It is easy to see that the hypersurface of the present falls into the last category since all its points except that occupied by the observer are outside the light cones.Given an event E, the light cone classifies all events in spacetime into 5 distinct categories:
- Events on the future light cone of E.
- Events on the past light cone of E.
- Events inside the future light cone of E are those which are affected by a material particle emitted at E.
- Events inside the past light cone of E are those which can emit a material particle and affect what is happening at E.
- All other events are in the (absolute) elsewhere of E and are those that will never affect and can never be affected by E
"I find this counter-intuitive, so how do I know it's 'really' that way or just conspires to act that way in all respects?"
IMO SRT has put forward a counter intuitive proposition, that observers at relative velocity do not share the same Hyper surface of the present [ other wise known as "now"] I ask is there evidence to support accepting such a counter intuitive proposition?
Simultaneity is a definition not a physical state, though that definition cannot run afoul of effect preceding cause. The simple logical fact is that if two separated observers cannot agree on the rate of time they cannot agree on the simultaneity of separated events. You even conceded the time dilation in the OP. The relativity of simultaneity simply derived an operational definition that all observers can agree with. The simultaneity of two event at the same point in space are never in question.
SR was derived under the logical positivist school of thought. I don't strictly hold to such a school of thought but its strength is that it remains mathematically valid regardless of what interpretation you put on it. Conceding time dilation but questioning the relativity of simultaneity is a lot like conceding Earth has a surface but questioning whether it has a center or not.
good counter argument and enquiry thanks...
if evidence can be obtained to support the non-simultaneity of t=thsp of observers at rel. velocity I would be a lot happier.
I am aware that the compounding nature of time dilation would intuitively lead to non-simultaneity however to confirm that non-simultaneity is actual and not merely a theoretical outcome of compounding time dilation effects would make the theory rock solid.
Not finding evidence would not in any way diminish the theory but being thorough would be great.
Yes, during to time I was chasing SR in circles to search for holes I much appreciated empirical data in spite of apparent logical consistencies. Here the existence of matter waves is given as direct experimental evidence of the relativity of simultaneity. See the section on De Broglie waves.
http://en.wikibooks.org/wiki/Special_Relativity/Simultaneity,_time_dilation_and_length_contraction
This one is probably easier to follow. This guy goes to great lengths to very pictorially show how Stellar Aberration is a direct observational result of the Relativity of Simultaneity.
http://www.pitt.edu/~jdnorton/Goodies/rel_of_sim/index.html
That is probably the one you need to spend time to understand. If you want a downloadable PDF version go here;
http://philsci-archive.pitt.edu/archive/00002734/