The science blogosphere is abuzz about Lisa Randall’s op-ed article in the New York Times. See comments at Hogg’s Universe, Not Even Wrong, Lubos Motl’s Reference Frame, and Cosmic Variance. The article just made me happy: read the following paragraph

“The uncertainty principle” is another frequently abused term. It is sometimes interpreted as a limitation on observers and their ability to make measurements. But it is not about intrinsic limitations on any one particular measurement; it is about the inability to precisely measure particular pairs of quantities simultaneously. The first interpretation is perhaps more engaging from a philosophical or political perspective. It’s just not what the science is about.

There is nothing that makes my Monday mornings brighter than a correct popular explanation of the uncertainty principle.

I assume it would be the least to expect from a practising physicist to understand the Uncertainty Principle correctly, and be able communicate said comprehension in a legible fashion.

In other news, I’m not allowed to tell you my advisor’s prize until Tuesday.

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Well, you’d be amazed how many “practicing physicists” get the uncertaintly principle wrong! I won’t name names

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That’s an excellent article. There needs to be more like it in the unintelligent design debate…

Oh yea, Dave, I was happy to see her correctly describe the uncertainty principle!

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As far as I know the interpretation was messy since the very beginning, as Pauli pointed out in his book about ‘wave mechanics’ (circa 1933).

According to Pauli quantum theorists (and also Heisenberg) used different terms, depending on the specific meaning (or interpretation) they were talking about.

Ungenauigheit = inexactness

Unbekanntheit = unknowability

Unsicherheit = uncertainty

Unbestimmtheit = indeterminacy

I do not know if, at present, we know the ultimate answers to questions like these:

- Do uncertainty relations apply to a single system or to ensembles (all in the same state)?

- Do u.r. imply a mere limitation on making certain kinds of measurements simultaneously?

- Do u.r. imply a limitation on the possible

knowledge obtainable about a system?

- Do u.r. imply a limitation on the properties

that can be ascribed to a quantum system?

s.

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scerir, interesting to hear about the uncertainty in the uncertainty principle!

Here are my answers to your questions (for fun, not religion). I’m sure these answers are very naive, and I’d love to hear others comments on these questions!

- Do uncertainty relations apply to a single system or to ensembles (all in the same state)?

The uncertainty relations apply to the statistics of multiple experiments with the same preparation. They have no meaning for a single experiment, since, from a single experiment, I can never even compute these statistics.

- Do u.r. imply a mere limitation on making certain kinds of measurements simultaneously?

Yes. Well, you ask whether they imply other things, certainly one can go from uncertainly relations to other interesting statements about quantum theory. But this is almost as broad as saying “what else does quantum theory imply?”

Also while I like Lisa’s statment of the uncertainty principle, I really also have a problem with phrasing the principle as about “simultaneous measurements.” Certainly I have no idea what this concept means. For example, consider experiements for a measurement of position and for a measurement of momentum. I can do one before the other and then take the limit as these measurements go to zero. But is it really possible to measure these two things at once? The problem, of course, is that most people think about the uncertainty principle in terms of limits on the values we ascribe to a system (like: in classical theory we can ascribe position and momentum.) But this interpretation seems to me to be way off mark. But I’m much more content with the simultaneously measurable language, than with most other language I hear about the uncertainty principle

- Do u.r. imply a limitation on the possible

knowledge obtainable about a system?

Certainly there is the notion of information disturbance in learning about the value of the amplitudes of a quantum state.

- Do u.r. imply a limitation on the properties

that can be ascribed to a quantum system?

Not as far as I understand. This question is the relm of the Kochen-Specker theorem or even Bell inequalities. But, like I said above, certainly non-commutativity is central to the KS theorem. It would be interesting to try to go from a theory with only uncertainty relations (quantum theory is not the only one!) and then derive a Kochen-Specker violation.

One problem with all these questions is that the uncertainty principle is a simple consequence of the non-commutativity of operators on our Hilbert space. And pretty much everything in quantum theory that is interesting is a result of non-commutativity. Indeed everything that is interesting in our classical world is also non-commutative (that turn the steering wheel before I push the accelerator yields far different consequence for the grandma in front of the car that if I had done these things in the opposite order!) Thus it seems arbitrary to say that the uncertainty principle has a fundamental status for helping answer the questions you ask. This would be like trying to use the fact that orbits in Newtonian gravity are ellipses to try to explain deep properties of Newtonian gravity.

Like I said, my answers are naive. One question I’ve always found fascinating is the limits of the arguments put forth by Heissenberg in his microscope thought experiment.

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Why do physicists like Michio Kaku make provacative statements as they do? In the Science Channel series “Atom”, he states, “If you want to see a physicist turn green, ask about the problem of measurement”. Is he one of the “practicing physicists” who’s got it wrong?

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