Can Analogies Reveal the Laws of Physics? | Hacker News Reader

Can Analogies Reveal the Laws of Physics?

nautil.us

50 pointsrbanffy13 comments

> Hartmann argues that experimenting on sonic black holes may indeed shed light on real ones because there might be a “common cause” underlying their similar mathematics. In the same way, yellow fingers and heart disease are both caused by smoking, and detecting one can be evidence of the other.

That seems like a terrible way to make this point. Honestly it practically argues against it.

Physical analogues occupy exactly the same epistemological status as numerical models. Before computers were used, scientists used to build physical analogues.

My favorite example: The U.S. Army Corps of Engineers Bay Model, a functional 128,000 sq. ft. hydraulic model of the San Francisco Bay.

https://en.wikipedia.org/wiki/U.S._Army_Corps_of_Engineers_B... https://www.youtube.com/watch?v=i70wkxmumAw

This is not true. With numerical models one can quantify the level of error one introduces and introduce a rigorous error analysis around the method.

You can also quantify the error introduced by physical models. For example, figuring out the amplitude of the line noise on your bank of capacitors and op-amps that are making up an analog computer. Electrical engineers know (and knew) a great deal about noise in their analog systems.

Here are some cool analog computers: http://www.analogmuseum.org/english/impressions/

You might be thinking of numerical error, which rarely dominates the full uncertainty if one is doing the computation right.

You can quantify the full uncertainty in both scale/analogue models and numerical models. In my experience the full uncertainty is much more often quantified in scale and analogue models than numerical models, by the way.

Analogous to numerical error, if the systems under study differ slightly you can quantify the error introduced from the "distortion" as it is often called in the literature.

>On the flip side, many black hole experts put no stock in the analogy and consider it potentially misleading, since it isn’t known whether Hawking’s math, upon which the analogy is based, actually does describe black holes.

That is the key issue. You can't do an experiment in a system X that can be described by similar math as system Y and conclude things about Y without first making sure that Y is actually behaving in the same way. These analogue experiments might be good tools to explore the consequences of the mathematics and come up with new theories, but in the end you only get results on system Y under the condition that your theories about it are correct. That doesn't sound too interesting, especially if you just confirm effects that you already derived theoretically. In that case you already know that if they behave according to your math then you'd see that effect.

Does this not apply even to experimental result interpretation? e.g. One can argue that the GRACE satellite program didn't image gravity, but showed the theory and the effect of the theory.

Sure, it has happened before that we found a different theory that's also compatible with the experimental evidence.

Demonstrations of effects are playing important role in teaching, so analogies may or may not reveal new laws of physics, but they certainly will inspire new scientists.

This is especially important when we're talking about something as difficult to observe, measure, and test as astronomical phenomena. Staring at

    F = G * m_1 * m_2 / r^2

may not provide an intuitive sense of what's happening for many students.

Many equations in physics are just not that complicated. A few constants, a multiplication here, a division there, and a square or square root operation describe most of the mathematics. If you can come up with a physical analogy that operates on the same mathematics (like using electric charges and Coulomb's Law - which matches the above equation - to simulate gravity), you can do interesting tests on a workbench with some wires and charged spheres where real world tests would be impractical. This is really cool and useful!

However, conveying understanding of an existing law that we already know isn't the same as revealing new physics. Coulomb's law and Newton's law of universal gravitation are the same; that's not to say you can hook up the electrical charges in a Coulomb's Law demonstrator to an electric circuit and reveal something that could be done with gravity.

https://plato.stanford.edu/entries/reasoning-analogy/

http://changingminds.org/disciplines/argument/types_reasonin...

https://en.wikipedia.org/wiki/As_above,_so_below

This might be most interesting to tackle emergent behavior theories like turbulence, where the fundamentals are known, but how they line up to cause an effect is still a mystery.

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