> On 11 Jun 2018, at 14:48, Bruce Kellett <[email protected]> wrote:
>
> From: Bruno Marchal <[email protected] <mailto:[email protected]>>
>>> On 11 Jun 2018, at 03:37, Bruce Kellett <
>>> <mailto:[email protected]>[email protected]
>>> <mailto:[email protected]>> wrote:
>>>
>>> From: Bruno Marchal <[email protected] <mailto:[email protected]>
>>>>> On 8 Jun 2018, at 14:55, Bruce Kellett <
>>>>> <mailto:[email protected]>[email protected]
>>>>> <mailto:[email protected]>> wrote:
>>>>>
>>>>> The choice of basis makes all the difference in the world.
>>>>
>>>> Everett prove the contrary, and he convinced me when I read it. I found
>>>> “his proof” used in many books on quantum computing, although with
>>>> different motivation. Thee result of an experiment, obviously depend of
>>>> what you measure, but when you embed the observer in the wave, you get
>>>> that what they find is independent of the choice of the base used to
>>>> describe the “observer” and the “observed”. If not, the MW would already
>>>> be refuted.
>>>
>>> In that case, MW is refuted. Clearly, what the observer finds is dependent
>>> on the basis in which he is described.
>>
>> ?
>>
>> I disagree. The finding can depend on what the observer decide to measure,
>> which is akin to choosing a base,
>
> I think there is more to it than this. We can choose a base in which to
> describe the state, but we are not able to choose the base for the actual
> measurement result.
I am not sure I understand. It seems to me that the base for the measurement
result will be decided by the observer (already or later, even at the last
moment, perhaps, like in Aspect experience).
> In a spin measurement of a spin half particle, we can decide to orient the
> magnet at any angle to the direction of motion. For convenience in
> understanding the dynamics, we then expand the spin wave function in the
> basis corresponding to that orientation; that is choosing what to measure.
Yes.
> But the result of our measurement in that orientation is that the particle
> emerges from the S-G magnet on either the up or down trajectory.
OK.
> The actual measurement is then made at screen downstream of the magnet. We do
> not have any control over the basis for the resulting position measurement.
Ah! If that is what you mean, I am OK. But that will be a slight dispersion. Of
course some electron, going to down could appears on the up, because the
“position-wave" are spread, but that should be negligible with the down/up spin
prediction.
> Decoherence decides that for us, and the stable basis for position
> measurements is the set of delta functions at each point along the spatial
> axis. Why do we not see the 'up' or 'down' result as a superposition of a lot
> of different positions on the screen? We don't because such superpositions
> are not stable under decoherence.
I will have to meditate on this. I take that decoherence is already in Everett,
and is simply entanglement. The why our brain prefer position is a refinement,
by Zeh indeed, and Zurek. I have not yet completely solved all problems raised
by this.
>
>> but the couple “observer + that chosen base” can be studied in any base, and
>> the same result will described in the memories of the observer. I will
>> search Everett proofs of this, as he is the one who convinced me on this.
>
> The situation as I understand it is the following. The original wave function
> |psi> can be expanded in any basis that spans the corresponding Hilbert
> space. So we can have
>
> |psi> = Sum_i c_i |a_i>
> = Sum_j d_j |b_j>,
>
> where the |a_i> and |b_j> are sets of vectors which independently span the
> space. The expansion coefficients are different, so in general the c_i =/=
> d_j.
>
> If we measure in one basis, say that of the |a_i>, the result is one of the
> |a_i> with probability |c_i|^2. However, if the measurement corresponds to
> the other basis (that will be a different operator in the Hilbert space), we
> will, in general, get a different result, one of the |b_j> with probability
> |d_j|^2.
OK.
> The results of these measurement will be different. If we now decohere these
> states with the environment, in one case the environment will be entangled
> with the |a_i> states, and in the other case, the environment (including the
> observer) will be entangled with the |b_j> states.
OK. But here, the choice of the measurement just determines the future results
of the measurement for the observer in some branches. The choice of the base
determines our possible continuations.
> So the observer will see different things according to the basis in which he
> is working and the measurement made.
In that sense above, I agree.
My sense is well explained by Everett in the Graham DeWitt selected papers,
page 38.
>
> Now since the bases both relate to the same Hilbert space, and the same
> original state is expanded, the basis vectors (and the expansion
> coefficients) are related, so we can always express one set in terms of the
> other:
>
> |a_i> = Sum_j f_{ij} |b_j>.
>
> So in this sense, the basis chosen does not matter in the overall description.
OK.
> But once we take environmental decoherence into account, only one basis will
> be stable, say the |a_i> basis, and if we describe things in the |b_j> basis,
> those basis states are immediately decohered into the corresponding |a_i>
> states. Consequently, any observer will only ever see results, or be located
> in branches (worlds), corresponding the the stable decohered base.
OK. We certainly needs that to have sharp memories enough to have a stable
first person history.
> Describing things in terms of another base doesn't change the reality, just
> as describing the orbit of the Moon in terms of a coordinate system based on
> Jupiter doesn't actually change the orbit of the Moon, it just makes the
> description a lot more complicated. However, in the absence of decoherence to
> a preferred stable basis, the results in the }a_i> and }b_j> bases are
> different.
OK.
>
>
>
>
>>> Or else experiments would not have definite results when described in the
>>> laboratory from the 1p perspective.
>>
>> I don’t see why.
>
> Without decoherence, measurements in the |b_j> basis are superpositions of
> the |a_i> states, and by construction, only the |a_i> states are stable under
> decoherence, corresponding to definite results.
I understand what you meant.
>
>
>
>>> Even if you take the 'bird' view of the whole multiverse -- which is, I
>>> agree, independent of the basis
>>
>> OK. At least we agree on that.
>>
>>
>>> in which it is described -- the view of any observer embedded in the
>>> multiverse is totally basis-dependent.
>>
>> Only in the sense that the biological brain has evolved through decoherence
>> with respect to some base, but as you say, that process lead to the same
>> result from the 1p perspective of those who have chosen the base, or have
>> the base imposed through decoherence and evolution, say.
>> If not then QM would be inconsistent, and had to different laws of physics
>> for different observers.
>
> That would be the result absent decoherence to the stable basis for any
> measurement.
OK. We don’t differ on the fundamentals. I would need to revise Zurek and Zeh
to assures myself that some base are more stable than other for physical reason
(and not simply Everett-anthropic one), but when I do that I eventually put
myself on a slope leading to the problem of marrying the quantum and gravity, a
nightmare from which I come back to mechanism rather quickly :)
Bruno
>
> Bruce
>
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