Einstein frame vs Jordan frame, About their strong and weakness point Recently i am interested in scalar gravity and its extension. 
In many context, they deal with Einstein frame and Jordan frame. 
From Wikipedia, 
Einstein frame is usual one with no scalar (or dilaton in front), $i.e$, $R$ in the action, but Jordan frame is like $\Phi R$. 
Performing conformal transformation, one can transform Jordan frame and Einstein frame and vice versa. 
Are they equivalent? 
In the action level, they can be transformed into each other, but in the equation of motion level, their dynamics seems pretty different.

At this moment i have two questions. 


*

*What is the physical frame between them?  


Wiki says it is controversial problem. 
(I just want your thoughts with some plausible reason)


*What is the strong and weak point for each frame? 


(If first problem is too abstract, then why some people use Jordan frame?) 
 A: *

*What is the physical frame between them?


Jordan frame is obtained by a conformal rescaling of the metric of the Einstein frame. Hence, it will have an extra scalar degree of freedom unless that scalar is already present in the Einstein frame. If the d.o.f. are kept the same, then both frames are physical. That means any physical process which takes place in Einstien frame will also be valid in Jordan frame since there is nothing special about it except being a coordinate transformation. That is one argument why it should be considered physical. 
However, it can be shown that the 2nd law of thermodynamics is broken in the Jordan frame (due to violation of the null energy condition). And that was cited as one of the reasons why that frame is unphysical. 
We did the analysis and it turns out that if we are willing to generalize the null energy condition (NEC) then the physicality is restored. 


*What is the strong and weak point for each frame?


In short,
Einstein frame - Best frame to discuss physical processes. Things are usually simpler.
Jordan frame - Extremely helpful in analyzing f(R) theories which can be reduced to a scalar-tensor theory in the Jordan frame. The Jordan frame helps to identify if the theory is unstable and if they have ghosts.
