On Fri, Aug 9, 2019 at 3:22 AM Bruno Marchal <marc...@ulb.ac.be> wrote:
>
> On 8 Aug 2019, at 17:41, Jason Resch <jasonre...@gmail.com> wrote:
>
>
>
> On Thu, Aug 8, 2019, 5:51 AM 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.
>>
>>
>>
>>
>> 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.
>>
>>
>>
>>
>> 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).
>>
>>
>>
>>
>> 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.
>>
>>
>>
>> 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.
>>
>> 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.
>>
>
> Bruno,
>
> Forgive me if I have asked this before, but can you elaborate on the
> how/why the math suggests negative interference?
>
> I currently have no intuition for why this should be.
>
> I recall reading something on continuous probability as being more natural
> and leading to something much like the probability formulas in quantum
> mechanics. Is that related?
>
>
>
> It is not intuitive at all. With the UDA, we can have have the intuition
> coming from the first person indeterminacy on all all computational
> continuation in arithmetic, but in the AUDA (the Arithmetical UDA), the
> probabilities are constrained by the logic of self-reference G and G*. So
> the reason why we can hope for negative amplitude of probability comes from
> the fact that modal variant of the first person on the (halting)
> computations, which is given by the arithmetical interpretation of:
>
> []p & p
>
> or
>
> []p & <>t
>
> or
>
> []p & <>t & p
>
> With, as usual, [] = Beweisbar, and p is an arbitrary sigma_1 sentences
> (partial computable formula).
>
> They all give a quantum logic enough close to Dalla Chiara’s presentation
> of them, to have the quantum features like complimentary observable, and
> what I have called a sort of abstract linear evolution build on a highly
> symmetrical core (than to LASE: the little Schroeder equation: p -> []<>p,
> which provides a quantisation of the sigma_1 arithmetical reality.
>
> It is mainly the presence of this quantisation which justify that the
> probabilities behave in a quantum non boolean way, but this is hard to
> verify because the nesting of boxes in the G* translation makes those
> formula … well, probably in need of a quantum computer to be evaluated. But
> normally, if mechanism (and QM) are correct this should work.
>
> This is explained with more detail in “Conscience et Mécanisme”.
>
> Bruno
>
>
Thank you Bruno for your explanation and references. Regarding “Conscience
et Mécanisme”, is there a web/html or English version available?
Unfortunately my browser cannot do translations of PDFs but can translate
web pages. If not don't worry, I can copy and paste into a translator.
Jason
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