What has changed since the Copenhagen interpretation?

[Auto-Didact]

I don't see any relation between those two things. Why do you think that they might be related?

I was hoping you might have already thought deeper about it than I have. I recall Feynman (in his lectures, w.r.t. his path integral and in 1979 w.r.t. particle jets) and Veneziano talking about such things.

Given Feynman's statements, Abbott & Wise's demonstration, as well as BM trajectories clearly being fractals, this naturally suggests to me that zooming in on a particle trajectory in standard QM/BM should produce richness undreamt of, very much in line with what you describe in section 5.2 of your latest paper.

Of course, the specifics of all of this would depend on the trajectories' exact (multi)fractal characteristics in question. Given that you explicitly say Galilean and non-Lorentzian though, this would imply much less constraint than is usually considered. Is there overlap between your idea and Amelino-Camelia or Magueijo's DSR?

 

[DarMM]

I assume you are asking for something deeper than how the calculation works like shown in Tipler's paper. I only have my own incomplete idea: First, how do Alice and Bob even know which basis is up? It must be because they have a shared reference frame. I imagine the measurement basis represents a new dimension, defined relative to that reference. When the "split" happens, the copies of Alice/Bob diverge into that new dimension. So when they come into contact the matching subsystems will overlap.

I've now read Tipler's paper and to be honest I don't see how it solves the issue, to me it just simply declares that the evolution must be local because you could reorder it in another frame due to the events being spacelike separated. However the usual issue is more so that there is a tying together of results at spacelike separated points regardless of their temporal ordering in a frame. I couldn't see much discussion on Tipler's paper, which is surprising for such a bold claim, so I might return to it.

It led me on to reading the Deustch-Hayden paper and the surrounding literature.

I don't see how local dynamics can lead to non-local states, but I think it's a consequence of considering gauge-equivalent states to be physically equivalent. At least most of the papers I've seen that aim to show unitary QM is local work in the Deutsch-Hayden picture, and that feature of gauge-sensitivity is not in debate.

From having a look it seems it is in debate, with Wallace and Tipler, MWI proponents themselves, disagreeing with Deustsch's analysis. Wallace himself thinks that states in MWI are nonlocal, simply because the quantum state itself is nonlocal so if you take it as ontic you have nonlocal physical states. I've read Deustch's follow up paper, but to me he takes a very weak notion of "local reality" where the density matrix of one of the quantum systems (with the other system traced out) is taken as the physical state of the system, the "element of reality" to use Einstein's words. This is very strange to me, but perhaps it works out, however the details seem to be lacking in Deustch's paper.

Considering it's controversial within MWI circles and due to the modified/weakened notion of "local reality", I'm not sure what to make of these arguments, so I'm not 100% convinced MWI is local. Food for thought.

 

[Demystifier]

Given Feynman's statements, Abbott & Wise's demonstration, as well as BM trajectories clearly being fractals, this naturally suggests to me that zooming in on a particle trajectory in standard QM/BM should produce richness undreamt of, very much in line with what you describe in section 5.2 of your latest paper.

Note that the fractal nature in the Abbott & Wise case is caused by measurement. On the other hand, unmeasured BM trajectories do not have a fractal nature. Experiment of the Abbott & Wise type probably cannot easily test Lorentz invariance. On the other hand, Lorentz invariance can be tested by scattering experiments with particle accelerators. The currently strongest particle accelerator (LHC) sees nothing beyond the Standard Model, but my theory predicts that a much much stronger accelerator should see new particles with Lorentz non-invariant cross sections.

Is there overlap between your idea and Amelino-Camelia or Magueijo's DSR?

Not much.

 

[Demystifier]

so I'm not 100% convinced MWI is local. Food for thought.

As I argue in http://de.arxiv.org/abs/1703.08341 , MWI is neither local nor non-local. It is alocal.

 

[DarMM]

Considering it's controversial within MWI circles and due to the modified/weakened notion of "local reality", I'm not sure what to make of these arguments, so I'm not 100% convinced MWI is local. Food for thought.

As a simpler version of this, since it is the case that the wavefunction for two particles ##\psi(x_1,t_1;x_2,t_2)## can be non-zero, even if the points ##(x_1,t_1)## and ##(x_2,t_2)## are spacelike separated and since the wavefunction is ontic in MWI (in fact it is the fundamental object), then there is a real physical quantity associated with spacelike separated pairs.

I don't see how one can avoid this, the wavefunction lives in the space of functions over ##n##-fold products of Minkowski space/a hypersurface thereof (depending on Schrodinger/Heisenberg picture), not Minkowski space. You could show that predictions/observations don't violate locality, but that's no different to Bohmian Mechanics. The fundamental ontology is not local.

While writing I saw @Demystifier 's post, alocal is probably a better word.

 

[DarMM]

As I argue in http://de.arxiv.org/abs/1703.08341 , MWI is neither local nor non-local. It is alocal.

Thanks for this @Demystifier , it actually leads into one of the most confusing points of MWI for me.

In MWI the wavefunction is all there is, a single point in ##\mathcal{H}##, the Hilbert space. It then "just so happens" that ##\mathcal{H}## is isomorphic to ##\mathcal{L}^{2}\left(\Sigma\right)## with ##\Sigma## a space of functions over a hypersurface of a Lorentzian manifold. Due to ##\mathcal{H}## having this structure and assuming it eventually reaches the point where it has a stable decomposition into:
$$\mathcal{H} = \mathcal{E} \times \mathcal{S}$$
with ##\mathcal{E}## the environment Hilbert space and assuming ##\mathcal{E}## has properties that make it pseudo-classical and also assuming time evolution behaves in a certain way (not overtly entangling) then one can show that components in ##\mathcal{S}## decohere in such a manner that their time evolution is approximately isomorphic to (multiple copies of) objects living in ##\mathcal{M}^{4}##, a Lorentzian manifold (Minkowski space for ease let's say).

I just find the whole picture hard to accept. Minkowski space is essentially an illusion arising only from the fact that ##\mathcal{H}## is isomorphic to a very abstract space built over it, combined with the emergence (somehow) of a stable decomposition where one part is pseudo-classical and thermal and a fortunate evolution law.

 

[DarMM]

the wavefunction lives in the space of functions over ##n##-fold products of Minkowski space/a hypersurface thereof

Note: In QFT this would be "the space of square-integrable functions over tempered Schwartz distributions over a Lorentzian hypersurface, with integrable defined with respect to the only measure that leaves the Hamiltonian finite".

Quite an abstract object.

 

[akvadrako]

I don't think it matters that the fundamental object is naturally interpreted as alocal. For a theory to be local, it must be possible to write down the states in a local manner, where all the "elements of reality" are confined to a region. As I understand, this is what Deutsch and Tipler show in their papers. Though I agree it's not totally convincing and remains an open question.

But to demonstrate that many worlds is non-local, one would have to provide an example experiment which can't be described with any quantum model that involves only local states and dynamics. So far I haven't come across this claim.

Also perhaps relevant: Against Wavefunction Realism (Wallace, 2017). He's saying that you shouldn't take Hilbert space as the fundamental ontology in many worlds, but instead consider the non-fundamental ontologies implied by a specific models. My point in linking this is to show that many worlds does not necessarily imply any specific decomposition.

 

[akvadrako]

However the usual issue is more so that there is a tying together of results at spacelike separated points regardless of their temporal ordering in a frame. I couldn't see much discussion on Tipler's paper, which is surprising for such a bold claim, so I might return to it.

Perhaps there is no discussion because like me, he doesn't see how it's an issue. Basically there are these "labels" attached to all the elements of the systems that encode the information necessary to know which systems they overlap with. Can you help me understand your objection a little better? Is it about the encoding of that information at the ontic level or about the mechanism which matches up those overlapping systems? I don't know how it's implemented, but I can't see any reason why it would be problematic.

 

[Demystifier]

Thanks for this @Demystifier , it actually leads into one of the most confusing points of MWI for me.

In MWI the wavefunction is all there is, a single point in ##\mathcal{H}##, the Hilbert space. It then "just so happens" that ##\mathcal{H}## is isomorphic to ##\mathcal{L}^{2}\left(\Sigma\right)## with ##\Sigma## a space of functions over a hypersurface of a Lorentzian manifold. Due to ##\mathcal{H}## having this structure and assuming it eventually reaches the point where it has a stable decomposition into:
$$\mathcal{H} = \mathcal{E} \times \mathcal{S}$$
with ##\mathcal{E}## the environment Hilbert space and assuming ##\mathcal{E}## has properties that make it pseudo-classical and also assuming time evolution behaves in a certain way (not overtly entangling) then one can show that components in ##\mathcal{S}## decohere in such a manner that their time evolution is approximately isomorphic to (multiple copies of) objects living in ##\mathcal{M}^{4}##, a Lorentzian manifold (Minkowski space for ease let's say).

I just find the whole picture hard to accept. Minkowski space is essentially an illusion arising only from the fact that ##\mathcal{H}## is isomorphic to a very abstract space built over it, combined with the emergence (somehow) of a stable decomposition where one part is pseudo-classical and thermal and a fortunate evolution law.

Yes, I think that's essentially the same problem as the problem I discuss in Sec. 3.3.

 

[martinbn]

It then "just so happens" that ##\mathcal{H}## is isomorphic to ##\mathcal{L}^{2}\left(\Sigma\right)## with ##\Sigma## a space of functions over a hypersurface of a Lorentzian manifold.

How is that?

 

[DarMM]

How is that?

What do you mean?

 

[Demystifier]

How is that?

You must read what he means, not what he writes.

 

[DarMM]

I don't think it matters that the fundamental object is naturally interpreted as alocal. For a theory to be local, it must be possible to write down the states in a local manner, where all the "elements of reality" are confined to a region.

What are those elements of reality in Tipler's paper? In Deutsch's work they are the reduced density matricies, I'm not really sure what they are in Tipler's case.

Tipler presents the evolution of the global state from Alice's perspective and then from Bob's and then says because the evolution has different time orderings from these two perspectives there's nothing nonlocal. To be honest I don't fully understand that, but my first sentence above is more important. What are the local elements of reality in his picture?

Also perhaps relevant: Against Wavefunction Realism (Wallace, 2017). He's saying that you shouldn't take Hilbert space as the fundamental ontology in many worlds, but instead consider the non-fundamental ontologies implied by a specific models. My point in linking this is to show that many worlds does not necessarily imply any specific decomposition.

Of course, but this really reduces to the case of ##\mathcal{H} = \mathcal{L}^{2}(Q)## with ##Q## model dependent. I get and I think agree with Wallace's point, but I don't think it affects this discussion as the state, regardless of how it is represented, seems to have these properties (even if formulated as a functional on a C*-algebra) and you need the environmental decomposition I mentioned earlier, again regardless of ##Q## or even if you don't view the theory through a Hilbert space lens the issue can be reposed in an Algebraic approach, it remains fundamentally the same issue.

Perhaps there is no discussion because like me, he doesn't see how it's an issue.

I meant there seems to be no discussion of his paper by other authors. Everybody who references him does it mostly to say either "Tippler thinks otherwise" or "Here's a many worlds treatment of entanglement", there's no real discussion.

Can you help me understand your objection a little better? Is it about the encoding of that information at the ontic level or about the mechanism which matches up those overlapping systems? I don't know how it's implemented, but I can't see any reason why it would be problematic.

Both, I'm certainly not saying there is a no-go theorem that means it can't be done, but it hasn't been done and I'm not sure it could be done. Very simply, as above, Tipler looks at the global state from Alice/Bob's view. However what you'd really need is what are the actual local degrees of freedom? The global state isn't a valid candidate. What element of reality/degree of freedom exists in Bob's spacetime region where he does the measurement?

Deutsch says the density matrix, is that what Tipler is saying?

 

[DarMM]

You must read what he means, not what he writes.

Let's hope I don't forget what I meant or we'd have a real paradox.

To explain that's the basic form of the Hilbert space in QFT, as space of square integrable functions over fixed time classical fields, with fixed time classical fields being the aforementioned functions on a hypersurface. Though this is being informal, correctly they are tempered distributions over a hypersurface.

 

[martinbn]

What I am confused about is that you say that the Hilbert space is an ##L^2## space over a space of functions. But what is the measure in that space of functions?

 

[DarMM]

What I am confused about is that you say that the Hilbert space is an ##L^2## space over a space of functions. But what is the measure in that space of functions?

Depends on the field theoretic Hamiltonian, unlike non-relativistic QM there isn't a unique (up to Unitary transformations) measure from the Stone-VonNeumann theorem. This is related to the issue of renormalization.

 

[martinbn]

Depends on the field theoretic Hamiltonian, unlike non-relativistic QM there isn't a unique (up to Unitary transformations) measure from the Stone-VonNeumann theorem. This is related to the issue of renormalization.

Any examples?

 

[DarMM]

Any examples?

It's quite technical, the measures are more proven to exist rather than being directly quotable. James Glimm's "Boson fields with the ##:\phi^4:## interaction in three dimensions", Comm. Math. Phys. 10(1) p.1-47, is one of the gentler introductions.

Also his book with Arthur Jaffe, Quantum Physics: A Functional Integral Point of View.

Though his paper derives their existence more directly.

Some properties of the measure and the closest to an easily quotable example is given in:
Reed, M. & Rosen, L. "Support properties of the free measure for Boson fields" Commun. Math. Phys. (1974) 36: 123

The case here being the measure for the free field.

 

[atyy]

As I argue in http://de.arxiv.org/abs/1703.08341 , MWI is neither local nor non-local. It is alocal.

I guess you would say MWI is a-nonlocal?

 

[Auto-Didact]

Not much.

Great, saves me the time of reading those again!

Note that the fractal nature in the Abbott & Wise case is caused by measurement. On the other hand, unmeasured BM trajectories do not have a fractal nature.

I see. On a related note, see this thread.

The currently strongest particle accelerator (LHC) sees nothing beyond the Standard Model, but my theory predicts that a much much stronger accelerator should see new particles with Lorentz non-invariant cross sections.

Any specific energy scale in mind? And if so, is that some physically derived scale or just an ad hoc guess?

 

[Demystifier]

Any specific energy scale in mind? And if so, is that some physically derived scale or just an ad hoc guess?

It's ad hoc, but my first guess would be Planck scale. However, one terminological notion is in order. In the context of violated Lorentz invariance, I would not talk about energy scale. I would talk about length scale or its inverse 3-momentum scale.

 

[Auto-Didact]

It's ad hoc, but my first guess would be Planck scale.

Okay. Last question for now: I probably missed it, but does your model, being fundamentally non-relativistic, have any strong explicit predictions about the existence, modification or non-existence of zitterbewegung? I ask mainly due to the arguments made in Hestenes 1990 that zitterbewegung need not be regarded as a purely relativistic phenomenon, instead amenable to a geometric algebra reinterpretation consistent with the Madelung reformulation of the SE.

However, one terminological notion is in order. In the context of violated Lorentz invariance, I would not talk about energy scale. I would talk about length scale or its inverse 3-momentum scale.

Ha, of course. As Poincaré said: We must use language, and our language is necessarily steeped in preconceived ideas.

 

[akvadrako]

I meant there seems to be no discussion of his paper by other authors. Everybody who references him does it mostly to say either "Tippler thinks otherwise" or "Here's a many worlds treatment of entanglement", there's no real discussion.

Ah, I agree with that. The original Deutsch-Hayden paper received a fair amount of citations, but after his latest reply to the most common criticisms there has been very little discussion. I'm not sure if it's because researchers aren't interested in the locality of many worlds or they don't know where to take it from there.

What are those elements of reality in Tipler's paper?

I like this question :) There are four "elements of reality" or local wave packets after Alice and Bob's measurements. One is Alice's copy of the "global state from Alice's perspective" when she measures q=0 at pos x=1, time t=1 and environment E, along with the other combinations:

Alice0(q=0,x=1,t=1,E) & Alice1(q=1,x=1,t=1,E)
Bob0(q=0,x=2,t=1,E) & Bob1(q=1,x=2,t=1,E)

After the measurement Bob moves to Alice and the wave packets evolve to x=1, t=2. The non-orthogonal wave packets overlap because now both have x=1, creating:

AB0(q=0,x=1,t=2,E) & AB1(q=1,x=1,t=2,E)

We need a degree of freedom to store q, but this is something Alice and Bob both can do, for example by writing it down - it's encoded in the degrees of freedom on the paper. It's not a global state, but local to that wave packet: even Alice0 and Alice1 disagree about the value. The majority of the local state (E) contains a rough copy of the world - everything that wave packet "knows" about its environment. If you are talking about Alice's experience, that knowledge must be encoded in the relations between atoms in the brain.

If you take a very simple system with limited degrees of freedom, the world it resides in will also be much simpler. Say Alice's lab doesn't have any spare degrees of freedom so they decide to erase the measurement of q completely; then there should be just one Alice system, overlapping with both Bob0 and Bob1. If you restrict Alice even further so she doesn't even know if it's Bob or Buster coming to meet her, she'll encounter both of them. So any local degree of freedom will suffice, but it actually does need to be recorded.

The global wavefunction then becomes the union of all local wave packets. This is how it's decomposed into local elements of reality and why Wallace's paper is relevant.

One of the aspects I'm unclear about above is how nature knows that Alice's q and Bob's q are the same basis, which is why I mentioned the shared reference frame before.

 

[Demystifier]

Okay. Last question for now: I probably missed it, but does your model, being fundamentally non-relativistic, have any strong explicit predictions about the existence, modification or non-existence of zitterbewegung? I ask mainly due to the arguments made in Hestenes 1990 that zitterbewegung need not be regarded as a purely relativistic phenomenon, instead amenable to a geometric algebra reinterpretation consistent with the Madelung reformulation of the SE.

For non-relativistic Bohmian treatment of spin see e.g. http://de.arxiv.org/abs/1305.1280 .
As you can see on Fig. 2, typical trajectories do not exhibit zitterbewegung.

 

[DarMM]

The global wavefunction then becomes the union of all local wave packets. This is how it's decomposed into local elements of reality and why Wallace's paper is relevant.

Firstly thanks for the post. I still don't fully understand, perhaps something just hasn't clicked yet. It's basically that I'd like to know what "global state from Alice's perspective" is mathematically. I'll elaborate.

From reading Wallace's paper I see that regarding local degrees of freedom he is essentially discussing his work with Timpson (and ideas like it) in:
Wallace, D., and C.G. Timpson. 2010. Quantum mechanics on spacetime I: Spacetime state realism. The British Journal for the Philosophy of Science 61(4): 697–727.

Where he also says, like Deutsch, that what are real are the reduced density matrices associated with a region, or (if one wishes to be abstract) the state on the local algebra of that region formed by restricting the global state (which is ultimately a non-pure state on the local algebra and thus a mixed state). Do you think that Tipler's local degree's of freedom are basically this or fundamentally different? If so, do you take the Deutsch-Wallace's or Tipler's view of what the local elements of reality are?

 

[akvadrako]

Do you think that Tipler's local degree's of freedom are basically this or fundamentally different? If so, do you take the Deutsch-Wallace's or Tipler's view of what the local elements of reality are?

In the latest Deutsch-Hayden paper (the vindication one), he says the factual information of each qubit or sub-network is encoded in its Heisenberg observables. A typical Schrodinger-picture density matrix is not enough because it misses some of the entanglement correlations with other sub-networks.

In Tipler's 2014 paper he is using pure states, it seems, though it's less clear. Each sub-system (Alice0, Bob1, ...) has its own pure-state view of the universe.

I think both approaches contain the same information. In contrast, the Wallace-Timpson view is explicitly non-local, though oddly they reference a companion paper that doesn't exist which is supposed to talk about the locality in the Deutsch-Hayden picture: Quantum mechanics on spacetime II: Quantum gauge freedom.

 

[DarMM]

Okay so I've read all these papers and the literature around them. Quite a morass I must say.

From the point of view of Algebraic QFT, one has the algebra of observables ##\mathcal{A}## and a state ##\rho## on that algebra. It is simply a fact that for a pure state it's restriction to the algebra of a region, i.e. ##\rho|_{\mathcal{A}(\mathcal{O})}##, is going to be a mixed state.

At this point you can say that only pure states are ontic objects, like standard Everett MWI, in which case you have to accept that the element of reality is alocal, in a sense "outside of spacetime".

Or alternatively you can say that density matricies are real ontic objects, which allows ##\rho|_{\mathcal{A}(\mathcal{O})}## to be an element of reality, this is what Wallace and Timpson do in their Spacetime realism interpretation (an alternate form of MWI). However this to me is pretty odd, as the density matricies carry classical Kolmolgorov probaility, standard "ignorance" based probability. It seems strange to view this as an element of reality, as the density operator at a point describes statistics of experiments even in a ##\psi##-ontic view!

Deutsch seems to take an even more radical approach, saying the ontic object associated to a region is ##\mathcal{A}(\mathcal{O})##, the algebra itself and not the quantum state! This cannot be considered Everett MWI, but a new interpretation, as it is algebra-ontic not ##\psi##-ontic like MWI. Now the evolution of ##\mathcal{A}(\mathcal{O})## and properties of regional algebras in general are local, so this is an advantage, but this is a completely undeveloped view. There's no measurement theory for example. It'll take a lot of work to show equivalence with standard QM. How does decoherence work? How does the algebra "effectively" become a function algebra in order to be classical? Will that be multiple function algebras or not, i.e. will there be more than one world?

As for Tipler, I have no idea what kind of mathematical object "Alice's pure state view" is and how it connects with ##\rho|_{\mathcal{A}(\mathcal{O})}##, the entire paper is very vague to me and I don't see how it is demonstrating anything beyond no signalling.

 

[ftr]

Quite a morass I must say.

But isn't all this about some mathematical formalism but does not answer the real important question as to where is the electron in the hydrogen atom at some point in time.

 

[DarMM]

But isn't all this about some mathematical formalism but does not answer the real important question as to where is the electron in the hydrogen atom at some point in time.

No, Many Worlds attempts to explain what is actually going on. Although "where the electron is in the hydrogen atom at some point in time" might not have a valid answer depending on the interpretation. In some interpretations there is no electron in the hydrogen atom.

 

[ftr]

In some interpretations there is no electron in the hydrogen atom.

wow, I knew some "models" hinted at that but not an "interpretation", which interpretation is that?

 

[DarMM]

wow, I knew some "models" hinted at that but not an "interpretation", which interpretation is that?

Relational Block World so far as I understand it, some takes on QBism for interpretations of QM.

In QFT many would take this view even ignoring the issue of interpreting QM in general, since an electron number operator isn't defined on hydrogen states in the Hilbert space of two flavor QED or whatever QFT you are using that contains hydrogen.

This is a general feature of QFT where particle number isn't defined on the interacting Hilbert space.

 

[akvadrako]

Okay so I've read all these papers and the literature around them. Quite a morass I must say.

Thanks for the followup and such a clear post.

From the point of view of Algebraic QFT, one has the algebra of observables ##\mathcal{A}## and a state ##\rho## on that algebra. It is simply a fact that for a pure state it's restriction to the algebra of a region, i.e. ##\rho|_{\mathcal{A}(\mathcal{O})}##, is going to be a mixed state.

At this point you can say that only pure states are ontic objects, like standard Everett MWI, in which case you have to accept that the element of reality is alocal, in a sense "outside of spacetime".

When taking the global wavefunction and restricting it to a spacetime region, you'll definitely have a mixed state. At the very least because multiple worlds will be occupying that region. But I don't see why that makes anything alocal; a mixed state is multiple pure states, so if pure states are ontic surely multiple pure states are too.

More practically, if you are restricting your view to a single region (say Alice's lab) and only considering a single world, then you should have a pure state again.

Deutsch seems to take an even more radical approach, saying the ontic object associated to a region is ##\mathcal{A}(\mathcal{O})##, the algebra itself and not the quantum state! This cannot be considered Everett MWI, but a new interpretation, as it is algebra-ontic not ##\psi##-ontic like MWI.

Hum, this is really beyond my understanding, but it directly contradicts a claim he reiterated at few times; that they are equivalent. I suppose one way out is to assume the algebra is encoded in ##\psi## itself. I'm not even sure what you mean by algebra - is that just the observables and the state?

 

[DarMM]

Hum, this is really beyond my understanding, but it directly contradicts a claim he reiterated at few times; that they are equivalent. I suppose one way out is to assume the algebra is encoded in ψ\psi itself. I'm not even sure what you mean by algebra - is that just the observables and the state?

Just the observables (not the state). See the last section of the vindication paper about "algebra-stuff". He says they'll be equivalent, maybe they are, but I think a theory with only observables as physically real needs a much more justification.

When taking the global wavefunction and restricting it to a spacetime region, you'll definitely have a mixed state. At the very least because multiple worlds will be occupying that region. But I don't see why that makes anything alocal; a mixed state is multiple pure states, so if pure states are ontic surely multiple pure states are too.

More practically, if you are restricting your view to a single region (say Alice's lab) and only considering a single world, then you should have a pure state again.

Firstly I just want to separate two things, I'm saying the claim that the global state is ontic is an alocal ontology. The view where the density matricies are ontic, not the global state (as Wallace and Timpson do), is not alocal as mentioned in #168.

The global pure state is alocal, that just follows from the fact that it is a state on the entire observable algebra ##\mathcal{A}(\mathcal{M}^4)##, with ##\mathcal{M}^{4}## the spacetime and obtains nonseperable relations between spacelike regions. If this is ontic, then you have ontic alocality. That's not to say the theory is signalling, which is a separate issue. This is what motivates Wallace and Timpson to not have the global state as the ontic object, i.e. to reject wavefunction realism.

Secondly, Wallace and Timpson avoid this by saying that what's actually ontic are the local density matrices. This would make things local, but it's a very strange ontology. Density matrices contain normal Kolmolgorov probabilities and imbuing that with the meaning of multiple worlds seems odd, as you don't do that in any other application of Kolmolgorov probabilities. Also I'd have several questions about the ontology, what's the ontic difference between Kolmolgorov mixing and non-Kolmolgorov superposition, since both now exist? Also the density matrix normally only has statistical meaning, what is its non-statistical meaning?
Also note that proper and improper mixtures are the same ontic situation under this picture. It seems odd to me that there really is no difference between one electron of an entangled pair (improper mixed state) and an electron fired at random from a silver oven (proper mixed state). In this picture they are identical because the classical uncertainty in the latter case has ontic status.

 

[akvadrako]

Just the observables (not the state). See the last section of the vindication paper about "algebra-stuff". He says they'll be equivalent, maybe they are, but I think a theory with only observables as physically real needs a much more justification.

How does this require more than the well-known equivalence between the Heisenberg and Schrodinger pictures, given the algebra stuff is the Heisenberg observables?

Firstly I just want to separate two things, I'm saying the claim that the global state is ontic is an alocal ontology.

I did see how they were separate points, though for now I'm ignoring the Wallace/Timpson picture; it's not very compelling. Let me see if I understand what you are saying about the global pure state. You're saying that because when it's defined on an algebra without spacetime it's alocal by definition and when defined on an algebra with spacetime ##(\mathcal{M}^4)## as a primitive element that it contains global properties and becomes non-local.

This isn't the definition of *local I'm using. A theory is local if it possibly can be reformulated in terms of separate regions, so that actions on separated regions don't effect each other. And for the example of many worlds, those separate regions are located in configuration space (which includes spacetime dimensions).

Ignoring the algebra stuff part, Deutsch's paper shows you don't need to think about spacetime at all. If you show a theory is qubit-local, along with the universality of quantum computers and the fact they can be built in our spacetime, that demonstrates there is a spacetime picture available.

So to show many worlds is local, it would be enough to show that non-interacting qubits can't effect each other. Maybe there is a more intuitive way than Deutsch's paper. What defines a qubit but it's correlation with other qubits? So if we have a bunch of qubits in Bob's lab can Alice effect their correlations at all? Well, the amount of entanglement between her lab and Bob's lab stays the same. She can cause Bob's qubits to appear entangled from her point of view, but the information defining that entanglement is necessarily encoded in her lab. I'll think more about this.