Jack Shutzman

Time Travel and the Universe

Intuition and Common senseWhat falls faster 1/2Lb of feathers or

20Lb of lead?We’ll have to forgo some of our common

senseA 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/hrHow fast does the flashlight’s beam go?

If your answer was c+60You’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 - 1676Discovered 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

M, M’ are the middle points - T on the train, E outside

v - The train moves at 200,000 km/sec c - The speed of light 300,000 km/sec

E sees lightning hit A and B at the same time

What does T see?

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

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

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 dilationTo simplify calculations we’ll call the

term: 1/sqrt(1-v^2/c^2) gamma : γ (or the Lorentz factor)

So: Time dilated = Time/γExample:

v= c/2; γ=1/sqrt(1-(c/2)^2/c^2) ≈ 1.155So 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) ≈ 50So 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 trianglesAEF is similar to ADB (same angles), AD=AE*γSo 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 upwardThe 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 byBodies 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 gravityThe 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