tomclarke wrote: Fair enough. And easily done.
You have claimed your SR-demons have:
(i) The ability to communicate instantaneously with one another when spatially separated as well as when moving relative to one another;
This statement is only well-defined if frame-independent simultaneity ("instantaneous") is well defined.
Why do you think I chose the term "demons" just as Maxwell has chosen the same term for a being that can control a gate which allows fast molecules through but not slow molecules through. We all know that such a demon with such powers cannot exist.
To now say that my demons must act within the constraints of the Lorentz transformation if I allow them, as demons, to be in instantaneous contact one another, is deliberately and wilfully inserting an irrelevant argument just for the sake of raising any argument. From your previous posts I should have expected this reaction from you.
I can come to the same conclusion when allowing two pilots on a spacehip to, beforehand, agree on the experiments with people who stay behind; and then having the spaceship sweeping past several times while switching on lights in the nose and tail of the spacship at different times during each passing by.
To make sure that such an assinine argument, like your present one, will not be used again in future, I will rewrite my demon post when I have the time by using real pilots, which are subject to the laws that make the Lorentz transformation valid.
If you wish to qualify this, saying that you view any two events with spacelike separation to be "instantaneous" that is fine by me.
It is of course nonsense to state that any two events that are space-separated
must occur at the same time. There is nothing to prevent one event to occur at an earlier or later time than the other.
Of course it does violence to the normally accepted notion of simultaneity because it would mean either that the concept is not transitive, or that all events are instantaneous including those happening at different local times in a given frame.
GobblyGook! Local times within an inertial refrence frame are not different: They are exactly the same. It should be clear to any logical thinker that within an inertial refrence frame, all the clocks that are stationary within this reference frame, will keep time at exactly the same rate. It is a simple task to synchronise all these clocks so that when one shows certain time ALL of them show the same time no matter how far they are seprated from one another. This means that at any separation, two events which occur at the
same time on the synchronsed clocks at these two positions
will be simultaneous events.
or, maybe your definition of instantaneous is arbitrary and relative to some given and constant but unspecified frame of reference.
Where is it arbitrary? Within any inertial refrence frame two events at different positions are simultaneous when the synchronised clocks at these posittions show the same time.
In that case it needs to be so stated in the definition of the demons?
Why? They are demons and not subject to the laws of physics but only used in the sense that Maxwell also used his demon.
(Note that having a consistent notion of simultaneity throughout space in one frame, this can be extended to different reference frames by at every point making a local time comparision with the preferred frame.
Obviously, you can do this by instantaneously stopping the two reference frames from moving further relative to one another. If the clocks within the two reference frames are synchronised to show the same time within each reference frame respectively, and if, before stopping the relative motion a clock within K has been synchronised with a clock within Kp, and then the clocks within K were all synchronised with the clock that is synchronised with a clock within Kp, and the clocks within Kp were then all synchronised with the clock within Kp that is now synccronised with all the clocks within K, then on stopping the motion one will find that all the clocks within K AND Kp will show
exactly the same time. If not, then Einstein's first postulate on which he based his Special Theory of Relativity will be null and void.