Definition of Frame of Reference

[ghwellsjr]

I never mentioned the Standard Configuration in any of my posts. I don't know where you guys got the idea that I was restricting my thinking to the Standard Configuration. Also, I might mention that, even in the Standard Configuration, the orientation of the x-axis in 4D spacetime is not the same as the orientation of the x' axis. I've been working with, and deriving, much more-advanced forms of the Lorentz Transformation than the simple form specific to Standard Configuration.

Chet

I was using the definition of the Standard Configuration presented in the wikipedia article on the Lorentz transformation which is identical to the one that Einstein presented in section 3 of his 1905 paper so I don't know why you state that it is something different. In any case, my point was that the geometric relationship between two Frames of Reference is not the same as the transformation process. I'm sure that each of the more advanced forms that you are working with starts with a description of the geometric relationship and then determines the transformation process to convert the coordinates of events from one to the other.

 

[Vandam]

I really do not understand why you guys are still debating this topic. My post with diagram shows and explains it all.

 

[Chestermiller]

... and what about an event that was at the middle of a rigid ruler where there was no clock or an event that was in the middle of a clock? How would you define those events? And think about what happens when you take the coordinates of an event in one FoR and convert them into the coordinates of the same event in a second FoR moving with respect to the first one, the calculation can result in an arbitrary location where there may not be a clock if you follow the physical idea of a FoR.

I'm sure you've heard the term Linear Interpolation. We engineers use it all the time in analyzing problems numerically, so that our finite difference grid or finite element grid does not have to be infinitely fine (and completely fill every iota of space). But wait, ..., is the functionality we are dealing with in the SR situation we are examining linear? Why yes it is.

Chet

 

[ghwellsjr]

I'm sure you've heard the term Linear Interpolation. We engineers use it all the time in analyzing problems numerically, so that our finite difference grid or finite element grid does not have to be infinitely fine (and completely fill every iota of space). But wait, ..., is the functionality we are dealing with in the SR situation we are examining linear? Why yes it is.

Chet

OK, now you're coming full circle. As long as you're going to allow for the determination of coordinates to include events for which there is no physical object at the time and place of the event, then you're simply imagining what a physical clock and ruler would determine the coordinates of the event to be, correct? And as long as you recognize that there is a 3D finite element grid with a previously synchronized clock at each finite element (as opposed to a small number of randomly located physical objects all at mutual rest) and you can interpolate anywhere else, then all you have to do is imagine that you have a very course grid with elements only at the extremities and you can interpolate to find the coordinates of any event anywhere you want. The final step is to simply imagine that even the elements at the extremities are also imaginary.

But I don't want to lose sight of the import of this thread which is your claim that only objects that are at mutual rest with a Frame of Reference belong to that Frame of Reference. I want to make sure you recognize that Einstein's definition of a Frame of Reference does not contain any physical objects, but an infinite number of imaginary objects (rigid rulers and synchronized clocks in the finite element grid) and you use these to specify the positions and motions of any number of physical objects. (Of course, in our thought problems, even these "physical objects" are imaginary, but we image that they are actually physical, whereas we image that the coordinate rulers and clocks are actually imaginary.)