Explanation of list reference

Gregory Ewing greg.ewing at canterbury.ac.nz
Sat Feb 15 12:29:20 CET 2014


Steven D'Aprano wrote:
> (1) General relativity tells us that not all observers will agree on the 
> space-time coordinates of two objects, since not all observers agree on a 
> single frame of reference.

But that doesn't mean they won't agree about whether
objects are identical or not! The coordinates they
use to describe spacetime locations may differ, but
they will agree on whether or not they are equal.
A Lorentz transformation can't cause a single point
in spacetime to split into two, or two distinct points
to merge into one.

> (2) Quantum mechanics tells us that objects are not located at a single 
> space-time coordinate. Objects are "smeared out" over space (and time). 
> We cannot really talk about the location of an object, but only about the 
> probability of a measurement registering the object at a certain location.

But that doesn't mean you can stuff two objects into
the same space at the same time. What we perceive as
solid objects are composed of fermions, which obey
the Pauli exclusion principle. That means you can't
have more than one of them in a given quantum state.
While you *could* have two of them equally spread out
over all of space, they would then have to be
separated in some other dimension such as momentum
or spin.

So if you replace "space-time coordinates" with
"quantum state", the original statement remains
essentially true.

-- 
Greg



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