Question

The Earth, effectively a non-inertial frame of reference, is where Newton concluded his laws of motion. However, Newton's first law only holds in an inertial frame of reference.

In the process of inventing the Newton's laws of motion, since almost all (I suppose) the experiments were done in a non-inertial frame of reference i.e. the Earth, why were people confident enough to believe that Newton's first law is true (to some extent, I am not talking about relativity etc.) in an inertial frame of reference?

I am not trying to say that Newton's laws of motion are lies. I just had a logical question: since the research was done in a non-inertial frame of reference, how can we invent the laws regarding motion in an inertial frame of reference?

I suppose that's because the Earth can be approximated to an inertial frame of reference as the effect of the self-rotation (which causes the Earth to be a non-inertial frame of reference, in my opinion) of the Earth on the objects on the Earth is quite small. And, therefore when people did the experiments, the uncertainty caused by the self-rotation of the Earth is too small to be significant (or, maybe they didn't even find/realise such an uncertainty!). And therefore, by inference (or guessing?), we can invent the laws of motion regarding objects in an inertial frame of reference. In theory, if we do the same experiment in a true inertial frame of reference, we will effectively get the same/similar results. (This is just my explanation, which can be very debatable!)

I want to hear how other people think about this question. Thank you!

Answer 1

The confidence in Newton's first law being applicable in an inertial frame of reference, despite Earth being non-inertial, stems from Earth closely approximating an inertial frame for most practical purposes. The minor deviations didn't significantly affect experimental outcomes, leading to the laws' acceptance.

Step-by-step explanation:

The confidence in Newton's first law of motion being true in an inertial frame of reference, despite most experiments being conducted on Earth (a non-inertial frame), emerges from the fact that the effects causing non-inertial behavior on Earth are relatively minor. When we examine the frames of reference used, for practical purposes, Earth approximates an inertial frame closely enough that the deviations are not significant for most experiments. For example, a car passenger feels forces when the car turns, which are due to their inertia and not a physical force, demonstrating the experience from within a non-inertial frame. However, when observing the same scenario from the Earth's frame of reference, which is nearly inertial, the forces have identifiable origins (like friction or tension), aligning with Newton's dynamics.

The laws of physics, including Newton's laws, are simplest in inertial frames, as observed in an airplane flying at a constant velocity, which resembles standing still on Earth's surface. While Newton's laws were formulated based on such observable phenomena, Einstein's special relativity further acknowledged that the laws of physics should be the same in all inertial frames. Consequently, Newton's first law is seen not just as a physical principle, but also as a tool for defining inertial reference frames. It is this profound simplicity and universality that led to the acceptance of Newton's laws and their continued use in accurately describing the physical world, before the additional complexities introduced by special relativity were considered.