How do non-inertial frames affect special relativity?

[Nugatory]

Inertial frame. A frame of reference in which bodies are not accelerated. The Penguin Dictionary of Science.

Something is wrong with that definition - at the very least it must include a qualifier about the object not being subject to external forces.

In free fall under the action of gravity objects are generally accelerated.

Objects in free fall under the action of gravity are not accelerating in a (local) inertial frame. An object dropped on the surface of the Earth is accelerating downwards in the frame in which the surface of the Earth is at rest. That's how we know that that frame is not an inertial frame.

 

[Ibix]

Inertial frame. A frame of reference in which bodies are not accelerated. The Penguin Dictionary of Science. In free fall under the action of gravity objects are generally accelerated.

In addition to @Nugatory's comments, this fails to make a distinction between proper acceleration and coordinate acceleration. Free-falling bodies do not experience proper acceleration, and whether or not there is coordinate acceleration is up to your choice of coordinates. So your statement is oversimplified at best.

 

[A.T.]

Inertial frame. A frame of reference in which bodies are not accelerated. The Penguin Dictionary of Science.

Says pretty much nothing. Bodies can be accelerating in inertial and non-inertial frames.

In free fall under the action of gravity objects are generally accelerated.

Which frame is inertial in a gravitational field depends on whether you use Newton or GR.

 

[PeroK]

Inertial frame. A frame of reference in which bodies are not accelerated. The Penguin Dictionary of Science.

The Penguin definition is incorrect. I suggest it was written by a lexicographer and not a physicist.

Wikipedia gives a better version:

"An inertial frame of reference, in classical physics, is a frame of reference in which bodies, whose net force acting upon them is zero, are not accelerated; that is they are at rest or they move at a constant velocity in a straight line."

In free fall under the action of gravity objects are generally accelerated.

If we take gravity to be a force, then this is correct. But, taking gravity as a fictitious force, objects in freefall are accelerating in a non-inertial reference frame: rest frame of the Earth's surface, say.. And objects, as they fall, are in a (local) inertial reference frame.

 

[Dragon27]

The Penguin definition is incorrect. I suggest it was written by a lexicographer and not a physicist.

It would look much better if one just inserts the (very important) word "free" before "bodies". Like here.

 

[kent davidge]

Which frame is inertial in a gravitational field depends on whether you use Newton or GR.

Can you elaborate on this? Is it because in GR we can make whatever frame locally inertial while in Newton we can't?

If we take gravity to be a force, then this is correct. But, taking gravity as a fictitious force, objects in freefall are accelerating in a non-inertial reference frame: rest frame of the Earth's surface, say.. And objects, as they fall, are in a (local) inertial reference frame.

Interesting point. Thanks for bringing this up.

 

[Ibix]

Can you elaborate on this? Is it because in GR we can make whatever frame locally inertial while in Newton we can't?

In GR gravity isn't a force, so a particle in a gravitational field isn't experiencing a force and is inertial. In Newtonian physics gravity is a force, so a particle in a gravitational field is experiencing a force so is not inertial.