Relative potential energy vs Absolute potential energy I have seen in many textbooks and sources which say that we can't experimentally measure potential energy but we can measure differences in potential energy.
$$\Delta U_g=-W_g$$ 
Choosing zero potential (reference point) at the ground.
Now if I measure change in gravitational potential energy from zero point to a point where an object thrown upwards attains zero velocity, then $U_g$ at that point would just be negative of the work done.
If potential energy at that point can be calculated then why is it said that absolute potential energy at a point can't be calculated?
 A: Simply put, potential energy is the energy an object possesses because of its position. Position, or location, is always relative. Therefore there is no such thing as an exact or absolute position in space and consequently no exact potential energy. 
Potential energy must be measured relative to something.  Suppose a 1 Kg ball is suspended 1 meter above the surface of the earth. Relative to the surface of the earth it has a potential energy of 9.81 Joules.  But suppose we put a 0.5 m high table underneath the ball.  Relative to the surface of the table it has a potential energy of 4.9 Joules. 
We haven't moved the ball, so which is the real potential energy?
A: It's because the "zero point" you mentioned is arbitrary, and doesn't have to be zero. I could just as say that $GPE(y = 0) = 10 \text{J}$ or any other arbitrary number. In that case, even thought I could find $GPE$ at whatever height the ball reaches, I couldn't unique determine it, since it would depend on how I defined $GPE(y = 0)$.
Hope that helps! 
A: We can measure potential energy. For example, we know that the electrostatic potential energy between a proton and a electron in a hydrogen atom is negative, and equal to -27.2 eV. This negative energy is what makes the mass of hydrogen atom be less than the sum of the proton and electron masses.
In special relativity, we know that mass, energy, and momentum of a system are related by $m^2=E^2-p^2$ (in units where $c=1$), and the energy $E$ in this equation includes all forms of energy, including potential energy. So, unlike in Newtonian physics, it is not true that only potential energy differences matter.
The electrostatic potential energy between two point charges is $q_1 q_2/r$ (in Gaussian units), not this plus an arbitrary constant. When the two charges are infinitely far apart, there is no potential energy.
Similarly, the gravitational potential energy between two point masses is $-G m_1 m_2/r$, not this plus an arbitrary constant. When two masses are infinitely far apart, there is no potential energy.
We know that this is true in the case of gravity because, in the post-Newtonian approximation of General Relativity, the negative gravitational potential energy affects the force of gravity. This has been tested in the dynamics of the solar system.
Only in Newtonian mechanics, which we have known is wrong for more than a century, is it true that only differences in potential energy matter. We know better now.
