Thursday, June 2, 2011

Time dilation

    According to Euclid, we live in a 3-dimensional world, being able to pinpoint our position using three coordinates: x, y and z. Einstein saw this in a different light- 4 dimensions. According to his special theory of relativity "The four dimensional space-time continuum of the theory of relativity , in its most essential formal properties, shows a profound relationship to the Euclidian geometrical space. In order to give due prominence to this relationship, we must replace the usual time coordinate t by an imaginary magnitude by (√-1)* ct proportional to it." Just as space is fluctuary, time changes as well.
    One feature that distinguishes time from space in how it is changed, is that motion changes time relatively. To illustrate that, imagine that an observer, person A, is on a stationary platform, and I have another person, person B, also on that platform, sitting in a spaceship. They are both experiencing, at that moment the same rate of time. Now the spaceship launches and it is accelerating. If he is traveling at 0.5c (half the speed of light) What feels like one day to person B, is 1.15 relative days for person A. As he gets closer to the speed of light, 0.99c, one day for person B is over a week back at the platform. Time goes up rapidly from there. at0.99999999999999c, for one day for person B, person A is long dead having almost 2000 years pass on his platform.
     This data is all based upon the Lorentz factor, which is represented by the equation below, with:
t = time
v = velocity
c = constant, the speed of light

 Rest Frame Time Elapsed per Day on Ship        
v/c                           Days        Years
0.0                           1.00         0.003  
0.1                           1.01         0.003  
0.2                           1.02         0.003  
0.3                           1.05         0.003  
0.4                           1.09         0.003  
0.5                           1.15         0.003  
0.6                           1.25         0.003  
0.7                           1.40         0.004  
0.8                           1.67         0.005  
0.9                           2.29         0.006  
0.95                          3.20         0.009  
0.97                          4.11         0.011  
0.99                          7.09         0.019  
0.995                        10.01         0.027  
0.999                        22.37         0.061  
0.9999                       70.71         0.194  
0.99999                     223.61         0.613  
0.999999                    707.11         1.937  
0.9999999                  2236.07         6.126  
0.99999999                 7071.07        19.373 
0.999999999               22360.68        61.262 
0.9999999999              70710.68       193.728
0.99999999999            223606.79       612.621
0.999999999999           707114.60      1937.300       
0.9999999999999         2235720.41      6125.261       
0.99999999999999        7073895.38     19380.535      
0.999999999999999      22369621.33     61286.634      
Sincerely,
Space Cadet