The First Postulate (2)

We know that motion is always connected with reference frames.

Let's take the example of a falling apple. Let's say an apple is falling from a tree. To a person under the tree, the apple is falling vertically; to a passenger in a train passing by, the apple is falling along a curved line.

This seems contradicting of the first postulate, so velocity itself should not be a physical law。

observer under tree observer in moving train

How about acceleration? Acceleration is also related to reference frames.
After some calculation, we find that the two observers get the same number.

So, the first postulate is closely related to acceleration, not velocity.
This should not be a surprise. A physical law is about a cause and effect relationship. This kind of relationship is only reflected by acceleration, not by velocity.

In which physical law does acceleration appear? In Newton's second law of motion!
Let's see if the first postulate is supported by the second law of motion.