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13 votes
3 answers
7k views

What is an inertial frame? [duplicate]

Throughout my life I've been told that an inertial frame is one that is not accelerating and I was satisfied with that. Well up to this day, until I asked: accelerating with respect to what ? Now this ...
37 votes
8 answers
11k views

What determines which frames are inertial frames?

I understand that you can (in principle) measure whether "free particles" (no forces) experience accelerations in order to tell whether a frame is inertial. But fundamentally, what determines which ...
1 vote
3 answers
219 views

Is the definition of inertial reference frame circular?

In elementary physics classes, inertial reference frames are defined as a coordinate system which is in constant rectilinear motion (or at least that is how it was defined by my professor). How then ...
2 votes
0 answers
123 views

About the definition of world-line in Arnold's book

I am reading Arnold's Mathematical Methods of Classical Mechanics. I have some questions about the definition of world-line. The book says: A curve in Galilean space which appears in some (and ...
0 votes
3 answers
107 views

What does it mean that two frames are " in a state of constant, rectilinear motion with respect to one another"?

This expression ( applied to reference frames) " being in a state of constant, rectilinear motion with respect to one another "is frequently used as self explanatory . Though I might appear as stupid, ...
8 votes
4 answers
1k views

What is the difference between a translation and a Galilean transformation?

What is the difference between a translation and a Galilean transformation?
0 votes
0 answers
54 views

Inertial frame definition in Rindler Introduction to STR vs Landau' & Lifshitz Mechanics

Juxtaposing Rindler's Introduction to STR (page 7) vs Landau's Mechanics (page 5) inertial frame definition,I get that rindler assumes frame moving uniformly w.r.t inertial frame as an inertial frame ...
1 vote
3 answers
256 views

Defining what it means for a reference frame to move with a velocity $\mathbf{u}$ with respect to another

In describing a Galilean transformation, for example, one might say that if a reference frame $S'$ is moving at a velocity $\mathbf{u}$ with respect to $S$, then an object traveling at a velocity $\...
2 votes
1 answer
497 views

Definition of Galilean structure in Arnold's book?

I am reading Arnold's Mathematical Methods of Classical Mechanics. He quickly introduces the notion of Galilean structure. The universe is defined as the affine space $A^4$ and time is defined as a ...
1 vote
2 answers
1k views

What does a Galilean transformation actually mean?

What does a Galilean transformation actually mean? I'm having trouble defining the equation for displacement shifts $x'=x-vt$. Does it mean that to any event $C$ the displacement in the primed ...