Willie Soon sent me a link to a cute 3-weeks-old article,
For Some Reason, These Quantum Mechanics Toys Didn’t Catch On (IEEE.org)Allison Marsh described metallic element objects that are belike the only objects inwards the world's museums related to quantum mechanics!
It's a collection of 21 aluminum cubes – around of them convey a 1-inch side (boxes to learn quantum mechanics to newborns), others convey a 4-inch side (those are for the kindergartens) – which are labeled past times symbols such every bit \(\sigma_x\) together with other operators on a two-dimensional Hilbert space.
With a fourth dimension machine, Julian Schwinger could convey used these toys piece pedagogy the course of written report 251a Quantum Mechanics at Harvard because mortal created them for him after he stopped pedagogy the course. I precisely checked my mailbox – I wasn't ever pedagogy this detail course of written report (Hau together with Halperin did it when I was there) but I taught a like undergraduate course of written report 143b together with if these cubes were slow to access, I would convey used them.
When I saw the article sent past times Willie Soon for the commencement time, I was unimpressed. Why? Because I idea that the boxes were only dull, passive pieces of a metallic element that you lot may role instead of writing the operators on the two-dimensional Hilbert infinite such every bit \(\ket{+}\bra{-}\) together with their linear combinations.
However, at around moment, I lastly read the article somewhat carefully together with saw what was going on. These aluminum boxes were really active together with manipulated the 2D states inwards a agency that was equivalent to quantum mechanics on the 2-dimensional Hilbert space.
How did it work? Polarized lite was mostly going through the boxes together with at that topographic point were Polaroid polarizers inside. The photon's polarization states \(\ket x\) together with \(\ket y\) generate around other 2-dimensional Hilbert space. Photons are really sent through these toys. Well, many photons create the same affair but the mathematics remains the same. Instead of measurement probabilities, you lot may stair out the intensity of the lite at the end. That's the simplest event of a classical limit.
There is a technical newspaper inwards Physics inwards Perspective that describes these toys.
These toys never became popular. Sadly, nosotros mightiness say. But fifty-fifty though he hasn't used them, either, they stand upwards for Schwinger's school's unlike approach to pedagogy of quantum mechanics. He really wanted around quantum mechanical intuition to live the primary affair that babies (such every bit Harvard students) acquire that is related to quantum mechanics. Conventional courses don't pigment quantum mechanics every bit the "first insight inwards a chain" but every bit a "second" or "later insight inwards a chain" – every bit an extension of classical physics.
If people were starting to acquire quantum mechanics from scratch, every bit a standalone theory, they could convey a amend adventure to really empathise the 20th century theory. But they're ever learning quantum mechanics every bit if it were something "derived from classical physics" or "built on classical physics", around "classical physics plus" – together with inwards this picture, they virtually universally convey a psychological occupation amongst the "plus" because they're encouraged inwards their persuasion to translate classical physics every bit a "golden standard" that amend theories should "match". But quantum mechanics doesn't depend on whatever classical theory together with it surpasses together with partly invalidates, non only matches, the really framework of classical physics.
Homework practice for you: Can you lot figure out why you lot can't easily construct a elementary quantum reckoner out of slightly larger aluminum boxes of Schwinger's type? ;-)