The Postulates — Question 7

Question 7

Acceleration can be detected without an external landmark

In inertial S, a freely drifting marker has $x=0$. An observer uses $x\prime=x-X(t)$ and the same t, where $X(t)=Vt+\tfrac12at^2$. Treat this as a low-speed local model.

1. Find the marker velocity and acceleration in the observer coordinates.

2. Compare $a=0$ with $a\ne0$ and state which motion can be detected by this free-marker test.

Question 7 - Solution

Acceleration can be detected without an external landmark

(a) Method and calculation

$$x\prime=-Vt-\tfrac12at^2,\qquad\dot x\prime=-V-at.$$$$\boxed{\ddot x\prime=-a}.$$

(b) Interpretation and further calculation

$$a=0:\quad\ddot x\prime=0\ \text{for every constant }V.$$$$a\ne0:\quad\boxed{\text{free marker accelerates relative to the observer}}.$$

Physical check

Uniform translational velocity supplies no absolute-rest test; acceleration relative to inertial free motion is locally detectable.