CALCULATIONS: Sum Velocity
This program was a direct result from our Internet discussions on the alt.physics.new-theories. It compares the velocity sum for Special Relativity and Autodynamics.
Basic Program Listing
10 REM A particle with 200 MeV of motion mass and 150 MeV of KE,
20 REM is in motion in System X which is moving with respect to
30 REM System X' with velocity B2=.75.
40 PRINT, "VELOCITY SUM IN AD"
50 MV=200 'Motion mass MV in MeV.
60 B2=.75
70 PRINT "MV="MV "Particle motion mass MV in MeV."
80 KE1=50 'Particle KE1 en MeV in System X.
90 PRINT "KE1="KE1 "Particle KE in MeV in System X."
100 MO=MV+KE1 'particle rest mass in MeV.
110 PRINT "MO="MO "Particle rest mass in MeV."
120 B1#=SQR(1-(1-(KE1/MO))^2) 'Beta1.
130 PRINT "B1="B1# "Beta1 with MO and Ke1."
140 B12#=SQR(1-(MV/(KE1+MV))^2) 'B12 with MV and KE1.
150 PRINT "B12="B12# "B12 with MV and KE1."
160 KE1T#=MO*(1-SQR(1-B1#^2)) 'KE1 test in MeV.
170 PRINT "KE1T="KE1T# "KE1 test in MeV."
180 M2=MO*SQR(1-B1#^2) 'Motion mass of MO in MeV.
190 PRINT "M2="M2 "Motion mass of MO in MeV."
200 PRINT "B2="B2 "Velocity of System X with respect to X'.
210 KE2#=MV*(1-SQR(1-B2^2)) 'KE of mass MV in MeV in System X'."
220 PRINT "KE2="KE2# "KE of mass M2 in MeV.
230 KE3#=KE1+KE2# 'Sum of KE1 plus KE2# in MeV.
240 PRINT "KE3="KE3#"Sum of KE1 plus KE2# in MeV.
250 B3#=SQR(1-(1-(KE3#/MO))^2) 'Beta3 with KE SUM and MO.
260 PRINT "B3="B3# "Beta3 with KE SUM and MO."
270 VS#=SQR(1-((1-B1#^2)*(1-B2^2))) 'Beta3 Sum velocities in AD.
280 PRINT "VS="VS# "*** Velocity SUM in AUTODYNAMICS ***"
290 PRINT
300 PRINT "-----------> Beta 1="B1#
310 PRINT " |"
320 PRINT " ------------> Beta 2="B2
330 PRINT "-----------------------> Beta 3="B3#"***","VS="VS#
340 PRINT
350 PRINT,"VELOCITY SUM IN SR"
360 REM The example will be calculated with the same values. It is
370 REM possible to see that the SR equation give wrong values
380 REM that is, the velocities SUM equation give approximate values.
390 PRINT
400 BR1#=SQR(1-(1-(KE1/MV))^2)'Working out MO with MV=MO/SQR(1-Beta^2).
410 PRINT "BR1="BR1#,"KE1="KE1,"MV="MV
420 MRO#=MV*SQR(1-BR1#^2)
430 PRINT "MRO="MRO#
440 MRV=MRO#/SQR(1-BR1#^2)
450 PRINT "MRV="MRV "(TEST)"
460 KERT=MRO#*((1/SQR(1-BR1#^2))-1)
470 PRINT "KERT="KERT "(Test)","MRV="MRV,"BR1="BR1#
480 PRINT
490 PRINT "B2="B2
500 KER2#=MV*((1/(1-B2^2))-1)
510 PRINT "KER2="KER2#,"MV="MV,"B2="B2
520 VS1#=(BR1#+B2)/(1+(BR1#*B2))
530 PRINT "VS1="VS1#"***","BR1="BR1#,"B2="B2"(VELOCITY SUM)"
540 KES1#=KE1+KER2# 'KE SUM.
550 PRINT "KES1="KES1#, "KE1="KE1, "KER2="KER2#
560 BT1#=SQR(1-(1/(1+(KES1#/MRO#))^2))
570 PRINT "BT1="BT1#"***","KES1="KES1#,"MRO="MRO#
580 PRINT "-------->>>>>"
Basic Program Output
VELOCITY SUM IN AD
MV = 200 Particle motion mass MV in MeV.
KE1 = 50 Particle KE in MeV in System X.
MO = 250 Particle rest mass in MeV.
B1 = .600 000 023 841 857 9 Beta1 with MO and KE1.
B12 = .600 000 023 841 857 9 Beta12 with MV and KE1 (Test).
KE1T = 49.999 996 185 302 74 KE1 test in MeV.
M2 = 200 Motion mass of MO in MeV.
B2 = .75 Velocity of System X with respect to X'.
KE2 = 67.712 440 490 722 66 KE of mass M2 in MeV.
KE3 = 117.712 440 490 722 27 Sum of KE1 plus KE2# in MeV.
B3 = .848 528 146 743 774 Beta3 with KE SUM and MO.
VS = .848 528 146 743 774 ***Velocity SUM in AUTODYNAMICS***
-------------> Beta1 = .600 000 023 841 857 9
|------------> Beta2 = .75
--------------------------> Beta3 = .848 528 146 743 774 4
*** Velocity SUM in AD *** VS = .848 528 146 743 774 4
VELOCITY SUM IN SR
BR1=.661 437 809 467 315 7 KE1=50 MV=200
MRO=150
MRV=200 (TEST)
KERT=50.000 01 (Test) MRV=200 BR1=.661 437 809 467
B2=.75
KER2=257.142 883 300 781 3 MV=200 B2=.75
VS1=.943 425 057 095 798 9 *** Br1=.661 437 809 467 B2=.75
KES1=307.142 883 300 781 3 KE1=50 KER2=257.142 883 300
BT1=.944 634 318 351 745 6 *** KES1=307.142 883 300 MRO=150
-------------> BetaR1 = .661 437 809 467 315 7
|------------> Beta2 = .75
--------------------------> BetaT1 = .944 634 318 351 745 6
*** Velocity SUM in SR *** VS1 = .943 425 057 095 798 9
VELOCITY SUM IN AD
With MV = 600 MeV and KE1 = 50 MeV.
-------------> Beta1 = .384 615 421 295 166
|------------> Beta2 = .75
--------------------------> Beta3 = .791 971 564 292 907 7
*** Velocity SUM in AD *** VS = .791 971 564 292 907 7
VELOCITY SUM IN SR
With MV = 600 MeV and KE1 = 50 MeV
-------------> BetaR1 = .399 652 600 288 391 1
|------------> Beta2 = .75
--------------------------> BetaT1 = .916 059 792 041 778 6
*** Velocity SUM in SR *** VS1 = .884 525 433 229 770 9