This question just arose in a discussion with George Disman and Kåre Olaussen on ResearchGate: ""https://www.researchgate.net/publication/242304447_Abraham-like_return_to_constant_c_in_general_relativit_y_R_R_R_R-theorem_demonstrated_in_Schwarzschild_metric?tab=comments&focusedCommentId=5a6c581eb53d2f0bba4e230a"
This is an important question.
Depending on how we define physcial equivalence, the answer is Yes. For example, let s1,s2 be states in a finite state space S. A state is represented by a real vector. Let $\mathcal{E}(S)$ (briefly, $\mathcal{E}$ denote the effects on S. State s1 is physically equivalent to s2, provided
there is a unit-preserving affine bijection
\begin{align*}
\Phi: &\mathcal{E}\rightarrow \mathcal{E}\mbox{s.th.} \\
& \Phi(s1) = \Phi(e)(s2)\forall e\in \mathcal{E}.
\end{align*}
This is Definition 1 on page 5 in
Article Physical Equivalence of Pure States and Derivation of Qubit ...
This leads to Proposition 1 (page 1) in this paper:
Proposition 1. Physical equivalence $\cong$ is an equivalence relation.
This is an important question.
Depending on how we define physcial equivalence, the answer is Yes. For example, let s1,s2 be states in a finite state space S. A state is represented by a real vector. Let $\mathcal{E}(S)$ (briefly, $\mathcal{E}$ denote the effects on S. State s1 is physically equivalent to s2, provided
there is a unit-preserving affine bijection
\begin{align*}
\Phi: &\mathcal{E}\rightarrow \mathcal{E}\mbox{s.th.} \\
& \Phi(s1) = \Phi(e)(s2)\forall e\in \mathcal{E}.
\end{align*}
This is Definition 1 on page 5 in
Article Physical Equivalence of Pure States and Derivation of Qubit ...
This leads to Proposition 1 (page 1) in this paper:
Proposition 1. Physical equivalence $\cong$ is an equivalence relation.
Dear Jack:
Thank you very much for your text.
As far as I can see, you do not strictly hold fast to the global-c postulate. Rather you essentially follow Einstein in no longer assuming this constraint. Am I right?
Or more concretely speaking: Would your solution support the global-c version of the Schwarzschild metric which I introduced in my Abraham paper?
I will very much appreciate your kind answer.
P.S.: I had in mind the paper http://lhc-concern.info/wp-content/uploads/2009/01/fullpreprint.pdf
which appeared in print later.
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