The question being asked is, "what is the correlation between these two variables": is it positive, negative, or zero (null). The null hypothesis is the baseline you start from because the overwhelming majority of variables from physical observations are uncorrelated (e.g. what is the correlation between "how many people in the treatment group of this clinical trial made a full recovery" and "the price of eggs in Slovakia").

Measurements of some physical quantity are a different kind of experiment, you cannot phrase it as a question about the correlation between two variables. Instead you take measurements and put error bars on them (unless what you're measuring is an indirect proxy for the actual quantity, in which case the null hypothesis and p-value testing does become relevant again).

In fact, you can express measurement of g as a linear correlation between y-y0 and (t-t0)^0.5.