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Spaceship Relativity

Spaceship Relativity. by Robert J. Nemiroff Michigan Technological University. Physics X: About This Course. Pronounced "Fiziks Ecks" Reviews the coolest concepts in physics Being taught for credit at Michigan Tech Michigan Tech course PH4999 Aimed at upper level physics majors

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Spaceship Relativity

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  1. Spaceship Relativity by Robert J. Nemiroff Michigan Technological University

  2. Physics X: About This Course • Pronounced "Fiziks Ecks" • Reviews the coolest concepts in physics • Being taught for credit at Michigan Tech • Michigan Tech course PH4999 • Aimed at upper level physics majors • Light on math, heavy on concepts • Anyone anywhere is welcome • No textbook required • Wikipedia, web links, and lectures only

  3. Special Relativity: Ehrenfest Paradox A rigid ring is rotated about its center.  Does it's radius decrease? Reformulated: Train cars sit on a circular track connected by taut strings. The train cars all begin to circle the track at once, faster and faster, eventually reaching relativistic speed. What happens to the strings? • The strings droop.  • The strings break.  • The strings remain the same.  • Did Ehrenfest think of this?  Then ask him!

  4. Special Relativity: Ehrenfest Paradox  2. The strings break. Length contraction makes the length of the train cars plus the strings contract, so that the strings break.  (Assuming circular symmetry.) Every observer at rest sees the radius as constant.  However, observers rotating with the ring measure a larger circumference than observers at rest: F' = F / (1 - v2/c2)1/2 .  The train cars plus strings are not long enough to cover this larger circumference. Einstein himself agreed with this solution.

  5. Special Relativity: Bell's Spaceship Paradox Two spaceships connected by a string both accelerate.  What will happen to the string? (Yes, it's the same Bell who created Bell's Inequality.)

  6. Special Relativity: Bell's Spaceship Paradox • The sting will droop. Since length contracts, the string will cover less length and bunch up. • The string will break.   Since length contracts, the string between the ships contracts but still must cover the same distance as seen in the rest frame. The string cannot cover this extra distance and will break.  • The string will remain the same.  Assume you are in the spacecrafts frame.  A passing observer will not cause your string to break no matter how fast they pass.

  7. Special Relativity: ParadoxesBell's Spaceship Paradox Controversial!  Sets of accelerations should exist that do NOT break the string, in particular when the lead spaceship should have lower acceleration than the trailing spaceship. Simultaneity is important. Can this be mapped into the Ehrenfest paradox? If so, then for those cases the string must break.

  8. Spaceship Relativity Is it possible for a human to go anywhere in the visible universe in a human lifetime without violating the laws of physics?  1. No, one must travel faster than c to do that.  2. Yes, you do not need to travel faster than c.  3. Did you think that Star Trek was real?

  9. Spaceship Relativity  2. Yes, you do not need to travel faster than c. A spaceship traveling at 1 g (comfortable!) can go anywhere in the visible universe in a normal human life span.  This is essentially the twin paradox, with you being the twin that leaves. As the ship accelerates, it approaches c in the "home twin"'s reference frame.  The universe "contracts" as well.  You can go anywhere.   See:  http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html

  10. Where How far Spaceship time at 1 g (low speed arrival) Nearest star 4.3 light years 3.6 years Vega (star) 27 light years 6.6 years Center of Galaxy 30,000 light years 20 years M31 2 million light years 28 years z = 1 11 billion light years (comoving radial) 45 years Microwave background 45 billion light years (comoving radial) 48 years General Formula n light years 1.94*arccosh(n/1.94+1) Spaceship Relativity

  11. Spaceship Relativity: Warp Speed Using Special Relativity, it is possible to "interpret" warp speed not as a true faster-than light speed but rather as distance in the Earth frame divided by time in the moving frame. For example: "warp one" would be the speed a spacecraft must take to travel one light year, as measured in Earth's frame, by one year's time, as measured on a starship. This corresponds to a specific velocity between the spacecraft and Earth. 

  12. Spaceship Relativity: Warp Speed In other words, how fast must one go to travel one light year away while experiencing the passing of one year's worth of time?  Answer: Warp one.  How fast must one travel to go ten light years away while experiencing only one year's worth of time passing? Answer: Warp 10.

  13. Special Relativity: A MovieWhat it looks like to move near c

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