# Special & General Relativity Questions and Answers

## If you traveled at the speed of light, would the universe appear instantaneous?

Yes. Lets take a look at the mathematics of special relativity! The famous equation that describes the amount of time dilation you experience is given by:

t0 T = -------------------- [ 1 - (v/c)^2 ]^1/2where T is the time interval measured by the twin that stayed behind on earth, and t0 is the time interval experienced by the moving twin travelling at a relative velocity of v. Lets now use the approximation formula for relativistic speeds in the limit where v = c - e where c is the speed of light and e is how close you are to the speed of light in the same velocity units. Lets also assume that t0 is one second as measured on the clock carried by the traveling twin.

'Warp factor' V e T .................................................... 1 0.9c 2.29 sec 2 0.99c 7.08 sec 3 0.999c 22.36 4 0.9999c 70.71 5 0.99999c 223.6 6 0.999999c 707.1 7 0.9999999c 2236.0 ....................................................At 'Warp 7' you are traveling at a speed which is within ( 1 - .9999999) x 300,000 kilometers/sec = 30 meters/sec of the speed of light. It will take you 4.2 years/2236 = 16.2 hours to travel to the nearest star 4.2 light years distant, but your twin back on Earth will see it take you 4.2 YEARS. The center of our Milky Way is 26,000 light years away, but this will take you only 11.6 years at this speed. An electron sitting in your frame of reference will be seen as having an energy of 2236 x mc^2 = 1.1 GeV which is the mass of a proton! We can push this story even further:

Warp Factor e t0 .................................................. 9 3 cm/sec 22360 16 300 Angstroms/sec 71 million 25 ..... 2.2 trillion 30 ..... 700 trillion 37 ..... 2 billion billion ...............................................................At 'Warp' 9, you can travel to the Galactic center in 1.1 years. At Warp 16, you can travel to the current distance of the visible horizon to the universe some 15 billion light years distant, in 212 years. At Warp 25, this takes only 2.4 days, and at Warp 37 ( 0.99999...37 times) the journey across the universe takes only 0.2 SECONDS! The journey may only take a second for you, but outside, it still takes 15 billion years. At this speed, if we live in a closed universe with only finite spatial volume and lifetime, you will witness the collapse of the universe in a few seconds! The universe will literally have passed in and out of existence in less time than it takes you to take a breath!

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All answers are provided by Dr. Sten Odenwald (Raytheon STX) for the NASA Astronomy Cafe, part of the NASA Education and Public Outreach program.