# relativity length contraction for twin clock experiment

The question im going to ask is based on scenario given here https://www.scientificamerican.com/article/how-does-relativity-theor/ Only thing that's different is that spacecraft has a length of 1 light year ($1ly$) and traveler is sitting on extreme rear. When the traveler reach the star after 8 years (in traveler's clock), the extreme front end has a explosion. The coordinate of this event for traveler is $(1 ly, 0, 0, 8)$. The transformed coordinate for homebody is $((1 ly +8*0.6c)*1.25, 0, 0, (8+1*0.6c/c^2)*1.25)$. Where 1.25 is $\gamma$ at $v=0.6c$. It means the position of explosion as seen homebody (i.e. the x-coordinate of explosion) is $(1 ly +8*0.6c)*1.25=7.25 ly$.

So here is my question: if the spacecraft is contracted in length due to travelling at $v=0.6c$, the coordinate of explosion should come out to be between 6ly and 7ly for the homebody because the star is already 6ly distance away (proper distance) and the $1ly$ long spaceship has contracted due to length contraction formula. But it is even more than 7ly. Where am i going wrong with it?

## 1 Answer

Allow me to just answer with a graphic (also sent via private e-mail):

It should be self-explanatory but... $(t_1,x_1)=(0,0)$ is the traveler's ($T$) position in his own reference frame at the beginning of the journey, $(t_2,x_2)=(0,1)$ is the position of the other end of his spaceship; $(t_3,x_3)=(8,0)$ and $(t_4,x_4)=(8,1)$ are the same at the end of the journey, and the prime denotes the same events in the "homebody's" ($H$) frame.

• All the equations in STR are specifically tailored to prove that light has invariant constant speed. Its not hard, its impossible to prove otherwise using any of the equations that have been formulated under STR. I replaced the 'c' in what I was doing with a general velocity 'u' other than c. That 'u' was now displaying invariant characteristic i.e. both rays travelling with u reached at the screen simultaneously. LOL – Gaurav Goyal Nov 26 '16 at 21:14
• Of course the equations are special relativity are "tailored" this way. After all, the constancy of c is one of special relativity's fundamental postulates. So if it predicted anything other than constant c, it would be logically inconsistent. – Viktor Toth Nov 26 '16 at 21:27
• Well its very nice. Im just wondering what would've happened if Michelson-Morley were testing speed of anything other than light....Would we be using that speed as universal constant today? – Gaurav Goyal Nov 26 '16 at 21:37
• Probably not, because there is no other experimentally known speed that is the same for all observers, so if Michelson and Morley tested high energy electrons, they would have found the speeds to depend on kinetic energies and the observer. However, if we found that there are two distinct speeds, both invariant for all observers, it would be time for so-called bimetric theories. (By way of example, when a couple of years ago, there was brief excitement about the possibility that neutrinos were moving faster than light, bimetric theory was one of the proposals offered by way of explanation.) – Viktor Toth Nov 26 '16 at 21:56
• Andrzej Trautman: How bats have proved the theory of relativity to be wrong. W.A. von Ignatowsk: Derived Lorentz transformations using only relativity principle i.e. he didnt consider light speed constant. Plus, you must be aware of news and journal articles where researchers have stopped light and restarted it while others proved mathematically that light propagates in leap-frog manner. And im not sure if its true or not, but I read somewhere that speed of light is decreasing over time. – Gaurav Goyal Nov 26 '16 at 22:12
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