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S p a c e - T i m e D i m e n s i o n s a n d N a t u r a l U n i t V a l u e s

o fP h y s i c a l Q u a n t i t i e s

byRonald W. Satz, Ph.D.*Transpower Corporation

Abstract

This paper presents the derivation of the space-time dimensions and the natural unit values of physical quantities in theReciprocal System. The factors include space, s, and time, t, only (with auxiliary units of cycles, revolutions, radians, andsteradians). The appropriate time-space region (macroscopic) value and/or time region (microscopic) value of space is usedfor the various mechanical, electrical, magnetic, thermal, and photonic units. The dimensional system of the ReciprocalSystem is unique: no previous system compares.

keywords: space, time, dimensional systems, natural physical units, mechanical units, electrical units, magnetic units,thermal units, photonic units

*The author is president of Transpower Corporation, a commercial and custom software manufacturing company and engineering/physicsconsultancy. Mailing address: P. O. Box 7132, Penndel, PA 19047. He is a full member of ASME, SAE, INFORMS, ISUS, and SIAM.

space_time_dimensions_units.mcd 2

Introduction and Literature Survey

Many dimensional systems exist; Ref. [3], pp. 146-166 and pp. 386-418, provides the most detailed treatment of these.Included are the dynamical system, the gravitational system, the astrophysical system, the electrophysical system, theelectrotechnical system, the "definitive" system, the "practical" system, the energetical system, the electrostatic system,the electromagnetic system, the thermophysical system, the thermotechnical system, the Gaussian or cgs system, and theMKS or SI system. None of these systems is "natural" in the sense of being based on the fundamental properties ofspace and time.

Dewey B. Larson, the originator of the Reciprocal System of theory, was the first theoretician to ground a dimensionalsystem on the true physical realities of space and time. He presented his new dimensional system in Ref. [1], first ed.,pp.25-27, pp. 73-83, pp. 210-211; Ref. [1], second ed., pp. 157-171; and Ref. [2], pp. 102-111, pp. 183-186, pp. 219-229.

This paper extends the work to the calculation of the space-time units, the cgs units, and the SI units of all mechanical,electrical, magnetic, thermal, and photonic physical quantities for the time-space region and/or the time region, asappropriate. A convenient table summarizing the results is presented at the end.

Ref. [4], [5], [6], and [7] provide conversion factors for going to and from the cgs and SI systems. Most of the factorsprovided are given to three decimal places only. For more precise work, one would have to use the conversion factors inRef. [5], pp. 1-23 to 1-32, which are expressed to five or six decimal places.

James Clerk Maxwell, in Ref. [8], Vol. 2, p. 267, gives a table of electric and magnetic dimensions which are quitebizarre--yet this physicist is considered to be the greatest of the 19th century. Nonetheless he did provide one very usefulsuggestion in Vol. 1, p. 5: "If we adopt the units of length and time derived from the vibrations of light, then the unit ofvelocity is the velocity of light." Unfortunately, Maxwell didn't follow up on his own suggestion, but Larson did!

The space-time dimensions given in this paper apply to our half of the universe, the material sector. The space-timedimensions for the other half of the universe, the cosmic sector, are just the inverse, with space and time interchanged.


Nomenclature for Natural Units--see Table at end of paper for values in space-time, cgs, and SI units

Au = area (time-space region)

Au = magnetic vector potential

At_u = area (time region)

Av = Avogadro's number

au = linear acceleration (time-space region)

au = thermal diffusivity

at_u = linear acceleration (time region)

Be_u = photonic energy brightness (per steradian)

B_u = photonic brightness in given direction

Bu = magnetic flux density (time-space region)

Bt_u = magnetic flux density (time region)

Cu = capacitance

cp_u = specific heat at constant pressure (molar)

cv_u = specific heat at constant volume (molar)


cu = speed of light

Du, du = space (atomic diameter)

Du = electric flux density (time-space region)

Dt_u = electric flux density (time region)

Du = electric displacement (time_space region)

Dt_u = electric displacement (time region)

Ea_u = photonic irradiance (absorbed)

Eu = energy, work, heat (time-space region); includes electric energy

Eu = electric field intensity (time-space region)

Eu = photonic illuminance (intensity of illumination over )

Eu_photon = energy of unit frequency photon

Et_u = energy, work, heat (time region)

Et_u = electric field intensity (time region)

FM_u = magnetomotive force (time-space region)

FM_t_u = magnetomotive force (time region)


Fu = force (time-space region)

Ft_u = force (time region)

frot = rotational vibration frequency (subscript rev = revolutions/sec, subscript rad = radians/sec)

Gu = electric conductance

Ha_u = luminous exposure solid angle

He_u = radiant energy exposure

Hu = magnetic field intensity (time-space region)

Ht_u = magnetic field intensity (time region)

hu_G = specific molar enthalpy of gas

hu_SL = specific molar enthalpy of solid/liquid

hu_V = specific molar enthalpy of vapor

Ia_u = illuminance (intensity of illumination over solid angle )

Ie_u = radiant intensity (per steradian)

IR = inter-regional ratio

Iu_G = specific molar internal energy of gas


Iu_SL = specific molar internal energy of solid/liquid

Iu_V = specific molar internal energy of vapor

Iu = moment of inertia (time-space region)

It_u = moment of inertia (time region)

iu = electric current

ju = electric current density (time-space region)

jt_u = electric current density (time region)

Lu = rotational momentum

Lu = magnetic inductance

Me_u = luminosity (radiance, emitted)

Mu = linear momentum

Mu = magnetic charge or flux

MM_u = magnetization (time-space region)

MM_t_u = magnetization (time region)

mu = mass


PG_u, Pu = pressure (gas)

PL_u = pressure (liquid)

PM_u = magnetic polarization (time-space region)

PM_t_u = magnetic polarization (time region)

PS_u = pressure (solid)

PV_u, Pu = pressure (vapor)

Pu = electric polarization (time-space region)

Pt_u = electric polarization (time region)

pu = power (time-space region); includes electric power

pu = electric dipole moment

pt_u = power (time region)

pt_u = electric dipole moment (time region)

Qu = electric charge or flux

Qu = luminous energy (for solid angle )

qu = electric quantity

R = linear vibration frequency


Re_u = luminance (radiance, emitted over solid angle )

RM_u = magnetic reluctance

Ru = electric resistance

Ru = luminance (radiance, emitted over )

R_u = thermal resistance

Su = molar specific entropy

S_u = thermal conductance

su = space (time-space region)

st_u = space (time region)

TG_u = temperature (gas)

TSL_u = temperature (solid, liquid)

TV_u = temperature (vapor)

Tu = torque (time-space region)

Tt_u = torque (time region)

tu = time

Vu = volume (time-space region)


Vu = specific volume (time-space region)

Vu = electric voltage or potential

Vt_u = volume (time region)

Vt_u = specific volume (time region)

vrot, u = rotational velocity

vu = linear velocity (time-space region)

vt_u= linear velocity (time region)

u = angular acceleration (subscript rev = rev/sec2, subscript rad = rad/sec2)

u = thermal diffusivity (gas)

t_u = thermal diffusivity (solid, liquid)

L_u = surface tension (liquid)

e_u = radiant flux

v_u = luminous flux (for solid angle )

0 = electric permittivity (free space)

u = dynamic viscosity


u = thermal conductivity

0 = magnetic permeability (free space)

c_u = magnetic moment from curret (time-space region)

c_t_u = magnetic moment from curret (time region)

L = Larson magneton (atomic magnetic moment)

u = magnetic dipole moment (time-space region)

t_u = magnetic dipole moment (time region

u = kinematic viscosity

u = linear vibration frequency

u, du = density (time-space region)

u = electric charge volume density (time-space region)

t_u = electric charge volume density (time region)

t_u = electric resistivity

u = electric resistivity

t_u, dt_u = density (time region--atoms)


_u = thermal resistivity

tu = electric conductivity

_u = magnetic susceptibility (free space)

_u = electric susceptibility (free space)

Note 1: A black square in the upper right of an equation means that the equation is disabled from running in Mathcad. This is done because not allvariables in the equation have, as yet, been given numerical values at that point in the program.

Note 2: We have attempted to use the same symbols here as in other papers and books on the Reciprocal System, but given the large number ofsymbols necessary, there will be some differences. Please consult the nomenclature of each individual paper for the symbols used in that paper. Also,in a few cases, duplicate symbols for different properties have been used, but no ambiguity should result; always consider the context.

Note 3: In the following equations, the subscript "u" in the variables will apply to the natural space-time units (stated in cm, sec, and auxiliary units, ifany); for cgs values, the subscript cgs will be used; and for SI values, the subscript SI will be used. If only cm and sec and auxiliary units are used, thecgs subscript will usually be left off. The subscript t means the time region value.

Note 4: The calculated values of the natural units are given to six decimal places. Because there is some uncertainty in the speed of light and theRydberg frequency of H1 there is uncertainty in the 5th and 6th decimal place. For most scientific and engineering work, four decimal places shouldsuffice; the slight differences in the values given in the various books and papers of the Reciprocal System are de minimis.


1. Mechanical Units

a. space, time, translational speed

In pure natural units, the Reciprocal System time-space region equation for velocity is, of course,

natural_unit_speed natural_unit_spacenatural_unit_time

(1a)

1 11

(1b)

All natural physical units in the Reciprocal System are 1, of course! To get anything useful out of the theory we must identifythe corresponding physical quantities expressed in conventional units, such as in cgs or SI. Obviously, the speed of light isthe natural unit speed of the universe, and so we have:

c 11

(1c)

In many Reciprocal System books and papers we use this cgs value for c:

cu 2.997925 1010 cm/sec (1d)


The physics/chemistry establishment (Ref. [5], p. 1-1) has recently "fixed" the value at

cu 2.99792458 1010 (1e)cm/sec

In Ref. [1], 2nd ed., p. 160, Larson used this value:

(1f)cu 2.997930 1010 cm/sec

Depending on which particular value one chooses, the values of the resultant natural unit of space and natural unit of timeexpressed in conventional units will be slightly different.

In order to get the natural unit of time, we use the Rydberg frequency of H1--this is the natural unit frequency. In most ReciprocalSystem books and papers, we use this value for R (with the auxiliary unit cycles):

R 3.288057 1015 cycles/sec νu R (2)

Unfortunately, the physics/chemistry establishment has switched to the "infinite mass" definition for this constant, rather thanthat based on the unit mass of H1. We think this is an error, and so we will continue to use the above value.

In the unit linear vibration of a Rydberg photon, there are two units of space and two units of time, one of each for up and one ofeach for down. The natural unit value of time can therefore be calculated by taking 1/2 the inverse of R:

tu1

2 R tu 1.520655 10 16 sec (3)


With cu and tu known, su can be found:

(4a)su cu tu su 4.558809 10 6 cm

But this value is bit lower than what we have commonly used in the Reciprocal System:

su 4.558816 10 6 cm (4b)

This implies that the "true" speed of light is

cusutu

cu 2.997929 1010 cm/sec vu cu (1g)

As you can see, there is some uncertainty in the last two digits. For our purposes here, and to stay consistent with previouswork, we will stick with using the value of su from Eq. (4b) and the value of cu from Eq. (1g). All of the values of c round to thevalue given by Larson, regardless. (In the Table below, the value from Eq. (1d) will be put below the value from Eq. (1g), as analternate.)

The SI values are

su_SI 4.558816 10 8 m (4c)

cu_SI 2.997929 108 m/sec vu_SI cu_SI (1h)


The above values are all for the macroscopic time-space region. For the microscopic time region values, we must divide bythe inter-regional ratio (see Ref. [1], 2nd ed., p. 154, p. 162):

(5)IR 156.4444

st_usuIR

st_u 2.914017 10 8 cm (6a)

(6b)st_u_SI 2.914017 10 10 m

A specialized length unit is used for atomic diameter. In the Reciprocal System, the atom is the same size as the supposed"nucleus" of the conventional atomic theory. Using the Reciprocal System alpha-particle scattering theory and a reflectionangle of 156o, the standard angle used, the natural unit value of atomic diameter can be shown to be

Du 3.359 10 13 cm (7a)

Du_SI 3.359 10 15 m (7b)

(See Appendix 1 for a derivation.)

The time-region unit velocity is obviously

(8a)vt_ust_utu

vt_u 1.916291 108 cm/sec

(8b)vt_u_SI 1.916291 106 m/sec


b. area and volume

Au su2 Au 2.078280 10 11 cm2 (9a)

Au_SI 10 4 Au Au_SI 2.078280 10 15 m2 (9b)

(10a)At_u st_u2 At_u 8.491494 10 16 cm2

At_u_SI 10 4 At_u (10b)At_u_SI 8.491494 10 20 m2

Vu su3 cm3 (11a)Vu 9.474498 10 17

Vu_SI 10 6 Vu Vu_SI 9.474498 10 23 m3 (11b)

Vt_u st_u3 Vt_u 2.474435 10 23 cm3 (12a)

Vt_u_SI 10 6 Vt_u Vt_u_SI 2.474435 10 29 m3 (12b)

space_time_dimensions_units.mcd 17c. rotational speed and frequency

The unit rotational speeds are the same as the unit translational speeds. But the natural unit rotational vibration frequencyis different from the natural unit linear vibration frequency. By inspection,

frot_rev2 R

π or frot_rev

1π tu

frot_rev 2.093242 1015 rev/sec (13a)

In terms of radians: frot_rad2tu

frot_rad 1.315223 1016 rad/sec (13b)

space_time_dimensions_units.mcd 18d. acceleration

The various acceleration values follow, by definition:

ausu

tu2

au 1.971473 1026 cm/sec2 (14a)

au_SI 10 2 au au_SI 1.971473 1024 m/sec2 (14b)

at_ust_u

tu2

at_u 1.260175 1024 cm/sec2 (15a)

at_u_SI 10 2 at_u at_u_SI 1.260175 1022 m/sec2 (15b)

αu_rev1

π tu2

αu_rev 1.376540 1031 rev/sec2 (16a)

In terms of radians,

αu_rad2

tu2

αu_rad 8.649055 1031 rad/sec2 (16b)


e. mass

Mass in the Reciprocal System is

mutu

3

su3

mu 3.711383 10 32 sec3/cm3 (17a)

There is no time region value! Unit atomic mass, 1 amu (not u), can be identified as the conventional equivalent. Therefore

(17b)mu_cgs 1.659790 10 24 g

mu_SI 1.659790 10 27 (17c)kg


f. density

The density values then follow, by inspection:

ρutu

3

su6

ρu 3.917235 10 16 sec3/cm6 (18a)

ρu_cgsmu_cgs

su3

ρu_cgs 1.751850 10 8 g/cm3 (18b)

ρu_SImu_SI

su_SI3

ρu_SI 1.751850 10 5 kg/m3 (18c)

ρt_u

tu3

su3

st_u3

ρt_u 1.499891 10 9 sec3/cm6 (19a)

ρt_u_cgsmu_cgs

st_u3

ρt_u_cgs 6.707752 10 2 g/cm3 (19b)

ρt_u_SI 103ρt_u_cgs ρt_u_SI 6.707752 101 kg/m3 (19c)


g. specific volume

Specific volume is the inverse of density.

Vusu

3

tu3

su3

Vu 2.552821 1015 cm6/sec3 (20a)

Vu_cgssu

3

mu_cgs Vu_cgs 5.708251 107 cm3/g (20b)

Vu_SIsu_SI

3

mu_SI Vu_SI 5.708251 104 m3/kg (20c)

Vt_ust_u

3

tu3

su3

Vt_u 6.667151 108 cm6/sec3 (21a)

Vt_u_cgsst_u

3

mu_cgs Vt_u_cgs 1.490812 101 cm3/g (21b)

m3/kgVt_u_SI 10 3 Vt_u_cgs Vt_u_SI 1.490812 10 2 (21c)


h. linear momentum

Linear momentum is simply mass times velocity.

Mutu

2

su2

Mu 1.112646 10 21 sec2/cm2 (22a)

Mu_cgs mu_cgs vu Mu_cgs 4.975933 10 14 g cm/sec (22b)

(22c)Mu_SI mu_SI vu_SI Mu_SI 4.975933 10 19 kg m/sec

Mt_utu

3

su3

st_utu

Mt_u 7.112089 10 24 sec2/cm2 (23a)

Mt_u_cgs mu_cgs vt_u Mt_u_cgs 3.180640 10 16 g cm/sec (23b)

Mt_u_SI 10 5 Mt_u_cgs Mt_u_SI 3.180640 10 21 kg m/sec (23c)


i. rotational momentum

By definition:

(24a)Lutu

2

su Lu 5.072351 10 27 sec2/cm

(24b)Lu_cgs mu_cgs vu su Lu_cgs 2.268436 10 19 g cm2/sec

Lu_SI mu_SI vu_SI su_SI (24c)Lu_SI 2.268436 10 26 kg m2/sec

Lt_utu

3

su3

st_u2

tu Lt_u 2.072475 10 31 sec2/cm (25a)

Lt_u_cgs mu_cgs vt_u st_u Lt_u_cgs 9.268438 10 24 g cm2/sec (25b)

Lt_u_SI 10 7 Lt_u_cgs Lt_u_SI 9.268438 10 31 kg m2/sec (25c)


j. force

Force is mass times acceleration.

(26a)Futu

su2

Fu 7.316890 10 6 sec/cm2

Fu_cgs mu_cgs au (26b)Fu_cgs 3.272230 102 dynes

Fu_SI 10 5 Fu_cgs Fu_SI 3.272230 10 3 N (26c)

Ft_u mu at_u Ft_u 4.676991 10 8 sec/cm2 (27a)

Ft_u_cgs mu_cgs at_u Ft_u_cgs 2.091625 dynes (27b)

Ft_u_SI 10 5 Ft_u_cgs Ft_u_SI 2.091625 10 5 N (27c)

The mechanical time region values are appropriate to use for nanotechnology machines. But whereas gravitational forcemay usually be neglected for time-space calculations, the reverse gravitational and progression forces must usually beconsidered when doing time region calculations. See Appendix 2.


k. pressure

Pressure is force divided by area.

(28a)Putu

su4

Pu 3.520646 105 sec/cm4

Pu_cgsFu_cgs

su2

Pu_cgs 1.574489 1013 dynes/cm2 PG_u Pu_cgs (28b)

Pu_SI 10 1 Pu_cgs (28c)Pu_SI 1.574489 1012 N/m2

This is the natural unit of pressure for ideal gases. Because of inter-atomic attraction in solids, liquids, and vapors (and realgases) the pressure is different for these states of matter.

For solids, we use the time region expression for force but keep the time-space region expression for area (becausepressure is a macroscopic property).

PS_u_cgsFt_u_cgs

su2

PS_u_cgs 1.006421 1011 (29a)dynes/cm2

(29b)PS_u_SI 10 1 PS_u_cgs PS_u_SI 1.006421 1010 N/m2

For liquids, which have 2/3 of the cohesion of solids, we must multiply the solid value by 2/3 and divide by another IR.


(30a)PL_u23

tu

su4

1

IR2

PL_u 9.589834 sec/cm4

PL_u_cgs

23

PS_u_cgs

IR PL_u_cgs 4.288727 108 dynes/cm2 (30b)

PL_u_SI 10 1 PL_u_cgs PL_u_SI 4.288727 107 N/m2 (30c)

For vapors, which have 1/3 of the cohesion of solids, we must multiply the solid value by 1/3 and divide by still another IR.

PV_u13

tu

su4

1

IR3

PV_u 3.064934 10 2 sec/cm4 (31a)

PV_u_cgs13

PS_u_cgs

IR2

PV_u_cgs 1.370687 106 dynes/cm2 (31b)

PV_u_SI 10 1 PV_u_cgs PV_u_SI 1.370687 105 N/m2 (31c)


l. torque

Torque is simply force times distance.

Tutusu

Tu 3.335636 10 11 sec/cm (32a)

Tu_cgs Fu_cgs su Tu_cgs 1.491750 10 3 dynes cm (32b)

Tu_SI 10 7 Tu_cgs Tu_SI 1.491750 10 10 N m (32c)

(33a)Tt_u mu at_u st_u Tt_u 1.362883 10 15 sec/cm

Tt_u_cgs Ft_u_cgs st_u Tt_u_cgs 6.095031 10 8 dynes cm (33b)

Tt_u_SI 10 7 Tt_u_cgs Tt_u_SI 6.095031 10 15 N m (33c)


m. moment of inertia

The moment of inertia is defined as mass times distance squared.

(34a)Iutu

3

su3

su2 Iu 7.713295 10 43 sec3/cm

Iu_cgs mu_cgs su2 Iu_cgs 3.449509 10 35 g cm2 (34b)

Iu_SI mu_SI su_SI2 Iu_SI 3.449509 10 42 kg m2 (34c)

It_utu

3

su3

st_u2 It_u 3.151519 10 47 sec3/cm (35a)

It_u_cgs mu_cgs st_u2 (35b)It_u_cgs 1.409410 10 39 g cm2

It_u_SI mu_SI st_u2 (35c)It_u_SI 1.409410 10 42 kg m2


n. dynamic and kinematic viscosity

Dynamic viscosity and kinematic viscosity are macroscopic properties of liquids and so only time-space region values apply.

ηutu

2

su4

ηu 5.353688 10 11 sec2/cm4 (36a)

ηu_cgsMu_cgs

su2

ηu_cgs 2.394255 10 3 poise (36b)

ηu_SIMu_SI

su_SI2

ηu_SI 2.394255 10 4 N sec/m2 (36c)

We commonly use centipoise, instead of poise.

ηu_cgs 2.394255 10 1 centipose (36d)

Kinematic viscosity is dynamic viscosity divided by density.

νusu

2

tu νu 1.366701 105 cm2/sec (37a)

νu_cgs 1.366701 107 centistokes (37b)

νu_SI 1.366701 105 stokes (37c)


o. surface tension

Surface tension is 1/3 the natural unit of pressure times the natural unit of distance divided by the cube of the inter-regionalratio. It is a macroscopic one-dimensional property only.

γu13

Pu su

IR3

γu 1.397247 10 7 sec/cm3 (38a)

γu_cgs13

Pu_cgs su

IR3

γu_cgs 6.248712 dynes/cm (38b)

γu_SI 10 3γu_cgs γu_SI 6.248712 10 3 N/m (38c)


p. energy

Energy is the inverse of velocity, or force times distance.

Eutusu

Eu 3.335636 10 11 sec/cm (39a)

Eu_cgs Fu_cgs su Eu_cgs 1.491750 10 3 ergs (39b)

Eu_SI Fu_SI su_SI Eu_SI 1.491750 10 10 J (39c)

Et_u Ft_u st_u Et_u 1.362883 10 15 sec/cm (40a)

(40b)Et_u_cgs Ft_u_cgs st_u Et_u_cgs 6.095031 10 8 ergs

Et_u_SI Ft_u_SI st_u_SI Et_u_SI 6.095031 10 15 J (40c)

For Einstein's famous equation:

Eu 3.335636 10 11 sec/cm mu cu2 3.335636 10 11 sec/cm [checks]


q. power

Power is energy per unit time.

Pu1su

Pu 2.193552 105 cm-1 (41a)

Pu_cgsEu_cgs

tu Pu_cgs 9.809916 1012 ergs/sec (41b)

Pu_SIEu_SI

tu Pu_SI 9.809916 105 J/sec (41c)

Pt_u1

st_u Pt_u 3.431689 107 cm-1 (42a)

Pt_u_cgsEt_u_cgs

tu Pt_u_cgs 4.008162 108 ergs/sec (42b)

Pt_u_SIEt_u_SI

tu Pt_u_SI 4.008162 101 J/sec (42c)


2. Electrical Units

We will give both the time-space region and time region values here as appropriate.

a. electric quantity

Electric quantity is simply one natural unit of space whether using the time-space region value or the time region value.From Larson, Ref. [2], p. 111: "...the unit of space in the region inside unit distance, the time region, as we are calling it, isinherently just as large as the unit of space in the region outside unit distance, but as measured it is reduced by theinter-regional ratio, 156.4444, for reasons previously explained. We cannot legitimately regard this quantity as somethingless than a full unit, since, as we saw in Volume I [Ref. [1]], it has the same status in the time region that the full-sized naturalunit of space has in the region outside unit distance. The logical way of handling this situation appears to be to take thestand there are two different natural units of distance (one-dimensional space), a simple unit and a compound unit, thatapply under different circumstances." Time-space values will apply to quantities which are not per distance or per areaor per volume; those which are per distance or per area or per volume can have either time-space or time regionvalues.

qu su qu 4.558816 10 6 cm (43a)

qu_cgs 4.802870 10 10 esuquantity (43b)

qu_SI 1.602062 10 19 coulombsquantity (43c)

Unlike conventional theory, the Reciprocal System distinguishes between electric quantity and electric charge; they havedifferent dimensions, hence the subscript.


b. electric current

Ordinary electric current is the flow of massless, chargeless electrons.

iusutu

iu 2.997929 1010 cm/sec (44a)

iu_cgsqu_cgs

tu iu_cgs 3.158422 106 esuquantity/sec (44b)

iu_SIqu_SI

tu iu_SI 1.053534 10 3 amps (44c)


c. electric current density

Electric current density is electric current per unit area.

(45a)juiu

su2

ju 1.442505 1021 cm-1sec-1

ju_cgsiu_cgs

su2

ju_cgs 1.519729 1017 (esuquantity/sec)/cm2 (45b)

ju_SIiu_SI

su_SI2

ju_SI 5.069260 1011 amps/m2 (45c)

jt_uiu

st_u2

jt_u 3.530509 1025 cm-1sec-1 (46a)

jt_u_cgsiu_cgs

st_u2

jt_u_cgs 3.719513 1021 (esuquantity/sec)/cm2 (46b)

jt_u_SIiu_SI

st_u_SI2

jt_u_SI 1.240693 1016 amps/m2 (46c)


d. electric charge or flux

Electric charge or flux is the unit charge of the electron. Notice that the dimensions of charge are different from those ofquantity.

Qutusu

Qu 3.335636 10 11 sec/cm (47a)

Qu_cgs 4.802870 10 10 esucharge (47b)

Qu_SI 1.602062 10 19 coulombscharge (47c)


e. electric dipole moment

Electric dipole moment is electric charge times distance.

pu Qu su pu 1.520655 10 16 sec (48a)

pu_cgs Qu_cgs su pu_cgs 2.189540 10 15 esucharge cm (48b)

pu_SI Qu_SI su_SI pu_SI 7.303506 10 27 coulombscharge m (48c)

pt_u Qu st_u pt_u 9.720098 10 19 sec (49a)

pt_u_cgs Qu_cgs st_u pt_u_cgs 1.399564 10 17 esucharge cm (49b)

pt_u_SI Qu_SI st_u_SI pt_u_SI 4.668436 10 29 coulombscharge m (49c)


f. electric charge volume density

Electric charge volume density is charge per unit volume.

ρuQu

su3

ρu 3.520646 105 sec/cm4 (50a)

ρu_cgsQu_cgs

su3

ρu_cgs 5.069261 106 esucharge/cm3 (50b)

ρu_SIQu_SI

su_SI3

ρu_SI 1.690920 103 coulombscharge/m3 (50c)

ρt_uQu

st_u3

ρt_u 1.348039 1012 sec/cm4 (51a)

(51b)ρt_u_cgs

Qu_cgs

st_u3

ρt_u_cgs 1.940996 1013 esucharge/cm3

ρt_u_SIQu_SI

st_u_SI3

ρt_u_SI 6.474453 109 coulombscharge/m3 (51c)


g. electric energy

The natural unit of electric energy is the same as the natural unit of mechanical energy.

Eutusu

Eu 3.335636 10 11 sec/cm (52a)

(52b)Eu_cgs Fu_cgs su Eu_cgs 1.491750 10 3 ergs

(52c)Eu_SI Fu_SI su_SI JEu_SI 1.491750 10 10


h. electric power

The natural unit of electric power is the same as the natural unit mechanical power.

Pu1su

Pu 2.193552 105 cm-1 (53a)

(53b)Pu_cgsEu_cgs

tu Pu_cgs 9.809916 1012 ergs/sec

Pu_SIEu_SI

tu Pu_SI 9.809916 105 J/sec (53c)


i. electric voltage

Electric voltage is simply electric force. It is unit power divided by unit current.

Vutu

su2

Vu 7.316890 10 6 sec/cm2 (54a)

(54b)Vu_cgsPu_cgsiu_cgs

Vu_cgs 3.105955 106 statvolts

(54c)Vu_SI

Pu_SIiu_SI

Vu_SI 9.311435 108 volts


j. electric field intensity

Electric field intensity is electric voltage per unit distance.

Eutu

su3

Eu 1.604998 sec/cm3 (55a)

(55b)Eu_cgsVu_cgs

su Eu_cgs 6.813073 1011 statvolts/cm

(55c)Eu_SI

Vu_SIsu_SI

Eu_SI 2.042512 1016 volts/m

(56a)Et_utu

su2 st_u

Et_u 2.510929 102 sec/cm3

(56b)Et_u_cgsVu_cgs

st_u Et_u_cgs 1.065867 1014 statvolt/cm

Et_u_SIVu_SI

st_u_SI Et_u_SI 3.195395 1018 volts/m (56c)


k. electric flux density

Electric flux density is electric charge per unit area.

Du

tusu

su2

Du 1.604998 sec/cm3 (57a)

Du_cgsQu_cgs

su2

Du_cgs 2.310983 101 esucharge/cm2 (57b)

Du_SIQu_SI

su_SI2

Du_SI 7.708594 10 5 coulombscharge/m2 (57c)

(58a)Dt_u

tusu

st_u2

Dt_u 3.928208 104 sec/cm3

Dt_u_cgsQu_cgs

st_u2

Dt_u_cgs 5.656096 105 esucharge/cm2 (58b)

Dt_u_SIQu_SI

st_u_SI2

Dt_u_SI 1.886667 coulombscharge/m2 (59c)


l. electric resistance

Electric resistance is electric voltage divided by electric current. It's also equal to mass per unit time.

Ru

tu3

su3

tu Ru 2.440648 10 16 sec2/cm3 (60a)

Ru_cgsVu_cgsiu_cgs

Ru_cgs 9.833881 10 1 statohms (60b)

Ru_SIVu_SIiu_SI

Ru_SI 8.838284 1011 ohms (60c)

Eutusu

Eu 3.335636 10 11 sec/cm iu2 Ru tu 3.335636 10 11 sec/cm [checks]


m. electric conductance

Electric conductance is the inverse of electric resistance.

Gutu

tu3

su3

Gu 4.097273 1015 cm3/sec2 (61a)

Gu_cgsiu_cgsVu_cgs

Gu_cgs 1.016893 statmhos (61b)

Gu_SIiu_SIVu_SI

Gu_SI 1.131441 10 12 mhos (61c)


n. electric resistivity

Electric resistivity is resistance times distance. Crystal unit cell parameters determine this value, and so the time regionunit of space must be used.

ρt_u Ru st_u ρt_u 7.112089 10 24 sec2/cm2 (62a)

ρt_u_cgs Ru_cgs st_u ρt_u_cgs 2.865609 10 8 statohms cm (62b)

ρt_u_SI Ru_SI st_u_SI ρt_u_SI 2.575491 102 ohms m (62c)

o. electric conductivity

Electric conductivity is the inverse of electric resistivity.

σt_u1

ρt_u σt_u 1.406057 1023 cm2/sec2 (63a)

σt_u_cgs1

ρt_u_cgs σt_u_cgs 3.489659 107 statmhos/cm (63b)

σt_u_SI1

ρt_u_SI σt_u_SI 3.882755 10 3 mhos/m (63c)


p. electric permittivity (free space)

(64a)ε0

su2

tu ε0 1.366701 105 cm2/sec

ε0_cgs 1 (by definition in cgs) (64b)

(64c)ε0_SI 8.854188 10 12 farad/m (by definition in SI)

q. electric susceptibility (free space)

By definition,

ε0_r 1 (relative permittivity of free space) (65a)

χε_u 1 ε0_r χε_u 0.000000 χε_u_cgs 0 χε_u_SI 0 (65b)

The cgs and SI units are also the same: 0.


r. electric capacitance

Only the time-space region value applies, because unit capacitance is equal to the unit of time divided by the unit ofresistance.

(66a)Cusu

3

tu Cu 6.230538 10 1 cm3/sec

To get the corresponding cgs and SI units, we note that the time constant, RC, of an RC DC circuit, must be equal tounit time.

Cu_cgstu

Ru_cgs Cu_cgs 1.546343 10 16 statfarads (66b)

Cu_SItu

Ru_SI Cu_SI 1.720532 10 28 farads (66c)

Note that

Cu_SI Vu_SI 1.602062 10 19 coulombs_q as it should

Also:Eu

tusu

Eu 3.335636 10 11 sec/cm Cu Vu2 3.335636 10 11 sec/cm [checks]


s. electric displacement

By definition, electric displacement is electric quantity per unit area:

Dusu

su2

Du 2.193552 105 cm-1 (67a)

Du_cgsqu_cgs

su2

Du_cgs 2.310983 101 esuquantity/cm2 (67b)

Du_SIqu_SI

su_SI2

Du_SI 7.708594 10 5 coulombsquantity/m2 (67c)

Dt_usu

st_u2

Dt_u 5.368686 109 cm-1 (68a)

Dt_u_cgsqu_cgs

st_u2

Dt_u_cgs 5.656096 105 esuquantity/cm2 (68b)

Dt_u_SI 1.886667 coulombsquantity/m2 (68c)Dt_u_SIqu_SI

st_u_SI2


t. electric polarization

By definition, electric polarization is electric displacement minus the permittivity of free space times the electric fieldintensity. Therefore the natural units are the same as those for electric displacement.

Pusu

su2

Pu 2.193552 105 cm-1 (69a)

Pu_cgsqu_cgs

su2

Pu_cgs 2.310983 101 esuquantity/cm2 (69b)

Pu_SIqu_SI

su_SI2

Pu_SI 7.708594 10 5 coulombsquantity/m2 (69c)

Pt_usu

st_u2

Pt_u 5.368686 109 cm-1 (70a)

Pt_u_cgsqu_cgs

st_u2

Pt_u_cgs 5.656096 105 esuquantity/cm2 (70b)

Pt_u_SI 4.008162 101 coulombsquantity/m2 (70c)Pt_u_SIqu_SI

st_u_SI2

Note that, unlike conventional theory, the esu and coulombs here are electric quantities, not electric charges: ordinarycapacitors store massless, chargeless electrons, not charged electrons.


3. Magnetic Units

Magnetic quantities which are analogous to electric quantities have the dimensions of the corresponding electric quantitiesmultiplied by t/s.

a. magnetic charge or flux

Real magnetic charges exist in the Reciprocal System, unlike in Quantum Mechanics.

Mutu

2

su2

Mu 1.112646 10 21 sec2/cm2 (70a)

Mu_cgsQu_cgs

cu Mu_cgs 1.602062 10 20 emu (70b)

(70c)Mu_SI Mu_cgs 299.7925 Mu_SI 4.802863 10 18 weber


b. Larson magneton

This is to the Reciprocal System what the Bohr magneton is to Quantum Mechanics.

Du 3.359 10 13 cm

Du_SI 3.359 10 15 m

(71a)μL_u

tu2

su2

Du μL_u 3.737380 10 34 sec2/cm

(71b)μL_cgs

Mu_cgs Du

cu1

μL_cgs 3.107984 10 38 emu cm

(71c)μL_SI

Mu_SI Du_SI

cu_SI1

μL_SI 9.317503 10 37 weber m


c. magnetic dipole moment

Magnetic dipole moment is magnetic charge times distance.

μutu

2

su μu 5.072351 10 27 sec2/cm (72a)

μu_cgs Mu_cgs su μu_cgs 7.303508 10 26 emu cm (72b)

μu_SI Mu_SI su_SI μu_SI 0.000000 weber m (72c)

μt_utu

2

su2

st_u μt_u 3.242271 10 29 sec2/cm (73a)

μt_u_cgs Mu_cgs st_u μt_u_cgs 4.668437 10 28 emu cm (73b)

μt_u_SI Mu_SI st_u_SI μt_u_SI 1.399562 10 27 weber m (73c)


d. magnetic moment from current

μc_usutu

su2 μc_u 6.230538 10 1 cm3/sec (74a)

μc_u_cgs iu_cgs su2 μc_u_cgs 6.564086 10 5 (esuquantity/sec) cm2 (74b)

μc_u_SI iu_SI su_SI2 μc_u_SI 2.189539 10 18 amps m2 (74c)

μc_t_usutu

st_u2 μc_t_u 2.545690 10 5 cm3/sec (75a)

μc_t_u_cgs iu_cgs st_u2 μc_t_u_cgs 2.681972 10 9 (esuquantity/sec) cm2 (75b)

μc_t_u_SI iu_SI st_u_SI2 μc_t_u_SI 8.946081 10 23 amps m2 (75c)


e. magnetic flux density

Magnetic flux density is magnetic charge per unit area.

(76a)Butu

2

su4

Bu 5.353688 10 11 sec2/cm4

(76b)Bu_cgsMu_cgs

su2

Bu_cgs 7.708596 10 10 emu/cm2

Bu_SIMu_SI

su_SI2

Bu_SI 2.310979 10 3 weber/m2 (76c)

(77a)Bt_utu

2

su2 st_u

2 Bt_u 1.310307 10 6 sec2/cm4

Bt_u_cgsMu_cgs

st_u2

Bt_u_cgs 1.886667 10 5 emu/cm2 (77b)

Bt_u_SIMu_SI

st_u_SI2

Bt_u_SI 5.656086 101 weber/m2 (77c)

Incidentally, 1 weber/m2 = 1 tesla = 10000 gauss.


f. magnetic permeability (free space)

μ0tu

3

su4

μ0 8.141112 10 27 sec3/cm4 (78a)

μ0_cgs 1 μ0_cgs 1.000000 (dimensionless) (78b)

μ0_SI 4 π 10 7 μ0_SI 1.256637 10 6 henries/m (78c)

g. magnetic susceptibility (freespace)

By definition,

μ0_r 1 (relativity permeability of free space) (79a)

χμ_u 1 μ0_r χμ_u 0.000000 χμ_u_cgs 0 χμ_u_SI 0 (79b)

The cgs and SI units are also the same: 0. Remember that

χμ_cgsχμ_SI

4 π


h. magnetic field intensity

Magnetic field intensity is defined as magnetic flux density divided by magnetic permeability. We generally prefer to useexternal magnetic flux density (divided by 0) rather than this.

HuBuμ0

Hu 6.576114 1015 sec-1 (80a)

Hu_cgsBu_cgsμ0_cgs

Hu_cgs 7.708596 10 10 (80b)emu/cm2

Hu_SIBu_SIμ0_SI

Hu_SI 1.839019 103 (weber/m)/(henry) (80c)

Ht_uBt_uμ0

Ht_u 1.609494 1020 sec-1 (81a)

(81b)Ht_u_cgsBt_u_cgsμ0_cgs

Ht_u_cgs 1.886667 10 5 emu/cm2

(81c)Ht_u_SIBt_u_SIμ0_SI

Ht_u_SI 4.500971 107 (weber/m)/(henry)


i. magnetomotive force and magnetic vector potential

Magnetomotive force and magnetic vector potential are the same: electric force times t/s.

FM_utu

2

su3

FM_u 2.440648 10 16 sec2/cm3 (82a)

The conventional units for magnetomotive force are mistakenly defined thusly:

FM_u_cgs iu_cgs μ0_cgs FM_u_cgs 3.158422 106 "(esuquantity/sec) turns"

FM_u_SI iu_SI μ0_SI FM_u_SI 1.323910 10 9 "amp turns"

But magnetic force cannot have the dimensions given. The correct values are

FM_u_cgsMu_cgs

su FM_u_cgs 3.514207 10 15 emu/cm (82b)

FM_u_SIMu_SIsu_SI

FM_u_SI 1.053533 10 10 weber/m (82c)

Note: If using magnetic vector potential instead of magnetomotive force, subsitute Au for FM_u in the above equations.


For the time region:

FM_t_utu

2

su2 st_u

FM_t_u 3.818257 10 14 sec2/cm3 (83a)

FM_t_u_cgsMu_cgs

st_u FM_t_u_cgs 5.497780 10 13 emu/cm (83b)

FM_t_u_SIMu_SIst_u_SI

FM_t_u_SI 1.648193 10 8 weber/m (83c)

Note: If using magnetic vector potential instead of magnetormotive force, substitue At_u for FM_t_u in the above equations.


j. magnetic polarization

Magnetic polarization has the same dimensions as magnetic flux density.

(84a)PM_utu

2

su4

PM_u 5.353688 10 11 sec2/cm4

(84b)PM_u_cgsMu_cgs

su2

PM_u_cgs 7.708596 10 10 emu/cm2

PM_u_SIMu_SI

su_SI2

PM_u_SI 2.310979 10 3 webers/m2 (84c)

(85a)PM_t_utu

2

su2 st_u

2 PM_t_u 1.310307 10 6 sec2/cm4

PM_t_u_cgsMu_cgs

st_u2

PM_t_u_cgs 1.886667 10 5 emu/cm2 (85b)

PM_t_u_SIMu_SI

st_u_SI2

PM_t_u_SI 5.656086 101 webers/m2 (85c)


k. magnetic inductance

By reason of consistency with the resistance units, only the time-space value applies.

Lutu

3

su3

Lu 3.711383 10 32 sec3/cm3 (86a)

Lu_cgs Ru_cgs tu Lu_cgs 1.495394 10 16 stathenries (86b)

Lu_SI Ru_SI tu Lu_SI 1.343998 10 4 henries (86c)

Eutusu

Eu 3.335636 10 11 sec/cm Lu iu2 3.335636 10 11 sec/cm [checks]


l. magnetization

Magnetization has the same dimensions and natural units as magnetic field intensity.

MM_u Hu MM_u 6.576114 1015 sec-1 (87a)

MM_u_cgs Hu_cgs MM_u_cgs 7.708596 10 10 (87b)emu/cm2

MM_u_SI Hu_SI MM_u_SI 1.839019 103 (weber/m)/(henry) (87c)

MM_t_u Ht_u MM_t_u 1.609494 1020 sec-1 (88a)

(88b)MM_t_u_cgs Ht_u_cgs MM_t_u_cgs 1.886667 10 5 emu/cm2

(88c)MM_t_u_SI Ht_u_SI MM_t_u_SI 4.500971 107 (weber/m)/(henry)


m. magnetic reluctance

Reluctance is the inverse of inductance.

RM_usu

3

tu3

RM_u 2.694413 1031 cm3/sec3 (89a)

RM_u_cgs1

Lu_cgs RM_u_cgs 6.687201 1015 stathenries-1 (89b)

RM_u_SI1

Lu_SI RM_u_SI 7.440487 103 henries-1 (89c)


Supplement: The Maxwell Relations

cgs: cu 2.997929 1010 cm/sec 1ε0_r μ0_r

1.000000 (relative to c)

SI: cu_SI 2.997929 108 m/sec 1ε0_SI μ0_SI

2.997925 108 m/sec

cu 2.997929 1010 cm/sec 1ε0 μ0

2.997929 1010 cm/sec

For cgs we have to use the relative permittivity and relative permeability of free space. Otherwise, the calculationscome out to the speed of light, as required.

Incidentally, here is a comparison of the natural unit ratios and the conventional ratios:

ε0μ0

1.678764 1031ε0_SIμ0_SI

7.045939 10 6 (The SI values are arbitrarily selected.)


4. Thermal Units

a. temperature

Gas constant (given): Rcgs 1.9869 cal/mol K

convcaltoJ 4.1868 RSI convcaltoJ Rcgs RSI 8.318753 J/mol K

convcaltoergs 4.1868 107 Rerg Rcgs convcaltoergs Rerg 8.318753 107 erg/mol K

Avogadro's number (given): Av 6.02486 1023 (atoms or molecules)/gram-mole

Boltzmann's constant (calculated): kBRergAv

kB 1.380738 10 16 ergs/K peratom ormolecule

Natural unit of energy (from above): Eu_cgs Fu_cgs su Eu_cgs 1.491750 10 3 ergs

Natural unit of gas temperature: TG_uEu_cgs

32

kB TG_u 7.202668 1012 K (90)


Larson's calculated value in Ref. [2], p. 59 is 7.20423 x 1012. 7.20423 1012

7.202668 10121.000217 a minor difference

(Both values will be displayed in the Table below.)

The thermal energy of radiation is proportional to the fourth power of temperature--this is known as theStefan-Boltzmann law. When the thermal motion reaches the time region boundary, the thermal energy becomesproportional to the third power of temperature. Therefore, for the vapor state:

TV_u TG_u

34 TV_u 4.396631 109 K (91a)

Larson, Ref. [2], p. 59, points out that "...the thermal motion is a motion of matter and involves the 2/9 vibrationaladdition to the rotationally distributed linear motion of the atoms. This reduces the effective temperature by thefactor 1 + 2/9."

Natural unit of vapor temperature: TV_uTG_u

34

1 29

TV_u 3.597244 109 K (91b)

Larson's calculates 3.5978 x 109 K. Given the uncertainty in kB we can continue to use the values given inRef. [2]. Both values will be given in the Table.


For the condensed states of matter, solids and liquids, we reduce the above three-dimensional unit to theone-dimensional basis and multiply by 1/3.

Natural unit of liquid and solid temperature:

(92)TSL_u

13

TV_u

13 TSL_u 510.742549 K

Larson calculates 510.8 K for this, and we can continue to use this value--it's close enough given theuncertainties, and will also be displayed in the Table below.


b. specific heat (molar)

Gas constant (given): Rcgs 1.9869 cal/mol K

RSI 8.318753 J/mol K

Rerg 8.318753 107 erg/mol K

Convert erg to natural energy units: RnRerg

Fu_cgs su Rn 5.576507 1010 natural_energy_units/mol K

Convert natural energy units to sec/cm: Ru Rntusu Ru 1.860120 (sec/cm)/mol K

Specific heat at constant volume (ideal gas):

cv_u32

Ru cv_u 2.790180 (sec/cm)/mol K (93a)

(93b)cv_u_cgs32

Rcgs cv_u_cgs 2.980350 cal/mol K

(93c)cv_u_SI32

RSI cv_u_SI 12.478129 J/mol K

Note: the specific heat at constant pressure has the same natural unit as the specific heat at constant volume. Foran ideal gas, it is equal to R + the specific heat at constant volume.


Specific heat at constant pressure (ideal gas):

cp_u52

Ru cp_u 4.650299 (sec/cm)/mol K (94a)

cp_u_cgs52

Rcgs cp_u_cgs 4.967250 cal/mol K (94b)

cp_u_SI52

RSI cp_u_SI 20.796882 J/mol K (94c)

The maximum thermal specific heat for solids is 3R (= 2 natural units) and this is also the basis for the specific heatcalculation of liquids; see Ref. [2] and Ref. [10]. Note that for solids and liquids the specific heat at constant pressureis really more fundamental than that at constant volume.


c. specific enthalpy (molar)

Gas

hu_G cp_u TG_u hu_G 3.349456 1013 (sec/cm)/mol (95a)

hu_G_cgs cp_u_cgs TG_u hu_G_cgs 3.577745 1013 cal/mol (95b)

hu_G_SI cp_u_SI TG_u (95c)hu_G_SI 1.497930 1014 J/mol

Vapor

(96a)hu_V cp_u TV_u (sec/cm)/molhu_V 1.672826 1010

hu_V_cgs cp_u_cgs TV_u (96b)hu_V_cgs 1.786841 1010 cal/mol

hu_V_SI cp_u_SI TV_u hu_V_SI 7.481146 1010 J/mol (96c)

Solid/Liquid

cp_u cv_u cp_u_cgs cv_u_cgs cp_u_SI cv_u_SI

(97a)hu_SL cp_u TSL_u hu_SL 1.425063 103 (sec/cm)/mol

hu_SL_cgs cp_u_cgs TSL_u (97b)hu_SL_cgs 1.522192 103 cal/mol

hu_SL_SI cp_u_SI TSL_u hu_SL_SI 6.373112 103 J/mol (97c)

Note that for solids and liquids, there is very little difference in specific heat at constant pressure and at constant volume;the specific heat at constant pressure is just a little higher.


c. specific internal energy (molar)

Gas

cv_u32

Ru cv_u_cgs32

Rcgs cv_u_SI32

RSI

iu_G cv_u TG_u iu_G 2.009674 1013 (sec/cm)/mol (98a)

iu_G_cgs cv_u_cgs TG_u iu_G_cgs 2.146647 1013 cal/mol (98b)

iu_G_SI cv_u_SI TG_u (98c)iu_G_SI 8.987583 1013 J/mol

Vapor

(99a)iu_V cv_u TV_u (sec/cm)/moliu_V 1.003696 1010

iu_V_cgs cv_u_cgs TV_u (99b)iu_V_cgs 1.072105 1010 cal/mol

iu_V_SI cv_u_SI TV_u hu_V_SI 7.481146 1010 J/mol (99c)

Solid/Liquid

(100a)iu_SL cv_u TSL_u iu_SL 1.425063 103 (sec/cm)/mol

iu_SL_cgs cv_u_cgs TSL_u (100b)iu_SL_cgs 1.522192 103 cal/mol

iu_SL_SI cv_u_SI TSL_u iu_SL_SI 6.373112 103 J/mol (100c)

For solids and liquids, actual internal energy is just a little less than the enthalpy.


d. specific entropy (molar)

The natural unit of specific entropy is the same as the natural unit of specific heat.

Su cv_u Su 2.790180 (sec/cm)/mol K (101a)

Su_cgs cv_u_cgs Su_cgs 2.980350 cal/mol K (101b)

Su_SI cv_u_SI Su_SI 12.478129 J/mol K (101c)


e. thermal resistance

Natural unit of energy: Eu_cgs Fu_cgs su Eu_cgs 1.491750 10 3 ergs

Eu_SI Fu_SI su_SI Eu_SI 1.491750 10 10 J

Natural unit of power: Pu1su

Pu 2.193552 105 cm-1

Pu_cgsEu_cgs

tu Pu_cgs 9.809916 1012 ergs/sec

Pu_SIEu_SI

tu Pu_SI 9.809916 105 J/sec (watts)

Natural unit of thermal resistance:

Rθ_uTG_u

Pu Rθ_u 3.283564 107 K cm (102a)

Rθ_u_cgsTG_u

Pu_cgs Rθ_u_cgs 7.342233 10 1 K/(ergs/sec) (102b)

Rθ_u_SITG_uPu_SI

Rθ_u_SI 7.342233 106 K/watt (102c)

Like electrical resistance, there is no distinction here between the time-space region and time region. The massless,chargeless electrons in a solid are like a gas.


f. thermal conductance

Thermal conductance is the inverse of thermal resistance.

(103a)Sθ_u1

Rθ_u Sθ_u 3.045471 10 8 1/(K cm)

Sθ_u_cgs1

Rθ_u_cgs Sθ_u_cgs 1.361984 (erg/sec)/K (103b)

(103c)Sθ_u_SI1

Rθ_u_SI Sθ_u_SI 1.361984 10 7 watt/K


g. thermal resistivity

Thermal resistivity is thermal resistance times distance. As with electrical resistivity, here we have to use the timeregion value of space.

ρθ_u Rθ_u st_u ρθ_u 9.568360 10 1 cm sec (104a)

ρθ_u_cgs Rθ_u_cgs st_u ρθ_u_cgs 2.139539 10 8 K cm sec/erg (104b)

ρθ_u_SI Rθ_u_SI st_u_SI ρθ_u_SI 2.139539 10 3 K m / watt (104c)

A common unit used in practice is K cm / watt, giving a natural unit of .2139539.


h. thermal conductivity

Thermal conductivity is the inverse of thermal resistivity.

κθ_u1

ρθ_u κθ_u 1.045111 cm-1 sec-1 (105a)

κθ_u_cgs1

ρθ_u_cgs κθ_u_cgs 4.673904 107 (erg/sec)/(K cm) (105b)

κθ_u_SI1

ρθ_u_SI κθ_u_SI 4.673904 102 watt/(K m) (105c)

A common unit used in practice is watt/(K cm), giving a natural unit of 4.673904.


i. thermal diffusivity

By definition:

Gases (time-space region)

αusu

2

tu αu 1.366701 105 cm2/sec (106a)

αu_cgs αu αu_cgs 1.366701 105 cm2/sec (106b)

αu_SIsu_SI

2

tu αu_SI 1.366701 101 m2/sec (106c)

Solids and Liquids (time region)

αt_ust_u

2

tu αt_u 5.584103 cm2/sec (107a)

αt_u_cgs αt_u αt_u_cgs 5.584103 cm2/sec (107b)

αt_u_SIst_u_SI

2

tu αt_u_SI 5.584104 10 4 m2/sec (107c)


5. Photonic Units

See Ref. [6], pp. 12-14, for a good review of these units. These are defined for large numbers of photons, and so only thetime-space region values apply.

a. energy of unit frequency photon

Eutusu

Eu 3.335636 10 11 sec/cm

Eu_cgs Fu_cgs su Eu_cgs 1.491750 10 3 ergs

h 4.14 10 15 eV sec (Planck's constant)

conveVtoergs 1.602 10 12 conveVtoJ 1.602 10 19

Eu_photon h R Eu_photon 13.612556 eV (108a)

Eu_photon_cgs h R conveVtoergs Eu_photon_cgs 2.180731 10 11 ergs (108b)

Eu_photon_SI h R conveVtoJ Eu_photon_SI 2.180731 10 18 J (108c)

In terms of sec/cm: Eu_photon_cgsEu

Eu_cgs 4.876238 10 19 sec/cm (108d)


b. radiant energy exposure

Radiant energy exposure is defined as the ratio of energy of radiation falling on a surface to the area of the surface.

He_uEu

su2

He_u 1.604998 (109a)sec/cm3

He_u_cgsEu_cgs

su2

He_u_cgs 7.177808 107 ergs/cm2 (109b)

He_u_SIEu_SI

su_SI2

He_u_SI 7.177808 104 J/m2(109c)

The subscript "e" used here can be mean either "exposure" or "emitted"--the context determines which. The subscript"a" will be used for "absorbed" or "impinged."


c. radiant flux

Radiant flux is defined as the ratio of radiation energy to the time interval of the radiation transfer (which significantlyexceeds the period of oscillations).

Φe_uEutu

Φe_u 2.193552 105 cm-1 (110a)

Φe_u_cgsEu_cgs

tu Φe_u_cgs 9.809916 1012 ergs/sec (110b)

Φe_u_SIEu_SI

tu Φe_u_SI 9.809916 105 J/sec (watts) (110c)


d. luminosity (radiance, emitted)

Luminosity is defined as the ratio of the radiant flux to the surface area from which this radiation is emitted.

Me_uEu

tu su2

Me_u 1.055465 1016 cm-3 (111a)

Me_u_cgsEu_cgs

tu su2

Me_u_cgs 4.720208 1023 (ergs/sec)/cm2 (111b)

Me_u_SIEu_SI

tu su_SI2

Me_u_SI 4.720208 1020 (J/sec)/m2 (111c)


e. irradiance (absorbed)

Irradiance is the ratio of radiant flux to the area by which this radiance is absorbed. This has the same natural units asluminosity.

Ea_uEu

tu su2

Ea_u 1.055465 1016 cm-3 (112a)

Ea_u_cgsEu_cgs

tu su2

Ea_u_cgs 4.720208 1023 (ergs/sec)/cm2 (112b)

Ea_u_SIEu_SI

tu su_SI2

Ea_u_SI 4.720208 1020 (J/sec)/m2 (112c)


f. radiant intensity per steradian

Radiant intensity per steradian is defined as the ratio of the radiant flux of a source to a solid angle (= 1 steradian)within which this radiation is propagated.

Ie_uEutu

Ie_u 2.193552 105 cm-1 sterad-1 (113a)

Ie_u_cgsEu_cgs

tu Ie_u_cgs 9.809916 1012 (ergs/sec)/sterad (113b)

Ie_u_SIEu_SI

tu Ie_u_SI 9.809916 105 (J/sec)/sterad (113c)

Incidentally, a "candela" is equal to 1/683 (J/sec) per steradian. Therefore the natural unit in candelas is

683 Ie_u_SI 6.700172 108 candelas

A common candle emits one candela.


g. energy brightness per steradian

Energy brightness per steradian is defined as the ratio of radiant intensity of a surface element to the area of theprojection of this element on a plane perpendicular to the observed direction.

(114a)Be_uIe_u

su2

Be_u 1.055465 1016 sterad-1 cm-3

Be_u_cgsIe_u_cgs

su2

Be_u_cgs 4.720208 1023 (ergs/sec)/(cm2 sterad) (114b)

Be_u_SIIe_u_SI

su_SI2

Be_u_SI 4.720208 1020 (J/sec)/(m2 sterad) (114c)


h. luminous flux for a solid angle of 1 steradian

Luminous flux for a solid angle of 1 steradian is defined as the product of the light intensity and this solid angle.

Φv_u Ie_u Φv_u 2.193552 105 steradian/cm (115a)

Φv_u_cgs Ie_u_cgsΦv_u_cgs 9.809916 1012 (ergs/sec) steradian (115b)

Φv_u_SI Ie_u_SI Φv_u_SI 9.809916 105 (J/sec) steradian (115c)

Incidentally, a lumen is equal to 1 candela times 1 steradian.


i. luminous energy

Luminous energy is equal to the the luminous flux produced over time t during which luminous flux is emitted or received.

Qu Φv_u tu Qu 3.335636 10 11 steradian sec/cm (116a)

Qu_cgs Φv_u_cgs tu Qu_cgs 1.491750 10 3 steradian ergs (116b)

Qu_SI Φv_u_SI tu Qu_SI 1.491750 10 10 steradian J (116c)


j. brightness in given direction

Brightness of a luminous surface in a given direction is define as the ratio of luminous intensity in this direction inrelation to the area of the projection of the luminous surface on a plane perpendicular to that direction. We assumethat = 1 radian.

Bϕ_uIe_u

su2 cos 1( )

Bϕ_u 1.953471 1016 cm-3 (117a)

Bϕ_u_cgsIe_u_cgs

su2 cos 1( )

Bϕ_u_cgs 8.736235 1023 (ergs/sec)/cm2 (117b)

Bϕ_u_SIIe_u_SI

su_SI2 cos 1( )

Bϕ_u_SI 8.736235 1020 (J/sec)/m2 (117c)


k. luminance (radiance, emitted over 1 steradian)

Luminance (radiance) is defined as the ratio of luminous flux emitted by a luminous surface in relation to its area.

Re_uΦv_u

su2

Re_u 1.055465 1016 steradian/cm3 (118a)

Re_u_cgsΦv_u_cgs

su2

Re_u_cgs 4.720208 1023 (ergs/sec) steradian/cm2 (118b)

Re_u_SIΦv_u_SI

su_SI2

Re_u_SI 4.720208 1020 (J/sec) steradian/m2 (118c)


l. illuminance (intensity of illumination over 1 steradian)

Illuminance is defined as the ratio of luminous flux falling on a surface element, in relation to the area of this element.

Ia_uΦv_u

su2

Ia_u 1.055465 1016 steradian/cm3 (119a)

Ia_u_cgsΦv_u_cgs

su2

Ia_u_cgs 4.720208 1023 steradian (ergs/sec)/cm2 (119b)

Ia_u_SIΦv_u_SI

su_SI2

Ia_u_SI 4.720208 1020 steradian (J/sec)/m2 (119c)

Incidentally, a lux = 1 lumen per meter2.


m. luminous exposure over 1 steradian

Luminous exposure is defined as the illuminance produced over time t during which the radiation occurs.

Ha_u Ia_u tu Ha_u 1.604998 steradian sec/cm3 (120a)

Ha_u_cgs Ia_u_cgs tu Ha_u_cgs 7.177808 107 steradian (ergs/cm2) (120b)

Ha_u_SI Ia_u_SI tu Ha_u_SI 7.177808 104 steradian (J/m2) (120c)


6. Interconversion of Units

Given that all physical quantities may be expressed in space-time units, it is possible to convert units in one group of units tounits of another group. We'll give just two examples.

a. mass and inductance

By inspection:

Lutu

3

su3

Lu 3.711383 10 32 sec3/cm3

Ru_SIVu_SIiu_SI

Ru_SI 8.838284 1011 ohms

Lu_SI Ru_SI tu Lu_SI 1.343998 10 4 henries

mutu

3

su3

mu 3.711383 10 32 sec3/cm3

mu_SI 1.659790 10 27 kg

mu_SILu_SI

1.234965 10 23 kg/henry


b. mechanical force and voltage

Vutu

su2

Vu 7.316890 10 6 sec/cm2

Vu_SIPu_SIiu_SI

Vu_SI 9.311435 108 volts

Futu

su2

Fu 7.316890 10 6 sec/cm2

Fu_SI 10 5 Fu_cgs Fu_SI 3.272230 10 3 N

Fu_SIVu_SI

3.514206 10 12 N/volts

The Table summarizing all of the results follows.


Physical Quantity Symbol Space-Time Dimensions

Reciprocal System Natural Unit Value

Stated in terms of cm and sec


Stated in normal cgs units

Reciprocal System Natural

Unit Value Stated in normal

SI units

space (time-space region) su su 4 .558 816e-06 cm 4.55 8816 e-0 6 cm 4.5 5881 6e-08 m

space (time region) st_u su/IR 2 .914 017e-08 cm 2.91 4017 e-0 8 cm 2.9 1401 7e-10 m

space (atomic diameter) Du,du k1su 3 .359 e-1 3 cm 3.35 9e-13 cm 3.3 59e-15 m

area (time-space region) Au su2 2 .078 280e-11 cm2 2.07 8280 e-1 1 cm2 2.0 7828 0e-15 m2

area (time region) At_u st_u2 8 .491 494e-16 cm2 8.49 1494 e-1 6 cm2 8.4 9149 4e-20 m2

volume (t ime-space region) Vu su3 9 .474 498e-17 cm3 9.47 4498 e-1 7 cm3 9.4 7449 8e-23 m3

volume (t ime region--atoms) Vt_u st_u3 2 .474 435e-23 cm3 2.47 4435 e-2 3 cm3 2.4 7443 5e-29 m3

time t u t u 1 .520 655e-16 sec 1.52 0655 e-1 6 sec 1.5 2065 5e-16 sec

linear velocit y (t ime-space region) vu su/tu 2 .997 929e+ 10 cm/sec 2 .997 925e+ 10 cm/sec

2.99 7929 e+ 10 cm/sec

2.9 9792 9e+ 08 m/sec

linear velocit y (t ime region--atoms) vt_u st_u/t u 1 .916 291e+ 08 cm/sec 1.91 6291 e+ 08 cm/sec

1.9 1629 1e+ 06 m/sec

linear vibration frequency R, u 1 /(2 x tu) 3 .288 057e+ 15 cycles/sec 3.28 8057 e+ 15 cycles/sec

3.2 8805 7e+ 15 cycles/sec

rotat ional frequency in rev/sec f rot _rev 1 /( x tu) 2 .093 242e+ 15 rev/sec 2.09 3242 e+ 15 rev/sec

2.0 9324 2e+ 15 rev/sec

rotat ional frequency in rad/sec f rot _rad 2 /tu 1 .315 223e+ 16 rad/sec 1.31 5223 e+ 16 rad/sec

1.3 1522 3e+ 16 rad/sec

linear acceleration (t ime-space region) au su/tu

2 1 .971 473e+ 26 cm/sec2 1.97 1473 e+ 26 cm/sec2

1.9 7147 2e+ 24 m/sec2

linear acceleration (t ime region) at_u st _u/t u2 1 .260 175e+ 24 cm/sec2

1.26 0175 e+ 24 cm/sec2

1.2 6017 5e+ 22 m/sec2

angular accelerat ion in rev/sec2 u_rev 1 /( x tu2) 1 .376 540e+ 31 rev/sec2 1.37 6540 e+ 31

rev/sec2 1.3 7654 0e+ 31 rev/sec2

angular accelerat ion in rad/sec2 u_rad 2 /tu2 8 .649 055e+ 31 rad/sec2

8.64 9055 e+ 31 rad/sec2

8.6 4905 5e+ 31 rad/sec2









SI units

mass mu t u3/su

3 3 .711 383e-32 sec3/cm3 1.65 9790 e-2 4 g (= 1 amu = .9 99682 2 u)

1.6 5979 0e-27 kg (= 1 amu= .999 6822 u

densit y (t ime-space region) u, du t u3/su

6 3 .917 235e-16 sec3/cm6 1.75 1850 e-0 8 g/cm3 1.7 5185 0e-05 kg/m3

densit y (t ime region--atoms) t_u, dt_u

(tu3/su

3)/st_u3 1 .499 891e-09 sec3/cm6 6.70 7752 e-0 2 g/cm3

6.7 0775 2e+ 01 kg/m3

specific volume (time-space region) Vu su3/( t u

3/su3) 2 .552 821e+ 15 cm6/sec3 5.70 8251 e+ 07 cm3/g

5.7 0825 1e+ 04 m3/kg

specific volume (time region--atoms) Vt_u st_u

3/( t u3/su

3) 6 .667 151e+ 08 cm6/sec3 1.49 0812 e+ 01 cm3/g (not including close packing factor .7 071)

1.4 9081 2e-02 m3/kg

linear momentum (t ime-space region) Mu t u

2/su2 1 .112 646e-21 sec2/cm2

4.97 5933 e-1 4 g cm/sec

4.9 7593 3e-19 kg m/sec

linear momentum (t ime regon) Mt _u (tu3 /su

3)(st _u/t u) 7 .112 089e-24 sec2/cm2 3.18 0640 e-1 6 g cm/sec

3.1 8064 0e-21 kg m/sec

rotat ional moment um (t ime-space region) Lu t u

2/su 5 .072 351e-27 sec2/cm 2.26 8436 e-1 9 g cm2/sec

2.2 6843 6e-26 kg m2/sec

rotat ional moment um (t ime region) Lt_u t u3 /su

3)(st _u2 /tu) 2 .072 475e-31 sec2/cm 9.26 8438 e-2 4 g

cm2/sec 9.2 6843 8e-31 g cm2/sec

force (time-space region) Fu t u/su2 7 .316 891e-06 sec/cm2 3.27 2230 e+ 02 dynes 3.2 7223 0e-03 N

force (time region--at oms) Ft_u (tu3/su

3)st_u/tu

2 1 .025 922e-02 sec/cm2 2.09 1625 dynes 2.0 9162 5e-05 N

pressure (gas) PG_u,Pu (tu/su4) 3 .520 647e+ 05 sec/cm4

1.57 4489 e+ 13 dynes/cm2

1.5 7448 9e+ 12 N/m2

pressure (solid) PS_u (tu3/su

5)st_u/tu2 2 .250 414e+ 03 sec/cm4

1.00 6421 e+ 11 dynes/cm2

1.0 0642 1e+ 10 N/m2

pressure (liquid) PL_u (2 /3) (tu

3/su5IR)st_u/tu

2 9 .589 834 sec/cm4 4.28 8727 e+ 08 dynes/cm2

4.2 8872 7e+ 07 N/m2

pressure (vapor) PV_u (1 /3) (tu

3/su5IR

2)st_u/t u2

3 .064 934e-2 sec/cm4 1.37 0687 e+ 06 dynes/cm2

1.3 7068 7e+ 05 N/m2









SI units

torque (time-space region) Tu t u/su 3 .335 636e-11 sec/cm 1.49 1750 e-0 3 dynes cm 1.4 9175 0e-10 N m

torque (time region) Tt_u (tu3 /su

3)st _u2 /tu 1 .362 883e-15 sec/cm 6.09 5031 e-0 8 dynes

cm 6.0 9503 1e-15 N m

moment of inert ia (time-space region) Iu t u

3/su 7 .713 295e-43 sec3/cm 3.44 9509 e-3 5 g cm2 3.4 4950 9e-42 kg m2

moment of inert ia (time region) It_u (tu3 /su

3)(st _u2) 3 .151 519e-47 sec3/cm 1.40 9410 e-3 9 g cm2 1.4 0941 0e-42 kg

m2

dynamic viscosit y u t u2/su

4 5 .353 688e-11 sec2/cm4 2.39 4255 e-0 1 cent ipoise

2.3 9425 5e-03 poise

kinematic viscosity u su2/t u 1 .366 701e+ 05 cm2/sec

1.36 6701 e+ 07 cent istoke

1.3 6670 1e+ 05 stokes

surface t ension L_u (1 /3)tu/(su3IR

3) 1 .397 247e-07 sec/cm3 6.24 8712 dynes/cm 6.2 4871 2e-03 N/m

energy, work, and heat (time-space region) Eu t u/su 3 .335 636e-11 sec/cm 1.49 1750 e-0 3 ergs 1.4 9175 0e-10 J

energy, work, and heat (time-region--atoms) Et_u (tu

3/su3)(st_u

2/tu2

) 1 .362 883e-15 sec/cm 6.09 5031 e-0 8 ergs 6.0 9503 1e-15 J

pow er (t ime-space region) pu 1 /su 2 .193 552e+ 05 cm-1 9.80 9916 e+ 12 ergs/sec

9.8 0991 6e+ 05 J/sec

pow er (t ime region--atoms) pt_u (tu

3/su3)(st_u

2/tu2

)/ tu 8 .962 474 cm-1 4.00 8162 e+ 08

ergs/sec 4.0 0816 2e+ 01 J/sec

electric quant ity qu su 4 .558 816e-06 cm 4.80 2870 e-1 0 esuquantit y 1.6 0206 2e-19 coulombsquantity

electric current iu su/tu 2 .997 929e+ 10 cm/sec 3.15 8422 e+ 06 esuquanti ty/ sec

1.0 5353 4e-03 amps

electric current density (time-space region ju 1 /(sut u) 1 .442 505e+ 21 cm-1sec-1

1.51 9729 e+ 17 (esuquantity /sec)/cm2

5.0 6925 0e+ 11 amps/m2

electric current density (time region) jt _u (su/tu)/st _u

2 3 .530 509e+ 25 cm-1sec-1 3.71 9513 e+ 21 (esuquantity /sec)/cm2

1.2 4069 3e+ 16 amps/m2

electric charge or flux Qu t u/su 3 .335 636e-11 sec/cm 4.80 2870 e-1 0 esucharge 1.6 0206 2e-19 coulombscharge









SI unitselectric dipole moment (t ime-space region) pu t u 1 .520 655e-16 sec 2.18 9540 e-1 5 esucharge

cm 7.3 0350 6e-27 coulombscharge m

electric dipole moment (t ime region) pt _u (tu/su)st _u 9 .720 098e-19 sec 1.39 9564 e-1 7 esucharge

cm 4.6 6843 6e-29 coulombscharge m

electric charge volume densit y (time-space region) u t u/st_u

4 3 .520 646e+ 05 sec/cm4 5.06 9261 e+ 06 esucharge /cm3

1.6 9092 0e+ 03 coulombscharge/cm3

electric charge volume densit y (time region) t_u (tu/su)/st _u

3 1 .348 039e+ 12 sec/ 1.94 0996 e+ 13 esucharge /cm3

6.4 7445 3e+ 09 coulombscharge/cm3

electric energy Eu t u/su 3 .335 636e+ 11 sec/cm 1.49 1750 e-0 3 ergs 1.4 9175 0e-10 J

electric pow er Pu 1 /su 2 .193 552e+ 05 cm-1 9.80 9916 e+ 12 ergs/ec

9.8 0991 6e+ 05 J/sec

electric voltage or potent ial Vu t u/su2 7 .316 890e-06 sec/cm2

3.10 5955 e+ 06 statvolt s

9.3 1143 5e+ 08 volts

electric f ield intensity (t ime-space region) Eu t u/su

3 1 .604 998 sec/cm3 6.81 3073 e+ 11 statvolt s/cm

2.0 4251 2e+ 16 volts/m

electric f ield intensity (t ime region) Et _u t u/(su2st_u) 2 .510 929e+ 2 sec/cm3 1.06 5867 e+ 14

statvolt s/cm 3.1 9539 5e+ 18 volts/m

electric f lux densit y (t ime-space region) Du (tu/su)/su

2 1 .604 998 sec/cm3 2.31 0983 e+ 01 esucharge/ cm2

7.7 0859 4e-05 coulombscharge/m2

electric f lux densit y (t ime region) Dt_u (tu/su)/st _u2 3 .928 208e+ 04 sec/cm3 5.65 6096 e+ 05

esucharge/ cm2 1.8 8666 7 coulombscharge/m2

electric resistance Ru t u2/su

3 2 .440 648e-16 sec2/cm3 9.83 3881 e-0 1 statohms

8.8 3828 4e+ 11 ohms

electric conductance Gu su3/tu

2 4 .097 273e+ 15 cm3/sec2 1.01 6893 statmhos 1.1 3144 1e-12 mhos

electric resistivity t_u (tu2 /su

3)st _u 7 .112 089e-24 sec2/cm2 2.86 5609 e-0 8 statohms cm

2.5 7549 1e+ 02 ohms m

electric conductivit y t _u su3/(t u

2st _u) 1 .406 057e+ 23 cm2/sec2 3.48 9659 e+ 07 statmhos/cm

3.8 8275 5e-03 mhos/cm

electric permit tivit y (f ree space) 0 su2/t u 1 .366 701e+ 05 cm2/sec 1 (dimensionless) 8.8 5418 8e-12

farad/m









SI units

electric susceptibility (free space) E_u 0 0 0 0

capacitance Cu su3/tu 6 .230 538e-01 cm3/sec

1.54 6343 e-1 6 statfarads 1.7 2053 2e-28 F

electric displacement (t ime-space region) Du 1/su 2 .193 552e+ 05 cm-1

2.31 0983 e+ 01 esuquanti ty/ cm2

7.7 0859 4e-05 coulombsquantity /m2

electric displacement (t ime region) Dt_u su/st _u2 5 .368 686e+ 09 cm-1


1.8 8666 7 coulombsquantity /m2

electric polarization (t ime-space region) Pu 1/su 2 .193 552e+ 05 cm-1


7.7 0859 4e-05 coulombsquantity /m2

electric polarization (t ime region) Pt _u su/st _u2 5 .368 686e+ 09 cm-1


1.8 8666 7 coulombsquantity /m2

magnet ic charge or flux Mu t u2/su

2 1 .112 646e-21 sec2/cm2 1.60 2062 e-2 0 emu 4.8 0286 31e-18 weber

Larson magneton (magnetic moment ) L_u (tu

2/su2)Du

3 .737 380e-34 sec2/cm 3.10 7984 e-3 8 emu cm 9.3 1750 3e-37 weber m

magnet ic dipole moment (time-space region) u t u

2/su 5 .072 351e-27 sec2/cm 7.30 3508 e-2 6 emu cm 2.1 8953 7e-25 weber m

magnet ic dipole moment (time region) u_t (tu

2 /su2)st _u 3 .242 271e-29 sec2/cm 4.66 8437 e-2 8 emu cm 1.3 9956 2e-27

weber m

magnet ic moment f rom current (time-space region) c_u su

3/t u 6 .230 538e-01 cm3/sec 6.56 4086 e-0 5 (esuquantity /sec) cm2

2.1 8953 9e-18 amps m2

magnet ic moment f rom current (time region) c_t _u (su/tu)st _u

2 2 .545 690e-05 cm3/sec 2.68 1972 e-0 9 8.9 4608 1e-23 amps m2

magnet ic flux density (time-space region) Bu t u

2/st_u4 5 .353 688e-11 sec2/cm4

7.70 8596 e-1 0 emu/cm2

2.3 1097 9e-03 weber/m2

magnet ic flux density (time region) Bt_u (tu2 /su

2)/st _u2 1 .310 307e-06 sec2/cm4 1.88 6667 e-0 5

emu/cm2 5.6 5608 6e+ 01 weber/m2

magnet ic permeabilit y 0 t u3/su

4 8 .141 112e-27 sec3/cm4 1 [dimensionless in cgs]

1.2 5663 7e-06 henries/m

magnet ic suscept ibilit y _u 0 0 0 0









SI unitsmagnet ic field int ensity (time-space region) Hu 1/tu 6 .576 114e+ 15 sec-1

7.70 8596 e-1 0 emu/cm2

1.8 3901 9e+ 03 (w eber/m)/henry

magnet ic field int ensity (time region) Ht_u (su

2/t u)/st_u2 1 .609 494e+ 20 sec-1 1.88 6667 e-0 5

emu/cm2 4.5 0097 1e+ 07 (w eber/m)/henry

magnetomotive f orce (t ime-space region) FM_u t u

2/su3 2 .440 648e-16 sec2/cm3 3.15 4207 e-1 5 emu/cm 1.0 5353 3e-10

weber/m

magnetomotive f orce (t ime region) FM_t_u (tu2/su

2)/st_u 3 .818 257e-14 sec2/cm3 5.49 7780 e-1 3 emu/cm 1.6 4819 3e-08 weber/m

magnet ic polarizat ion (t ime-space region) PM_u t u

2/st_u4 5 .353 688e-11 sec2/cm4

7.70 8596 e-1 0 emu/cm2

2.3 1097 9e-03 weber/m2

magnet ic polarizat ion (t ime region) PM _t _u (tu2 /su

2)/st _u2 1 .310 307e-06 sec2/cm4 1.88 6667 e-0 5

emu/cm2 5.6 5608 6e+ 01 weber/m2

magnet ic inductance Lu t u3/su

3 3 .711 383e-32 sec3/cm3 1.49 5394 e-1 6 stathenries

1.3 4399 8e-04 henries

magnet ization (time-space region) MM_u 1 /tu 6 .576 114e+ 15 sec-1 7.70 8596 e-1 0 emu/cm2

1.8 3901 9e+ 03 (w eber/m)/henry

magnet ization (time region) MM_t_u (su2/t u)/st_u

2 1 .609 494e+ 20 sec-1 1.88 6667 e-0 5 emu/cm2

4.5 0097 1e+ 07 (w eber/m)/henry

reluctance RM_u su3/tu

3 2 .694 413e+ 31 cm3/sec3 6.68 7201 e+ 15 stathenries-1

7.4 4048 7e+ 03 henries-1

temperature (gas) TG_u (tu/su)/((3 /2)kB) 3 .335 636e-11 (sec/cm)/((3/2)kB)

7.20 2668 e+ 12 K, 7.20 4230 e+ 12 K

7.2 0266 8e+ 12 K, 7.2 0423 0e+ 12 K

temperature (vapor) TV_u TG_u3 /4 / (1+ 2/9)

[3.3 35636 e-1 1 (sec/cm)/((3/2)kB)] 3/ 4/ (1+ 2/9 )

3.59 7244 e+ 09 K, 3.59 7800 e+ 09 K

3.5 9724 4e+ 09 K,3.5 9780 0e+ 09 K

temperature (solid, liquid) TSL_u (1 /3)TV_u1/ 3

1 /3 [[3.3356 36e-11 (sec/cm)/((3/2)kB)] 3/ 4/ (1+ 2/9 )]1/3

510.7425 49 K, 510.8 K

510 .742 549 K, 510 .8 K

specific heat (molar) cv_u, cp_u

(3 /2)Ru (Gas Constant)

2 .790 180 (sec/cm)/mol K 2.98 0350 cal/mol K 12.4781 29 J/mol K

specific molar enthalpy (gas) hu_G cp_uTG_u 3 .349 456e+ 13 (sec/cm)/mol

3.57 7745 e+ 13 cal/mol

1.4 9793 0e+ 14 J/mol









SI units

specific molar enthalpy (vapor) hu_V cp_uTV_u 1 .672 826e+ 10 (sec/cm)/mol

1.78 6841 e+ 10 cal/mol

7.4 8114 6e+ 10 J/mol

specific molar enthalpy (solid, liquid) hu_SL cp_uTSL_u

1 .425 063e+ 03 (sec/cm)/mol

1.52 2192 e+ 03 cal/mol

6.3 7311 2e+ 03 J/mol

specific molar internal energy(gas) iu_G cv_uTG_u 2 .009 674e+ 13 (sec/cm)/mol

2.14 6647 e+ 13 cal/mol

8.9 8758 3e+ 13 cal/mol

specific molar internal energy (vapor) iu_V cv_uTV_u

1 .003 696e+ 10 (sec/cm)/mol

1.07 2105 e+ 10 cal/mol

7.4 8114 6e+ 10 J/mol

specific molar internal energy (solid, liquid) iu_SL cv_uTSL_u

1 .425 063e+ 03 (sec/cm)/mol

1.52 2192 e+ 03 cal/mol

6.3 7311 2e+ 03 J/mol

specific molar entropy Su (3 /2)Ru (Gas Const ant) 2 .790 180 (sec/cm)/mol K 2.98 0350 cal/mol K 12.4781 29 J/mol K

thermal resist ance R_u TG_u/Pu 3 .283 564e+ 07 K cm 7.34 2233 e-0 1 K/ (ergs/sec)

7.3 4223 3e+ 06 K/wat t

thermal conduct ance S_u Pu/TG_u 3 .045 471e-08 (K cm)-1 1.36 1984 (erg/sec)/K 1.3 6198 4e-07 wat t/K

thermal resist ivit y _u R_ust _u 9 .568 360e-01 cm sec 2.13 9539 e-0 8 K cm sec/erg

2.1 3953 9e-03 K m /w at t

thermal conduct ivity u 1/( R_ust _u) 1 .045 111 cm-1 sec-1 4.67 3904 e+ 07 (erg/sec)/(K cm)

4.6 7390 4e+ 02 wat t/ (K m)

thermal diff usivity (gas) u su2/t u 1 .366 701e+ 05 cm2/sec 1.36 6701 e+ 05

cm2/sec 1.3 6670 1e+ 01 m2/sec

thermal diff usivity (solid, liquid) t_u st _u2 /tu 5 .584 103 cm2/sec 5.58 4103 cm2/sec 5.5 8410 4e-04

m2/sec

energy of unit frequency phot on Eu_phot on hR 4 .876 238e-19 sec/cm 2.18 0731 e-1 1 ergs 2.1 8073 1e-18 J

radiant energy exposure He_u t u/su3 1 .604 998 sec/cm3

7.17 7808 e+ 07 ergs/cm2

7.1 7780 8e+ 04 J/m2

radiant f lux e_u 1/su 2 .193 552e+ 05 cm-1 9.80 9916 e+ 12 ergs/sec

9.8 0991 6e+ 05 J/sec

luminosit y (radiance, emit ted) M e_u 1/su3 1 .055 465e+ 16 cm-3

4.72 0208 e+ 23 (ergs/sec)/cm2

4.7 2020 8e+ 20 (J/sec)/m2









SI units

irradiance (absorbed) E a_u 1/su3 1 .055 465e+ 16 cm-3

4.72 0208 e+ 23 (ergs/sec)/cm2

4.7 2020 8e+ 20 (J/sec)/m2

radiant int ensity (per st eradian) I e_u 1/su sterad-1 2 .193 552e+ 05 -1 sterad-

1 cm-1 ( = 1 ) 9.80 9916 e+ 12 ergs/sec per sterad

9.8 0991 6e+ 05 J/sec per sterad

energy bright ness (per st eradian) Be_u 1/su3 sterad-1 1 .055 465e+ 16 -1 sterad-

1 cm-3 ( = 1)

4.72 0208 e+ 23 (ergs/sec)/cm2 per sterad

4.7 2020 8e+ 20 (J/sec)/m2 per sterad

luminous flux (for solid angle ) v_u /su 2 .193 552e+ 05 cm-1 sterad ( = 1 )

9.80 9916 e+ 12 sterad ergs/sec

9.8 0991 6e+ 05 sterad J/sec

luminous energy (f or solid angle ) Qu t u/su 3 .335 636e-11 sterad cm-1 ( = 1) sec/cm

1.49 1750 e-0 3 sterad ergs

1.4 9175 0e-10 sterad J

bright ness in given direction B_u 1/su3 1 .953 471e+ 16 cm-3 [ =

1 rad] 8.73 6235 e+ 23 (ergs/sec)/cm2

8.7 3623 5e+ 20 (J/sec)/m2

luminance (radiance, emit ted over ) Re_u /su

3 1 .055 465e+ 16 sterad cm-3 ( = 1)

4.72 0208 e+ 23 sterad (ergs/sec)/cm2

4.7 2020 8e+ 20 sterad (J/sec)/m2

illuminance (intensit y of illumination over ) Ia_u /su

3 1 .055 465e+ 16 sterad cm-3 ( = 1)

4.72 0208 e+ 23 sterad (ergs/sec)/cm2

4.7 2020 8e+ 20 sterad (J/sec)/m2

luminous exposure over Ha_u t u/ su3

1 .604 998 sterad sec/cm3 ( = 1 )

7.17 7808 e+ 07 sterad ergs/cm2

7.1 7780 8e+ 04 sterad J/m2

Table 1. Space-Time Dimensions and Natural Unit Values of Physical Quantities


Table Notes:

1. Values are given to six decimal places, but there is uncertainty in the fifth and sixth places. This is so because there isuncertainty in the true value of the speed of light, the Rydberg hydrogen frequency, Avogadro's number, Boltzmann's number, etc.,which have been used in converting from the natural units to conventional units.

2. Values may be slightly different from those in other Reciprocal System papers and books. The differences are de minimis.

3. In some cells, alternate values are given; again, the differences are de minimis.

4. Some physical quantities have only time-space region values; others have only only time region values; and still others haveboth.

5. Given the large number of symbols, there are some duplications; context determines which is appropriate.


Conclusion

The Reciprocal System supercedes all other physical theories and dimensional systems. Unlike other systems, in theReciprocal System all physical quantities are expressed in terms of space, s, and time, t, only. Mass and charge,therefore, are derived quantities, as is everything else. This paper adds to existing Reciprocal System literature inproviding the natural unit values in cgs and SI of not only the mechanical and electrical quantities, but also the magneticand thermal and photonic quantities. A convenient table is included, summarizing the results.


Acknowledgements

Funding for this work came from my company, Transpower Corporation. Of course, great thanks go to Dewey B. Larson,who served as my theoretical physics mentor from 1965 until his death in 1990. He was, by far, the most intelligent and mostlogical of any individual I've ever known.

References

[1] D. Larson, The Structure of the Physical Universe (Portland, OR: North Pacific Publishers, 1959); Nothing ButMotion (Portland, OR: North Pacific Publishers, 1979). The latter is Volume I of the 2nd ed. of The Structure of thePhysical Universe.

[2] D. Larson, Basic Properties of Matter (Salt Lake City, UT: International Society of Unified Science, 1988). This isVolume II of the revised and enlarged The Structure of the Physical Universe.

[3] O. Eshbach, M. Souders, ed., Handbook of Engineering Fundamentals, 3rd ed. (New York, NY: John Wiley & Sons,1975).

[4] D. Halliday, R. Resnick, Physics--Part I and Part II (New York, NY: John Wiley & Sons, 1962).

[5] D. Lide, ed., CRC Handbook of Chemistry and Physics, 88th ed. (Boca Raton, FL: CRC Press, 2008).

[6] I. Grigoriev, E. Meilikhov, ed., Handbook of Physical Quantities (Boca Raton, FL: CRC Press, 1997).

[7] W. Martienssen, H. Warlimont, ed., Springer Handbook of Condensed Matter and Materials Data (Berlin, Germany:Springer, 2005).

[8] J. Maxwell, A Treatise on Electricity and Magnetism, 3rd ed. (New York, NY: Dover Publications, Inc., 1891--reprinted1954).

[9] R. Satz, "Theory of Dielectrics, Diamagnets, Paramagnets, and Ferromagnets, including the Calculation of Electricand Magnetic Susceptibilities," http://transpower.wordpress.com, last updated 06/19/2012.


[10] R. Satz, "Theory of Liquids, Vapors, and Gases," http://transpower.wordpress.com, last updated 11/18/2012.

[11] R. Satz, "Proposal for a Modified Rutherford Experiment," http://transpower.wordpress.com, last updated01/04/2011.

last updated 02/11/2013--fixed another typo and added natural unit form of Einstein's famous equationupdated 01/20/2013 and 01/22/2013--fixed various typos


Appendix 1. Determination of Reciprocal System Natural Unit Value for Atomic Diameter

See Ref. [11] for the derivation of the Reciprocal System alpha particle scattering equations. The impact parameter, whichis the effective radius of the target atom, is

(A1)bKG

2 su_SI2 Ek

cot Θ deg2

where KG is the repulsion coefficient, Ek is the kinetic energy of the alpha particle, and is the resultant scatteringangle. The repulsion coefficient is expressed as

KGFu_SI su_SI

4

IR4

LntM4 (A2)

The factor LntM depends on the rotational characteristics of the target atom and is not of importance here. What we'relooking for is the coefficient for Eq. (A1). The usual alpha particle energy is

Ek 7.03 10 13 J (A3)

(or 4.39 MeV). The value of is usually set to 156.5 degrees to determine the effective size of the target atom. Then

Θ 156.5 degrees (A4)


(A5)bFu_SI su_SI

4

IR4 2 su_SI

2 Ekcot Θ deg

2

LntM4

Then

Du_SI2 Fu_SI su_SI

4

IR4 2 su_SI

2 Ekcot Θ deg

2

(A6)

Du_SI 3.359 10 15 m

which is the value used in the paper proper. Use of this value, together with the calculation of LntM gives values foratomic diameters which are very close to those calculated by 2r0A1/3 for the "nucleus" of conventional theory (r0 isthe "Fermi radius" and A is the mass number here).


Appendix 2. Special Dimensions for Interatomic Distance Calculation in the Time Region

Larson explains this clearly in Ref. [2], pp. 6-7:

"As explained in introducing the concept of the time region in Chapter 8 of Vol. I, equivalent space 1/t replaces space in thetime region, and velocity is therefore 1/t2. Energy, the one-dimensional equivalent of mass, which takes the place of mass inthe time region expression of the force equation, because the three rotations of the atom act separately, rather than jointly,in this region, is the reciprocal of this expression, or t2. Acceleration is velocity divided by time: 1/t3. The time regionequivalent of the equation F = ma [for the purpose of interatomic distance calculation] is therefore F = Ea = t2 x 1/t3 = 1/t ineach distance." The reader can follow the remainder of the discussion in Ref. [2].

A nanotechnology force could be applied to individual atoms in the time region and the appropriate natural unit would beFt_u_cgs or Ft_u_SI as given in the paper proper but this force must be added to the interatomic force given by Larson'smodified expression above.

[academic] mathcad - space time dimensions units · pdf file2/11/2013 · this paper...

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