Special Relativity II: Paradoxes by Robert Nemiroff Michigan Tech

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

Special Relativity: Doppler effect Doppler effect Doppler effect Object moving toward you o appears more blue -- called blueshift o appears to speed up (clock looks faster) o appears elongated Object moving away from you o appears more red -- called redshift o appears to slow down (clock looks slower) o appears contracted

Special Relativity: Doppler Related Effects Doppler effect: moving toward a uniform color background o A green background ahead of you appears blue o A green background behind you appears red Transverse Doppler Effect o The time dilation effect of special relativity is directly measured for an object moving transverse (neither toward nor away) from you

Special Relativity: Doppler Effects Aberational effect: moving toward a uniform star fieldAberational effect o Stars in your direction of motion appear to bunch o Stars behind your direction of motion appear to spread out

Special Relativity: Doppler effects Earth's motion with respect to the cosmic microwave background radiation

Special Relativity: Superluminal Blinking Paradox Can a wavefront of blinking lights appear superluminal? Example: A row of lights blinks in sequence. Each light seen to blink one second after the one to its right. You now find out that the lights are far away and separated by light years. Does the "wave" of blinking exceed c? 1.Yes. 2.No. 3.Lights can't blink that fast.

Special Relativity: Paradoxes Superluminal Blinking Yes: blinking light sequence may appear to have v > c. No information is transferred with v > c. Observers located elsewhere may see different blinking pattern. No observer can use the blinking lights to communicate with v > c.

Superluminal Flashlight Sweep You shine a flashlight inside a distant spherical dome one light year away. In one second, you swing the light from shining to your left to shining to your right. How fast does the spot from the flashlight move on the dome? 1.Slower than c. 2.c. 3.Faster than c. 4.5 sqrt(alpha - 2 gamma).

Superluminal Flashlight Sweep 3. Faster than c. Although you would have to wait for two years to see the spot move at all, when you saw it, the spot would move many light years across the sky in one second. The spot is not a physical thing, however, and the spot can carry no information.

Special Relativity: Quasar Motion Paradox Quasar Motion Paradox Quasar Motion Paradox A source moving with speed v>cat an angle θ < pi/2 from the line of sight may appear to be moving faster than c in projection onto the sky because the light travel time is reduced by t cos( θ ) (v/c) in time t.