For example, the electric potential can be expressed as follows: $$ V(\mathbf{r})=V_0 + \frac{1}{4\pi\epsilon_0}\frac{q_i}{|\mathbf{r}- \mathbf{r_i}|} $$
It can be written as a representation of the difference relative to a reference value ($V_0$). However, this expression for potential possesses a very peculiar characteristic that is entirely different from all other physical quantities.
Most physical quantities, such as length, time, and mass, are expressed as ratios to a chosen reference.
Therefore, if the reference is changed, the value also changes. For example, if we change from inches to meters, the numerical value representing a given distance changes as well.
In this case, the numerical value changes, but the change rate is proportional to the change in the standard.
However, in the case of potential, infinity is often chosen as the reference point, effectively making the reference value zero. In cases of other physical quantities, if the reference is set to zero, the value typically loses its physical meaning, but potential is treated as an exception.
Of course, the reference point for potential can also be chosen arbitrarily, rather than at infinity. However, in such cases, potential loses the second characteristic seen in other physical quantities — that is, it is independent of the change rate of the reference value.
This peculiar behavior of potential arises from its mathematical properties. That is, the meaningful physical quantity is not the potential itself, but its gradient, and in particular, the potential difference in the case of conservative fields.
Nevertheless, considering phenomena such as the Aharonov-Bohm effect, I find myself raising many questions, such as whether it is appropriate to disregard the value of the potential itself.
