Hbar=e^2/e0c

[Garry Denke]

hbar=e^2*z0 ; hbar=e^2/e0*c ; hbar=e^2*u0*c

 

Garry W. Denke, Geologist/Geophysicist

Copyright © 1st April 2002

All rights reserved

 

 

Abstract:

 

hbar = e^2*z0

hbar = [(1.6021765(31) x 10^-19 A-s)^2] * (3.767303134... x 10^2 kg-m^2-sr/A^2-s^3)

hbar = 9.6705527(59) x 10^-36 kg-m^2-sr/s

 

hbar = e^2/e0*c

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 = 9.6705527(59) x 10^-36 kg-m^2-sr/s

 

hbar = e^2*u0*c

hbar = [(1.6021765(31) x 10^-19 A-s)^2] * (1.256637061... x 10^-6 kg-m-sr/A^2-s^2) * (2.99792458 x 10^8 m/s)

hbar = 9.6705527(59) x 10^-36 kg-m^2-sr/s

 

 

Introduction:

 

reduced Planck constant: hbar = 9.6705527(59) x 10^-36 kg-m^2-sr/s

elementary charge: e = 1.6021765(31) x 10^-19 A-s

impedance of vacuum: z0 = 3.767303134... x 10^2 kg-m^2-sr/A^2-s^3

electric constant: e0 = 8.854187817... x 10^-12 A^2-s^4/kg-m^3-sr

speed of light in vacuum: c = 2.99792458 x 10^8 m/s

magnetic constant: u0 = 1.256637061... x 10^-6 kg-m-sr/A^2-s^2

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

Planck constant: h = 6.6260693(11) x 10^-34 kg-m^2/s

molar mass: M = 3.2858629(47) x 10^16 kg/mol

dielectric constant: ke = 1.4594705(10) x 10^-2 sr

 

 

Derivation:

 

1) temperature: [(h*c^5/G)^1/2]/k = 3.5518626(92) x 10^32 K

2) electric current: e/[(h*G/c^5)^1/2] = 1.1857531(48) x 10^24 A

3) dielectric constant: e^2/(e0*h*c) = 1.4594705(14) x 10^-2 sr

4) fine-structure constant: e^2/(2*e0*h*c) = 7.2973525(68) x 10^-3 rad

5) mass: (h*c/G)^1/2 = 5.4563031(18) x 10^-8 kg

6) amount of substance: [(h*c/G)^1/2]/M = 1.6605388(62) x 10^-24 mol

7) length: (h*G/c^3)^1/2 = 4.0507625(15) x 10^-35 m

8) luminous intensity: [(h*G/c^5)^1/2]/ke = 9.2580762(94) x 10^-42 cd

9) time: (h*G/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) inverse 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) molar concentration = 2.4982661(10) x 10^79 mol/m^3

012) surface tension = 2.9885899(39) x 10^78 kg/s^2

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) surface concentration = 1.0119882(71) x 10^45 mol/m^2

026) force = 1.2106068(10) x 10^44 kg-m/s^2

027) frequency = 7.4008895(10) x 10^42 /s

028) inverse luminous intensity = 1.0801379(99) x 10^41 /cd

029) angular velocity = 5.4006900(07) x 10^40 rad/s

030) mass flow rate = 4.0381496(51) x 10^35 kg/s

031) wave number = 2.4686710(13) x 10^34 /m

032) molar energy = 2.9531863(41) x 10^33 kg-m^2/s^2-mol

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) luminous flux density = 8.2346001(27) x 10^25 cd-sr/m^2

039) electric current = 1.1857531(48) x 10^24 A

040) Avogadro constant = 6.0221415(04) x 10^23 /mol

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) displacement = 4.4930474(34) x 10^18 kg-s/m^2

044) luminous density = 2.7467669(40) x 10^17 cd-sr-s/m^3

045) absorbed dose = 8.987551787… x 10^16 m^2/s^2

046) molar mass = 3.2858629(47) x 10^16 kg/mol

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 = 8.987551788... x 10^9 kg-m^3-sr/A^2-s^4-(4pi)

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) inverse mass = 1.8327427(53) x 10^7 /kg

054) Faraday constant = 9.6485337(83) x 10^4 A-s/mol

055) von Klitzing constant = 2.5812807(51) x 10^4 kg-m^2/A^2-s^3

056) inverse conductance quantum = 1.2906403(76) x 10^4 kg-m^2-rad/A^2-s^3-sr

057) impedance of vacuum = 3.767303134… x 10^2 kg-m^2-sr/A^2-s^3

058) inverse fine-structure constant = 1.3703599(91) x 10^2 /rad

059) relative permeability = 6.8517999(54) x 10^1 /sr

060) momentum = 1.6357585(24) x 10^1 kg-m/s

061) molar gas constant = 8.3144721(42) x 10^0 kg-m^2/s^2-mol-K

062) spin two = 2.00000000 x 10^0 sr/rad

063) spin one = 1.00000000 x 10^0 rad/rad, sr/sr

064) spin one-half = 5.00000000 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 quantum = 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) mass = 5.4563031(18) x 10^-8 kg

073) radiant distribution = 3.335640952... x 10^-9 s/m

074) Stefan-Boltzmann constant = 1.3897144(61) x 10^-9 kg/s^3-K^4

075) molar Planck constant = 3.9903127(01) x 10^-10 kg-m^2/s-mol

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 quantum = 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 spectral radiance = 1.1910428(22) x 10^-16 kg-m^4-sr/s^3-rad

086) first radiation = 5.9552141(09) x 10^-17 kg-m^4-rad-(4pi)/s^3-sr

087) molality = 3.0433405(66) x 10^-17 mol/kg

088) elementary charge = 1.6021765(31) x 10^-19 A-s

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) amount of substance = 1.6605388(62) x 10^-24 mol

092) inverse electric current = 8.4334585(30) x 10^-25 /A

093) kinematic viscosity = 1.2143880(51) x 10^-26 m^2/s

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^-80 m^3/mol

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:

 

1. Whilhelm Frederick Denke, Sr "H-BAR" (1888) GDG

2. William Herman Denke, Sr "H-Bar" (1947) GDG

3. http://physics.nist.gov/cuu/Constants

[Queso]

so um...what's that supposed to mean?

[UncleAl]

This idiot has spammed bulletin boards and sci.physics (where he got his ears pinned back but good) with this trash. Ban him and purge his spam.

[infamous]

This idiot has spammed bulletin boards and sci.physics (where he got his ears pinned back but good) with this trash. Ban him and purge his spam.

 

I agree Uncle, What's this guy trying to prove anyway???

[sanctus]

As an admin: Even if you are right uncle al (that he spammed elsewhere), you are not supposed to insult him (calling him an idiot). This is a reminder.

[Garry Denke]

so um...what's that supposed to mean?

hbar=e^2/e0c means Dirac's constant is in error, orbsycli.

 

Garry Denke

[Qfwfq]

I agree with Sanctus, Uncle Al.

 

hbar=e^2/e0c means Dirac's constant is in error

What is Dirac's constant, Garry?

[Garry Denke]

What is Dirac's constant, Garry?

The reduced Planck constant, Qfwfq.

 

Planck invented hbar=h/(2 pi)

e^2/e0c shows hbar=e^2/e0c

 

Uncle Al is mad because Planck's error, the reduced Planck constant,

also known as Dirac's constant, affects his theories containing hbar.

 

Planck's error is not my fault, Qfwfq.

 

Garry Denke

[infamous]

The reduced Planck constant, Qfwfq.

 

Planck invented hbar=h/(2 pi)

e^2/e0c shows hbar=e^2/e0c

 

Uncle Al is mad because Planck's error, the reduced Planck constant,

also known as Dirac's constant, affects his theories containing hbar.

 

Planck's error is not my fault, Qfwfq.

 

Garry Denke

 

Why do you show e= 1.6021765 E-19 when it should be (1.6021765 E-19 times c, 2.99792458E+8 (10E-20) or in simpler terms: 4.80320431085E-10 esu.

 

Also; the fine structure constant = e^2/h-bar*c

 

(4.803043108 E-10^2) = 2.3069223097 E-19

 

The fine structure = 7.297325 E-3 =( 2.3069223097 E-19 / h-bar * 2.99792458 E+10 )

 

h-bar= (2.3069223097 E-19/(2.99792458 E+10 * 7.297325 E-3)

 

h-bar = 1.05450483969 E-27 (cgs units)

 

These figures diverge from CODATA slightly, but I chose to use the figures you gave in fairness to you.

[Garry Denke]

Why do you show e= 1.6021765 E-19 when it should be (1.6021765 E-19

times c, 2.99792458E+8 (10E-20) or in simpler terms: 4.80320431085E-10 esu.

Because, infamous, e =

http://physics.nist.gov/cgi-bin/cuu/Value?e|search_for=elecmag_in!

and Coulomb © is A-s

 

Garry Denke

[Garry Denke]

I agree Uncle, What's this guy trying to prove anyway???

In short the dielectric constant is in steradians

 

e/e0=ke

electric permittivity: e = 1.2922426(01) x 10^-13 A^2-s^4/kg-m^3

electric constant: e0 = 8.854187817... x 10^-12 A^2-s^4/kg-m^3-sr

dielectric constant: ke = 1.4594705(14) x 10^-2 sr

 

because the magnetic constant is in steradians

 

u/u0=km

magnetic permeability: u = 8.6102257(82) x 10^-5 kg-m/A^2-s^2

magnetic constant: u0 = 1.256637061... x 10^-6 kg-m-sr/A^2-s^2

relative permeability: km = 6.8517999(54) x 10^1 /sr

 

and electromagnetically ke times km = 1 unity.

 

hbar=e^2/e0c

reduced Planck constant: hbar = 9.6705527(59) x 10^-36 kg-m^2-sr/s

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

speed of light in vacuum: c = 2.99792458 x 10^8 m/s

 

h=e^2/e0c ke

Planck constant: h = 6.6260693(11) x 10^-34 kg-m^2/s

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

speed of light in vacuum: c = 2.99792458 x 10^8 m/s

dielectric constant: ke = 1.4594705(10) x 10^-2 sr

 

I hope this helps, infamous.

 

Garry Denke

[infamous]

In short the dielectric constant is in steradians

 

e/e0=ke

electric permittivity: e = 1.2922426(01) x 10^-13 A^2-s^4/kg-m^3

electric constant: e0 = 8.854187817... x 10^-12 A^2-s^4/kg-m^3-sr

dielectric constant: ke = 1.4594705(14) x 10^-2 sr

 

because the magnetic constant is in steradians

 

u/u0=km

magnetic permeability: u = 8.6102257(82) x 10^-5 kg-m/A^2-s^2

magnetic constant: u0 = 1.256637061... x 10^-6 kg-m-sr/A^2-s^2

relative permeability: km = 6.8517999(54) x 10^1 /sr

 

and electromagnetically ke times km = 1 unity.

 

hbar=e^2/e0c

reduced Planck constant: hbar = 9.6705527(59) x 10^-36 kg-m^2-sr/s

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

speed of light in vacuum: c = 2.99792458 x 10^8 m/s

 

h=e^2/e0c ke

Planck constant: h = 6.6260693(11) x 10^-34 kg-m^2/s

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

speed of light in vacuum: c = 2.99792458 x 10^8 m/s

dielectric constant: ke = 1.4594705(10) x 10^-2 sr

 

I hope this helps, infamous.

 

Garry Denke

 

Are you saying that h-bar is not equal to h/2pi, if you are, I must disagree.

 

Let e= 1.60217733E-20 emu,times 2.99792458E+10 (cm X sec.^-1)=(4.8032068E-10 esu)

 

Solve: e^2/h-bar*c = fine structure constant

 

Are you saying that e^2 does not equal (4.8032068E-10)^2, if you are, I must disagree.

 

For: e^2/(a * c) = h-bar

 

For: 2.307079556E-19/(7.29735308E-3 * 2.99792458E+10) = (1.05457266E-27)

[Dark Mind]

Can't wait to get to college so I can understand this stuff :hyper:, way over my head. I must be the youngest Moderator of a science forum ever :rant:. Oh well, I'll learn eventually :eek:.

[Qfwfq]

Don't worry to much Dark Mind, most of the definitions of these constants are more technical than scientific. Some of it is more of historical interest. I'll have a go now at figuring what scientific point Garry is trying to make...

 

Planck invented hbar=h/(2 pi)

e^2/e0c shows hbar=e^2/e0c

Planck defined Planck's constant h and then, in the early QM days, it proved useful to define hbar simply to save a bit of ink here and there. Even more ink can be saved by choosing units in which hbar = 1. Why do you say that Planck invented hbar?

 

Uncle Al is mad because Planck's error, the reduced Planck constant,

also known as Dirac's constant, affects his theories containing hbar.

Why do you call the reduced Planck constant "Planck's error"? Why does hbar=e^2/e0c mean that it's in error?

 

I did not mean it's your fault, anyway.

[nkt]

I have no idea what the point of posting the OP was.

 

It isn't a proof, nor is it even useful, and is will only serve to confuse people looking for the true values of those constants he has changed slightly.

 

Planck is pretty unlikely to be wrong, and if he had been, the various proofs would fail at various stages too. I remember we covered this and determined the values for h and hbar in various classes at uni, both experimentally and theoretically. h is used all over the place, and h(bar) is simply a mathematical construct to save ink, as Infamous correctly states.

h(bar) MUST be h/2PI, as this is its definition!

 

E = hν and λ = h / p are pretty exactly known.

 

This led directly to the development of our complete quantum theory of matter, quantum mechanics. h appears in the Shrodinger Equation of non-relativistic quantum mechanics, and the Dirac Equation of relativistic quantum mechanics. In quantum mechanical analysis, it turns out that the quantity most often used is h/2PI, and this is given the special symbol h(bar).

 

If, as a construct, it was wrong, then the deviance from theory would have been spotted in the experimental results for things such as laser interferometry, which is about as accurate as things get in the real world.

 

I agree with Al. If the guy isn't an idiot, then, he is even worse, and doing this on purpose. :hyper:

[infamous]

 

I agree with Al. If the guy isn't an idiot, then, he is even worse, and doing this on purpose. :hyper:

 

Thank you nkt for that well defined response, I believe however that he is neither an idiot nor is he purposely trying to mislead anyone. What he is, simply put is, mistaken. He has failed to understand that : e=1.60217733E-20 (emu) must be multiplyed by c= 2.99792458E+10 to equal 4.8032068E-10 (esu).

[sanctus]

Nkt, same reminder to you as to uncle al.