CarlLaMagouille wrote:To Monika,
I'd say you are right about this, but I think you would need 3 detectors to trinagulate an event in 2+1d, and 4 in 3+1d.
I am thinking of detectors that can see the source of light emission (and of course record a time when they receive it). So 2 detectors are enough. Each of them can find out a line on which the event lies. Intersecting two lines results in a point.
2 detectors cannot make the difference between events on the bissecting plane between them, for instance.
Okay, so you're using detectors that can only record when the signal arrived, but they don't see the source, right?
I am not sure which type is used by GPS. I guess it could be the type of detector you are thinking of, so 4 detectors would indeed be needed.
steve waterman wrote:Monika
Your thought experiment is right on the issue, well done.
Great. So you understand now that when we say "observer 1 observed order event 1 and event 2 to be simultaneous" we do in fact NOT mean "observer 1 received the signals from event 1 and event 2 at the same time", right? So you will stop saying "reception time is irrelevant here!", right?
With that in mind Monica, I hope you do not mind too much, that I also get a chance for the brief comments below .
if we have 1 receiver, it only gets to record their PERSONAL receipt sequence
Not sure if you mean 1 observer (1 reference frame) or you mean 1 detector (of which there could be several in a reference frame) and which style of detector you mean, but if you mean 1 detector and you mean a style-II detector that can record both the light source (direction) and the time then I agree, it cannot figure out the sending sequence.
if we have 2 receivers, they get to know the hyperboloid of possible POINTS for the transmission site
Not sure how you mean that, can you make a picture of that?
If we have 3 receivers, they get to know the transmission time and transmission site
unless the receipt times are all equal, then the possible transmission site is some point on the line,
perpendicular to the plane that the 3 receivers sites mathematically define.
You realize there are infinitely many such lines? Actually any point is on some line that is perpendicular to that triangle.
if we have 4 receivers not all in the same plane, they get to know the transmission time and transmission site
What do your "receivers" (which seem to be detectors, not observers / reference frames) record?
Do they see the light source, i.e. from which direction the light is coming? (Style II) Or do they only record the time when the light is received? (Style I)
Obviously they are not working like police speed guns that also measure the distance.