Download K - Christian J. Bordé

h or me
h or me
By additivity the link between a macroscopic
mass and a frequency is thus unavoidable.
On the unit of mass:
If one accepts to redefine the unit of mass from
The
mass
of ascale,
macroscopic
object isassociated
the sum
At
the
atomic
mass
is
directly
that of a microscopic particle such as the electron,
of that
ofaall
its microscopic
constituents
and
with
frequency
via
Planck
constant.
then the link with the unit of time is ipso facto
of frequency
a weak approximately
calculable
This
can
be
measured
established with a relative uncertaintydirectly
much better
interaction
term.
for
atoms
and
molecules
-8
than 10 . Both units are de facto linked by the
This
hypothesis
is quite
implicit
in both
possible
even
though
it
is
a
large
frequency.
Planck constant to better than 10-8.
2/h
new definitions
ofare
thepresently
unit of mass.
Measurements
of
mc
It seems difficult to ignore thisperformed
link
-8.
The
concept
of mass must
bebetter
identical
with
a
relative
uncertainty
much
than
10
and not to inscribe it in the formulation of the
at all scales.
system of units, especially since it leads to
a reduction of the number of independent units.
0 or e
On electrical units:
In the present SI, the values of μ0 and ε0 are fixed and
thus the propagation properties of the electromagnetic field
in the vacuum are also fixed:
- propagation velocity
- vacuum impedance
c0  1/  00
Z 0  0 /  0
- electric and magnetic energy densities  0 E 2 / 2
0 H 2 / 2
and
2
gives the radiation pressure and
 E
0
c 0 E
2
gives the intensity and the number of photons
This system is perfectly adapted to the propagation of light
in vacuum: no charges but also no ether.
Let us now introduce charges.
The values of μ0 and ε0 are related to the positron charge e
by the fine structure constant:
dimensionless constant imposed by nature, extraordinarily
well-known today since its present uncertainty is 0.7x10-9.
The free electromagnetic field is coupled to charges through
this constant, which thus appears as a property of electrons
and not as a property of the free electromagnetic field.
is just another way to write the positron charge
choice adopted by field-theory experts.
On electrical units:
The electron is an excitation of the vacuum.
It is an object whose ultimate structure is not known (string ?).
Its bare charge is infinite and it requires a renormalization
process to account for the experimentally observed charge.
If one chooses to fix this renormalized charge e,
one will unfortunately lose the consistency in the free
propagation properties of electromagnetic fields in the vacuum,
since μ0 and ε0 will be determined by the measured value of α.
The uncertainty of this measurement is therefore transferred to
the vacuum properties. One reintroduces a kind of ether,
which satisfies some theoreticians who see there the possibility
to introduce hypothetical scalar fields suggested by string theory
Is there any other advantage for electrical measurements ?
On electrical units:
It clarifies future issues to introduce a specific notation for the
approximate theoretical expressions of RK and KJ :
( 0)
RK
 h/e
2
(0)
KJ
 2e / h
in order to distinguish them from the true experimental constant
RK and KJ which are related to the previous ones by:
RK  RK( 0) (1   K ) K J  K J( 0) (1   J )
(0)
(0)
RK and K J
Fix h and e would fix the constants
but not RK and KJ which would keep an uncertainty.
This uncertainty is not that related to the determination
of e and h in the SI but to our lack of knowledge
of the correction terms to the expressions of RK and KJ.
Let us recall that the present estimate of the value of εK
is of the order of 2.10-8 and that of εJ of the order of 2.10-7
with important uncertainties.
The fact that the universality of these constants has been
demonstrated to a much better level simply suggests that
possible corrections would involve other combinations of
fundamental constants: functions of α, mass ratios, …
The hydrogen spectrum provides an illustrating example
of a similar situation. The energy of the levels of atomic
hydrogen is given to the lowest order by Bohr formula,
which can also be derived through a topological argument.
Nevertheless there are many corrections to this first term
involving various fundamental constants.
It is not because the spectrum of hydrogen is universal that
we may ignore these corrections and restrict ourselves
to Bohr formula.
Let us not forget that Cooper pairs are not elementary particles.
They exist through a coupling with a lattice and the two
electrons may have all kinds of other interactions.
2
3




me 11 2 28 
3
14

R
 H 1S1/ 2  2S1/ 2   R c 1 
  
ln  2   P   ...
4
9 
9  C 
 mP 48

1 2 me c
R  
2
h
g e  21  ae 
1
( 4)   
ae 
 Ce    ....
2
 
2
2
3




me 11 2 28 
3
14

R
 H 1S1/ 2  2S1/ 2   R c 1 
  
ln  2   P   ...
4
9 
9  C 
 mP 48

1 2 me c
R  
2
h
g e  21  ae 
1
( 4)   
ae 
 Ce    .
2
 
2
Let us not forget that Cooper pairs are not elementary
particles. They exist through a coupling with a lattice and
the two electrons may have all kinds of other interactions.
Conclusion on electrical units:
Even if e is fixed, there remains a large
uncertainty for RK and KJ and in addition
vacuum properties acquire an uncertainty.
There seems to be no real advantage
in fixing the value of e rather than that of μ0.
Conclusion on electrical units:
One possiblity is to define a unit of current
simply as a number of electrons per unit time,
but to keep
for the positron charge in units
of a fixed natural unit for charge
.
Mise en pratique
The chain for the mise en pratique would
thus include, as a primary realization of the
definition, the calculable Thompson Lampard capacitor, which materializes the
best the vacuum properties and, especially
the vacuum impedance Z0 (with a relative
uncertainty equal to a few 10-8 to-day and
to 10-8 in the near future).
From there, one can determine not only RK
by direct comparison with Z0 (Lampard
experiment), but also determine KJ thanks
to the watt balance used with Z0 instead of
RK, without any hypothesis on the formulas
which connect these constants to e, h and
.
Planck vs Boltzmann
Action S
Quantum 


Entropy S
Quantum kB
Time
t

Temperature 1/T
Liouville - Von Neumann equation:

i
 H ,  
t
Bloch equation:
Complex time:

  H

i
t 
2
1

kBT
On the unit of temperature:
The Boltzmann constant
comes into play
at the microscopic level
through its ratio
to the Planck constant.
Any future redefinition
of the kelvin should
take into account
this association,
according to the future
definition of the unit of mass.