity of
the photon
 1284 m / sec
B) Deflection angle is the ratio of the transverse
velocity to the forward speed.

  vtrans c  4.3 10 6 rad
Deflection of photon
by the Sun –
Off from GR result by
factor of 2
 0.88 arcseconds
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Problem: SP2-13 Calculus Proof
b
The photon is accelerated by gravity
db
v
dvT  aT dt  aT
where aT 
r
GM
cos 
r2

ro
dvT
Sun
Deflection is very small so we can assume
that light is very close to original path, so

vT   aT

thus
vT 

db
GM cos 

db
v  v r 2
GM
v
with
r  ro sec 
b  ro tan 
& db  ro sec 2  d
 /2

cos 
GM 2
ro sec 2  d 
2
2

r
sec
v ro
/2 o


now
But on the previous slide we had
v
2GM 1
 T 
v
ro c 2

vT asunte GM 2ro 1 2GM 1

 2

v
c
ro c c
ro c 2
Checks!
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3
Principle of Relativity
Relativity




There is no absolute motion.
Everything is relative.
Suppose two people are alone in space and traveling
towards one another:
 Which one is moving?
 They can’t tell!
Example –



A train is moving at 65 mph relative to the tracks.
If the people inside the train cannot see out and the track is
very smooth, they can not tell they are moving!
Example 2 –

The earth moves around the sun at 30 km/sec. Can you
tell?
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Aside on Albert Einstein

Perhaps the greatest physicist of all time.

1905: Published papers on




Special Relativity
Photoelectric effect (photons carry energy
proportional to their frequency)
Brownian motion (random movement of particles
in a fluid)

General Relativity – theory of gravity

Critical opalescence

Atomic transition probabilities

Statistical physics




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See Wikipedia entry
1879 - 1955
Including relativistic cosmology
Explains why the sky is blue
Includes “stimulated” emission which led to lasers
Bose-Einstein statistics - bosons
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4
Principle of Relativity
Special Theory of Relativity

Postulates:

Albert Einstein (1905)
1879 - 1955
1. The speed of light is the same to all
observers, irrespective of their motion.
2. The laws of physics are the same
everywhere no matter what the speed of the
observer.
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The speed of light is constant.

Person in boat moving towards shore shines
a beam of light at a person on the shore.
Flashlight
c
vboat

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The velocity of light as seen by the person in
the boat and on the shore is the same, c.
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Principle of Relativity
Same/Different in Different Frames

Not necessarily the same –

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Same –

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Space separations, time separations, velocities, accelerations,
forces, and field (such as electric and magnetic fields)
Physical laws and physical constants in these laws
Examples:

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
Speed of light
Speed of a particle
Charge on an electron
Kinetic energy of proton
Time between two events
Newton’s first law
same
not necessarily the same
same
not necessarily the same
not necessarily the same
same
Law of Inertia: A remains at rest or
at constant velocity unless acted on
by an external, unbalanced force.
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Simultaneity

The simultaneity of events is in the eye of the
beholder.
v

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A light bulb in the center of a high speed train
flashes. An observer on the train sees the light reach
the front and back simultaneously
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Principle of Relativity
From outside the train




Simultaneity is in the eye
of the beholder.

Simultaneity is relative!
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To the outside observer
the light reaches the
back first.
The back moves towards
the light and the front
away.
Not simultaneous!
Flash goes off
v
Flash reaches back wall first
Principle of Relativity
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