relativity by albert einstein
TRANSCRIPT
Relativityby
Albert EinsteinPrepared by:
Sir Antonio Salvador Jr.
The Relativity Principle
Galileo Galilei 1564 - 1642
The Ptolemaic Model
The Copernican Model
Problem: If the earth were moving wouldn’t we feel it?
A coordinate system moving at a constant velocity is called an inertial
reference frame. The Galilean Relativity Principle: All physical laws are the same in all inertial reference frames.
Other Examples:
As long as you move at constant velocity you are in an inertial reference frame.
Galilean Relativity
– “Relativity” refers in general to the way physical measurements made in a given inertial frame are related to measurements in another frame.
– An inertial observer is one whose rest frame is inertial.
– A quantity is invariant if all inertial observers obtain the same value.
– Under Galilean relativity, measurements are transformed simply by adding or subtracting the velocity difference between frames:
– vball(measured on ground)=vtrain (measured on ground)+vball(measured
on train) 12 m/s = 10m/s + 2 m/s– Vball(measured on train)=vground(measured on train)+ vball(measured on
ground) 2 m/s = 10m/s + 12 m/s10 m/s
2 m/s
12 m/s
ElectromagnetismA wave solution traveling at the speed of light
c = 3.00 x 108 m/s
Maxwell: Light is an EM wave!
Problem: The equations don’t tell what light is traveling with respect to
James Clerk Maxwell 1831 - 1879
Einstein’s Approach to Physics
Albert Einstein 1879 - 1955
1. (Thought) Experiments
E.g., if we could travel next to a light wave, what would we see?
2. “The Einstein Principle”:
If two phenomena are indistinguishable by experiments then they are the same thing.
Einstein’s Approach to Physics2. “The Einstein Principle”:
If two phenomena are indistinguishable by experiments then they are the same thing.
A magnet moving A coil moving towards a magnet
Both produce the same currentImplies that they are the same phenomenon
towards a coil
Albert Einstein 1879 - 1955
current
current
Einstein’s Approach to Physics1. Gedanken (Thought) Experiments
E.g., if we could travel next to a light wave, what would we see?
c
c
We would see an EM wave frozen in space next to usProblem: EM equations don’t predict stationary waves
Albert Einstein 1879 - 1955
ElectromagnetismAnother Problem: Every experiment measured the speed of light to be c regardless of motion
The observer on the ground should measure the speed of this wave as c + 15 m/s
Both observers actually measure the speed of this wave as c!
Special Relativity Postulates
• The Relativity Postulate: The laws of physics are the same in every inertial reference frame.
• The Speed of Light Postulate: The speed of light in vacuum, measured in any inertial reference frame, always has the same value of c.
Einstein: Start with 2 assumptions & deduce all else
This is a literal interpretation of the EM equations
Special Relativity PostulatesLooking through Einstein’s eyes:
Both observers (by the postulates) should measure the speed of this wave as c
Consequences:
• Time behaves very differently than expected
• Space behaves very differently than expected
Einstein’s Special Relativity
1,000,000 ms-1
0 ms-1
300,000,000 ms-1
Both spacemen measure the speed of the approaching ray of light. How fast do they measure the speed of light to be?
Einstein’s Special Relativity
• Stationary man– 300,000,000 ms-1
• Man travelling at 1,000,000 ms-1
– 301,000,000 ms-1?– Wrong!
• The Speed of Light is the same for all observers
Three effects• 3 strange effects of special
relativity
– Lorentz Transformations
– Relativistic Doppler Effect
– Headlight Effect
Lorentz Transformations
■ Light from the top of the bar has further to travel.
■ It therefore takes longer to reach the eye.
■ So, the bar appears bent.
■ Weird!
Doppler Effect• The pitch of the siren:
– Rises as the ambulance approaches– Falls once the ambulance has passed.
• The same applies to light!– Approaching objects appear blue (Blue-
shift)– Receding objects appear red (Red-shift)
Headlight effect
• Beam becomes focused.• Same amount of light concentrated in a
smaller area• Torch appears brighter!
V
Warp• Program used to visualise the three
effects
Demo . . .
Fun stuff
• Website:http://www.adamauton.com/warp/
Eiffel Tower Stonehenge
Time DilationOne consequence: Time Changes
Equipment needed: a light clock and a fast space ship.
Time DilationIn Bob’s reference frame the time between A & B is Δt0
Sallyon earth
Bob
Beginning Event A
Ending Event B
cDt 2
0
D
Δt0
Bob
Time DilationIn Sally’s reference frame the time between A & B is Δt
Bob
A BSallyon earth
22 2 22 2 2
2v ts D L D
Length of path for the light ray:
cst 2
and
Δt
Time Dilation2
2 2 22 2 22
v ts D L D
Length of path for the light ray:
cst 2
and
Solve for Δt:22 /1
/2
cv
cDt
cDt /20
Time measured by Bob
220
/1 cv
tt
Time Dilation
220
/1 cv
tt
Δt0 = the time between A & B measured by Bob
Δt = the time between A & B measured by Sally
v = the speed of one observer relative to the other
Time Dilation = Moving clocks slow down
If Δt0 = 1s, v = .999 c then: s 500999.1s 1
2
t
Time Dilation
• Bob’s watch always displays his proper time
• Sally’s watch always displays her proper time
How do we define time?
The flow of time each observer experiences is measured by their watch – we call this the proper time
• If they are moving relative to each other they will not agree
Time DilationA Real Life Example: Lifetime of muons
Muon’s rest lifetime = 2.2x10-6 seconds
Many muons in the upper atmosphere (or in the laboratory) travel at high speed.
If v = 0.999 c. What will be its average lifetime as seen by an observer at rest?
s 101.1999.1
s 102.2/1
3
2
6
220
cv
tt
Length ContractionBob’s reference frame:
The distance measured by the spacecraft is shorterSally’s reference frame:
Sally
Bob
0
0
LLvt t
The relative speed v is the same for both observers:
220
/1 cv
tt
220 /1 cvLL
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