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Suppose I am sitting around floating in the middle of intergalactic space minding my own business, when all of a sudden WOOSH a really weird massive ellipsoid thing starts rushing by me at .99c (where relative gamma is about 7). The thing appears to be 100,000/7 light years across (take the length of our galaxy and divide it by 7 to get the relativistic contraction). Simultaneously, the inhabitants of the galaxy are going "WTF? that flat-person-looking thing is going at .99c." (According to Einstein no inertial reference frame is better than an other so both viewpoints are equally valid as far as each of them can tell). Now let's say that each inhabitant of this galaxy has a watch and all of their watches are synchronized to the exact same time (assume they are all in the same inertial reference with each other). So, as I'm passing the first one I see by (close enough so that time between messages is neglible), I take my flashlight out and morse-code really quickly "sup d00d, what time you got". Immediately, he replies "I got t=0", so I synchronize my watch to t = 0 years. So, after 100,000/7 years (The galaxy is practically traveling at c so it should take 100,000/7 years for it to completely pass by me), I decide to take out my flashlights and talk to one of the inhabitants again. I figure since the galaxy is passing by me at .99c, time in the galaxy is going by 7 times slower than my time, 100,000/49 years should have passed. The inhabitant sees me rushing by not long after hearing the news from the first inhabitant through their intergalactic morse-code network. He figures that since his galaxy is 100,000 light-years across, the message must have been sent at t = 0, and the traveller(me) took a little more than 100,000 years to traverse the galaxy. He decides he wants to be smart and realizes that time must have been going 7x as slow for me as it was for him so he morse-codes me "Hey your clock reads t = 100,000/7 years, right?" I also wanted to be smart and realized that time for him must have been going 7 times slower than it was for me so I morse-code him "Yup, and your clock reads t = 100,000/49, right?". "Wrong, it reads t = 100,000." He replied.
So what was wrong with this?
So what was wrong with this?