The Unified Family of all physical quantities

Table 1. Symbols of the physical quantities of the Unified Family

a) dynamical plane

Row Column Dimension Symbol Physical quantity

-3

1

vector

G

gravitational factor

-2

0

scalar

f2

frequency square

-2

1

vector

a

acceleration

-2

2

bivector

c2

squared velocity of light

-2

3

vector

fF

temporal change of force

-2

4

scalar

P

power

-1

0

bivector

f

frequency

-1

1

vector

c

velocity of light

-1

2

scalar

Φf

circulation (flux of frequency)

-1

3

vector

F

force

-1

4

bivector

W

energy

0

-3

vector

n

spatial density

0

-2

bivector

Laplace operator

0

-1

vector

k

wave vector

0

0

scalar

1

universal unity

0

1

vector

r

length

0

2

bivector

A

area

0

3

vector

p

momentum

0

4

scalar

J

action

1

-2

scalar

σ

electric conductivity

1

-1

vector

ρm

mass density

1

0

bivector

t

time

1

1

vector

km

linear distribution of mass

1

2

scalar

m

mass

2

-2

bivector

ε

dielectric factor

2

-1

vector

εr

dielectric length

2

0

scalar

Φε

optical area (flux of ε)

Table 1. Symbols of the physical quantities of the Unified Family

b) electrodynamic plane

Row Column Dimension Symbol Physical quantity

-1

0

bivector

Bf

temporal change of magnetic induction

-1

1

vector

fH

temporal change of magnetic field

-1

2

scalar

E

electric field

-1

3

vector

U

electric potential

-1

4

bivector

ΦE

flux of electric field

0

-2

bivector

B∆

planar distribution of magnetic induction

0

-1

vector

Bk

linear distribution of magnetic induction

0

0

scalar

j

(planar) current density

0

1

vector

H

magnetic field

0

2

bivector

i

electric current

0

3

vector

ΦH

flux of magnetic field

0

4

scalar

µ~

magnetic dipole moment

1

-1

vector

ρq

electric charge density

1

0

bivector

D

planar distribution of electric charge

1

1

vector

kq

linear distribution of electric charge

1

2

scalar

q

electric charge

1

3

vector

qr

electric dipole moment

Table 2. The frequently used physical quantities equivalent to one of the „basic“ quantities of the Unified Family (listed in Table 1)

(The equivalent quantities are sorted here alphabetically; d means the dynamical plane, e means the electrodynamical plane of the unified family)

Equivalent
physical quantity
Equivalent symbol Corresponding „basic“ quantity „Basic“ symbol Plane

angular momentum

J

action

J

d

diffusion coefficient

D

circulation

Φf

d

elastic force coefficient

k

circulation

Φf

d

magnetic induction

B

planar current density

j

e

electric inductance

L

length

r

d

electric resistance

R

light velocity

c

d

electric resistivity

ρ

circulation

Φf

d

electrical mobility

µn

planar distribution of electric charge

D

e

energy density

ρW

light velocity

c

d

frequency flux

J/m

circulation

Φf

d

heat flow

G

squared light velocity

c2

d

length cube

r3

momentum

p

d

magnetic flux density

B

planar current density

j

e

magnetic induction

B

planar current density

j

e

nabla-minus operator

wave vector

k

d

optical path

nλ

time

t

d

optical path square

εr2

optical area

Φε

d

period

T

time

t

d

planar density

k2

Laplace operator

d

pressure

p

light velocity

c

d

quantum of rotation

K

circulation

Φf

d

radiation intensity

S

squared light velocity

c2

d

reciprocal length

1/r

wave vector

k

d

reciprocal velocity

1/c

mass density

ρm

d

reciprocal volume

1/V

spatial density

n

d

refraction index

n

mass density

ρm

d

refraction index square

n2

dielectric factor

ε

d

rotation

ω

frequency

f

d

second time derivative

2/∂t2

frequency square

f2

d

spatial density of current

i/V

linear distribution of magnetic induction

Bk

e

temporal force density

F/∂t

temporal change of force

fF

d

thermodynamical mobility

Bn

Laplace operator

d

time derivative

/∂t

frequency

f

d

time derivative of B

B/∂t

temporal change of magnetic induction

Bf

e

time derivative of H

H/∂t

temporal change of magnetic field

fH

e

time square

t2

optical area

Φε

d

velocity

v

light velocity

c

d

viscosity coefficient

η

length

r

d

voltage

U

electric potential

U

e

volume

V

momentum

p

d

volume expansion

V/∂t

force

F

d

vorticity

Ω

frequency

f

d

wavelength

λ

length

r

d

work

W

energy*

W

d

(*) Note that we have to use (because of our unification) the equivalent symbol W for energy if we wish to use simultaneously the electric field E having no common equivalent symbol.

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