🚀 go-pugleaf

In article <1992Jan24.191554.6217@sunova.ssc.gov> brian@helium.ssc.gov (Brian Scipioni) writes:
>I know the twin paradox has been beaten to death, and I know what the
>mainstream viewpoint is. It is simple and straightforward to understand.
>
>My problem continues to be the unsupported assertion that information - 
>which does not contain matter or energy - travels, and is limited to the
>speed of light. You can send information using light if you like, but the
>speed belongs to the light.
>
>You can also use your observations coupled with a knowledge of physical
>laws to deduce information about events not directly accessible to
>you through observation.
>
>When information is created does it have a location? Does it appear throughout
>the universe at once?

Well, you're entitled to use the word however you want, and in some
senses of the word you might be right in saying that information is
"created" or "appears throughout the universe at once."  But there is a
well-defined concept of information which is what people are using when
they say that no information travels faster than the speed of light.
Actually, I bet most people who say this only have a fuzzy notion of
information, but I'll give them the benefit of the doubt.  :-)

In quantum theory (or even classical theory) observables are represented
by elements in an algebra (e.g. an operator algebra).  In relativistic
physics we may assign to each nice (e.g. open) subset of spacetime the
algebra of observables that can be measured within that subset.  The
state of a physical system is represented by a linear functional on the
algebra of observables (which should satisfy some properties).  In nice
cases we can actually measure the information of a state, also called
its entropy.  For example if the state is represented as a density
matrix (as often done in quantum statistical mechanics), say D, then 
the information is  Tr (D ln D).   (The sign is a frequent nuisance in
discussing information.  Here it's chosen so that a pure state, which
carries the most information about what'd going on with the system, has
zero information, while mixed states have less information (a negative
amount, actually, but you can add any number you like if negative
numbers freak you out.))  Using these notions you can rigorously say
what you mean about information not traveling faster than light.  (Left
as a nontrivial exercise to the reader.)