# Special Relativity Assumption

In the Book "The Geometry of Minkowski spacetime" by Naber, he says we may assume the following:

Any two admissible observers agree on the temporal order of any two events on the worldline of a photon, i.e., if two such events have coordinates $(x^1, x^2, x^3, x^4)$ and $(x^1_0, x^2_0, x^3_0, x^4_0)$ in $S$ and $(\hat{x}^1, \hat{x}^2, \hat{x}^3, \hat{x}^4)$ and $(\hat{x}^1_0, \hat{x}^2_0, \hat{x}^3_0, \hat{x}^4_0)$ in $\hat{S}$ then $x^4 - x^4_0$ and $\hat{x}^4 - \hat{x}^4_0$ have the same sign.

i.e. that two observers agree upon the ordering of events in spacetime. Why is he making this assumption? Isn't the whole point of SR to say that simultaneity is relative?

• See: physics.stackexchange.com/questions/169631/… Two events on the worldline of a photon are lightlike separated. Dec 24 '17 at 3:45
• Please don't post images of text: transcribe the text into the post as a bloack quote (use > for markup). This has two advantages: first the quote is machine readable and therefore searchable and second it is possible for user to cut-n-paste from the block quote to highlight important points. Dec 24 '17 at 5:37
• Here's an important point that should be highlighted: the author does not make this claim for arbitrary pairs of points, he makes it for "any two events on the worldline of a photon". That is a very restricted case, and you have to analyze the situation with that in mind. Dec 24 '17 at 5:38

3. For each admissible observer the speed of light in vacuo as determined by the Fizeau procedure is independent of when the experiment is performed, the arrangement of the apparatus (i.e., the choice of P), the frequency (energy) of the signal and, moreover, has the same numerical value c (approximately $3.0 \times 10^8$ meters per second) for all such observers.
4. "causality assumption": Any two admissible observers agree on the temporal order of any two events on the worldline of a photon, i.e., if two such events have coordinates $(x^1, x^2, x^3, x^4)$ and $(x^1_0, x^2_0, x^3_0, x^4_0)$ in S and $(\hat x^1, \hat x^2, \hat x^3, \hat x^4 )$ and $(\hat x^1_0, \hat x^2_0, \hat x^3_0, \hat x^4_0 )$ in $\hat S$, then $x^4 − x^4_0$ and $\hat x^4 − \hat x^4_0$ have the same sign.