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Jack Shutzman Time Travel and the Universe

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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.

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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?

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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?

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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?

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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?

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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.

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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

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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?

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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

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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

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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)

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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)

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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

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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

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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)

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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

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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.

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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

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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

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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.

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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

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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

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The eclipse experiment made Einstein an instant celebrity Relativity claims that space is curved by Bodies in space-time

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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.

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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

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The Milky Way We have a black hole in the center of the galaxy more than 1 million times the mass of the sun.

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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.

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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

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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.

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With the aid of the Hubble telescope floating in space here is what we see: http://www.youtube.com/watch?v=fgg2tpUVbXQ&feature=related

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Announcements Exam 3 is scheduled for Wednesday April 8. Will be pushed back to Monday April 13 Tentatively will cover the rest of Chapter 4, all of Chapters.

Announcements Exam 3 is scheduled for Wednesday April 8. Will be pushed back to Monday April 13 Tentatively will cover the rest of Chapter 4, all of Chapters.

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