Transcript TT_and_the_Universe

Time Travel and the Universe
Jack Shutzman
Intuition and Common sense
 What falls faster 1/2Lb of feathers or
20Lb of lead?
 We’ll have to forgo some of our common
sense
 A Einstein: Common sense is the
collection of biases you accumulate
before you reach 18.
A simple case (space)
 A train with a table on it, and a person
bouncing a ping-pong ball once a second
 The train travels at 90 miles/hr
 How is it viewed from the outside?
Adding / Subtracting velocities
 A person walks on an airport moving strip
at 3 miles/hr
 The strip moves 3 miles/hr
 What does the observer on the outside
see?
What about a case of light?
 The person on the train holds a flashlight
and shines it in the moving direction
 Light travels at c
 The train moves at 60 miles/hr
 How fast does the flashlight’s beam go?
If your answer was c+60
 You’ll be wrong!
 Does it make sense?
 Who found it ? Who found the speed of
light?
 Does anyone here know the speed of
light?
Ole Chritensen Roemer - 1676
 Discovered that light is not instantaneous
 1887 - Albert Michelson & Edward
Morely - 186,000 miles/second
 More precisely: 299,792,458 meters/sec
 More importantly, the light speed is not
affected by movement.
Thought experiment 1
 Assumptions: The laws of physics (nature) are the
same for all inertial systems, and the speed of light is
constant in vacuum, about 300,000 km/sec
v - The train moves at 200,000 km/sec
c - The speed of light 300,000 km/sec
 M, M’ are the middle points - T on the train, E outside
E sees lightning hit A and B at the same time
What does T see?
E sees the lighting hit A and B simultaneously, 1/3 of a
second later (100,000 km from it)
T is moving, so we’ll need to set equations
A: T is moving away from the lightning, but the lightning is faster and
will catch T after t second:
t*300000 = t*200000+100000 /equating distance => t=1
B: T is moving toward the lightning and will see it in t’ sec
t’*300000 + t’*200000 = 100000 => t= 1/5 sec
Conclusion: T does not think the lightning
on A and B occurred at the same time
So we’ve arrived at another ‘illogical’
conclusion: Time is not absolute.
 I’ll try to convince you that time slows
down for the moving entity
 Another thought experiment (2), with a
truck
 We build clocks which are hollow tubes,
the size of c, with light beam and mirrors
The truck moves at the speed of v, which is
close to the speed of light
 The light beam moves through the tube from end to end in 1
second. One clock stays outside and one is on the truck
To the outside observer, the beam moves like the
Ball from the first experiment (diagonally)
Let’s calculate the time for the truck
driver (up to M)
 Using the Pythagorean Theorem
So x=SQRT(c^2 - v^2)= c*sqrt(1-v^2/c^2)
Conclusion : Time slows down when we
move fast
 We call it: Time dilation
 To simplify calculations we’ll call the
term: 1/sqrt(1-v^2/c^2) gamma : γ
(or the Lorentz factor)
 So: Time dilated = Time/γ
 Example:
v= c/2; γ=1/sqrt(1-(c/2)^2/c^2) ≈ 1.155
 So if we measure 10 seconds the driver
will measure 10/1.155= 8.66 seconds
A more extreme example 99% of the
speed of light
 Moving at 184,000 miles per second
 γ=1/sqrt(1-(0.99c)^2/c^2) ≈ 50
 So if you travel for 1 year at .99c, you’ll age by
one year, but your fellows will age by 50 years
 Optional home drill: Calculate what speed
you need, to ‘jump’ ahead to 3011 within a
year of your time
Other side effects
 Length contraction in the movement
direction - requires simultaneous check of
2 points. γ is used to calculate length too
as we’ll see.
 Rigidity of objects is weakened under
relativity (because nothing is faster than
light)
Two similar right triangles
AEF is similar to ADB (same angles), AD=AE*γ
So also DB=EF*γ= vγ. The Truck driver measures a
distance of vγ after his second passed, and we measure only v
What speed do we need for a
contraction by half?
 I’ll leave as a home exercise.
 So time is relative to the observer. We’ll then
add time to a coordinate system and we’ll use
space-time instead of space coordinates.
 Einstein could not rest with special relativity.
You need to accelerate to achieve speed.
Extending the principle of equivalence to
accelerating object
 Einstein determined that no experiment
can tell an observer if he or she are inside
and accelerating chamber, or resting in a
gravitational field
 Thought experiment 3
A space rocket is as long as c, has one
observer on top and second on bottom
 The top observer send light signal every second
to the bottom - The rocket is resting in space,
the bottom observer agrees (seeing the signal
precisely every second.)
 Now the rocket starts accelerating upward
 The intervals become shorter to the bottom
observer - He is moving faster and will get
closer to the light
We’ll use the principle of equivalence, so
the rocket could be resting in a
gravitational field
 Conclusion: time dilates closer to
gravitational field.
 A clock on the sun will gain 1 minute per
year - pretty small effect
 An experiment in 1962 with a water
tower and two very accurate clocks
showed the effect predicted.
You may think why use relativity, who
achieves such speeds or enormous
gravitation?
 A simple app. Like GPS would not have
been possible. Without corrections for
relativistic effects, a GPS would miss its
target by several miles.
 General relativity also predicted
gravitation changing light’s direction
In 1919, 4 years after the publishing of
general relativity, an experiment proves it
 An eclipse in west Africa and Brazil
The measurement of delta was the value predicted
The eclipse experiment made
Einstein an instant celebrity
 Relativity claims that space is curved by
 Bodies in space-time
The bodies in space-time move in geodesic
lines in the curved continuum
 On earth Geodesics are used by airline to
minimize flying distance across the
globe.
More about the universe and how we
discover facts about it
 We can see only 3 to 5 thousands stars
with the naked eye.
 There are about 100 Billion stars like the
sun in our galaxy, the Milky Way.
 There are about 100 Billion galaxies
similar to ours.
 The diameter of the Milky Way is about
100,000 light years
The Milky Way
 We have a black hole in the center of the
galaxy more than 1 million times the
mass of the sun.
That massive black hole has a visible star
rotating it at 3700 miles per second
 So one technique to find a black hole is to
check its gravitational effects.
 Scientists use parallax to measure distances of
medium length.
 They use star brightness and luminosity for
measuring distance to remote galaxies.
 They use color spectrum analysis to check
temperature.
Spectrum is used for other
important findings
 One such findings was the discovery of the
expanding universe, using the Doppler effect.
 On a large scale, the universe looks the same in
every direction, and also if observed from any
view point.
 This theory developed by a Russian astronomer
Alexander Friedman and verified by an
American: Edwin Hubble
Supernova - A massive explosion of
a star
 It collapses under its own gravity
 The Chinese recorded one in 1054, about 5000
light years away. It was so bright, you could see
it during the day and read by it at night.
 In 1604 is the last recorded (before the
telescope was invented).
 Our sun is a 2nd or 3rd generation star, which
formed from remnants of a supernova, 5 Billion
years ago.
With the aid of the Hubble telescope
floating in space here is what we see:
 http://www.youtube.com/watch?v=fgg2tpUVbXQ&feature=related