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Einstein
● Relativity principle in the restricted sense
○ 2 systems of coordinated - in uniform motion in relation to each other, the
uniform roles of the universe are the same for both
E5: Recent events suggest classical mechanics is insufficient for describing natural phenomenon.
- Investigations by physicists into the nature of light
- Speed of light = 186,000 miles/second (in a vacuum)
- Light travels from Earth to the moon in 1-2 seconds/ from the Sun in 8 minutes
First, light appears to travel at the same speed no matter the observer…
● Person A is on a train moving at a uniform velocity. A is holding a light source.
● Person B is on an embankment.
○ A + B both see/measure the speed of the light as c
■ True scientific fact about the nature of the universe
● Mathematics due to J. Maxwell
○ Backed up (from a calculation standpoint) what physicists saw experimentally
○ Light (electromagnetic energy) travels at speed c as a wave does through water
Electromagnetic Spectrum:
Infrared R O Y G B I V ultraviolet
● Caused by light moving at a particular frequency as a wave
● Scientists tried to detect the medium through which light travels - “ether”
○ (failed to find this)
● Relativity (Einstein's) concludes that this is not a problem
E6:
● Person A is on a train moving at a uniform velocity, and throws an object at a speed of w
● Person B is on an embankment
○ A sees the object moving at speed w
○ B sees the object moving at speed w+v (according to classical mechanics)
E7: Light moves at c to all observers
*Double star systems
- Rotational motion with respect to each other
Special Relativity
1. The laws of nature are independent of the reference frame.
2. Light moves at c.
E8: Time and Physics
● 2 lightning bolts strike 2 different locations on a railroad track ‘at the same time.’ (points
A and B)
● Person stands at the midpoint (M) between A and B and looks at both points
○ If the lightning strikes both A and B at the same time, they are simultaneous
● Simultaneity is defined in terms of time
○ Assumed that clocks move at the same rate if they have identical construction
● Two clocks are NOT in sync with each other if one of them is in motion.
E9: Simultaneity
● Points A and B (and midpoint M) are on an embankment
● Train is moving at a uniform velocity (V)
○ Person is at midpoint (M)
● Person on embankment watching A and B - sees the light simultaneously
● Person on the train does not - they are in relative motion to one of the light sources (B),
and they see this one first.
*Relativity of what is simultaneous
E11:
● The mathematics that allows us to meaningfully represent these two tenants of special
relativity implies all these seemingly absurd results
● One system moving in a relative motion to the other system
● x 1 = x 1vt v y 1 = y
√ c
z1 = z
t=
t v2 x
c
√1 2
v2
c
● Mathematics that allow scientists to verify Einstein's claims about reality.
E12:
● Person A on a train moving at a uniform velocity views a clock passing 1 second, and
holds a rod that is 1 meter long
● Person B on the embankment views the objects on the passing train
● Person A and B both see a different length of the rod and count a different amount of
time that passes on the clock.
Ex.
● Suppose v = 12 c
v2
c2
=
√1
(1/2 c)
c2
v2
c2
=
2 = 1/4 c
c2 = ¼
√3/4 =
√3
2
.866
1-.866 = what the person on the embankment (B) measures the rod as
*Time as a reciprocal of this
2
1.15... = time measured on the clock by the person on the embankment (B)
√3