Understanding first order versus second order, specifically in context of relativity and optics experiments
I'm reading the following seminal paper on experiments in relativity:
<PERSON>, <PERSON>; <PERSON>, <PERSON>; <PERSON>, <PERSON>; <PERSON>, <PERSON>; <PERSON>, <PERSON>; <PERSON>, <PERSON>; <PERSON>, <PERSON> (1990). Test of the isotropy of the one-way speed of light using hydrogen-maser frequency standards. Physical Review D, 42(2), 731–734. doi:10.1103/PhysRevD.42.731
And it starts with this text:
The constancy or isotropy of the velocity of light for inertial reference frames, first tested in the classic experiments of <PERSON> and <PERSON>,' is a fundamental postulate of the theory of special relativity. Because of the success of relativity, there is little reason to doubt the validity of this postulate. Nevertheless, in most previous tests of isotropy, light was propagated in a closed path instead of one way.* Consequently, round-trip propagation would be sensitive to an anisotropy which is of second order in the velocity of the reference frame of the experiment with respect to a hypothetical universal rest frame, but would be insensitive to an anisotropy which is of first order in this velocity.
Explain it to me like I'm a historian with a good grounding in physical machinery, an excellent grounding in relativity theory conceptually, but nothing above middle school math. 346
IE: I know the physical consequences of constancy and clearly grasp things like relative simultaneity, but still use ultra basic calculation methods to calculate the change factor only. (no more complex uses of the transform)
Also bear in mind I understand the issues with measuring the speed of light explained here on Veritassium's channel.
Yet I'm still having a hard time understanding this particular use of first and second order... The phrasing seems opaque. Heck, I can't even decode their use at a high level, no less what first and second order physically means in this context.
Are they meaning to say that within the confines of accepted relativity theory, a two-way round trip test could detect anisotropy of second order but could not detect first order anisotropy? The word "velocity" is really tripping me up here since they seem to be trying to pull in an "aether-like" frame comparison and leaving me with no idea what they mean.
If I've got the structure right, then what exactly do they mean physically by first and second order in the context of, say, an interferometer experiment or an example from the video above? What's a first order anisotropy in light's speed versus a second order isotropy?
The anisotropy laid out in the simple video above is obvious. Two trips can be unequal but average out... That's fine and makes sense. Is that first or second order and what is the other alternative scenario?
Thanks in advance for the careful and lengthy explanations required to skirt around concise math! I know it's an "ask." 562