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I came across the following distinction between frames and coordinate systems from Rindler,

“We should, strictly speaking, differentiate between an inertial frame and an inertial coordinate system, although in sloppy practice one usually calls both IFs. An inertial frame is simply an infinite set of point particles sitting still in space relative to each other. For stability they could be connected by a lattice of rigid rods, but free-floating particles are preferable, since keeping constant distances from each other is also a criterion of the non-rotation of the frame. A standard inertial coordinate system is any set of Cartesian (x,y,z) axes laid over such an inertial frame, plus synchronized clocks sitting on all the particles, as described above.”

By particles, is Rindler referring to an infinite set of observers? That is, the particles aren’t physical and don’t actually exist, but are just a way of thinking of the observer team which makes measurements within a frame once the coordinate system is chosen?

I assume a frame of reference can be essentially taken to be a grid of observers who share a rigid body motion attached to a physical body or feature of interest.

Here is the reference: http://www.scholarpedia.org/article/Special_relativity:_kinematics

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  • $\begingroup$ Well your question is more philosophical, since particles are regarded as both points and waves. Physics never made much sense to me, especially after QM. $\endgroup$ Feb 11, 2020 at 9:01
  • $\begingroup$ @MathematicalPhysicist I’m asking from a more technical standpoint. As if he’s describing a metaphorical grid which shares the rigid body motion of the object whose rest frame we are considering. $\endgroup$
    – 13509
    Feb 11, 2020 at 10:48
  • $\begingroup$ You might as well ask, how can you build point-like clocks as well? physics is ill-defined, everyone knows that. $\endgroup$ Feb 11, 2020 at 11:02
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    $\begingroup$ My guess would be that the particles should be thought of a reference points, so I can determine the position of a object by saying something like "It is half way between particle 2547 and particle 2548". This may help clear up questions when setting up SR such as "given that I am expecting effects such as length contraction to exist, how exactly do I define 'length'? How specifically do I measure distance?" $\endgroup$ Feb 11, 2020 at 12:12

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That is, the particles aren’t physical and don’t actually exist, but are just a way of thinking of the observer team which makes measurements within a frame once the coordinate system is chosen?

Basically yes.

Once an event takes place you can assign it a spacetime coordinate $(t,x,y,z)$ by looking at the particle in the grid $(x,y,z)$ nearest to the event and the time $t$ that particle's clock measures when the event happens. It is just a way of interpreting how spacetime coordinates relate to a specific inertial reference frame.

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