The Many Worlds Wiener Sausage is a very simple model that shows how some of the apparent non-locality in the infamous Einstein-Podolsky-Rosen paradox can arise simply by the world splitting into parallel universes. It can be understood by advanced high school students (and the quantum version is now also available on the preprint archive). But we saw that although it is a many worlds model, it is not a quantum world! Today we will make the model look like the great spaghetti monster. There are two aspects about this that I find amazing:
1) It can still be understood by high school students but is nevertheless correct quantum mechanics – not some cracked pot’s hidden variables nonsense.
2) It is one single and natural step that turns the model quantum, and this step has two important features:
- The step is obviously a local modification at one certain place of a classical and thus fundamentally local model, therefore the quantum model also still obeys Einstein locality! Since quantum physics cannot be both local and real, the “real” must have been modified. And it has.
- The crucial step obviously turns something that still can be described as a naïve direct realism into something that can no longer be so described, and again, not via philosophical sophistry or advanced math that rests more on authority than on what lay people can understand: After the crucial modification, a little arrow called “DirectlyReal”, short “DR”, is no longer able to point to the one real world it pointed to before.
Adding a single little arrow “DR” clarifies that the model is fundamentally a local realism. It is well known that such models cannot possibly describe quantum physics. Below it will be modified so that DR cannot point to a certain world anymore, or if it does, points with the wrong probability. At that point, the model will be quantum.(This article is one in a series - for further explanation of this picture please use the links provided.)
Much like Minkowski diagrams can resolve the relativistic twin paradox without mathematical equations, this novel model can explain to high school pupils the most difficult aspect at the core of quantum mechanics, its hall mark entanglement. The young generation, having been brought up in the information age with virtual realities and all that, are anyway more able to understand that the core is not* non-locality but true modal realism, the fact that your now reading this text supervenes on ‘you’ doing something else in another part of totality. As usual, the next generation will not understand what the big problem was previous generations struggled with.
So let’s get started already:
From Sausage to Spaghetti Monster
The classical Many Worlds Wiener Sausage model is just a sausage cut lengthwise with wires. The many cuts through the sausage approach each other from the two ends of the sausage, slicing the sausage into many wedge shaped strands. Because of Einstein-locality, Alice’s end of the sausage to the left cannot know about Bob’s end to the right, about at what angles the other side’s cuts are. We will now consider that the sausage is not split into parallel stripes called “branches”, but that the universe grows those branches instead.
At first, the sausage is empty, having no ‘meat’ except maybe for tightly along the x-axis. Imagine a large number Z of new branches, wedge-shaped and labeled by their angle around the x-axis, which grow like fiber bundles of meat shooting out of the measurement events at Alice’s and Bob’s ends of the sausage. (Z may be thought of as due to neglected microscopic degrees of freedom**.)
Wedge-shaped meat fibers represent the many parallel branches of the many worlds model. They race with light velocity to Alice where a similar growth of worlds happens, this represents so called "dislocation" of decoherence. Both growths will meet somewhere between Alice and Bob, but notice that Bob’s end has a low number of wedges per angle along the b-axis and a much higher number at 45degrees to the b-axis. Alice may have her a-axis rotated so that a high number of her world fibers meet a low number of Bob’s. The worlds do not match up when they meet. Also notice that the dark green “DirectlyReal” (DR) direction points out the one real world that direct realism insists on, which is the light green glowing world.
The fibers’ number density tells us how many fibers there are per angle. It depends on the angle from the crystal’s z-axis as discussed previously. Those that grow at Alice’s end have their number density, and those that grow at Bob’s end have theirs, but they still cannot know about each other; they do not know the random relative angle between Alice’s and Bob’s measurements. Therefore, the many fibers from Alice cannot join with the ones from Bob at almost any given angle around the x-axis, because their respective number densities will be different at most angles. Most meat fibers will be left hanging and not result in parallel worlds that continuously extend from left to right.
Turning the Many World Local Realistic Model into Quantum Physics: The Crucial Step
Non-locality may suggest modifying the model by letting Bob’s world fiber growth on the right depend on Alice’s to the left. Such would bring us back to suspecting superluminal hidden information. Instead, we modify the model as naturally expected from the way we developed it up to this point.
Alice’s act of observing Bob’s measurement constitutes another measurement. A further observation with different potential outcomes is necessary, and so the fibers should naturally branch again, because that is what we assume the model does: it grows new fibers for all the potential outcomes. This should already happen when Charlotte observes both results in the middle of the sausage, because she is the first one who can know the combined results - what ever must happen must have happened by then (in case it happens only once).
The previously considered cutting automatically made more and finer meat fibers when the propagating splits overlapped in the middle of the sausage, that was the beauty of it and resulted in the non-locality, but with many cutting surfaces on each side approaching, many of them may accidentally be in the same plane (like the two in the first picture above). Every pair of such coincident cuts make only one and the same cut, not two at an angle, and so they leave only two instead of four more worlds. That would change the resulting numbers in a way that is difficult to track.
Now the sausage takes care of measurements by growing new meat fibers instead; Charlotte’s observation is a new measurement; and the fibers meet at the point where previously the apparent non-locality came about by the appearance of more strands. This all indicates that new fibers grow when the old ones meet in the middle.
If all of Alice’s fibers grow according to the number densities of Bob’s fibers when they ‘bump against each other’, and Bob’s do the same vice versa according to the number density of the fiber’s they meet coming from Alice, the new number of fibers produced will be on both sides the same; they match up exactly. The number is proportional to the product of both, Alice’s and Bob’s number densities. This product can easily lead to the correct quantum factors.
The Unimportant versus the Crucial Points
The exact number densities are unimportant. It is not important whether the branches first grew according to the number densities and then multiply further according to the product, or whether they first split into only four worlds on each side and later branch into very many*** when meeting. In both and all possibilities in between these extremes, the introduction of the last, local branching accomplishes two crucial aspects at once:
(I) It turns the model into a quantum physical one, because the numbers of branches (parallel worlds) have ratios that can lead to the empirical probability being the observed quantum probability. ("Can" lead is already enough, as any classical model can of course not for example violate the Bell inequality!)
(II) It destroys the direct reality of the model. Before the last branching, DirectlyReal (DR) could have pointed all along to a certain future fiber (the green one above), which was perhaps subsequently labeled with a little label having the correct quantum probability P written on it, but DR pointed there with the classical probability as given by the volume of the cuts V, not the quantum probability P. After the last branching, DR does not point to a certain world at all anymore. It does not know where to point.
Just before the crucial step, DR may still point to a certain one of Alice’s fibers, but afterward, it points towards all the new ones that grew out of that fiber. A committed direct realist allowing for classical indeterminism may now opine that DR could randomly select one of the new ones. Sure, why not, but these new fibers that grow for example out of a (11) volume which DR pointed to previously, are all also (11) fibers! The naïve meta-probability V(11) does not change anymore, even if these new fibers are all among each other distinguishable micro-states. The probability ‘to go from’ a (11)-branch into one of the new (11)-branches is 100%, thus V(11) remains what it was.
It might be a good idea to read on empirical probability in order to understand why the ratios of numbers of parallel worlds are the correct probabilities. Once more: If a single, classical, directly real Alice at every measurement were to randomly select one from the newly grown fibers, she would end up in the sausage volume V(11) with probability V(11), regardless of how many new branches grow later. However, nothing selects anything in the quantum universe and there is no god that counts fibers either. After doing the experiment many times, past experience tells Alice the probabilities, and those are in the overwhelming number of worlds the quantum probabilities P, not V.
There are further implications of the EPR-paradox solving model as it should accelerate a paradigm change that is prerequisite to advance fundamental physics, discussed in Einstein could have solved EPR, Why he did not.
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)
*Non-local realism may perhaps be shown to be an equally valid dual description, but we should prefer a description that rests on philosophically self-evident tautologies while conserving Einstein locality (micro-causality in particle physics). Moreover, if non-locality should come necessarily in somehow in another way later on (say via gravity, holography), this does not change any conclusions, on the contrary, that would be re arranging the chairs in the foyer of modal realism.
** If the total number of fibers is to ensure one fiber at smallest angular resolution, say an angle of 0.01 degree, V(11) at Pi/2 will need to grow 1/sin2(0.01 degree) > 108 fibers. If there is no limit resolution, Z will be infinite and the cosmological measure problem has reared its head. We may not be able to normalize the probabilities. It is not obvious that Z can be accounted for by neglected microscopic degrees of freedom. Such considerations lead to Multiple Minds Interpretations and the view that probabilities are due to what rational agents expect as for example discussed in [D. Wallace: Quantum probability from subjective likelihood: improving on Deutsch’s proof of the probability rule. (2005)]
*** When growing only four (or even just two) fibers at each end, one will get the same quantum model if the volumes V(11) and V(00) grow new fibers according to the square of the cross product of the a and b axes, which is proportional to sin2(δ), while V(01) and V(10) grow according to the square of the dot product between a and b, which is proportional to cos2(δ).