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Speed of light
Theoretically, if you spin a long rope to just below the speed of light, will the end of the rope be moving faster than the speed of light, as it will have to travel faster to cover the greater distance?
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The answer to kwicky's conundrum is at the heart of relativity.
The Physics dictated by Newton says that two bodies with velocities of u and v approaching each other close at their combined velocity of (u+v). Einstein�s theories say that they close at
(u+v)
------------
(1+(uv/c2))
(where c is the speed of light)
Substituting low values for u and v results in very little difference between this formula and the simple (u+v) mentioned earlier. For example, two trains approaching each other and both travelling at 100 mph would have a closing velocity of 200mph under Newtonian principles and 199.99977mph using Einsteinian principles - very little difference and the approximation (u+v) is good enough for everyday calculation when the values of u and v are low.
If, however, we move on to consider the case of two spaceships both travelling towards each other with a velocity of 0.8c (about 150,000 miles per second!) relative to a fixed rendezvous point, the significance of Einstein's Theory becomes more obvious. Assuming that the passengers aboard the ships could survive the forces needed to accelerate their craft to such speeds, and the energy could be found to do so, their closing speed (as observed from either of them) would be 1.6c according to Newton. Einstein's calculation does not show this to be the case. Using the revised formula, their closing velocity would be, only 0.9756c.
Examination of the formula, in fact, will show that, provided the individual values of u and v do not exceed c (and this is impossible under Einstein's theories) then relative velocities cannot exceed c either.
The Physics dictated by Newton says that two bodies with velocities of u and v approaching each other close at their combined velocity of (u+v). Einstein�s theories say that they close at
(u+v)
------------
(1+(uv/c2))
(where c is the speed of light)
Substituting low values for u and v results in very little difference between this formula and the simple (u+v) mentioned earlier. For example, two trains approaching each other and both travelling at 100 mph would have a closing velocity of 200mph under Newtonian principles and 199.99977mph using Einsteinian principles - very little difference and the approximation (u+v) is good enough for everyday calculation when the values of u and v are low.
If, however, we move on to consider the case of two spaceships both travelling towards each other with a velocity of 0.8c (about 150,000 miles per second!) relative to a fixed rendezvous point, the significance of Einstein's Theory becomes more obvious. Assuming that the passengers aboard the ships could survive the forces needed to accelerate their craft to such speeds, and the energy could be found to do so, their closing speed (as observed from either of them) would be 1.6c according to Newton. Einstein's calculation does not show this to be the case. Using the revised formula, their closing velocity would be, only 0.9756c.
Examination of the formula, in fact, will show that, provided the individual values of u and v do not exceed c (and this is impossible under Einstein's theories) then relative velocities cannot exceed c either.
I asked something along the lines your on a while back and got this. http://www.theanswerbank.co.uk/Science/Questio n449036.html
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