Electron Mass - New Algorithm Discussion, continued

https://energywavetheory.com/subatomic-particles/electron/

(2) The electron mass:

error, dx, $e_m$

-0.0005446185946568205, 1e-34, 9.109383560899034e-31

-0.0004348416825593615, 1e-34, 9.110383560899034e-31

-0.0003250647704619025, 1e-34, 9.111383560899033e-31

-0.00021528785836444353, 1e-34, 9.112383560899032e-31

-0.0001055109462667625, 1e-34, 9.113383560899032e-31

0.0000042659658308075166, 1e-34, 9.114383560899031e-31

0.0000042659658308075166, 9.999999999999999e-36, 9.114383560899031e-31

0.0000042659658308075166, 1e-36, 9.114383560899031e-31

0.000003168196709646409, 1e-36, 9.11437356089903e-31

0.0000020704275887073464, 1e-36, 9.11436356089903e-31

9.726584677682837e-7, 1e-36, 9.11435356089903e-31

-1.2511065350384598e-7, 1e-36, 9.11434356089903e-31

-1.2511065350384598e-7, 9.999999999999999e-38, 9.11434356089903e-31

-1.5333741276712942e-8, 9.999999999999999e-38, 9.11434456089903e-31

-1.5333741276712942e-8, 9.999999999999998e-39, 9.11434456089903e-31

-4.356050076204099e-9, 9.999999999999998e-39, 9.11434466089903e-31

-4.356050076204099e-9, 9.999999999999998e-40, 9.11434466089903e-31

-3.2582810893799774e-9, 9.999999999999998e-40, 9.11434467089903e-31

-2.160511880511251e-9, 9.999999999999998e-40, 9.114344680899031e-31

-1.0627426716425248e-9, 9.999999999999998e-40, 9.114344690899031e-31

3.502664824850399e-11, 9.999999999999998e-40, 9.114344700899032e-31

(5) Permittivity of free space:

error, dx, $\epsilon_0$

-0.0005446185946568205, 1e-15, 8.854187817e-12

-0.0003186985089359551, 1e-15, 8.853187817e-12

-0.00009270185473797543, 1e-15, 8.852187817e-12

-0.00009270185473797543, 1.0000000000000001e-16, 8.852187817e-12

-0.00007009797671997386, 1.0000000000000001e-16, 8.852087817e-12

-0.00004749333263676103, 1.0000000000000001e-16, 8.851987817e-12

-0.00002488792245347593, 1.0000000000000001e-16, 8.851887817e-12

-0.0000022817461350355117, 1.0000000000000001e-16, 8.851787817000001e-12

-0.0000022817461350355117, 1e-17, 8.851787817000001e-12

-2.108636454334345e-8, 1e-17, 8.851777817000002e-12

-2.108636454334345e-8, 1e-18, 8.851777817000002e-12

-2.108636454334345e-8, 1.0000000000000001e-19, 8.851777817000002e-12

1.5202716863171872e-9, 1.0000000000000001e-19, 8.851777717000002e-12

1.5202716863171872e-9, 1.0000000000000001e-20, 8.851777717000002e-12

-7.403918589332648e-10, 1.0000000000000001e-20, 8.851777727000002e-12

-7.403918589332648e-10, 1.0000000000000001e-21, 8.851777727000002e-12

-5.143258041684362e-10, 1.0000000000000001e-21, 8.851777726000002e-12

-2.882593053143978e-10, 1.0000000000000001e-21, 8.851777725000002e-12

-6.219280646035941e-11, 1.0000000000000001e-21, 8.851777724000002e-12

(1) Planck's Constant:

error, dx, h

-0.0005446185946568205, 1e-37, 6.62607004e-34

-0.00009172484027375472, 1e-37, 6.62507004e-34

-0.00009172484027375472, 1.0000000000000001e-38, 6.62507004e-34

-0.00004642042436875382, 1.0000000000000001e-38, 6.62497004e-34

-0.0000011132730078911024, 1.0000000000000001e-38, 6.6248700400000005e-34

-0.0000011132730078911024, 1.0000000000000001e-39, 6.6248700400000005e-34

-0.0000011132730078911024, 1.0000000000000001e-40, 6.6248700400000005e-34

-6.601876793022043e-7, 1.0000000000000001e-40, 6.62486904e-34

-2.0710207759844224e-7, 1.0000000000000001e-40, 6.62486804e-34

-2.0710207759844224e-7, 1.0000000000000001e-41, 6.62486804e-34

-1.617935022624195e-7, 1.0000000000000001e-41, 6.62486794e-34

-1.1648492426186152e-7, 1.0000000000000001e-41, 6.62486784e-34

-7.117634359676828e-8, 1.0000000000000001e-41, 6.62486774e-34

-2.5867760267139772e-8, 1.0000000000000001e-41, 6.62486764e-34

1.9440826282135504e-8, 1.0000000000000001e-41, 6.62486754e-34

1.9440826282135504e-8, 1.0000000000000002e-42, 6.62486754e-34

1.4909967482878983e-8, 1.0000000000000002e-42, 6.62486755e-34

1.0379108905667067e-8, 1.0000000000000002e-42, 6.62486756e-34

5.848250106410546e-9, 1.0000000000000002e-42, 6.62486757e-34

1.3173915291986305e-9, 1.0000000000000002e-42, 6.62486758e-34

1.3173915291986305e-9, 1.0000000000000003e-43, 6.62486758e-34

8.643059601354253e-10, 1.0000000000000003e-43, 6.624867581e-34

4.1122016902761516e-10, 1.0000000000000003e-43, 6.624867581999999e-34

-4.1865733102497416e-11, 1.0000000000000003e-43, 6.624867582999999e-34

The fine-structure constant, $\alpha$ is squared, thus, like the proton radius going negative, $\alpha$  reduces the error towards ZERO (0) by increasing to a LARGE value.

Once a second set of constants is generated from the first step of the algorithm, the error will be compared to the original 0.000544 and comments/analysis made/continued.

Ongoing... ...note: these posts are investigative - will summarize findings after investigation.

BASIC code (simple) as of 5/20/2023:

10 PRINT "Hello World"

100 Rem New Algorith 1.1 5/15/2023 MR

102 count = 0

106 print "error, dx, q"

110 Dim x2(7),sign(7), dx(7)

120 Rem Init some vars

125 aminerr=1.0

132 res = 1e-10

200 xpi=3.14159265358979323846

250 rem 8 coefs here

255 Rem elementary charge (e)-0

260 x2(0)=1.60217662e-19

263 xorig(0)=x2(0)

265 Rem Planck's constant (h)-1

300 x2(1)=6.62607004e-34

325 xorig(1)=x2(1)

350 rem electron mass (Me)-2

400 x2(2)=9.109383560899034e-31

425 xorig(2)=x2(2)

450 Rem Proton radius (Rp)-3

500 x2(3)=8.41235640479985e-16

525 xorig(3)=x2(3)

550 Rem Rydberg Constant (R_H or R_{\infty})-4

600 x2(4)=10973731.5685083

605 xorig(4)=x2(4)

610 Rem Permittivity of free space (e0)-5

620 x2(5)=8.854187817e-12

650 xorig(5)=x2(5)

701 Rem Speed of Light (c)-6

702 x2(6)=299792458.0

704 xorig(6)=x2(6)

706 Rem fine-structure constant (\alpha)-7

708 x2(7)=0.00729735256

709 xorig(7)=x2(7)

710 For i = 0 to 7

720 sign(i)=0

730 next i

740 dx(0) = 0.001e-19

741 dx(1) = 0.001e-34

742 dx(2) = 0.001e-31

743 dx(3) = 1e-16

744 dx(4) = 10000000.0

745 dx(5) = 0.001e-12

746 dx(6) = 10000000.0

747 dx(7) = 0.001

750 Rem define bit to be twiddled here

1030 eold = err

1050 gosub 1600

1051 REM enter starting values here (temporary initial start)

1075 rem x2(0)=1.602e-19

1076 rem x2(1)=6.626e-34

1077 rem x2(2)=9.109e-31

1078 rem x2(3)=8.0e-16

1080 REM EDIT "i" to select constant 0,1,2... etc.

1090 i = 1 

1100 print err;", ";dx(i);", ";x2(i)

1150 rem Main Loop1 

1210 z1=x2(i)+dx(i)

1220 z2=x2(i)-dx(i)

1230 xsave=x2(i)

1240 x2(i)=z1

1250 eold = err

1260 gosub 1600

1270 e1=err

1280 x2(i)=z2

1290 gosub 1600

1300 e2=err

1310 x2(i)=xsave

1320 err = eold

1325 rem print x2(i),z1,z2

1327 rem print err,e1,e2

1330 if abs(e1) < abs(err) then x2(i)=z1

1332 if abs(e1) < abs(err) then aminerr=e1

1340 if abs(e2) < abs(err) then x2(i)=z2

1342 if abs(e2) < abs(err) then aminerr=e2

1350 if (abs(e1) >= abs(err)) and (abs(e2) >= abs(err)) then dx(i)=dx(i)/10.0

1360 if abs(aminerr) < res then goto 1500

1370 gosub 1600

1380 goto 1100

1500 gosub 1600

1510 print err;", ";dx(i);", ";x2(i)

1525 end

1550 REM Subroutines:

1600 rem starting error

1700 xerr1=x2(2)*x2(0)^4/(8*x2(6)*x2(5)^2*x2(1)^3*x2(4))

1800 yerr2=-xpi*x2(3)*x2(4)/(x2(7)^2)

1900 err = xerr1 + yerr2 - 1.0

2000 return

One slight modification to the polynomial is to use the $m_e\over m_p$ format, working with the proton mass, then calculating the radius afterwards...