How Does the Equation hbar=e^2/e0c Relate to Fundamental Physical Constants?

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SUMMARY

The equation hbar = e^2/e0c is derived from fundamental physical constants, where hbar represents the reduced Planck constant, e is the elementary charge, e0 is the electric constant, and c is the speed of light in vacuum. The calculated value of hbar from the derivation is approximately 9.670552746 x 10^-36 kg-m^2/s, while the theoretical value from NIST is 1.05457168 x 10^-34 kg-m^2/s. This discrepancy indicates that the two quantities are not equal, with the derived value being nearly 100 times smaller than the theoretical value, thus confirming that the derivation is incorrect.

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Garry Denke
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Abstract:
hbar=e^2/e0c
hbar=[1.6021765(31) x 10^-19 A-s]^2/[8.854187817... x 10^-12 A^2-s^4/kg-m^3-sr][2.99792458 x 10^8 m/s]
hbar=[2.5669696(36) x 10^-38 A^2-s^2]/[2.6544187(29) x 10^-3 A^2-s^3/kg-m^2-sr]
hbar=[9.6705527(59) x 10^-36 kg-m^2-sr/s]

Introduction:
Planck constant: h = 6.6260693(11) x 10^-34 kg-m^2/s
speed of light in vacuum: c = 2.99792458 x 10^8 m/s
Newtonian constant: G = 6.6723635(22) x 10^-11 m^3/kg-s^2
Boltzmann constant: k = 1.3806504(11) x 10^-23 kg-m^2/s^2-K
elementary charge: e = 1.6021765(31) x 10^-19 A-s
electric constant: e0 = 8.854187817... x 10^-12 A^2-s^4/kg-m^3-sr
molar mass: M = 3.2858629(47) x 10^19 kg/kmol
dielectric constant: ke = 1.4594705(10) x 10^-2 sr
fine-structure constant: a = 7.2973525(68) x 10^-3 rad

Derivation:
1) temperature: [(hc^5/G)^1/2]/k = 3.5518626(92) x 10^32 K
2) electric current: e/[(hG/c^5)^1/2] = 1.1857531(48) x 10^24 A
3) dielectric constant: e^2/(e0hc) = 1.4594705(14) x 10^-2 sr
4) fine-structure constant: e^2/(2e0hc) = 7.2973525(68) x 10^-3 rad
5) mass: (hc/G)^1/2 = 5.4563031(18) x 10^-8 kg
6) amount of substance: [(hc/G)^1/2]/M = 1.6605388(62) x 10^-27 kmol
7) length: (hG/c^3)^1/2 = 4.0507625(15) x 10^-35 m
8) luminous intensity: [(hG/c^5)^1/2]/ke = 9.2580762(94) x 10^-42 cd
9) time: (hG/c^5)^1/2 = 1.3511889(33) x 10^-43 s

Conclusion:
001) radiance = 1.5154964(57) x 10^123 kg/s^3-sr
002) irradiance = 2.2118223(93) x 10^121 kg/s^3
003) radiant density = 7.3778453(51) x 10^112 kg/m-s^2
004) density = 1.5044912(03) x 10^103 /m^3
005) mass density = 8.2089600(41) x 10^95 kg/m^3
006) i. luminous efficacy = 2.6860106(85) x 10^95 kg-m^2/cd-sr-s^3
007) electric current density = 7.2263787(71) x 10^92 A/m^2
008) thermal transfer = 6.2272181(80) x 10^88 kg/s^3-K
009) electric charge density = 2.4104604(96) x 10^84 A-s/m^3
010) angular acceleration = 3.9969910(02) x 10^83 rad/s^2
011) surface tension = 2.9885899(39) x 10^78 kg/s^2
012) molar concentration = 2.4982661(10) x 10^76 kmol/m^3
013) dynamic viscosity = 9.9688629(88) x 10^69 kg/m-s
014) inverse area = 6.0943365(69) x 10^68 /m^2
015) electric field strength = 7.5560138(75) x 10^62 kg-m/A-s^3
016) surface density = 3.3252547(62) x 10^61 kg/m^2
017) absorbed dose rate = 6.6515877(76) x 10^59 m^2/s^3
018) magnetic field strength = 2.9272344(25) x 10^58 A/m
019) thermal conductivity = 2.5224981(98) x 10^54 kg-m/s^3-K
020) magnetic flux density = 2.5204149(31) x 10^54 kg/A-s^2
021) radiant intensity = 2.4867291(78) x 10^54 kg-m^2/s^3-sr
022) power = 3.6293079(12) x 10^52 kg-m^2/s^3
023) field acceleration = 2.2187308(58) x 10^51 m/s^2
024) electric flux density = 9.7642030(22) x 10^49 A-s/m^2
025) force = 1.2106068(10) x 10^44 kg-m/s^2
026) frequency = 7.4008895(10) x 10^42 /s
027) surface concentration = 1.0119882(71) x 10^42 kmol/m^2
028) inverse luminous intensity = 1.0801379(99) x 10^41 /cd
029) angular velocity = 5.4006900(07) x 10^40 rad/s
030) molar energy = 2.9531863(41) x 10^36 kg-m^2/s^2-kmol
031) mass flow rate = 4.0381496(51) x 10^35 kg/s
032) wave number = 2.4686710(13) x 10^34 /m
033) temperature = 3.5518626(92) x 10^32 K
034) electric conductivity = 9.5637447(08) x 10^29 A^2-s^3/kg-m^3
035) electric potential = 3.0607617(77) x 10^28 kg-m^2/A-s^3
036) luminance = 5.6421832(93) x 10^27 cd/m^2
037) mass field = 1.3469817(34) x 10^27 kg/m
038) Avogadro constant = 6.0221415(04) x 10^26 /kmol
039) luminous flux density = 8.2346001(27) x 10^25 cd-sr/m^2
040) electric current = 1.1857531(48) x 10^24 A
041) thermal conductance = 1.0218041(14) x 10^20 kg-m^2/s^3-K
042) magnetic potential = 1.0209602(33) x 10^20 kg-m/A-s^2
043) molar mass = 3.2858629(47) x 10^19 kg/kmol
044) displacement = 4.4930474(34) x 10^18 kg-s/m^2
045) luminous density = 2.7467669(40) x 10^17 cd-sr-s/m^3
046) absorbed dose = 8.987551787… x 10^16 m^2/s^2
047) electric displacement = 3.9552467(59) x 10^15 A-s/m
048) Josephson quantum = 4.8359787(85) x 10^14 A-s^2-sr/kg-m^2-rad
049) Josephson constant = 2.4179893(93) x 10^14 A-s^2/kg-m^2
050) Coulomb constant = 7.7384850(15) x 10^12 kg-m^3/A^2-s^4
051) energy = 4.9038806(85) x 10^9 kg-m^2/s^2
052) speed of light in vacuum = 2.99792458 x 10^8 m/s
053) Faraday constant = 9.6485337(83) x 10^7 A-s/kmol
054) inverse mass = 1.8327427(53) x 10^7 /kg
055) von Klitzing constant = 2.5812807(51) x 10^4 kg-m^2/A^2-s^3
056) i. conductance q. = 1.2906403(76) x 10^4 kg-m^2-rad/A^2-s^3-sr
057) molar gas constant = 8.3144721(42) x 10^3 kg-m^2/s^2-kmol-K
058) impedance of vacuum = 3.767303134… x 10^2 kg-m^2-sr/A^2-s^3
059) inverse fine-structure constant = 1.3703599(91) x 10^2 /rad
060) relative permeability = 6.8517999(54) x 10^1 /sr
061) momentum = 1.6357585(24) x 10^1 kg-m/s
062) spin two = 2.0000000 x 10^0 sr/rad
063) spin one = 1.0000000 x 10^0 rad/rad, sr/sr
064) spin one-half = 5.0000000 x 10^-1 rad/sr
065) dielectric constant = 1.4594705(14) x 10^-2 sr
066) second radiation = 1.4387752(25) x 10^-2 m-K
067) fine-structure constant = 7.2973525(68) x 10^-3 rad
068) magnetic permeability = 8.6102257(82) x 10^-5 kg-m/A^2-s^2
069) conductance q. = 7.7480917(13) x 10^-5 A^2-s^3-sr/kg-m^2-rad
070) electric conductance = 3.8740458(57) x 10^-5 A^2-s^3/kg-m^2
071) magnetic constant = 1.256637061... x 10^-6 kg-m-sr/A^2-s^2
072) molar Planck constant = 3.9903127(01) x 10^-7 kg-m^2/s-kmol
073) mass = 5.4563031(18) x 10^-8 kg
074) radiant distribution = 3.335640952... x 10^-9 s/m
075) Stefan-Boltzmann constant = 1.3897144(61) x 10^-9 kg/s^3-K^4
076) density of states = 2.0392013(27) x 10^-10 s^2/kg-m^2
077) Newtonian constant = 6.6723635(22) x 10^-11 m^3/kg-s^2
078) magnetic pole strength = 4.8032044(04) x 10^-11 A-m
079) electric constant = 8.854187817... x 10^-12 A^2-s^4/kg-m^3-sr
080) magnetic exposure = 2.9363774(27) x 10^-12 A-s/kg
081) electric permittivity = 1.2922426(01) x 10^-13 A^2-s^4/kg-m^3
082) magnetic flux = 4.1356674(39) x 10^-15 kg-m^2/A-s^2
083) magnetic flux q. = 2.0678337(20) x 10^-15 kg-m^2-rad/A-s^2-sr
084) specific heat = 2.5303770(36) x 10^-16 m^2/s^2-K
085) first radiation = 1.1910428(22) x 10^-16 kg-m^4-sr/s^3-rad
086) radiation = 5.9552141(09) x 10^-17 kg-m^4/s^3
087) elementary charge = 1.6021765(31) x 10^-19 A-s
088) molality = 3.0433405(66) x 10^-20 kmol/kg
089) thermal resistance = 9.7866116(02) x 10^-21 s^3-K/kg-m^2
090) Boltzmann constant = 1.3806504(11) x 10^-23 kg-m^2/s^2-K
091) inverse electric current = 8.4334585(30) x 10^-25 /A
092) kinematic viscosity = 1.2143880(51) x 10^-26 m^2/s
093) amount of substance = 1.6605388(62) x 10^-27 kmol
094) electric resistivity = 1.0456155(31) x 10^-30 kg-m^3/A^2-s^3
095) relative expansion = 2.8154241(50) x 10^-33 /K
096) Planck constant = 6.6260693(11) x 10^-34 kg-m^2/s
097) length = 4.0507625(15) x 10^-35 m
098) reduced Planck constant = 9.6705527(59) x 10^-36 kg-m^2-sr/s
099) absorption-emission = 2.4763817(25) x 10^-36 s/kg
100) inductance = 3.4877979(84) x 10^-39 kg-m^2/A^2-s^2
101) luminous intensity = 9.2580762(94) x 10^-42 cd
102) moment = 2.2102188(14) x 10^-42 kg-m
103) luminous flux = 1.3511889(33) x 10^-43 cd-sr
104) time = 1.3511889(33) x 10^-43 s
105) magnetic moment = 1.9456640(35) x 10^-45 A-m^2
106) capacitance = 5.234567901... x 10^-48 A^2-s^4/kg-m^2
107) electric moment = 6.4900366(34) x 10^-54 A-s-m
108) area = 1.6408676(95) x 10^-69 m^2
109) fluidity = 1.0031234(27) x 10^-70 m-s/kg
110) inertial moment = 8.9530715(22) x 10^-77 kg-m^2
111) molar volume = 4.0027761(50) x 10^-77 m^3/kmol
112) electric charge volume = 4.1485848(93) x 10^-85 m^3/A-s
113) luminous energy = 1.8257115(33) x 10^-86 cd-sr-s
114) electric current volume = 1.3838189(66) x 10^-93 m^2/A
115) luminous efficacy = 3.7229933(79) x 10^-96 cd-sr-s^3/kg-m^2
116) mass volume = 1.2181811(03) x 10^-96 m^3/kg
117) volume = 6.6467653(52) x 10^-104 m^3
118) radiant volume = 1.3554092(73) x 10^-113 m-s^2/kg
119) inverse irradiance = 4.5211586(75) x 10^-122 s^3/kg
120) inverse radiance = 6.5984977(75) x 10^-124 s^3-sr/kg

Bibliography:
http://physics.nist.gov/cuu/Constants/
 
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hbar=e^2/e0c

Err... no it doesn't.
 
Rubbish. Off by two orders of magnitude!

edit:
\frac{e^2}{\epsilon_0 c}=9.668\times 10^{-36} \frac{C^2}{(F/m)(m/s)}=C\cdot V\cdot s=J\cdot s

\hbar=1.055*10^{-34} J\cdot s
 
Last edited by a moderator:
Planck constant, h, is a measured quantity, but hbar is not.

According to NIST measured quantity h
Planck constant: h = 6.6260693 x 10^-34 kg-m^2/s
http://physics.nist.gov/cgi-bin/cuu/Value?h|search_for=universal_in!

According to NIST theoretical quantity h/(2 pi)
Planck constant/(2 pi): hbar = 1.05457168 x 10^-34 kg-m^2/s
http://physics.nist.gov/cgi-bin/cuu/Value?hbar|search_for=universal_in!

Accurate Measurement of the Planck Constant
Edwin R. Williams, Richard L. Steiner, David B. Newell, and Paul T. Olsen
Physical Review Letters 81 (22) 2404-2407 (1998)

Planck constant, h, is a measured quantity, but hbar is not.

NIST derivation quantity e^2/e0c
e = 1.60217653 x 10^-19 A-s
http://physics.nist.gov/cgi-bin/cuu/Value?e|search_for=elecmag_in!
e0 = 8.854187817... x 10^-12 A^2-s^4/kg-m^3
http://physics.nist.gov/cgi-bin/cuu/Value?hbar|search_for=universal_in!
c = 299792458 m/s
http://physics.nist.gov/cgi-bin/cuu/Value?c|search_for=universal_in!

Solve: e^2/e0c = ?
[(1.60217653 x 10^-19 A-s)^2]/(8.854187817... x 10^-12 A^2-s^4/kg-m^3)(299792458 m/s) = ?
(2.566969633 x 10^-38 A^2-s^2)/(2.654418729... x 10^-3 A^2-s^3/kg-m^2) = ?
9.670552746 x 10^-36 kg-m^2/s

NIST theoretical quantity h/(2 pi)
h = 6.6260693 x 10^-34 kg-m^2/s
http://physics.nist.gov/cgi-bin/cuu/Value?h|search_for=universal_in!
(2 pi) = 6.283185307
http://physics.nist.gov/cgi-bin/cuu/Category?view=html&Universal.x=65&Universal.y=8

Solve: h/(2 pi)
(6.6260693 x 10^-34 kg-m^2/s)/(6.283185307)
1.05457168 x 10^-34 kg-m^2/s

Compare: hbar derivation / hbar theoretical
9.670552746 x 10^-36 kg-m^2/s (hbar derivation)
1.05457168 x 10^-34 kg-m^2/s (hbar theoretical)

Garry Denke
 
Don't quote unnecessary information.

Look at your numbers:
Compare: hbar derivation / hbar theoretical
9.670552746 x 10^-36 kg-m^2/s (hbar derivation)
1.05457168 x 10^-34 kg-m^2/s (hbar theoretical)
edit: emphasis added

\hbar is about 10^{-34}J\cdot s; \frac{e^2}{\epsilon_0 c} is about 10^{-36}J\cdot s. The second is almost a hundred times bigger than the first; they are not equal.
 
Last edited by a moderator:
rachmaninoff said:
Look at your numbers:
edit: emphasis added

\hbar is about 10^{-34}J\cdot s; \frac{e^2}{\epsilon_0 c} is about 10^{-36}J\cdot s. The second is almost a hundred times bigger than the first; they are not equal.
That is the point rachmaninoff.

e^2/e0c = hbar is a derivation,
h/(2 pi) = hbar is only a theory.

GarryDenke
 
This looks TD-worthy.

e^2/e0c = hbar is a derivation,

How did you think you derived it? (I'm just curious, it's obviously not correct).

h/(2 pi) = hbar is only a theory.
No, it's a definition.
 

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