|Subject: Information or propensities?
Date: Wed, 09 Jan 2002 12:29:40 +0200
From: "Dimiter G. Chakalov" <firstname.lastname@example.org>
To: Caslav Brukner <email@example.com>
CC: Karl Svozil <firstname.lastname@example.org>,
Johann Summhammer <email@example.com>,
Daniel Terno <firstname.lastname@example.org>,
Ark Jadczyk <email@example.com>, firstname.lastname@example.org,
Dear Dr. Brukner,
I found it difficult to agree with your final statement in your article "Young's Experiment and the Finiteness of Information" [Ref. 1]. It seems to me that the most basic notion of quantum mechanics is not information but *propensities*.
Let me try to explain what I understand by 'propensities', and then will ask you to help me find an algorithm for mapping 'propensities' to 'information', with POVM (a set of positive operators that may (hopefully) sum up to unity, in some highly contrived cases such as the one examined in [Ref. 1]).
The problem is, I believe, very simple: there is no way to translate/map 'information' to 'propensities', which casts a serious doubt on the whole enterprise. I think the reason is very simple too: we can define 'information' iff we can employ the relativistic causality, while in the case of 'propensities' the latter is simply inapplicable. The two entities, information and propensities, are totally different in nature, which is "the only mystery in QM", I believe.
By 'propensities' (always plural) I understand the Aristotelian 'potentialities' presented with conditional propositions about future observations: if "we do not know, not even in principle, which of the two paths the particle takes" [Ref. 1], then we don't have any *information* but two propensities pertaining to two physically incompatible outcomes. Hence 'propensities' denotes something totally different than 'information': the former can hold simultaneously two or more *potential* outcomes, such as a superposition of a cat and a dog [Ref. 2], while the latter can be either information about "this physical dog, here-and-now" OR "this physical cat, here-and-now". In the latter case, the dog and the cat are inevitably localized as 'events' and subsequently 'information', although no FTL communication is possible due to the so-called 'peaceful co-existence of QM and STR' a la Shimony.
In the case of 'propensities', however, we can not, even in principle, think of relativistic causality. If we try it, we'll end up with a jabberwocky:
If Alice and Bob are entangled, "before" Alice could emit a corresponding signal, Bob will know all about it, but "before" Bob could learn about Alice's intention to emit a corresponding signal, she should have "already" sent it.
Sounds like some tachyonic talk "during" the "entanglement time". (I don't know how one could break into this talk *and* keep it for some "quantum computing", but this is a bit different issue.)
To sum up, may I ask you to shed some light on the conversion/mapping
of 'propensities to information', and 'information
to propensities', with POVM.
It seems to me that you'll need the 'chooser' in QM, as explained by Pearle,
I extend this request to all physicists reading these lines.
Thank you very much in advance.
[Ref. 1] Caslav Brukner,
Anton Zeilinger. Young's Experiment and the Finiteness
of Information. Tue, 8 Jan 2002 17:07:09 GMT,
"Whenever we do not know, not even in principle, which of the two paths the particle takes, the quantum state can be written as [Eq. 1]
"In that case, no information whatsoever is available
about the slit the particle passes through. Indeed,
if one would ask in an experiment for a specific run
which path the particle takes, one would find with equal probability
the particle in either slit.
"From a fundamental perspective, this approach suggests
that the most basic notion of quantum mechanics is
information [A. Zeilinger, Found. Phys. 29, 631-643
[Ref. 2] E. Joos. Elements of Environmental
"There are many examples, where it is hard to find certain superpositions in the real world. The most famous example has been given by Schrödinger: A superposition of a dead and an alive cat
Psi = |dead cat> + |alive cat>
is never observed, contrary to what should be possible according to the superposition principle (and, in fact, must necessarily occur according to the Schrödinger equation). Another drastic situation is given by a state like
Psi = |cat> + |dog>
"Such a superposition looks truly absurd, but only because
we never observe states of this kind! (The obvious
objection that one cannot superpose states of "different
systems" seems to be inappropriate. For example, nobody hesitates
to superpose states with different numbers of particles.)"