# Re: What are wavefunctions?

`On Sun, Dec 29, 2013 at 6:52 PM, meekerdb <meeke...@verizon.net> wrote:`
```
>  On 12/29/2013 3:31 PM, Jason Resch wrote:
>
>
>
>
> On Sun, Dec 29, 2013 at 5:29 PM, meekerdb <meeke...@verizon.net> wrote:
>
>>  On 12/29/2013 2:01 PM, Jason Resch wrote:
>>
>>
>>
>>
>> On Sun, Dec 29, 2013 at 1:47 AM, meekerdb <meeke...@verizon.net> wrote:
>>
>>>  On 12/28/2013 6:41 PM, Jason Resch wrote:
>>>
>>>
>>>
>>>
>>> On Sat, Dec 28, 2013 at 8:32 PM, meekerdb <meeke...@verizon.net> wrote:
>>>
>>>>  On 12/28/2013 4:45 PM, Jason Resch wrote:
>>>>
>>>>
>>>>
>>>>
>>>> On Sat, Dec 28, 2013 at 7:12 PM, meekerdb <meeke...@verizon.net> wrote:
>>>>
>>>>>  On 12/27/2013 10:31 PM, Jason Resch wrote:
>>>>>
>>>>>  To that I would add the purely epistemic "non-intepretation" of
>>>>>> Peres and Fuchs.
>>>>>>
>>>>>
>>>>> "No interpretation needed" -- I can interpret this in two ways, one
>>>>> way is to just take the math and equations literally (this leads to
>>>>> Everett), the other is "shut up and calculate", which leads no where
>>>>> really.
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>  2. Determined by which observer? The cat is always either dead or
>>>>>>> alive. It's just a matter of someone making a measurement to find out.
>>>>>>>
>>>>>>
>>>>>>  So are you saying that before the measurement the cat is neither
>>>>>> alive nor dead, both alive and dead, or definitely alive or definitely
>>>>>> dead?  If you, (and I think you are), saying that the cat is always
>>>>>> atom?
>>>>>> Is it ever in a state of being decayed and not decayed? If you say no, it
>>>>>> sounds like you are denying the reality of the superposition, which some
>>>>>> interpretations do, but then this leads to difficulties explaining how
>>>>>> quantum computers work (which require the superposition to exist).
>>>>>>
>>>>>>
>>>>>>  Superposition is just a question of basis.  An eigenstate in one
>>>>>> basis is a superposition in another.
>>>>>>
>>>>>>
>>>>>  Can you provide a concrete example where some system can
>>>>> simultaneously be considered to be both in a superposition and not?  Is
>>>>> this like the superposition having collapsed for Wigner's friend while
>>>>> remaining for Wigner before he enters the room?
>>>>>
>>>>>
>>>>>>
>>>>>  ?? Every pure state can be written as a superposition of a complete
>>>>> set of basis states - that's just Hilbert space math.
>>>>>
>>>>>
>>>>  So then when is the system not in a superposition?
>>>>
>>>>
>>>>  When it's an incoherent mixture of pure states.
>>>>
>>>
>>>  What makes it incoherent though?
>>>
>>>
>>>  If the density matrix is not a projection operator, i.e. rho^2 =/= rho,
>>> it's incoherent.
>>>
>>> But really I just meant that in theory there is a basis in which any
>>> given pure state is just (1,0,0,...).  In theory there is a 'dead&alive'
>>> basis in which Schrodinger's cat can be represented just like a spin-up
>>> state is a superposition is a spin-left basis.
>>>
>>>
>>  So if someone keeps alternating between measuring the spin on the y
>> axis, and then the spin on the x axis, are they not multiplying themselves
>> continuously into diverging states (under MWI)?  Even though these states
>> only weakly interfere, are they not still superposed (that is, the
>> particles involved in a simultaneous combination of possessing many
>> different states for their properties)?
>>
>>
>>  Right, according to Everett, the world state becomes a superposition of
>> states of the form |x0,x1,...> where each xi is either +x, -x, +y, or -y.
>> And per the Bucky Ball, Young's slit experiment, the spins don't have to
>> observed by anyone.  If the silver atom just goes thru the Stern-Gerlach
>> apparatus and hits the laboratory wall, the superposition is still
>> created.  If it just goes out the window and into space...it's not so
>> clear.
>>
>>
>>
>>
>>>
>>>   An electron in a superposition, when measured, is still in a
>>> superposition according to MWI. It is just that the person doing the
>>> measurement is now also caught up in that superposition.
>>>
>>>  The only thing that can destroy this superposition is to move
>>> everything back into the same state it was originally for all the possible
>>> diverged states, which should practically never happen for a superposition
>>> that has leaked into the environment.
>>>
>>>
>>>  In Everett's interpretation a pure state can never evolve into a
>>> mixture because the evolution is via a Hermitian operator, the
>>> Hamiltonian.  Decoherence makes the submatrix corresponding to the
>>> system+instrument to approximate a mixture.  That's why it can be
>>> interpreted as giving classical probabilities.
>>>
>>
>>  Are there pure states in Everett's interpretation? Doesn't one have to
>> consider the wave function of the universe and consider it all the way into
>> the past?
>>
>>
>>  I suppose the universe could have started in a mixed state, but most
>> cosmologists would invoke Ockham and assume it started in a pure state -
>> which, assuming only unitary evolution, means it's still in a pure state.
>> Of course since inflation there can be entanglements across event horizons,
>> so FAPP that creates mixed states.
>>
>>
>>
>>  In any case, returning to the original point that began this tangent,
>> do agree that QM interpretations which are anti-realist (or deny the
>> reality of the superposition) are unable to describe where the intermediate
>> computations that produce the answer to a quantum computation, take place?
>>
>>
>>  They take place in a quantum computer.
>>
>>
>  And the quantum computer is a coherent, long-lived superposition with a
> number of real states exponential with the number of its qubits.
>
>
> I'm not sure what you mean by "a number of real states"?  It has only one
> state (which is in a complex Hilbert space), which can be written as a
> superposition of some set of basis states - but that's true of my
> refrigerator too.
>
>
I mean each particle could be considered to possess properties with more
than one value (for position, spin, momentum, etc.)

>
>
>   If superpositions are real and long-lived, and involve an arbitrary
> number of particles, it seems there is no reason that people could not also
> be in superpositions.
>
>
>>
>>
>>  What would Fuchs say about quantum computation?
>>
>>
>>  It's a physical process whose outcome is predicted by QM.
>>
>>
>
>
>  We limit the power and effectiveness our own theories and stifle
> progress, when we don't put forward theories that make bold statements
>
>
> And we divert progress when we adopt intuitively appealing theories with
> no operational content and try to reify them.
>
>
That is the only way to make progress.  Propose theories, and falsify them.
Ockham says between theories that make equal predictions, simpler ones are
better, and it for theories of equal simplicity, ones that can explain more
are also better.  Anti-realist interpretations of QM have no adequate
explanation for quantum computers.  They say "don't ask" on fundamental
questions, which is never a good attitude to have in science.

>
>   Bohr's (and seemingly Fuch's) positions are so conservative as to never
> be falsified,
>
>
> Nevertheless they both published more papers than Everett (whose
> interpretation doesn't seem testable either - if it were, it would be a
> theory instead of an intepretation).
>

Everett's idea is more properly a theory. It explains the phenomenon of
collapse without supposing it is the other ideas of QM that try to
interpret what is seen (without offering any explanation for them).

As Deutsch says, we wouldn't call dinosaurs an interpretation of fossils
when they are the very thing that explains the appearance of the fossils.
So it is with Everett and collapse.

>
>
>   but they also inhibit progress and new understandings. For example,
> general purpose quantum computers may not have been invented had Deutsch
> not been operating under Everett's paradigm.
>
>
> Feynman wrote about quantum computation well before Deutsch.
>
>
Yes, but not general purpose computers.  And Feynman also used a
many-worlds interpretation.

>
>
>  "You are the only contemporary physicist, besides
> Laue<http://en.wikipedia.org/wiki/Max_von_Laue>,
> who sees that one cannot get around the assumption of reality, if only one
> is honest. Most of them simply do not see what sort of risky game they are
> playing with realityâ€”reality as something independent of what is
> experimentally established." --- Einstein in a letter to Schrodinger
>
>
> Everybody believes in reality. Nobody agrees on what it is. :-)
>

True, but that "reality" is quite a different thing if it is only what is
captured by our measurements.

Jason

>
> Brent
>
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