Would Headlights Work at Light Speed?

If you were driving at the speed of light and turned on your headlights, what would happen?
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Sources and extras below!!

Thanks to Jude for asking me this question on twitter! https://twitter.com/stefanikj5/status/550865272895447041

“The Life of the Cosmos” by Lee Smolin: http://www.amazon.co.uk/The-Life-Cosmos-Lee-Smolin/dp/0195126645
“In Search of the Multiverse” by John Gribbin: http://www.amazon.co.uk/In-Search-Multiverse-John-Gribbin/dp/0141036117
“The Pig That Wants to be Eaten: by Julian Baggini: http://www.amazon.co.uk/The-Pig-That-Wants-Eaten/dp/1847081282

Relevant MinutePhysics videos:

light slowing down in glass: https://www.youtube.com/watch?v=FAivtXJOsiI
a different perspective from Sixty Symbols about light slowing down: https://www.youtube.com/watch?v=CiHN0ZWE5bk

Why is “c” the speed of light?

http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/c.html

Car at light speed:

http://www.sydneyobservatory.com.au/2010/what-happens-when-a-car-travelling-near-the-speed-of-light-turns-on-its-headlights/
https://van.physics.illinois.edu/qa/listing.php?id=1355
http://www.scienceforums.net/topic/82191-i-am-driving-my-car-at-the-speed-of-light-and-i-turn-on-my-headlights-what-do-i-see/
http://www.desy.de/user/projects/Physics/Relativity/SpeedOfLight/headlights.html

Light speed is the same in all inertial frames of reference:

http://www.physlink.com/Education/AskExperts/ae558.cfm
https://van.physics.illinois.edu/qa/listing.php?id=2605
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/mmhist.html#c1

Relativistic addition of velocities:

http://demonstrations.wolfram.com/EinsteinsFormulaForAddingVelocities/
http://cnx.org/contents/e3a41220-af3f-40c6-b8ba-1a5d1bcbed92@6/Relativistic_Addition_of_Veloc

doppler shift:

http://commons.wikimedia.org/wiki/File:XYCoordinates.gif#mediaviewer/File:Doppler-velocity89.jpg

Relativity:

http://www.refsmmat.com/jsphys/relativity/relativity.html
http://www.astro.virginia.edu/~jh8h/Foundations/quest7.html

Light speed and catching-up to light.

http://www.pitt.edu/~jdnorton/Goodies/Chasing_the_light/
http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html
http://www.askamathematician.com/2010/11/q-what-would-you-experience-if-you-were-going-the-speed-of-light/
http://scienceline.ucsb.edu/getkey.php?key=1571
https://van.physics.illinois.edu/qa/listing.php?id=1354

Other good relativity resources: http://newt.phys.unsw.edu.au/einsteinlight/

Light echo footage: http://www.spacetelescope.org/videos/heic0617a/

“fine-tuned” universe:

http://io9.com/5989467/how-does-the-anthropic-principle-change-the-meaning-of-the-universe
http://en.wikipedia.org/wiki/Fine-tuned_Universe
http://rationalwiki.org/wiki/Anthropic_principle

Irrational numbers: http://mathworld.wolfram.com/IrrationalNumber.html

a million digits of pi: http://www.piday.org/million/

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animated drawings by Guy Larsen https://twitter.com/guylar
rocketship animation by Eric Langay https://twitter.com/ericlanglay