Einstein vs Newton: The concept of inertial vs non inertial frames

[Dale]

A physical setup of "clocks and rulers" defines one and only one reference frame. Of course you can use different coordinates and different tetrads to "map it"

Remember, for me the reference frame is the coordinates or tetrad. So if you agree that you can use different coordinates and tetrads then you do in fact agree with the content of 2, just not the semantics.

In any case, perhaps I should have avoided the term reference frame since that it the term under contention. In neutral terms, the fact I was highlighting is that you can use any possible sufficient set of clocks and rulers to realize any possible coordinate system or tetrad. I assume, worded like that, you have no objection. My opinion (which I assume you disagree with) following from that fact (which I assume you agree with) is that since the two halves are so independent of each other, to me it makes little sense to try to lump them together in one term.

To understand my stance on this issue, consider “the mass of object A”. This could refer to either a mathematical variable $m$ in some equation or to the physical property of A that can be measured by placing A on a balance scale. This uses the same term for the map and the territory, but there is a unique physical quantity and a unique mathematical quantity assigned to represent it. The math and the measurements are isomorphic, so there is no ambiguity.

Now, consider the Coulomb gauge. That is purely mathematical. You can change to a different gauge without changing any of your voltmeters or grounding wires. The mathematical quantity is not isomorphic to any physical object or measurement. Because of this we do not try to assign the label “the Coulomb gauge” to any collection of measurement devices or physical objects. We keep the map and the territory distinct because there is no isomorphism between them.

As you yourself have mentioned, the freedom to select a coordinate system or tetrad is similar to choosing an EM gauge. Certainly a coordinate system has more in common mathematically and theoretically with an EM gauge than with mass. It makes sense that the language should reflect that similarity. Given the lack of an isomorphism between the math and the physics, we should not try to use the same word to refer to both.

but the physical observables are independent of this choice. This is guaranteed by general covariance

Precisely.

because physics is more than a mathematical formalism but it has the goal to describe the real world

I already told you multiple times that this is not a point of disagreement. I do not appreciate this repeated and completely asinine mischaracterization of my opinion. Simply because I do not wish to call a collection of clocks and rulers a “reference frame” does not mean that I cannot use rulers and clocks to measure and describe the real world!

In the end this is the only argument you have put forth for your position and it is a pure misrepresentation. This is intellectually dishonest.

 

[Dale]

Temporarily closed for moderation

 

[PeterDonis]

I have not misinterpreted your standpoint but disagree(d) with it, because physics is more than a mathematical formalism but it has the goal to describe the real world, i.e., quantitative observations and is not merely some mathematical system of axioms and theorems.

@Dale never denied what you are saying here, and indeed has explicitly said he agrees with it, so you are not disagreeing with him, you are misrepresenting his position, as he has said. The only thing you disagree with him on is the usage of the term "reference frame", which is just about words, not about physics.

In any case, this thread has gone far beyond answering the OP's question, which was answered many posts ago, so the thread will remain closed.