On Thu, Aug 8, 2019 at 8:51 PM Bruno Marchal <marc...@ulb.ac.be> wrote:
> On 8 Aug 2019, at 11:56, Bruce Kellett <bhkellet...@gmail.com> wrote:
>
> On Thu, Aug 8, 2019 at 7:21 PM Bruno Marchal <marc...@ulb.ac.be> wrote:
>
>> On 8 Aug 2019, at 02:23, Bruce Kellett <bhkellet...@gmail.com> wrote:
>>
>> On Wed, Aug 7, 2019 at 11:30 PM Bruno Marchal <marc...@ulb.ac.be> wrote:
>>
>>> On 7 Aug 2019, at 14:41, Bruce Kellett <bhkellet...@gmail.com> wrote:
>>>
>>>
>>> Superpositions are fine. It is just that they do not consist of
>>> "parallel worlds”.
>>>
>>>
>>> But then by QM linearity, it is easy to prepare a superposition with
>>> orthogonal histories, like me seing a cat dead and me seeing a cat alive,
>>> when I look at the Schoredinger cat. Yes, decoherence makes hard for me to
>>> detect the superposition I am in, but it does not make it going away
>>> (unless you invoke some wave packet reduction of course)
>>>
>>>
>>>
>>>> “Parallel worlds/histories” are just a popular name to describe a
>>>> superposition.
>>>>
>>>
>>> In your dreams, maybe. There is a clear and precise definition of
>>> separate worlds: they are orthogonal states that do not interact. The
>>> absence of possible interaction means that they are not superpositions.
>>>
>>>
>>> That is weird.
>>> The branches of a superposition never interact. The point is that they
>>> can interfere statistically, if not there is no superposition, nor
>>> interference, only a mixture.
>>>
>>
>> There some to be some fluidity is the concepts of superposition and basis
>> vectors inherent in this discussion. Any vector space can be spanned by a
>> set of orthogonal basis vectors. There are an infinite number of such
>> bases, plus the possibility of non-orthogonal bases given by any set of
>> vectors that span the space. If the basis vectors are orthogonal, these
>> basis vectors do not interact. But any general vector can be expressed as a
>> superposition of these orthogonal basis vectors. (Orthonormal basis for a
>> normed Hilbert space.)
>>
>> So the question whether the branches of a superposition can interact
>> (interfere) or not is simply a matter of whether the branches are
>> orthogonal or not. If we have a superposition of orthogonal basis vectors,
>> then the branches do not interact. However, if we have a superposition of
>> non-orthogonal vector, then the branches can interact.
>>
>> For example, the wave packet for a free electron is a superposition of
>> momentum eigenstates (and position eigenstates). These momentum eigenstates
>> are orthogonal and do not interact. The overlap function <p|p'> = 0 for all
>> p not equal to p'. This is the definition of orthogonal states. But this
>> does not mean that the wave packet of the electron is a mixture: It is a
>> pure state since there is a basis of the corresponding Hilbert space for
>> which the actual state is one of the basis vectors. (We can construct an
>> orthonormal set of basis vectors around this vector.) On the other hand,
>> the two paths that can be taken by a particle traversing a two-slit
>> interference experiment are not orthogonal, so these paths can interact. So
>> when the quantum state is written as a superposition of such paths, there
>> is interference.
>>
>> Orthogonality is the key difference between things that can interfere and
>> those that cannot. So if separate worlds are orthogonal, there can be no
>> interference between them, and the absence of such interaction defines the
>> worlds as separate.
>>
>>
>> What I use is the fact that when we have orthogonal states, like I0> and
>> I1>, I can prepare a state like (like I0> + I1>), and then I am myself in
>> the superposition state Ime>( I0> + I1>), Now, in that state, I have the
>> choice between measuring in the base {I0>, I1>} or in the base {I0> + I1>,
>> I0> - I1>). In the first case, the “parallel” history becomes indetectoble,
>> but not in the second case, so we have to take the superposition into
>> account to get the prediction right in all situations.
>>
>
> I don't think this is actually correct. Take a concrete example that we
> all understand. If we prepare a silver atom with spin 'up' in the
> x-direction, then a measurement in the x direction does not produce a
> superposition -- the answer is 'up' with 100% certainty. But is we measure
> this state in the transverse, y-direction, the result is either 'up-y' or
> 'down-y' with equal probabilities. This is because the initial state 'up-x'
> is already a superposition of 'up-y' and 'down-y'. When we measure this in
> the x-direction, there is no parallel history. When we measure in the
> y-direction, we get either 'up-y' or 'down-y'. MWI says that for either
> result, the alternative occurs in some other world. And that alternative
> result is just as undetectable as the 'down-x' result for the x-measurement.
>
>
>
> The pure state up-x is the same state as the superposition of up-y and
> down-y.
> Me in front of up-x and Me in front of up-y + down-y are only different
> description of the same state. When measuring that state in the
> x-direction, I don’t made that y-superposition disappears.
>
All you are saying here is that if you measure the up-x state in the x
direction, the state does not change -- it is still a superposition of up-y
and down-y. Of course, if the state is not changed it does not change.
Tautologies are not very useful.
> The point being that whatever measurement we perform, we get only one
> result, and the alternative results that may or may not have been possible
> are undetectable.
>
>
> Yes, that is why we can exploit the parallel worlds (aka superposition of
> states relative to me) only by isolating the computer from from me, so that
> I don’t get entangled with it.
>
You have nothing to do with it. Quantum computers require coherence, or
freedom from entanglement with the outside environment. But that says
nothing about parallel worlds. They exist, if at all, only as the result of
decoherence with the environment in measurement -- where there is the
suggestion that there are separate worlds for each possible measurement
outcome. Any other, non-decohered, interpretation of "other worlds" is just
a confusion of terminology.
However, it is interesting how this discussion has morphed. We started with
> the observation that a quantum computer does not demonstrate the existence
> of parallel worlds because its operation can be understood completely in
> terms of unitary rotations of the state vector in the one world of Hilbert
> space.
>
>
> Unitary rotations conserves the superposition (and the relative
> probabilities).
>
That is patently false. The unitary rotations in Hilbert space change the
weights of each component of the basis vectors in superposition, so they
change the superposition and the probabilities, by definition. There is
generally still a superposition (though not necessarily always), but the
nature of that superposition changes (even to the extent of vanishing if
the state vector is regarded as one of the basis vectors). You can always
change the superposition by changing the basis, after all. The relative
probabilities change along with the changes in the superposition.
Now we seem to have ended up with a discussion of the nature of
> superpositions, and the idea that unobserved outcomes from experiments have
> to be taken into account. How they are to be taken into account is never
> made clear.
>
>
> I don’t know why you say this. We need to take the superposition into
> account to get the probabilities right for arbitrary possible measurements.
>
We need only take the basic state vector into account. The nature of
whatever superpositions this represents depends on the basis chosen to
represent the state. It is nothing more than an abstract mathematical
manipulation, until you get the preferred measurement basis. And that is
only obtained by the measurement interaction entangling the system with the
rest of the environment.
They are orthogonal, in fact, and cannot interact with the observed result.
> Parallel worlds, whether they "exist" or not, have no consequences for
> physics or experimental results. So Everett and MWI are otiose -- they have
> no conceivable effects, particularly in quantum computers, so they are
> irrelevant.
>
>
> If the superposition are not relevant, then I don’t have any minimal
> physical realist account of the two slit experience, or even the stability
> of the atoms.
>
Don't be obtuse, Bruno. Of course there is a superposition of the paths in
the two slit experiment. But these are not orthogonal basis vectors. That
is why there is interference.
> My goal is not in finding working theory, just to see if the current
> modern theory given by the physicists is consistent with digital mechanism,
> and indeed, its MWI aspect is the easiest prediction of mechanism. Then the
> math suggest we get also the negative interference and that QM confirms
> Digital Mechanism, unless we add the collapse postulate, which indeed is an
> option for the non-computationalist. But the collapse itself is not
> something that we can detect or observe in any way.
>
Since digital mechanism is just an alternative parallel world, orthogonal
to the world of physics, we can safely ignore it as of no possible
consequence.
We cannot detect even one world. “World” are metaphysical notion. The old
> dream argument made this clear since long.
>
Only in your world, Bruno. The rest of us have well-defined ways of telling
the difference between dreams and objective reality.
Bruce
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