a harvard pole vaulter carries a pole that is just as long as a barn. he encounters a nj farmer....
Post on 21-Dec-2015
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A Harvard pole vaulter carries a pole that is just as long as a barn. He encounters a NJ farmer.
Overhead view:
Is this Nonsense? -- Space & Time are Relative
The farmer gathers 100 witnessesand this is what they see:
The pole vaulter then bursts through the second door. The witnesses ALL agree: THE FARMER WON
?According to the Pole Vaulter,
the Farmer cheats!!He shuts the front door before
the back one!
But, alas, not one witness agrees
A New Geometry for Space and Time
Space, Time, Simultaneity, Energy, Momentumare all relative
Yet, some things, like the speed of light,are absolutes (“invariants”)
ct
x
SPACE-TIME DIAGRAMWELCOME TO YOUR 4-DIMENSIONAL WORLD
Bob’sviewpoint
ct
x
SPACE-TIME DIAGRAM
an event
a worldline
light
y
x
SPACE-SPACE DIAGRAM
a point
y
x
SPACE-SPACE DIAGRAM
y’
x’
a point
xx '
yy '2222 '' yxyxbut
ct
SPACE-TIME DIAGRAM
light
x
Bob’sviewpoint
ct
SPACE-TIME DIAGRAM
lightct’
x
x’Alice’sviewpoint
ct
SPACE-TIME DIAGRAM
lightct’
x
x’
ct
SPACE-TIME DIAGRAM
ct’
x
x’an event
ct
SPACE-TIME DIAGRAM
ct’
x
x’an event
xx '
ctct '
2222 ')'()( xctxctbut
ct
TIME & SIMULTANEITY ARE RELATIVE
x
Farmer’sviewpoint
ct ct’
x
x’
TIME & SIMULTANEITY ARE RELATIVE
first
second
Pole vaulter’sviewpoint
Alice
Bobpeople
“Twin Paradox” Revisited
vAlice
Bob
v
The End
?
t
x
AT LAST: THE TWIN PARADOX
Alicetakesoff
Alicereturns
t
x
SPACE-TIME DIAGRAM
Alicetakesoff
Alicereturns
Bob’s“worldline”
t
x
SPACE-TIME DIAGRAM
Alicetakesoff
Alicereturns
Alice’s“worldline”
Kink: only Alicefeels acceleration
y
x
SPACE-SPACE DIAGRAM
Shortest distancebetween two points is a straight line
t
x
SPACE-TIME DIAGRAM
Alicetakesoff
Alicereturns
Alice’s“worldline”
Longest timebetween two events is a straight line
E = mc2
E = mrestc2