The Many Worlds Wiener Sausage is the first step in understanding the Einstein-Podolsky-Rosen (EPR) paradox. However, there are still three steps missing until we can resolve the EPR paradox correctly. One important step: Although it is a many-worlds model, with parallel universes and all that, and although it can reproduce certain quantum factors, it is not yet a quantum world!UPDATE: What is written in this post is now mostly much better accessed in this, extremely pedagogically written article: http://arxiv.org/abs/1311.5419
The Sausage is Real
Why is the sausage not a quantum world? Because you only need to imagine a little arrow called DR, which stands for "Directly Real", which is a vector that points out the “one true real world”, and the model is immediately a deterministic, classical, directly real world.
Adding a single little arrow “DR” clarifies that the model is fundamentally a local realism and thus cannot violate Bell’s inequality. No such model can describe quantum physics.
You could simulate the whole model in a classical computer. Therefore, it is impossible that the model describes quantum physics, because otherwise you could tackle the Quantum Randi Challenge (QRC) with it and win the Nobel Prize.
The arrow DR can serve as a local hidden variable that is carried by the photons in the EPR setup of Alice and Bob. Thus, if you could modify the model so that the volumes V of the sausage strips equal the quantum probabilities P, you would overcome the Quantum Randi Challenge, which cannot be overcome. V can never model P, whatever the shape of the sausage, whatever the density distribution of lean meat versus fat inside the sausage, whatever period.
Apparent Non-Locality versus "Non-Locality"
The sausage model has the simple ‘non-locality’ of the EPR setup, namely the photon at Alice’s place seems to immediately react to the measurement of the photon at Bob’s place far away. Two comments: 1) The sausage model shows that this kind of simple “spin-up-spin-down” anti-correlation between the two photons, this ‘non-locality’, does not necessitate a non-local model. 2) The non-locality that physics talks about goes deeper. This is one of the main aspects those many crackpots do not understand.
Although the 'non-local' anti-correlation exists in the sausage model, and although even the probabilities depend on the relative angle between widely separated detectors, there is no "quantum non-locality"! It might help to calculate the Bell inequality with the Bell angles that violate the inequality maximally. With the correct quantum probabilities P you get
[cos2(3π/8)] + [sin2(-π/4)] smaller than [cos2(π/8)] (in detail here),
but with the volumes V of the sausage strips you get instead
[1-2(3π/8)/π] + [2(π/4)/π] equal to [1-2(π/8)/π].
If the sausage model were non-local, you could expect the Bell inequality to be violated a little; maybe not violated to the same extend as quantum physics does it with the correct P, but still violated. However, the V do not violate the inequality even a tiny little bit.
Some pointless Philosophy
A crucial step, namely understanding the classicality of the simple sausage many world model via a pointer called DR, is now completed, and there are only two steps missing until the EPR paradox is resolved. Before I reveal those one, two steps, let me get into something that can be appreciated at this point but will be kind of beside the point once the model is completed.
The sin2(δ) dependence tells us that the world cannot be described by a local realism. With a δ/π dependence instead, we would not be having this discussion, but we know from simple optics involving polarization filters that it is sin2(δ). Surely, we would rather like to have a good reason for why we should have for example non-locality and then be able to derive functional dependencies and weird numerical factors from that. This is missing today.
Some say that the world is non-local because it is like a hologram, but this is also just derived from the weird factors. We know of no reason that lets us slap our forehead, exclaiming “Oh but of course it must be a hologram!” For relativity theory, there have always been such reasons. Profound symmetry arguments are what drove Einstein to sit down and learn Riemann’s math in the first place.
If I were to believe in realism, I would only come up with one reason for non-locality: Without, there is no reason why the left half of the model should not go twice as fast for a while, or say thousands of times faster than the right one. The nature of time itself is some “interaction” that keeps the whole synchronized.
However, this “reason” is so spooky, as in Einstein's “spooky action at a distance”, so unreal anyway, that it can only be part of the fundamental answer. The answer rests in a self-evident symmetry: The profound laws of nature are not there to make me toss heads instead of tails on some Tuesday afternoon! All such possibilities are cared for on equal terms relative to totality. The main problem with this is the open question about why different possibilities interfere. If we knew a good reason (like evolutionary coemergence as grounding of meaning in consistent stories), we would pretty much know everything there is to know.
These philosophical implications of the solution to the EPR problem are further discussed here.
--------------------------------------S. Vongehr: "Many Worlds Model resolving the Einstein Podolsky Rosen paradox via a Direct Realism to Modal Realism Transition that preserves Einstein Locality" arXiv:1108.1674v1 [quant-ph] (2011)
UPDATE: This reference is the first paper on the possibility of such models, but the models have now actually been constructed and are much better explained in:
S. Vongehr: “Against Absolute Actualization: Three "Non-Localities" and Failure of Model-External Randomness made easy with Many-Worlds Models including Stronger Bell-Violation and Correct QM Probability” http://arxiv.org/abs/1311.5419 (2013)