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David Kagan
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As I promised some time ago (see http://goo.gl/xF8d7p), I would return to discuss various aspects of my work with Jacob Barandes on interpretations of quantum theory. Over a series of posts, I'll explain why I think we need an interpretation of quantum theory, what our minimal modal interpretation is, and some critiques of other popular approaches. I'll try to keep the discussion relatively non-technical.

So, why do we need an interpretation of Quantum Theory?

The mathematics of a theory, whether it is classical Newtonian physics or quantum theory is a way of expressing relationships and definitions. The physics consists of the real-world phenomena that the theory is meant to describe. The interpretation is the glue that joins the mathematical structure to the real-world content.

Putting things this way makes it obvious that quantum theory must have an interpretation since all mathematical theories need to include some interpretation of the mathematics.

Perhaps you already understand this point, but assume that the math already comes equipped with a "standard" interpretation. "So really," you ask, "why not just stick to the standard approach to quantum theory, as laid out in most undergraduate texts?"

This attitude is not a ridiculous one, especially in light of how we typically learn Newtonian physics. In the Newtonian situation, the math still needs an interpretation, but there is a rather straightforward one available and it doesn't have any deep problems. For instance, when you were first introduced to the concept of a force as a push or a pull, that was a way of taking the symbol "F" and relating it to something in the real world---better yet, something very tangible. Things like position, velocity, and acceleration are geometrical concepts that relate very directly to the geometry of real-world things moving in space.

While the standard interpretation of Newtonian physics can be tidied up and made very precise, it is pretty robust and the bonus is that it tends to connect to various aspects of our own human experience of the world in a relatively direct way.

The situation is not really analogous in quantum theory. There is indeed a standard, textbook approach to thinking about the theory. It's an approach that works insofar as it gives us a way to extract predictions and confront the theory with observations and experiments. But it lacks a coherent, underlying notion of a real world. Thus, if you want to inject realism into how you think about quantum theory, you will be dissatisfied with the textbook approach. In addition to this issue, it's also the case that all of the interpretations of quantum theory---textbook or otherwise---do not have the direct appeal to experience that the standard interpretation of classical physics has. In fact, all consistent interpretations force you to give up on key aspects of how you think about the real world. For these reasons, the debate about quantum interpretations has raged since the very inception of quantum theory itself, and continues to be a fascinating topic explore today.

More to come soon.

#quantumphysics   #quantummechanics   #philosophy   #physics   #quantumfoundations  

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Jacob Barandes and I have posted two papers on the arXiv today detailing our new "minimal modal" interpretation of quantum theory. One paper is long:

http://arxiv.org/abs/1405.6755

The other is a more concise description:

http://arxiv.org/abs/1405.6754

Don't be put off by the word 'modal'! It merely means that our interpretation is decidedly a "single-world" one, in which we clearly distinguish between possible outcomes versus actual ones. It is neither instrumentalist (which does not posit anything about the underlying ontology of our universe), nor is it many-worldish.

Our interpretation should feel familiar and relatively intuitive to the practicing physicist. The goal was to develop a precise, realist interpretation in which collapse is replaced with an underlying dynamics. We found that this could be done with a minimal set of new ingredients added to those found in the standard, density-matrix formulation of quantum theory. Furthermore, although the ingredients are inherently quantum in nature, they are clearly motivated by classical counterparts.

While describing the motivation and formulation of our new interpretation, we also present a critique of some of the more popular interpretations (Bohmian quantum theory and the many-worlds interpretation in particular).

We make sure that our interpretation does not violate any of the well-known no-go theorems (such as Bell's) and that it provides consistent resolutions of various apparent paradoxes (such as the one involving Schrodinger's poor cat).

Please take a look! If you are in a rush, read the shorter version. If you want a more in depth perspective look at the longer one. I welcome your comments and questions!

In some future posts, I'll provide a more detailed description of the interpretation.


#spnetwork arxiv:1405.6755 arxiv:1405.6754

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Apparently those faster-than-light neutrinos appear to be the result of a loose fiber optic cable! (Mind you, we should all wait for an official announcement).

http://blogs.discovermagazine.com/cosmicvariance/2012/02/22/neutrinos-and-cables/

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Brian Greene, Pontus Ahlqvist, and I have a new paper out on the impact that warping of extra dimensions has on the statistical distribution of "vacua" or more colloquially "string theory solutions". You can check it out here

http://arxiv.org/abs/1202.3172

I'll likely do a post or two trying to explain the paper in plainer language on my blog. That should appear relatively shortly.

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I just wrote an article laying out some personal thoughts about Columbia's Frontiers of Science course and its place in a liberal arts education. This should mainly be of interest to other current and former Columbia students. You can find the article here:

http://www.columbiaspectator.com/2011/12/08/reflections-frontiers-science
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