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From: ellis@spar.UUCP (Michael Ellis)
Newsgroups: net.philosophy,net.physics
Subject: Einstein and causality
Message-ID: <660@spar.UUCP>
Date: Wed, 20-Nov-85 03:48:38 EST
Article-I.D.: spar.660
Posted: Wed Nov 20 03:48:38 1985
Date-Received: Sat, 23-Nov-85 00:31:00 EST
References: <1174@wucec2.UUCP> <27500182@ISM780B.UUCP>
Reply-To: ellis@spar.UUCP (Michael Ellis)
Organization: Schlumberger Palo Alto Research, CA
Lines: 39
Xref: watmath net.philosophy:3181 net.physics:3614

[Note- this is a partial response to a flame from Mr. Gwyn concerning
       a previous article of mine..]

>Consider simultaneity: before Einstein, it was assumed that simultaneity was
>an inherent property of the relationship between two events; either they
>were simultaneous or they were not.  But Einstein pointed out that
>whether two events are perceived as simultaneous depends upon the location of
>the observer.  *Any* two different events will be appear to be simultaneous 
>to an observer at the right location. - Jim Balter

    This is an overstatement -- only two events separated by a SPACELIKE
    4-distance can be seen as `simultaneous' by an appropriately chosen 
    observer.

    BTW, two events which can be causally connected must be separated
    by a TIMELIKE (or NULL, in the limiting case) 4-distance. 

    4-distance is invariant to all observers, whereas the spatial or
    temporal separations vary according to observers. The formula
    for 4-distance between two events is:

		      ------------
		    \/	x*x - t*t

	where x is the spatial distance (in terms of the speed of light)..
	      t is the amount of time..

              ..separating the two events. 4-distances are categorized:
	      
	      >0        Spacelike
	      =0        Null
	      imaginary Timelike

    Timelike and null intervals are crucial to modern notions of 
    causality. Since 4-distances are invariant, if I throw a 
    rock thereby breaking a window, all observers will agree
    on the order of events (I threw the rock, then the window broke).

-michael