[extropy-chat] Re: A view on cryonics, worlds, identities

[scerir]

Brett Paatsch: 

> I don't regard many-worlds theory as
> something that needs to be accomodated 
> or is worth accomodating.

This is perhaps something worthy of further, obstinate 
investigation :-) 

Imagine a quantum superposition state like this 
one:
    1/sqrt2 |spin_z +1>|m +1> + 
    1/sqrt2 |spin_z -1>|m -1> 

The state above is trivial enough, it describes
a superposition of spin-up/spin-down states, and 
the "entagled" (or, following here H. Everett III, 
the "relative") recording states |m +1>, |m -1>, of a 
recording device M.

Imagine we have now another measurement device K, 
to measure some observable (let us call it OBS) 
of the above quantum superposition state.

Let us choose (heh!) OBS such that the ray (or the subspace), 
generated by the quantum superposition state (above), 
is an eigenspace of OBS, corresponding to a certain 
definite eigenvalue, let us say the eigenvalue ONE. 

Because of this specific (indeed!) choice of OBS, *neither* 
component of the (above) quantum superposition state 
lies in the eigenspace of OBS. Hence OBS fails to commute 
with the spin_z observable, and of course fails to commute 
with the entangled M recording device observable. 

We can write down the following quantum superposition state,
before the 2nd measurement is performed by means of K:
  1/sqrt2 |spin_z +1>|m +1>|OBS uncertain> + 
  1/sqrt2 |spin_z -1>|m -1>|OBS uncertain>

We can write down the following quantum superposition state,
after the 2nd measurement is performed by means of K:
  1/sqrt2 |z-spin +1>|m +1>|OBS ONE> + 
  1/sqrt2 |z-spin -1>|m -1>|OBS ONE>

In MWI the superposition state has, usually, no actual meaning, 
since, in MWI, each term of the superposition is in one-to-one 
correspondence with a distinct "world" (not well defined). 
Notice that in MWI the quantum superposition state just means 
that a component is reificated in a "world", while another
component is reificated in another "world". Also notice that 
in each of the distinct (or decohering?) "worlds" the measurement 
devices - say M, or K - can incorporate the state of an observer 
(human) who perceives the outcome of the measurement.

In general terms, in MWI, a "world" instantiates an 
eigenvalue for an observable iff the superposition term 
associated with that "world" is an eigenstate of the 
observable corresponding to that eigenvalue. (The above 
is the MWI implementation of the usual eigenstate-eigenvalue 
link of the orthodox interpretation).  

Well, from the equivalence between MWI and orthodox 
interpretation we should get that the following "worlds"
"world" one -> 1/sqrt2 |spin_z +1>|m +1>|OBS uncertain>  
"world" two -> 1/sqrt2 |spin_z -1>|m -1>|OBS uncertain>
become, after the measurement performed by means of K, 
"world" one -> 1/sqrt2 |spin_z +1>|m +1>|OBS ONE>  
"world" two -> 1/sqrt2 |spin_z -1>|m -1>|OBS ONE>

In other words the fact that K would later record the state 
|OBS ONE> is fixed in advance, and no other "world" is allowed
here excepting the following two
"world" one -> 1/sqrt2 |spin_z +1>|m +1>|OBS ONE>  
"world" two -> 1/sqrt2 |spin_z -1>|m -1>|OBS ONE>

But it is worth noticing that in the first "world", say
    1/sqrt2 |spin_z +1>|m +1>|OBS uncertain> ,
the observable OBS, since it does not commute with
the spin_z observable, has no determinate value,
and thus the outcome of the measurement of the
observable OBS must occur *by chance*!

It is worth noticing that also in the second "world", say
    1/sqrt2 |spin_z -1>|m -1>|OBS uncertain>, 
the observable OBS, since it does not commute with
the spin_z observable, has no determinate value,
and thus the outcome of the measurement of the
observable OBS must occur *by chance*!

So, here we have reached - at least apparently! - a 
contradiction. Possible solution is, i.e., that the
"state" does not describe anything physical, but only
all available informations about the quantum system.
Or we can make appeal to magic properties of the SUUW
Schroedinger Unitary-evolving Universal Wave-function.
Or to some other possible super-rule.

Anyway, it seems important here that observers, and their 
individualities, could be attached to M (measuring 
the spin_z) or to K (measuring the observable OBS). 
So the situation seems to be rather messy and weird,
as usual.