How do you know if a reference frame is inertial?

Q: What makes a frame inertial?

An inertial frame is defined as one in which Newtons law of inertia holds—that is, any body which isnt being acted on by an outside force stays at rest if it is initially at rest, or continues to move at a constant velocity if thats what it was doing to begin with.

What you just realized in that freefall, even in Newtonian mechanics, looks locally like an inertial frame.

Table of Contents Show

How do you identify an inertial frame?
What makes a frame inertial?
How will you realize an inertial frame in practice?
What makes a non

This is called the equivalence principle, and led Einstein to postulate that gravity is not a "real force acting on the ball". In fact, gravity when we are standing "still" looks like the pseudo force we would observe in the elevator if we were to "place this elevator in the far reaches of the solar system sufficiently far from any planets" but have it accelerating.

Unfortunately, unlike the usual fictitious forces we encounter when studying Newtonian mechanics (Coriolis force, the centrifugal force), we can't make gravity easier to describe just by changing to a more appropriate coordinate system. Instead Einstein found we need to consider space-time curved.

And in GR, a free-fall frame is a locally inertial frame.

So your intuition was right.

And to answer your titled question:
Any linear transformation would preserve straight lines, but could make other physics look bizarre in those coordinates. So free floating objects moving in a straight line is not quite enough. Having the metric be -1,1,1,1 diagonal (or opposite sign) is usually what people mean by an inertial frame.

How do you identify an inertial frame?

Thus, it can be said that an inertial frame of reference either remains at rest or moves with a constant velocity. For example, a car at standstill or a bus moving with constant speed are considered to be inertial frames of reference. A non-inertial frame of reference is one which is in the state of acceleration.

What makes a frame inertial?

An inertial frame is defined as one in which Newton's law of inertia holds—that is, any body which isn't being acted on by an outside force stays at rest if it is initially at rest, or continues to move at a constant velocity if that's what it was doing to begin with.

How will you realize an inertial frame in practice?

A good example of an inertial frame is the Earth. If you leave an object rest, it will remain at rest forever, and one in motion will keep moving with a uniform motion provided no net external force acts on the object. In the Earth frame of reference, the law of inertia holds for most practical purposes.

What makes a non

A non-inertial reference frame is a frame of reference that undergoes acceleration with respect to an inertial frame. An accelerometer at rest in a non-inertial frame will, in general, detect a non-zero acceleration.