Does MWI predict spot size on screen

[fhenryco]

The wave function as it approaches the screen in the double split experiment is extended all over space. How does the MWI (multi worlds interpretation) account for the energy hf of the particle being deposited on a very small area and producing a spot there rather than in a more extended area hence producing a large patch ? in over words how MWI predicts the extension of the parts of the wave function that decohere from each others ?
I assume that within the MWI there is an infinite number of parrallel histories each corresponding to the oberver seeing the spot at a different location...

 

[PeterDonis]

I assume that within the MWI there is an infinite number of parrallel histories each corresponding to the oberver seeing the spot at a different location...

Yes. And this, in itself, answers your question, if you think about it.

 

[fhenryco]

Yes. And this, in itself, answers your question, if you think about it.

Ok the way i expressed it was not clear enough . why not an infinite number of parallel histories each corresponding to a large patch several centimeters large ( due to the volume of wave function that decoheres from other similar volumes is ~ several cm³) : that's all my question was about !

 

[PeterDonis]

why not an infinite number of parallel histories each corresponding to a large patch several centimeters large

This question is not particular to the MWI; it's not a question about interpretation, it's a question about how the detector screen works as a measuring device. For example, instead of the MWI, adopt a collapse interpretation like Copenhagen. Do you still have the same question?

 

[fhenryco]

i would not have the same question because within the Copenhaguen interprtation nobody pretends to describe physically the collapse mechanism whereas decoherence (here i consider decoherence to be MWI in its more modern version) pretends to describe as a result of the physics of the Schrödinger equation only the apparent collapse ...
if you prefer i can turn the question differently : does decoherence explain the size of the spot ?

 

[PeterDonis]

i would not have the same question

You should, because decoherence is not interpretation-dependent; it occurs regardless of which interpretation you adopt. So if you don't think decoherence answers your question about the size of the spot in the MWI, it won't answer the question in Copenhagen either.

within the Copenhaguen interprtation nobody pretends to describe physically the collapse mechanism

But the size of the spot in a collapse interpretation is not determined by the collapse mechanism; it's determined, as I said before, by the interaction between the particle and the detector screen, which needs to be analyzed by the interpretation-independent math of QM. Collapse, in a collapse interpretation, only explains why just one branch of all the possible branches (corresponding to all the different possible positions of the spot on the screen) survives; it doesn't explain the particular content of each branch (like the size of the spot on the screen).

does decoherence explain the size of the spot ?

In principle it should, yes. (And in any interpretation.) But I don't know if anyone has studied this particular case in detail in the context of decoherence, because it's hard to analyze compared to other simpler measurements (like spin measurements using Stern-Gerlach devices).

 

[fhenryco]

Collapse, in a collapse interpretation, only explains why just one branch of all the possible branches (corresponding to all the different possible positions of the spot on the screen) survives; it doesn't explain the particular content of each branch (like the size of the spot on the screen).

in a theory that does not try to derive but just postulates both the collapse and the collapse branch content as standard QM (copenhaguen interpretation, where may be the branch content is determined by the resolution of the apparatus) this distinction is not of particular interest anyway, On the other hand It's difficult to imagine that decoherence while deriving the apparent collapse from the evolution of the wave function according Schrödinger should not at the same time derive what is apparently collapsing (a spot ?, a large patch?, still resolution determined ?). Of course only focusing on simple cases where the collapse is between two alternatives (spin measurement) avoids the question but then also makes me suspect that something important was left aside which would make decoherence less attractive in the sense that we could imagine that decoherence which is also something quite trivial and well known in classical physics well before people started to question the very nature of the "collapse" in QM, this decoherence is overestimated when given a central trigger role for the apparent collapse. In particular there seems to be no particular role played by "hbar", i.e the Planck einstein relations which makes me suspect that decoherence by itself is not the trigger but rather quantization itself, the starting point of QM, the fact that energy must be exchanged in E=hf paquets. May be i missed something but i don't see a close and clear enough link between hbar and decoherence which makes me doubt about the actual relevance of decoherence in QM... not embarrassed by this ?

 

[Nugatory]

May be i missed something but i don't see a close and clear enough link between hbar and decoherence which makes me doubt about the actual relevance of decoherence in QM.

When we use the rules of QM to calculate how the state of a quantum system changes over time, we find that some terms quickly go to zero; we call this result decoherence. In experiments in which a photon hits a screen, the terms that disappear are the ones that do not correspond to a spot of some size and shape appearing somewhere on the screen. Thus, the relevance to QM should be clear: without decoherence the theory would not properly describe one important property of photon-screen interactions.

MWI and Copenhagen differ only in how they handle the terms that don't go to zero, so the effects of decoherence are the same for both.

You're not seeing an $\hbar$ in the result of these calculations because it cancels out partway through.

 

[fhenryco]

the terms that disappear are the ones that do not correspond to a spot of some size and shape appearing somewhere on the screen.

Do you have a reference showing that particular computation that leads to this prediction

When we use the rules of QM to calculate how the state of a quantum system changes over time, we find that some terms quickly go to zero

which specific rules of QM ? : i guess not simply the Schrödinger equation ... a wave function that propagates according for instance the free Schrödinger equation has nothing to do with QM since you can eliminate hbar from it (replacing the mass by hbar.omega_0) which shows that it is actually as a classical wave equation as the propagation equation for the electromagnetic field for instance ... So indeed a specifically QM rule is needed otherwise i admit that the decoherence argument in the case of the double slit experiment would look as strange for me as if someone would tell me that in an interference experiment with surface water waves (where it is also possible to suppress the interference by losing the coherence between the two sources of waves) this would ultimately lead to the observer, as a result of decoherence when the waves reach the caps, only seeing one localized vibration of only one cap among an alignment of caps at the water surface (playing the role of the screen) , the other caps only vibrating in the parrallel worlds...

 

[fhenryco]

I'm trying to catch the idea behind the formalism, that's why the discussion sounds not very rigorous

I guess the specific QM rule is something like : "the wave represents one single particle" or "the wave represents one energy-momentum quantum" which within the duality of the Copehaguen interpretation is a trivial statement , but much less obvious within a decoherence theory where we are supposed to have the wave and the wave only ...