The limits of my language are the limits of my world. 3 June 2011

Friday

One of the many famous aphorisms that have been plucked out of Wittgenstein’s Tractatus Logico-Philosophicus is, “The limits of my language are the limits of my world” (“Die grenzen meiner sprache sind die grenzen meiner welt” section 5.6). Like much in the Tractatus, this gnomic aphorism invites interpretation and can never be exhausted.

One way to construe this Wittgensteinism very broadly would be to think of it as the limits of my idiom are the limits of my world, with “idiom” construed broadly to include any way of talking about the world, and not merely a particular language. If you’re of a continental persuasion, you could say the limits of my discourse are the limits of my world. It amounts to pretty much the same thing.

Particular theories about the world are idioms for talking about the world, forms of discourse, if you will. Scientific theories are scientific idioms for talking about the world. Now, scientific theories often broaden our horizons and allow us to see and to understand things of which we were previously unaware. But a scientific theory, being a particular idiom as it is, may also limit us, and limit the way we see the world.

The limitations we take upon ourselves by thinking in terms of particular theories or speaking in particular ways are human limits that we have chosen for ourselves; they are not intrinsic limitations imposed upon us by the world, and this, of course, is something that Wittgenstein wanted to bring to our explicit attention.

We very frequently mistake the idioms we employ, and the particular ways in which we understand these idioms, to constitute the very fabric of the world. When in this frame of mind we make claims for our theories that are not supported by the theories themselves, but rather reflect our particular, limited understanding of very difficult matters. This has been the case with the general theory of relativity and quantum theory, both of which are very young sciences, but which now dominate physics. Because of the dominant position of these theories, and of particular interpretations of these theories, we forget how young they are, and how far we have to go in really coming to an adequate understanding of them.

Our inadequate understanding of quantum theory, in particular, has been glossed so many times by physicists seeking to give a popular account of quantum theory that one might be forgiven for supposing that quantum theory is a form of mysticism rather than of science. (For example: “For those who are not shocked when they first come across quantum theory cannot possibly have understood it.” Niels Bohr) It is inevitable that, as our understanding of the world gradually and incrementally improves, much in quantum theory that now seems inscrutable will eventually make sense to us, rather than the theory being a mere systematization of a mystery.

A recent paper in Science by Sacha Kocsis, Boris Braverman, Sylvain Ravets, Martin J. Stevens, Richard P. Mirin, L. Krister Shalm, and Aephraim M. Steinberg, Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer, points to new ways of thinking and talking about quantum theory. Here is the abstract of the paper:

“A consequence of the quantum mechanical uncertainty principle is that one may not discuss the path or “trajectory” that a quantum particle takes, because any measurement of position irrevocably disturbs the momentum, and vice versa. Using weak measurements, however, it is possible to operationally define a set of trajectories for an ensemble of quantum particles. We sent single photons emitted by a quantum dot through a double-slit interferometer and reconstructed these trajectories by performing a weak measurement of the photon momentum, postselected according to the result of a strong measurement of photon position in a series of planes. The results provide an observationally grounded description of the propagation of subensembles of quantum particles in a two-slit interferometer.”

There is a good article by Jason Palmer of the BBC, Quantum mechanics rule ‘bent’ in classic experiment, about the paper and its ramifications. Palmer writes that researchers, “say the feat ‘pulls back the veil’ on quantum reality in a way that was thought to be prohibited by theory.” If one wanted to go seeking headlines, one could say something dramatic like “Scientists break the laws of quantum physics” — you get the idea.

But what has been thought to be prohibited is in large measure a limitation upon the current language of quantum theory and, to a certain extent, an artifact of particular experiments. As more sophisticated experiments are conceived and conducted, we may someday know quite a bit more about quantum theory than has been thought possible to date.

In Palmer’s BBC story there is an excellent quote from Marlan Scully of Texas A&M University:

“The trouble with quantum mechanics is that while we’ve learned to calculate the outcomes of all sorts of experiments, we’ve lost much of our ability to describe what is really happening in any natural language.”

“I think that this has really hampered our ability to make progress, to come up with new ideas and see intuitively how new systems ought to behave.”

Progress in understanding quantum theory will, as implied by Scully, ultimately take the form of being able to discuss it in natural language and to formulate the theory in an intuitively perspicuous manner. We do not yet have the language or the concepts to do this, but each advance like the recent results reported in Science bring us a little closer, chipping away at the limits of our language that currently constitute the limits on our world.

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Since writing the above I have learned that the method used in the experiment described is called “weak measurement” (as mentioned in the abstract quoted above) and has been employed in other recent experiments (as well as having been criticized quite harshly). I have written further on weak measurement in some comments on the paper Observation of a quantum Cheshire Cat in a matter-wave interferometer experiment.

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