the false “twin paradox”steinh/ph115/slides_12_12_19.pdf · einstein: gravity distorts ......
TRANSCRIPT
v
Alice
Bobpeople
The false “Twin Paradox”
vAlice
people
Puzzler : g=10
Suppose Alice only shows a 3 minute videotape.
According to Bob, this take 30 minutes –Precisely the same time it takes for him to read his
magazine!So, according him, he can start and stop reading
his magazine simultaneous with the start and stop of the tape.
Yet Alice, who sees the tape last 3 minutes, measures that Bob takes 300 minutes to read his magazine.
How can that be? If they start and end simultaneously according to Bob, doesn’t it have to be simultaneous according to Alice??
ct
SPACE-TIME DIAGRAM
lightct’
x
x’
Bob reads for 30 minutes
Alice views TV for 3 minutes
Notice: Alice’sworldline is straight
& so is Bob’s & they do not endat the same place-- not quite thetwin paradox
So who is right aboutsimultaneity –Alice or Bob?
ct
x
AT LAST: THE REAL TWIN PARADOX
Alicetakesoff
Alicereturns
Bob’s frame
ct
x
AT LAST: THE REAL TWIN PARADOX
Alicetakesoff
Alicereturns
Bob’s frame
Bob’s“worldline”
Alice’s“worldline”
Kink: only Alicehas kinky worldline and
feels acceleration!!
y
x
SPACE-SPACE DIAGRAM
Shortest distancebetween two
points is a straight line
You OVERestimatethe distance
if you use theCrooked path
t
x
SPACE-TIME DIAGRAM
Alicetakesoff
Alicereturns
Longest timebetween two
events is a straight line
You UNDERestimatethe time
if you use thecrooked path
Einstein’s next problem:
So far relativity successfully revises:
Newton’s Laws of Motion
… and fits Maxwell’s Theory of Electromagnetism & Light
... but FAILS to work withNewton’s Universal Law of Gravity
Newton’s Gravity Einstein’s Relativity
Force depends on mass Mass is just a form of energy
Newton’s Gravity Einstein’s Relativity
Force depends on mass Mass is just a form of energy
Light does not gravitate Why not?
Force depends on separation Distance is relative
Newton’s Gravity Einstein’s Relativity
Force depends on mass Mass is just a form of energy
Light does not gravitate Why not?
Force depends on separation Distance is relative
Force on mass Bdepends on instantaneous
position of mass A
Instantaneous/simultaneousare relative
Inverse square law Must be modified
Galileo
1 kg 10 kg
a!
All objects fall with the same acceleration
Newton:Masses
acceleratedue to a force
that just happensto accelerate
all masses the same way !
Einstein:Gravity distorts
space ...and massesmove along
same “straight”path in curved
space!
Matter gets its marching orders locally, from the local geometry
Newton:Masses
acceleratedue to a force
that just happensto accelerate
all masses the same way !
Space is not Absolute!Mass distorts the space around it
Other masses move in straight linesin a curved space (geodesics)
General Relativity in a nutshell
• mass and energy cause spacetime to curve
• objects move in the straightest possible paths in a curved space-time
• space is not inert: it can stretch, contract & wiggle
New Phenomena
1. Gravitational lensing
2. Gravitational waves
3. Profound Implications for the Universe
COSMOLOGY
The study of the origin and evolution of the universe
Profound Implications for the Universe:
If space is filled with matter, radiation and other forms
of energy, then, generally speaking,
we should expect space to be contracting or expanding
COSMOLOGY
Universe is Evolving
What happens tothe temperatureas the universe
expands ?
Nobel Prize in Physics 2006:
evidence Universewas once hotter
than .1 eV
Wilkinson Microwave Anisotropy Probe
What is the Universe composed of?
<1930s100% protonsneutrons, electrons
“ordinary matter”
What is the Universe composed of?
1930s-1980s
most isDark Matter
5% ordinarymatter
95% darkmatter
What is the Universe composed of?
1990-today
most isDark Energy
5% ordinarymatter25% dark
matter
70% dark energy