Re: Superposed observers (was No new Einstein)
- From: "I.Vecchi" <vecchi@xxxxxxxxxxxxx>
- Date: Thu, 15 Sep 2005 05:42:11 +0000 (UTC)
rof@xxxxxxxxxxxx ha scritto:
> So you're saying that in some circumstances, a cat could be alive
> relative to somebody and dead relative to somebody else? Can you
> give an example of circumstances like those?
I already did . In the experiment we have been discussing, the
instances of Nick seeing the cat respectively dead and alive are the
"somebody" and "somebody else" you are asking for. And we outside
detect their interference patterns.
> Isn't that many worlds?
Arguably , but the observer-dependent nature of entanglement plays a
crucial role in my model and I find it far easier to formulate it in an
epistemic setting like RQM rather than in an ontological one like
many-worlds.
> >The key point is that the fact that the observer knows or not about it
> >(i.e. whether the information about it being up or down is encoded in
> >her version of the system's state vector ) MAKES A PHYSICALLY TESTABLE
> >DIFFERENCE for other observers (and indirectly for the observer in
> >question too). That holds for "it" being an electron, a coin, a person
> >or a star.
> When you say that there is a physically testable difference, do you
> just mean that a person who knows about something is physically
> different to a person who doesn't, for example in terms of the
> structure of their brain? If so, what does that have to do with
> quantum mechanics?
I mean that in an appropriate experimental setting, if I don't know
(no collapse yet) I will detect interference patterns, if I know (after
collapse) I won't. That's again the experiment we have been discussing
all along.
> Or possibly you mean that the "entanglement" (which I put in quotation
> marks because I know you have reservations about it) between the
> knower and the known is detectable. This is true - the entanglement
> should be detectable in principle, but you don't need RQM to know
> that.
NB: Thanks to Ruadhan's constructive persistence, in a series of
private exchanges we have managed to clarify our previous discussion
about the experiment beyond the "I already said this three times"-point
([1]). Here is the result.
RoF:
>>> The reason that I say that he'll be put into the superposition
>>> again is the following.
>>>
>>> 1. It is an axiom of quantum mechanics that after an observable has
>>> been measured, the system is in an eigenstate of that observable.
>>>
>>> 2. To detect the superposition, you need to use an observable
>>> which has |Nick seeing cat dead>+|Nick seeing cat alive> as
>>> one of its eigenvectors.
>>>
>>> 3. If |Nick seeing cat dead>+|Nick seeing cat alive> is one
>>> of its eigenvectors, then there is a determinate probability
>>> that the system will be in that superposed state after
>>> the measurement (namely after you have received information
>>> from your thin channel).
>>>
>>> 4. The probability of finding |final state> is calculated by using the
>>> formula
>>> P(final state)=|<initial state|final state>|^2.
>>>
>>> 5. If the initial state is |Nick seeing cat dead>, then the probability
>>> of finding the final state to be
>>> (|Nick seeing cat dead>+|Nick seeing cat alive>)/sqrt(2) is 50%,
>>> calculated by using the formula given in step 4.
>>>
>>> I think this is the crux of where we have been disagreeing.
>>> Let me know which step of the above, if any, you disagree with.
>>>
>>
IV:
>>The point is that when you agree beforehand with Nick and tell him "Kill
>>the cat" or "Put the coin head upwards" instead of "Let the Geiger do its
>>job" or "Toss the coin" you are changing the experiment. You are changing
>>your epistemic perspective and therefore the basis in which you extract
>>information. Whatever the result of the measurement to detect superposed
>>Nicks you will already know that the cat is dead or that the coin shows
>>head and that firing a split photon through the box will not change that.
>>You won't absorb/interpret information from the measurement readings in
>>the same way.
>>
>>I can elaborate on this but I think it's pretty clear.
RoF:
> You are changing the initial state of the system, but not the
> experimental arrangement used.
We are not talking about measuring Nick's states directly, but through
measurement outcomes that are entangled with them. The point I am
making is based on the fact that entanglement, being observer-dependent
, may change according to the observer's epistemic perspective.
As a simple step towards understanding my point consider the situation
where Nick is behind a wall and we agree before the experiment that if
he tosses a coin and gets head, he'll raise a red flag, otherwise he'll
raise a white flag. The white flag collapss me into the Nick-head
branch, the red flag gets me into the Nick-tail branch. Now consider
the situation where we agree before the experiment that if he tosses a
coin and gets head, he'll raise a white flag, otherwise he'll raise a
red flag. The white flag now collapses me into the
Nick-tail branch, the red flag gets me into the Nick-head branch.
In the two cases the same signals are entangled with different
eigenvectors.
In my full experiment you are not observing directly Nick or the cat,
but an outcome which is entangled with it. Again, entanglement is
observer-dependent. It depends on the epistemic perspective of the
observer. When you know that the initial state of the system is |Nick
seeing cat dead> you are changing the epistemic perspective, i.e, the
way in which the measurement outcomes are entangled with Nick's states.
> I can, for example, measure
> the position of an electron regardless of whether it starts
> off in one place or another. There's a single observable
> for position, rather than different observables for different
> positions. Similarly, in thise case, there is a single
> observable which has to be used when you want to detect
> superpositions, and it doesn't change just because the
> state of the system is different.
My epistemic perspective may change and that change the eigenvectors of
the system (which are just THE STATES IN WHICH I CAN EXPECT TO FIND
THE SYSTEM after measurement) . I know, based on my knowledge of the
experimental setting , that the system will stay in the |Nick seeing
cat dead> state.
>
> Let me try to explain it in a different way. You will
> do one experiment to detect superposition of observers.
> You will claim (correctly, if the experimental design
> is good) that finding the light on 100% of the time
> is evidence that a superposition is being detected.
>
> However, as in all such experiments, you need a control
> experiment, to demonstrate that when there *isn't* a
> superposition, you get different results.
Obviously.
> So you will
> have to do the same procedure with a Nick/cat system
> which isn't in a superposition. Now, when you do
> this control experiment, you will (if all goes well)
> find that the light goes on only 50% of the time.
>
> It is this control experiment, in which the observable
> being measured is the same (and hence has the same
> eigenvectors),
The only thing that I need to show is that the system yields different
response depending on how and when I extract information about the
cat's state. The observable changes, because the way your readings are
entangled with Nick's state changes.
> but in which the initial state of the
> system is different, which will resurrect cats and
> alter Nick's memory, 50% of the time. The proof is
> above, in steps 1-5.
>
> The crux is that you need to use an observable with
> an eigenstate like |Nick seeing cat dead>+|Nick seeing cat alive>
> if you want to detect superposition. If you have an
> observable with an eigenstate like that, then when you
> measure that observable, the system will sometimes
> end up in exactly that state. You won't be able to
> start with a system in the state |Nick seeing cat dead>,
> and then measure the interference observable and still
> leave the system in the |Nick seeing cat dead> state.
> That would be like measuring the x-spin of a spin-half
> particle without affecting the z-spin.
>
This is just different from what I am describing. I am talking about
measurements outcomes which are entangled with Nick's states.
Signs.
I've been articulating the description of my experimental model in more
detail as you've been raising your objections, which have provided this
exchange with a useful dialectic thread. You may have a look at [2]
to see what the experiment I have in mind actually looks like. Some of
the considerations in the paper are somewhat outdated, but the
experimental procedure described there is basically what I have been
referring to.
Cheers,
IV
[1]
http://groups.google.com/group/sci.physics.research/msg/efd4447ca2318931?
[2] http://xxx.lanl.gov/abs/quant-ph/0007117
.
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