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

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Discussion Overview

This discussion revolves around the equation hbar = e^2 / (e0 * c) and its relation to fundamental physical constants. Participants explore various derivations and implications of this equation, touching on theoretical aspects and numerical values of constants such as the Planck constant, speed of light, and elementary charge.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Exploratory

Main Points Raised

  • Some participants present the equation hbar = e^2 / (e0 * c) and provide detailed derivations involving fundamental constants.
  • Others discuss the numerical values of constants like the Planck constant, speed of light, and elementary charge, citing their significance in the equation.
  • A few participants propose that the derivation of temperature and electric current from the equation suggests deeper connections between these physical quantities.
  • Some participants express uncertainty about the implications of the derived values for physical interpretations, particularly regarding the relationships between constants.
  • There are mentions of various derived quantities such as mass, luminous intensity, and electric field strength, with participants questioning how these relate back to the original equation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the implications of the equation or the derived quantities. Multiple competing views remain regarding the interpretations and significance of the relationships between the constants.

Contextual Notes

Some participants note limitations in the assumptions made during derivations, particularly regarding the definitions of constants and the conditions under which they hold true. There is also mention of unresolved mathematical steps in the derivations presented.

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/
 
Physics news on Phys.org
hbar=e^2/e0c

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

edit:
[tex]\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[/tex]

[tex]\hbar=1.055*10^{-34} J\cdot s[/tex]
 
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

[tex]\hbar[/tex] is about [tex]10^{-34}J\cdot s[/tex]; [tex]\frac{e^2}{\epsilon_0 c}[/tex] is about [tex]10^{-36}J\cdot s[/tex]. 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

[tex]\hbar[/tex] is about [tex]10^{-34}J\cdot s[/tex]; [tex]\frac{e^2}{\epsilon_0 c}[/tex] is about [tex]10^{-36}J\cdot s[/tex]. 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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