Please check my quantum physics browser game for accuracy (linkingideasblog.wordpress.com)

It's as easy as running '$ appletviewer URL'

  IcedTea-Web java error manual log:
  Application title was not found in manifest. Check with application vendor
  IcedTea-Web java error - for more info see itweb-settings debug options or console. See http://icedtea.classpath.org/wiki/IcedTea-Web#Filing_bugs for help.

Second edit: It's because I had OpenJDK 7 as the default JRE. It works fine when I switch it to OpenJDK 8.

Tip: stick 4 spaces before the stack trace to not munge newlines.

Edit: If I run it with appletviewer, I get a more helpful exception:

    $ appletviewer http://tropic.org.uk/~crispin/quantum/
    java.lang.UnsupportedClassVersionError: quantum/GameWindow : Unsupported major.minor version 52.0
            at java.lang.ClassLoader.defineClass1(Native Method)
    [snip]

I'm also working on a game that at one point had a quantum mechanical theme, however it is more backstory than science. Quantum Traffic Control. Watch for it on the App Store sometime in this decade. Hopefully.

Remember there's no friction so if you accelerate over half the screen you need to decelerate over the other half if you're going to stop before the other side.

Level 2 can be solved by accelerating/decelerating to follow three straight lines (east-south-west) to the goal. Alternatively if you're feeling cocky you can accelerate east then throw in some south as you approach the corner: you'll bounce off the walls and break the wavefunction a bit but about 50% of the time the goal will trigger.

If you haven't discovered already you can also skip levels from the menu ;)

It's a bunch of QM applets I created about 12 years ago to aid in visualising different aspects of quantum mechanics. I was a grad student at the time, and made these as part of a fellowship. Several of these were used in corresponding homework assignments and lectures for both grad and undergrad QM classes.

http://www.pha.jhu.edu/~javalab/

I decided to apply for this fellowship after an enlightening experience seeing the time evolution of Coherent States of a quantum simple harmonic oscillator.

You can certainly talk about it in terms of Fourier components or that sort of thing, too. There's a degree to which the uncertainty principle as applied to the position/momentum degrees of freedom is nothing but a statement about Fourier transforms. But I don't think it's a bad conceptual shorthand, especially for students who aren't yet experts in thinking about Fourier stuff.

Are you saying then that by allowing people to directly observe the wavefunction I'm not really demonstrating uncertainty at all? As that only arises when you force observation via position/momentum?

Also if a massless quantum particle is dispersionless does that mean you can say "the particle is in this small area and will stay here forever"? Doesn't that violate uncertainty?

The uncertainty of position and momentum is fundamentally about the Fourier transform, and is definitely about the time dependence of the wave function. You don't even need a full description of quantum mechanics to get the uncertainty principle, "momentum is the Fourier transform of position" gets you there immediately.

> This is not true, spreading out is due to dispersion.

In this case, for a massive particle, the spreading out is due to the uncertainty principle. That uncertainty principle might be the cause of the dispersion, but you don't need to invoke anything else to get the spreading out.

>Why you don't see particle like wave packets on water surface? Also dispersion. In fact you can create particle like waves on a guitar string, which is pretty much dispersionless. Also you can describe massless particles in QM which are also dispersionless.

You can create particle like waves on water surface, on a guitar string (which IS dispersive, just not to first order), and in massless particles. They are called solitons, and are a pretty cool area of research.

Level 8 is odd. You thought more diffraction would occur with slower speed right? In the simulation it doesn't; bounce off the left wall and hit the grating fast to complete. I have to admit this bothers me. I can only assume this is because sidebands which would otherwise hit the grating itself move inwards to hit the 2% targets or something. Not good at all from a learning point of view.

Yes, the arrow keys impose a linear potential gradient while they are being held. It fades in gradually as well so no sharp transients (unless you differentiate). Not sure if that detail was required but it's there now.

The interference effects during motion are not wall reflections as far as I can tell. Some levels such as the traps don't have walls but (imperfect) absorbers and they exhibit it just as much. You're right, it's easy to see why this occurs in the rainbow mode but not so much in the amplitude mode. Genuine physics or artifact of simulation - presumably somebody can do some calculus and work that one out!

Decoherence, I acknowledge should involve multiple quantum particles. What we do see here though is an evolution from a single particle with coherent phase, which interferes with itself, into one with incoherent phase, that doesn't. Conceptually that seems similar to decoherence.

I think all your pedagogical points are good ones btw.

Like I said to evanb, if you would like to be acknowledged for your review I'm more than happy to. Best wishes.

> Decoherence doesn’t explain, though, why the wavefunction collapses to a singular thing we call “reality”. So quantum mysticism still has room to flourish.

No. Decoherence is the thing that lets you avoid the need to collapse at all. The point of decoherence is that many quantum particles interacting together looks like a quantum superposition of many classical systems. So if you "are" one of those particles and look around, you'll see things behaving classically---only if you are "outside" (ie. have full access to the wf) can you see anything quantum going on.

If the wavefunction doesn't collapse, why does it look like it does collapse?! Well, you're inside the wavefunction. Before the different classical possibilities decohere, you wait with anticipation. After decoherence, a version of you is in each branch of the wavefunction, each observing different outcomes, wondering how the wavefunction collapsed! But, it didn't---it's just hard to see that from where you're standing.

This is the claim of the Many Worlds interpretation --- the wavefunction never collapses. Everything just evolves according to the Schrodinger equation, forever. There is no place or regime where quantum mechanics breaks down. Every branch of the wavefunction is equally real and continues to exist forever.

So, why don't we see all sorts of zany, quantum effects in our every day life? Decoherence saves the day: even with a few dozen particles the different branches of the wavefunction have decohere enough that it'd take a massive, huge, gargantuan coincidence for two parts of the wavefunction to interfere. It's still possible! But it's extremely unlikely. Now scale up to Avogadro's number of particles, and forget it: things just look classical.

> You could also massively simplify particle interactions to make some reasonable gameplay; perhaps even simulate a quantum computer. Do get in touch with me if you want to do this; I’d be keen to help.

If you can find a way to simulate an arbitrarily-sized quantum computer with a reasonable amount of computing, you will get famous. A few particles should be possible but it won't scale well. You're right to worry about how to draw it. You might consider (fixed-in-space) spin systems instead, where you can draw the density matrix with (relative) simplicity. But then you lose the moving-around-in-space intuition.

> Feynman dedicates a lot of his book to two state systems, because these are ultimately responsible for the strong and weak nuclear forces. > Nuclear forces arise when you vary the size of the system, and the two possible stationary states display slightly different energy characteristics. This means the system has a lower energy at a certain size.

Oy. This is wrong.

Two state systems are interesting in-and-of-themselves because you can exactly solve them, they have many actual instatiations in nature (in fact, anything you might consider making a qubit out of!), and they provide toy models for many kinds of other physical systems.

Nuclear forces do not arise from two state systems. There is a pecularity in nuclear physics---the proton and the neutron look (almost) exactly the same. OK, they have different electric charge, but nuclear force doesn't care about electromagnetism. What's interesting is that they have almost exactly the same mass: m_Neutron = 939 MeV, m_Proton = 938 MeV. Well, that's quite surprising! Why should that be? Most particles we know have dramatically differing masses (eg. m_electron = 0.511 MeV, etc). So, what's making these masses come out the same? Moreover, people noticed empirically that the interaction between protons and neutrons seemed to look roughly the same (once you account for electromagnetism).

This led people to hypothesize a symmetry called isospin symmetry---the symmetry between protons and neutrons [isospin]. You can make a lot of progress by assuming that protons and neutrons form two-state system and that the nuclear force doesn't care which state you're in. Then, you can incorporate the slight differences on top.

In fact, you can get a lot farther once you have this idea in hand. You realize that the pions form an iso-triplet, the delta baryons form an iso-fourplet, etc [fourplet]. Then you find particles with strangeness, and you really get going. You wind up recognizing deeper underlying patterns that reveal beautiful symmetry.

Isospin symmetry is not a true symmetry of nature, but it's a very good approximation, and it's related in some ways to weak isospin [weak].

> Base states are arbitrary things, like a trap or a goal in QMM, but you can still ask what the chances are of a particle being in one of them.

You're right that basis states can be arbitrary. However, that's not their most important characteristic. We say we have a basis if we have a set of states that covers all the possibilities and they're not redundant. That is, if any state can be written as a unique sum of basis states.

> Stationary states are more like wavefunctions in QMM that have settled into a stable condition. Their phase may go on changing, but the amplitude doesn’t.

The set of stationary states is a special basis. It's the set that when evolved in time only change by a phase, as you suggest---these states don't get mixed together when time marches on. So, how can a system "settle" into such a state? In other words, if you rewind the Schrodinger equation, what state was the system in before? Simple: it was in the same stationary state!

Because stationary states form a basis, any non-stationary state is a unique sum of stationary states. In fact, if you know this basis and their corresponding energies you know all there is to know about a system's dynamics! If you take an arbitrary state and decompose it as a sum over stationary states (which is always possible, since they form a basis) then you immediately know how that state evolves in time, because you know how the individual components evolve in time.

Since the individual stationary-state components don't mix together, the only thing that changes in time is their relative phases. So, if a system doesn't start in a stationary state, it cannot possibly reach one, without there being some kind of perturbation (ie. alteration of the system).

Postscriptum

Not having played, I can't say that it's not faithful to a deep understanding of quantum mechanics. But, I am skeptical, because your write-up seems to have a lot of confusion about what QM actually is / says. That's OK---it's a tricky subject. But I would avoid trying to push your game as a pedagogical learning tool unless it's been thoroughly vetted by actual physicists, because you could easily confuse neophytes.

In some sense, the learning approach you have laid out stresses the parts of quantum mechanics that are the least interesting and least novel---they can be understood from playing with a wave equation. What's new is superposition, commutation of operators (or failure to commute), interference. That's why most modern approaches start with two-state systems (which immediately require bras and kets) and only go to systems with spatial extent later. In other words, it's better pedagogically to understand the operating system (quantum mechanics) before you start studying particular programs (particular systems).

When you study particular systems there's a lot of intricate detail that doesn't matter for you to learn the lesson. You don't really need to know about the Laguerre polynomials or whatever. The way you learn quantum mechanics is by showing a bunch of wavefunctions are orthogonal---it's not about performing integrals. You're better off understanding orthogonality, linearity, and unitarity.

> I found myself baffled trying to understand the connection between state notation, continuous wavefunctions...

Moving from bras and kets to wavefunctions is, honestly, trivial---if you have a firm understanding of what's going on. That's why I'm nervous about trying to translate your game (which again, may be faithful to QM---I haven't played) into actual education.

[continuity] https://en.wikipedia.org/wiki/Continuity_equation#Quantum_me...

[isospin] https://en.wikip...