Eugene Shubert
the new William Miller
Joined: 06 Apr 2002
Posts: 1006
Location: Richardson Texas
|
 Posted: Sun Aug 24, 2003 10:24 am Post subject: Causality and the Conventionality of Simultaneity |
 |
|
| Mark Szlazak wrote: | Can anyone explain _in plain English_ to a non-physicist, how David Malament in his 1977 paper "Causal Theories of Time and the Conventionality of Simultaneity" tried to show that standard simultaneity is the only possible simultaneity in the Minkowski spacetime of special relativity.
Also, what's the counter argument or problem with his results. |
The problem with David Malament’s argument is the existence of a counterexample. I will try to explain as simply as possible.
Understanding this is very easy. I will illustrate what the counterexample looks like in one spatial dimension.
Take any inertial frame of reference and declare it to be "an absolute frame of reference." (In flat Minkowski spacetime you have an infinite number of perfectly good choices to select from so don't let the seeming arbitrariness of my directions confuse you).
In your absolute frame of reference, you understand that clocks are synchronized so that the speed of light is c in both directions.
Now consider the following transformation equations:
x'=Y(v)(x-vt)
t'=t/Y(v)
Y(v)=1/sqrt(1-v^2/c^2)
These equations are just the Lorentz transformation equations in disguise. The disguise is that clocks are synchronized differently in the moving frame of reference. The effect is an alternative definition of simultaneity. With these clock synchronizations, in the moving frame of reference,
C(v) is the velocity of light in the direction of motion.
->
C(v) is the velocity of light opposite the direction of motion.
<-
C(v)= (Y(v)^2)(c-v)
->
C(v)= (Y(v)^2)(c+v)
<-
As you can imagine, you can define "Shubertian simultaneity" with these rules for the one-way speed of light in a moving frame.
The point of the links [1] and [2] is that this new sense of simultaneity is truly unique, i.e., it's the only physically meaningful notion of simultaneity that may be defined globally in a closed and bounded universe. |
|
FAQ
Search
Memberlist
Usergroups
Register
Profile
Log in
