Hey all,

My qustion is coming from a purely conceptual understanding of
physics, so if I'm just spouting nonesense, tell me. But I'd much
rather you explain where I am going wrong in my mental model, because
I have an interesting idea in my head.

So Special relativity, while enforcing the universal speed of light,
makes relative measurements of time and space. One consequence of
this is that two events determined by one observer to be simultaneous
might be determined by a different observer to occur at different
times. My question is how this phenomenon relates to causality. For
instance, two events that are causaly related must occur in sequence,
but if it is possible to observe the same two events happening
simultaneously or even in reverse order, then does this mean that SR
also destroys universal causality? Would observing two
causally-related events as simultaneous mean "spooky action at a
distance" is possible, or is the causality somehow destroyed when you
are moving at high relative speed?

If any of this makes sense, please point out to me where my
understanding is lacking or point me towards some good reference.

Thanks
Charlie Mezak

"Charlie Mezak" wrote in message
m...
Hey all,

My qustion is coming from a purely conceptual understanding of
physics, so if I'm just spouting nonesense, tell me. But I'd much
rather you explain where I am going wrong in my mental model, because
I have an interesting idea in my head.

So Special relativity, while enforcing the universal speed of light,
makes relative measurements of time and space. One consequence of
this is that two events determined by one observer to be simultaneous
might be determined by a different observer to occur at different
times. My question is how this phenomenon relates to causality. For
instance, two events that are causaly related must occur in sequence,
but if it is possible to observe the same two events happening
simultaneously or even in reverse order, then does this mean that SR
also destroys universal causality? Would observing two
causally-related events as simultaneous mean "spooky action at a
distance" is possible, or is the causality somehow destroyed when you
are moving at high relative speed?

Two events can only be causally related if A causes B. Since in SR
information can not be transmitted faster than light (and A causing B is
certainly transmitting information - well generally anyway - QM has some
interesting twists) then A and B must be what is called time like
intervals - which means they are connectable by a speed traveling less than
light. Time like intervals always have their ordering preserved hence
casualty is not violated. Space like intervals OTOH can not be connected by
a speed traveling less than or equal to light and their ordering can be
different - but that is no problem since they can not be casually connected
so causality is saved. See
http://www.physics.fsu.edu/users/Pro...y/Interval.htm
and
http://chaos.swarthmore.edu/courses/...lativity_4.pdf.

Thanks
Bill


If any of this makes sense, please point out to me where my
understanding is lacking or point me towards some good reference.

Thanks
Charlie Mezak

Charlie Mezak wrote:

Hey all,

My qustion is coming from a purely conceptual understanding of
physics, so if I'm just spouting nonesense, tell me. But I'd much
rather you explain where I am going wrong in my mental model, because
I have an interesting idea in my head.

So Special relativity, while enforcing the universal speed of light,
makes relative measurements of time and space. One consequence of
this is that two events determined by one observer to be simultaneous
might be determined by a different observer to occur at different
times. My question is how this phenomenon relates to causality. For
instance, two events that are causaly related must occur in sequence,
but if it is possible to observe the same two events happening
simultaneously or even in reverse order, then does this mean that SR
also destroys universal causality?

That's wrong. In order for two events to have different temporal
ordering according to different observers they need to be spacelike
separated. That means that there is no way that they can communicate
with each other to catch the "problem" unless they can communicate
faster than the speed of light.

SR is consistent on this.

John Anderson

Charlie Mezak wrote:

Hey all,

My qustion is coming from a purely conceptual understanding of
physics, so if I'm just spouting nonesense, tell me. But I'd much
rather you explain where I am going wrong in my mental model, because
I have an interesting idea in my head.

So Special relativity, while enforcing the universal speed of light,
makes relative measurements of time and space. One consequence of
this is that two events determined by one observer to be simultaneous
might be determined by a different observer to occur at different
times. My question is how this phenomenon relates to causality. For
instance, two events that are causaly related must occur in sequence,
but if it is possible to observe the same two events happening
simultaneously or even in reverse order, then does this mean that SR
also destroys universal causality? Would observing two
causally-related events as simultaneous mean "spooky action at a
distance" is possible, or is the causality somehow destroyed when you
are moving at high relative speed?


You're getting at the root of why SR doesn't allow faster than
light information transfer. I'll try to explain.

In the usual formalism, every "event" is devined by a position
and a time. Say we have two events: A and B, defined by
(xA,yA,zA,tA) and (xB,yB,zB,tB)
Event A could be, say, a button being pushed and event B could
be a buzzer going off. In our current physics A can "cause" B
ONLY if information could get from A to B in as much time as
light could, or less. Mathematically, the
means that the invariant
(xB-xA)^2+(yB-yA)^2+(zB-zA)^2 - c*(tB-tA)^2 = 0
These events are said to have a "timelike separation", which means
two things:
- There exists a frame of reference where the two events occur
a the same *location* at different *times*.
- There is NO frame where the order of the events changes; that is,
if A preceeds B in one frame, A' preceeds B' in any other
frame of reference.

On the other hand, if
(xB-xA)^2+(yB-yA)^2+(zB-zA)^2 - c*(tB-tA)^2 0
the two events are said to have a "spacelike separation", which
means:
- There exists a frame where the two events occur at the same
*time* at different *locations*.
- The order of the events may change in a different frame of
reference.

IF information is limited to the speed of light, then the only
events which can be causally linked are those with timelike
separation, which retain their order in any frame of
reference.

On the other hand, if information can travel faster than light,
then event A can cause event B *even if* the two have a spacelike
separation. Unfortunately, when viewed from a different frame
of reference, B preceeds A and the whole things doesn't make
sense.

I hope this helps.

-E









If any of this makes sense, please point out to me where my
understanding is lacking or point me towards some good reference.

Thanks
Charlie Mezak