Bohm trajectories and "protective" measurements?

Ilja

My argument about the Hamilton operator is indeed more formal, but it is also about a slightly different point than Maudlin. In the video lecture which has been linked here, he was ready to accept the configuration space as given as an additional structure. Then, one main argument is that the configuration space itself requires much more structure.

My point is that without additional structure you cannot identify the configuration space. This was an important point for me because it destroys claims that MWI needs less structure.

Quantumental

I am very interested in grasping this, but first I want to ask you if you've considered the "new" approach by Wallace and Timpson? It seems they no longer support the view of wavefunction realism in configuration space, but rather promote an idea called Space-Time state realism.
They have written a paper on it: http://philsci-archive.pitt.edu/4621...aterealism.pdf

bohm2

Just to add some more links to this topic since I'm also confused and yet very interested in trying to understand these arguments by Wallace, Ilja and Maudlin there is this series of videos by Tumulka discussing Wallace's paper that was linked by Quantumental:
http://www.youtube.com/user/rutgersphilos
(The relevant videos are Tumulka 1-Tumulka 6 (6 videos) and Tumulka audiende discussion with Q & A (3 videos)

Quantumental

I really struggle to grasp this.
If I remember correctly these (Maudlin, Tumulka etc) reject functionalism. So I wonder if that is their motivation, since people like Wallace etc. claims the ontology is there

Ilja

My first impression is that this accepts some of the arguments by Maudlin. So, they accept not only that the wave function is not only an element in a Hilbert space, but a complex function on the configuration space (introducing the first additional structure) but also that the configuration space itself has a complex structure of something living on ordinary space.

Of course, because of the relativistic background, all this on spacetime instead of space.

And, once it is a many worlds variant, only with a wave function, not with a configuration itself.

So, now we have a configuration space, moreover, with a structure which makes sense for a space of configurations living in a space - and all this with all the properties we would use to describe the actual configuration of the world as we see it - but without any configutions.

I would say there was, in the past, some interesting research program: Is it possible to start, with only a Hilbert space and the Hamilton operator on it, to derive everything else, including all the physics? My argument was that this program fails because one needs additional structure, already in the first step where one wants to recover the configuration space from the Hamilton operator, a step which, from mathematical point of view, was the most promising, because the usual Hamilton operator, looking like $p^2 + V(q)$, looks very different for p and q.

As far as I understand, the very program has been given up. The subdivision into systems, which was a central element, always had a weak point: There is no natural fundamental subdivision, and the subdivisions we have in real life, into observers, devices and so on have no fundamental origin, they make sense only in an environment of a particular configuration which contains at least the Solar system with the Earth.

Maybe looking for a replacement of the subdivision into subsystems they use the subdivision into spacetime regions? That would be fine with me, it makes sense. Unfortunately not for the aim of saving relativity, because
it would be an introduction of a background in a situation where the quantum gravity guys hope for background-independent theories. But it doesn't seem to be the case - at other places, it sounds like all the decoherence stuff is used as it is, without worrying about the definition of subsystems.

I see a circularity here: To define the real objects we observe, we have to apply this decoherence machine, which depends on the subdivision into systems. But the usual subdivisions into systems come from the real objects we observe.

A problem which is absent in dBB. There we always have a configuration, and if we consider the evolution of this configuration, we have to consider its environment in the configuration space. In this environment all the visible subsystems are already present and can be used as they are.

So far some ideas immediately after reading the paper, so, not very deep.

bohm2

I'm not sure if this paragraph by Jill North makes it any easier but here's a pretty good summary (I think) of Maudlin's argument:
The Structure of a Quantum World
http://philsci-archive.pitt.edu/9347...for_volume.pdf

bohm2

I'm still having some difficulty understanding the difference between weak versus protecive measurements although the authors in some of these papers seem to be suggesting that unlike weak measurements:
Protective Measurements
http://lanl.arxiv.org/pdf/0801.2761.pdf

So if I'm understanding this, then, it is different than weak measurements as summarized here by Demystifier:

Weak measurements in quantum mechanics and 2.6 children in an American family
http://www.physicsforums.com/blog.php?b=1226

I'm still not sure if this scheme of protective measurements is universally accepted primarily because of some critical papers on the topic but in a recent paper by Gao, he suggests that protective measurements rule out ψ-epistemic models as per PBR:
Comment on "Distinct Quantum States Can Be Compatible with a Single State of Reality"
http://philsci-archive.pitt.edu/9457..._on_PRL_v9.pdf

Demystifier

Both weak measurement (WM) and protective measurement (PM) measure an observable without destroying the state. But they achieve it in a different way.

PM does it with a single measurement. WM does it with a large number of measurements, each on another member of an ensemble of equally prepared systems.

For WM, the prepared state before the measurement may be arbitrary (but must be the same for each member of the ensemble). For PM, the prepared state before the measurement cannot be arbitrary; it must be an eigenstate of the observable which will be measured.

In a perfect measurement, one would measure an observable:
1. for an ARBITRARY initial state,
2. WITHOUT DESTROYING it, and
3. with only ONE measurement performed.
But in QM such a perfect measurement is not possible. Standard strong measurement violates 2, WM violates 3, and PM violates 1.

EDIT:
For the sake of completeness, let me also explain two additional kinds of measurement:
- first kind (FK) measurement and
- quantum non-demolition (QND) measurement.
Both FK and QND are types of standard strong measurement, so they both destroy the initial state. However, they have a nice property if, after the measurement, you measure the same observable again; they both give the same value of the observable which you obtained by the first measurement. The difference is that FK achieves this only immediately after the first measurement, while QND achieves this at an arbitrary later time. FK measurements are measurements which can be described by a wave-function collapse. Many (but not all !) actual measurements are FK. However, not many actual measurements are also QND.

bohm2

I don't fully understand this argument but this author tries to use protective measurement to rule out the MWI:
An Exceptionally Simple Argument Against the Many-worlds Interpretation: Further Consolidations
http://philsci-archive.pitt.edu/9494...further_v9.pdf

bohm2

Another paper came out today suggesting that ψ is ontic but relying on the concept of protective measurement:
Distinct Quantum States Cannot Be Compatible with a Single State of Reality.
http://philsci-archive.pitt.edu/9609/1/dqs_v6.pdf