Considering $E=mc^2$, what really is a Joule? A newton is defined as the force able to accelerate a mass of $1kg$ by $1m.s^{-2}$ : $1N=1kg.m.s^{-2}$.
Then, a joule is defined as the work done by a force of $1N$ moving an object by $1m$ : $1J = 1N.m = 1kg.m^2.s^{-2}$.
As Einstein redefined what mass is, with the $m=E/c^2$ formula, the kilogram definition should fundamentaly be derived from the joule : $1kg = 1J.m^{-2}.s^2$.
And from there a newton gets defined as a joule per meter : $1N=1kg.m.s^{-2}=1(J.m^{-2}.s^2).m.s^{-2}=1J.m^{-1}$.
All of this makes sense, but what fundamentally is a joule ? As it is defined from the kilogram... itself depending on the joule (!), I can't figure it out.
 A: As of 2019, it's arguable the Joule has a more fundamental definition than the kg,
A Joule is the unit of energy such that Planck's constant takes the exact value:
$$ 6.62607015 × 10^{-34} \, \mathrm{Joule \cdot second} $$
With the second being defined by the Cs hyperfine transition.
The post-2019 kg is derived as a consequence of this and the speed of light.
A: In the modern International System of Units, the chain of definitions goes as follows:

*

*The second is defined in relation to the frequency of a certain atomic transition in cesium vapor.


*The meter is defined from the second via the speed of light in a vacuum.


*The reduced Planck constant $\hbar$ is defined as the quantum of angular momentum.  Among other examples, $\hbar$ is the angular momentum carried by a single circularly-polarized photon, which can be used to drive a torsion pendulum.


*The quantum of charge on an electron or a proton is used to define macroscopic electric charges.
In principle you could define "the joule" just from the second and the Planck constant, using the relation between photon energy and frequency $E = hf$.  In practice, however, the transition between microscopic and macroscopic energies is made using electronics.  In the Josephson effect, a voltage (energy per unit charge) is quantized in units of ${\hbar\omega}/{e}$.  Meanwhile the quantum Hall effect has a resistance which is quantized in units of $h/e^2$.  From these two constants you can construct voltage and current standards, and therefore define electrical power $P = IV$.  Connection to macroscopic mechanical energies is made using the Kibble balance.
In the modern SI, force is derived from energy done per unit distance, rather than the other way around as in your question.
A: 
All of this makes sense, but what fundamentally is a joule ?

A joule is fundamentally a unit of energy. Since energy is defined as the capacity for doing work, the joule is defined as the capacity for doing an amount of work equal to the force of one newton applied over a displacement of one meter.
As has been pointed out by @Mauricio, Einstein did not redefine mass. Prior to $E=mc^2$ the laws of conservation of mass and conservation of energy were seen as two separate laws. With mass-energy equivalency the total mass may change, but the total energy remains constant.
Hope this helps.
