Another month, another rationality quotes thread. The rules are:
- Please post all quotes separately, so that they can be upvoted or downvoted separately. (If they are strongly related, reply to your own comments. If strongly ordered, then go ahead and post them together.)
- Do not quote yourself.
- Do not quote from Less Wrong itself, HPMoR, Eliezer Yudkowsky, or Robin Hanson. If you'd like to revive an old quote from one of those sources, please do so here.
- No more than 5 quotes per person per monthly thread, please.
- Provide sufficient information (URL, title, date, page number, etc.) to enable a reader to find the place where you read the quote, or its original source if available. Do not quote with only a name.
Coincidentally, I was actually heading out to meet my dad (a physics Ph.D.), and I mentioned the paper and blog post to him to get his reaction. He asked me to send him a link, but he also pointed me at Feynman's lecture on electrostatic analogs, which is based on one of those simple ideas that invites bullet-swallowing: The same equations have the same solutions.
This is one of those ideas that I get irrationally excited about, honestly. The first thing I thought of when you described these hydrodynamic experiments was the use of similitude in experimental modeling, which is a special case of the same idea: after you work out the equations that you would need to solve to calculate (for example) the flow of air around a wing, instead of doing a lot of intractable mathematics, you rewrite the equations in terms of dimensionless parameters like the Reynolds number and put a scale model of the wing in a wind tunnel. If you adjust the velocity, pressure, &c. correctly in your scale model, you can make the equations that you would need to solve for the scale model exactly the same as the equations for the full-sized wing ... and so, when you measure a number on the scale model, you can use that number the same way that you would use the solution to your equations, and get the number for the real wing. You can do this because the same equations have the same solutions.
For that matter, one of the stories my dad wrote on his blog about his Ph.D. research mentions a conversation in which another physicist pointed out a possible source of interesting complexity in gravitational waves by metaphor to electromagnetic waves - a metaphor whose validity came from the same equations having the same solutions.
I have to say, though, that my dad does not get excited about this kind of thing, and he explained to me why in a way which parallels Feynman's remark at the end of the lecture: these physical models, these analog computations, are approximate. Feynman talks about these similarities being used to design photomultiplier tubes, but explains - in a lecture delivered before 1964, mind - that "[f]or the most accurate work, it is better to determine the fields by numerical methods, using the large electronic computing machines." And at the end of section 4.7 of the paper you linked to:
On the basis of these factors, I think I would fully endorse Brady and Anderson's conclusions in the paper: that these experiments have potential as pedagogical tools, illuminating some of the confusing aspects of quantum mechanics - such as the way multiple particles interacting produce a waveform that is nevertheless defined by a single amplitude and phase at every point. By contrast, when the blogger you link to says:
...all I can think is, "does this person understand what the word 'analogue' means?" There is no earthy reason to imagine that the force of gravity on the droplet and liquid surface should have anything to do with gravity acting on particles in quantum waveforms. Actually, it's worse than that: we can know that it does not, in the same way that, among simple harmonic oscillators, the gravity force on pendulums has nothing to do with the gravity force on a mass on a spring. They are the same equations, and the equations in the latter case don't have gravity in them ... so whatever work gravity does in the solution of the first equation is work it doesn't do in the solution of the second.
I may be doing the man a gross injustice, but this ain't no way to run a railroad.
Why draw strong conclusions? Let papers be published and conferences held. It's a neat toy to look at, though.