Clean and simple derivation of Johnson Nyquist noise I am not sure to get the derivation of Johnson Nyquist noise. I would like to understand it under black-body radiation approach.
Consider this reference: http://www.pas.rochester.edu/~dmw/ast203/Lectures/Lect_20.pdf
Considering the Johnson Nyquist noise as a 1d blackbody version, what I expect is to say that we study a radiation that has thermalized with the electrical circuit at temperature T.
Then I need to compute the energy density per unit length (because 1D) and unit frequency.
In the 3D blackbody we consider stationnary waves. Here it seems it is the same. But why ?
Does that mean the wire must be connected to ground in x=0 and x=L ? If not, why can we impose stationnary waves in the derivation ?
Finally I dont get the point of putting two resistors. For me what matters is only to consider waves here. The fact we will be able to talk about power flow is just because of propagation, it is not related to the presence or not of a resistor.
I am very confused
 A: You do not need to "ground" a transmission line anywhere for Nyquist's derivation to work, you need to ground a transmission line at its ends if you do not want to get electrocuted while touching it. 
The role of the transmission line in this derivation is to allow for two resistors, one at each end, that are potentially at different temperatures to equilibrate thermally.  Having a simple transmission line connecting them constrains the possible electromagnetic modes by which the resistors exchange energy here forming a simple discrete sequence numbered by the possible standing waves given the length of the line. In thermal equilibrium one resistor emits as much wave energy, that is propagating waves, as it absorbs from the other end. If they are at different temperature then the one at higher temperature will emit, on the average, higher amplitude waves than it absorbs while the other will absorb more than it emits until they reach the same temperature at which point the resistors will be in a dynamic equilibrium with each other and with the propagating medium, here the transmission line.
If you connected the terminals of the resistors directly to one another (zero length transmission line) then they could never equilibrate within the confines of the laws of Kirchhoff (KVL, KIL), Ohm ($V=RI$) and Joule ($I^2R$) (ie. purely by electrical phenomena) for then their voltages would not be fluctuating independently one from another.

From the Master himself, see [1]: 

At any instant after equilibrium has been established, let the line be
  isolated from the conductors, say, by the application of short circuits at the
  two ends. Under these conditions there is complete reflection at the two
  ends and the energy which was on the line at the time of isolation remains
  trapped. Now, instead of describing the waves on the line as two trains
  traveling in opposite directions, it is permissible to describe the line as
  vibrating at its natural frequencies. Corresponding to the lowest frequency the voltage wave has a node at each end and no intermediate nodes. The
  frequency corresponding to this mode of vibration is $\nu/2l$. The next higher
  natural frequency is $2\nu/2l$. For this mode of vibration there is a node at each
  end and one in the middle. Similarly there are natural frequencies $3\nu/2l,
4\nu/2l$, etc. Consider a frequency range extending from $\nu$ cycles per second
  to $\nu+d\nu$ cycles per second, i.e., a frequency range of width $d\nu$. The number of modes of vibration, or degrees of freedom, lying within this range may be taken to be $2ld\nu/\nu$, provided $l$ is taken sufficiently large to make this expression a great number. Under this condition it is permissible to speak of the average energy per degree of freedom as a definite quantity. To each
  degree of freedom there corresponds an energy equal to $kT$ on the average,
  on the basis of the equipartition law, where $k$ is the Boltzmann constant.
  Of this energy, one-half is magnetic and one-half is electric. The total energy
  of the vibrations within the frequency interval $d\nu$ is then seen to be $2lkTd\nu/\nu$. But since there is no reflection this is the energy within that frequency interval which was transferred from the two conductors to the line during the time of transit $l/\nu$. The average power, transferred from each conductor to the line within the frequency interval $d\nu$ during the time interval $l/\nu$ is therefore $kTd\nu$."

[1] Nyquist: "THERMAL AGITATION OF ELECTRIC CHARGE IN CONDUCTORS" Phys. Rev. JULY, 1928, pp110-113
