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        SR < > NM            SRT vs. NM E

NM:   Vwrt x=0 = (x´/t) = (x´/I)c

SRT:   vwrt x=0=(x´/t´)=(x´/H)c

NM:   Vwrt* = (H/t) = (c´t)/t = c´

SRT:   vwrt * = (H/t´) = (ct´/t´) = c

Special Relativity (SRT) is an encryption of Newtonian Mechanics (NM)

Dr. Sherwood Kaip

El Paso, TX

<skaip799@gmail.com>;   cell: 1 (915) 309-6340

This material may be reproduced if author attribution is given.

     Three objects start from  x=0  and in one second travel  x1=40meters,  x2=400m, and  x3=4,000m .  Their speeds are obviously  V1=40m/s,  V2=400m/s ,  and  V3=4,000m/s .  If they go these distances in one microsecond  (µs), then according to Newtonian Mechanics (NM) their speeds would be  V1=40m/µs,  V2=400m/µs ,  and  V3=4,000m/µs .  

     Since light travels  300m/µs  and since nothing can exceed the speed of light,  c ,  according to Special Relativity (SRT),  V2 and  V3  are not possible.

     Consider three SRT speeds:  va=39.649116…m/µs ,  vb=240m/µs ,  and  vc=299.159793…m/µs .  These are not random choices.  How many meters will objects traveling at these SRT speeds travel in the  1.0µs  in which light travels  300m ?  The formula is  x=γvt  where  γ  is 1/(1–(v/c)2)½ .  (The full formula is  γ(vt+x)  but here  x=0  because it’s the non-moving reference frame.)  

     From the formula for  γ ,  

γa=1.00900919…,    γb=1.66… ,    γc=13.3707807…   .

According to the formula, each  x  equals  γ  times  v  times  1µs :

xa= 1.00900919… * 39.649116m/µs * 1µs = 40m

xb = 1.66… * 240m/µs * 1µs = 400m

xc = 13.3707807… * 299.159793…m/µs * 1µs = 4,000m

     Note that  xa=x1 ,  xb = x2 ,  and  xc = x3 .  Using the last example, according to NM,  x3  traveled  4,000meters  while the light traveled  300meters  during  1.0µs  and  xc also traveled 4,000meters while the light traveled  300m during  1.0µs  based on a SRT speed of only 299.159793…m/µs  which had to be multiplied by its  γ  to get the correct 4,000m.

     NM velocity  V  and SRT velocity  v  are related by

V = γv       or       v = V/γ    

V = x/t       or       v=x/γt

Thus, the NM velocity (V) is simply the distance traveled,  x  , divided by the time,  t ,  whereas the SRT velocity (v) is the (same) distance traveled,  x  , divided by  γt .

     Encryption converts the original representation of information into an alternative form.  For example, “Ifmmp” is an encryption of “Hello” by changing each letter to the next letter of the alphabet.  This could be done to the entire book “War and Peace”.  

     SRT has just been shown to be an encryption of NM  by changing NM velocity  V=x/t  to SRT velocity  v=x/γt .   At all speeds, in NM, x equals Vt ,  vs. the complicated  x equals γvt of SRT.  For every SRT depiction of events there is an equivalent accurate NM depiction which makes more sense and doesn’t have paradoxes.