The last post gave a possible answer to a very interesting question, namely “Why does the wave function collapse and where does the randomness come from?”. But we have also left out a few important details.
We have only seen a quantum measurement process for a single qubit, so what about more complex systems? There is a very elegant way to generalize the qubit measurement to systems of arbitrary size, and that is iterated bisection. Imagine the qubit process not acting on a two state system, but rather on two subspaces of a system. The result of one measurement process would then be a collapse to one subspace. This process can be iterated and surprisingly the splitting point for the subspaces and the number and order of the individual processes does not have any influence on the outcome, as long as there enough processes happening to fully reduce the state to one-dimensional outcomes.
Next, what about stability of the measurement? If you measure twice in a row, will the results be identical? The answer is yes, and in general the Born rule will hold again if the outcome of a measurement is measured once more. This is not a trivial result, and in fact it comes with an unexpected consequence concerning the observer’s memory of events. See my paper linked further down for the details.
The concept of an observer, does it not make all the observations very subjective? Is there an objective reality? Well, the observations we derived are subjective, but they are subjective in a weak way. That means, all other observers that look at the same event do get the same result in general, because they’re subject to the same constraints. So there is a universal subjective reality if you want.
So, this is not new physics, it is just an overlooked aspect of unitary quantum theory? It is new physics as it uncovers some earlier unknown consequences of observing unitary evolution and gives new mechanisms, but it is also established physics as it does not postulate anything new. It is even testable experimentally because the process of measurement is described in detail. In addition the same mechanism applied to a different scattering process can be shown to also produce two other projective outcomes that do not follow the Born rule but only work on single qubits. Those can also be verified experimentally.
Does this solve the quantum measurement problem? I think it does, but I am obviously biased. I believe it successfully follows the idea of replacing the requirement of an interpretation with an actual theory. Of course it remains to be seen if the arguments contain any factual errors.
Where can I read up on all the details?
So, finally, here is a link to my paper: http://arxiv.org/abs/1205.0293
Why is this only on arxiv and not in some peer reviewed journal? I am currently trying to get this published, but it is not easy to come up with something entirely new in a field that has been worked on for so long. The skepticism is great and many researchers follow their own school of thought without considering alternatives. This is why I chose to put it on arxiv for now and get feedback about the paper from other physicists first. This blog is to attract people to the idea and offer a gentle introduction to the derivations. I would like to know if it is well enough written to be understandable and if you consider the arguments sound. I will keep revising the paper based on the feedback I get and hopefully finally have it published with a peer reviewed journal.
This is where I need you. You can actively help me spread this idea, or contribute by giving me your feedback of any kind. You can comment here on the blog or send an email to the address on the paper.
Thank you for reading this far and please let me know what you think!