But you have specified a unique location as well as a frame of reference in an attempt to more precisely define simultenaeity. And you have still failed to do so in a manner that is physically meaningful.
False. The method I described to get simultaneity of clock displays at A & B locations is very physically meaningful AND can be extended to make a clock at location C be synchronized with them both, where C is any location (in the universe) that is at rest with clocks at A & B - that is in their same inertial frame.
Do you know what a "beat frequency" is?
Certainly. I have known for 70 years. I was a young radio amateur using code (not voice as my radiated power was only about 40W) and set my local RF oscillator to differ from the RF signal I was receiving by an audio frequency difference, making a beat frequency tone I could hear. I suspect you were not yet born when I understood beat frequencies well.
Any two oscillators of nearly the same natural frequency will not make a beat frequency if there is even a small amount of energy exchanged between them. For example two electrical generators driven by steam turbines feeding a common power line (by which they can exchange) will lock together in the same frequency. This is why power in the US is so precisely 60hz even though at times some thousands of the steam turbines if decoupled would be spin to make 59hz and others 61hz.
Thus the following from you is also FALSE and nonsense. Most electric clocks use the 60Hz power line frequency to advance their displays and are perfectly synchronized California to Mane, as the tiny energy exchange that gets them locked in phase goes both ways.
You can phase lock oscillators that are separated in time, and or space, but it is meaningless to specify simultaneity without an acceptable amount of error and/ or a specified time interval (which, as I have explained, appears to be an instant with respect to a particular location, at a particular time).
There is no error when phase locked by energy exchange. Every where in the USA, the power line is with its 60hz cycles having its peak voltages at the same time. Admittedly that would not happen if one were the master and sending synchronization signals to all the others - Then their peak voltage would not be simultaneous.
So yes if you don't understand well (your problem) that they must be part of a network feeding small mounts of energy to each other to keep phase locked, the oscillators can not be synchronized. That is, yes you can do it wrong, but that does not mean you can not do the synchronization right!
The same mathematical bozos who would have us believe that an origin of a coordinate system is something that can be meaningfully specified at some precise location in inertialess relativistic space agreed upon by more than one frame of reference are the same people who think they understand what simultanaeity is. They don't. You can't do relativity with only one observer, or only a single mathematical expression to describe what is observed.
Simultanaeity always requires at least two observers, and there is no guarantee that time dilation is exactly the same at both locations.
All false and egotistical. No observers are required if a phase locked network is sharing energy (more to the oscillators that would run too slowly and fall out of phase and taking energy from others trying to run too fast). Clocks in different inertial frames can not be synchronized, even with a million observers! You have at least heard of time dilation, but don't seem to understand what that implies.
As I noted it earlier post, 247, in bold, it is you who don't even distinguish between true synchronization / simultaneous (in one frame) and your personal perception of synchronization / simultaneous of two (or more) events. With your degree of ignorance / mis understanding etc. you are in no position to call those who know the subject well: "bozos."