I've heard of the apocryphal "half-silvered mirror", but I don't get why reflection isn't an observation/interaction there either.
I know this comment is going to get lost in the noise, but that is a really excellent point, one of the best that has been raised here so far. This is a point that is often glossed over, but it is actually really important, and quite challenging to explain without getting deep into the weeds. The answer is that passing through a half-silvered mirror is an observation/interaction, but it is special because it can be practically reversed by using additional mirrors so that you can get back to a state where you can no longer tell what the outcome of the "measurement" was. All measurements are reversible in principle, but some are irreversible in practice because the number of things you'd have to reverse is just too large. And in particular, by the time a measurement has affected the state of any macroscopic system (like a ball) it is absolutely impossible to reverse in practice, though not in principle. This process of becoming irreversible-in-practice is called "decoherence".
See [1] for a more detailed explanation.
[1] http://blog.rongarret.info/2014/10/parallel-universes-and-ar...
The weird part is precisely this: "you can get back to a state where you can no longer tell what the outcome of the 'measurement' was." In other words, at lunchtime you believed that a horizontally polarised photon hit your nose at 10am in morning, and you were right. Now it's dinner time, you don't believe that, and you would be wrong if you did. If the Everett interpretation doesn't pose a massive challenge to your ideas about reality and human identity, you haven't understood it. There are physics professors who picture photons choosing which way to go at a beam splitter, then transmitting the news backwards in time, because that seems more plausible to them.
Of course, interpretations are not science. Everyone agrees how an experiment would go: any attempt to reverse the interaction of the photon with your nose and brain would fail, because thermodynamics. From a purely scientific viewpoint, it simply doesn't matter how many other yous are superposed in parallel universes, because their existence or lack of it has no consequences that (any of?) you can observe. But scientists are as fascinated by this as everyone else is.
No, it isn't. I've said nothing about many-worlds, only reversibility. And on that point everyone agrees.
> Now it's dinner time, you don't believe that
You really need to read the link above. It goes into all that in great detail. But the TL;DR here is that if it's dinner time, you haven't actually reversed the measurement, notwithstanding your current mental state with respect to the photon.
I don't like claims to authority, but maybe you should read the papers I've published about Bell inequalities too? :-p
It sounds like you're saying that, in principle, physical processes are all reversible. (Although that is often thermodynamically impossible in practice.) You're also saying that it's impossible in principle for someone to learn the result of a measurement in the morning, then unlearn it when the measurement is reversed during the afternoon. I don't see how there could be a self-consistent interpretation of quantum measurement where both those things are true.
How am I supposed to do that? You haven't provided and references and your profile is empty.
> in principle, physical processes are all reversible
Correct. This is a straightforward mathematical property of the Schroedinger equation.
> it's impossible in principle for someone to learn the result of a measurement in the morning, then unlearn it when the measurement is reversed during the afternoon
That's right. But that's not because it's impossible to reverse the measurement. It's because when you reverse a measurement you don't just "unlearn" the result.
You really should read the reference I gave you.
Here you're hitting on the heart of the Measurement Problem. In QM as it is understood today, unlike classical mechanics, there are two fundamentally different kinds of interactions between objects: quantum interactions and measurement. Quantum interactions are linear changes to the wave function, while measurements perform a non-linear update to the wave function (it becomes one for the measured value and 0 everywhere else).
Unfortunately, we do not have any theory so far that explains what is the difference between a quantum interaction and a measurement. The experiment I described works with 'machines' that interact quantically with the 'balls', but does not reproduce if the machines measure the state of the balls.
I will note that in the Many Worlds Interpretation, the measurement problem is somewhat different - it states that the state of the universe is always described by a wave function, but that parts of the wave which are sufficiently separated can no longer perceive each other somehow, usually called branching. Precisely when, why or how this happens are just as unknown, though decoherence seems to play a role
However, the wave function at different places interacts with the environment and start to shift in phase, eventually becoming unable to interfere with itself - this is called decoherence, and is a valid explanation about why and how we can't observe wave-like behaviors at large scales or in hot systems.
On the other hand, we can only postulate, based on observations, that when a particle interacts with a measurement device, the measurement device will show a single value with a probability determined by the amplitude of the particle's wave function at that point. We can postulate that the wave function collapses, or we can postulate that the device branches out into different devices in different worlds (enough such devices&worlds to achieve the probability distribution through observer selection somehow), or many other ways of formulating the Born rule. But whichever way you put it, this rule must be added to your system to predict experimental results, it does not derive from the Schrodinger equation.
I suppose it's destructive interference. It's qualitatively interesting, but its observation is complicated by orthogonal states: when you multiply orthogonal states you get zero. If you can thoroughly dismantle the state to observe it, you still can do it only on microscale, then you'll have a problem lifting it to macroscale evading destructive interference while orthogonal states are all over the place. Anyway, Schrodinger equation describes behavior of quantum states with mathematical precision and the math is quite conclusive that a linear equation behaves in a linear way. When you feel intuition doesn't get you much, you can resort to math, that's why math is seen as an indispensable part of science, because intuition isn't guaranteed to work, which is exactly your case.
>it does not derive from the Schrodinger equation
MWI derives it from the Schrodinger equation. Observation is experience of the observer and can be calculated. Unless you assume that the observer is supernatural and is thus unknowable.
This posits the notion of an observer that only observes one outcome, whereas the SE predicts that an observer will observe several different outcomes with different amplitudes. The MWI is postulating that we should only look at each outcome separately.
Furthermore, it is not possible to derive the actual probability value from the wave function amplitude without some additional postulate equivalent to the Born rule, for example that the number of observers that observe one outcome is proportional to the wave function amplitude of that outcome.
>that the number of observers that observe one outcome is proportional to the wave function amplitude of that outcome
If you mean the number, the norm of each state of observer that observes the respective outcome can be calculated. The statistics over the outcomes can be calculated too.
But this sheds no light on quantum wave functions and quantum entanglement.
The non-classical properties of entanglement start appearing once you start measuring combinations of the redness and blueness of those balls.
Let's say that instead of looking at the balls, you pass them through some machine that will let a red ball pass through with some probability P that you control; if the ball is blue, the machine will let it pass with probability 1-P. Let's say further that you have three such machines. You set the first machine to P=1. You pass each ball falling from this machine through a second machine, which has P = 0. You will never see a ball pass through to the end - if it were red, it would pass the first machine, but not the second; if it were blue, it would not pass the first machine at all.
But, let's say you now put a third machine between the other two, and you set P = 0.5. With classical balls, nothing changes - a blue ball doesn't make it past the first machine, while a red ball goes through the first, may or may not pass the second, and never makes it through the third regardless.
However, a quantum ball actually has a chance to pass through the 3 machines if you set it up this way. In fact, that chance is pretty large - more than half of the balls will start passing once you add the middle filter machine.
Still, this is easy to explain if we assume that the middle machine actually paints the ball instead of just detecting its color. This is where the entanglement experiment comes in: if you pass the pair of balls through the three machines, with ball 1 passing through machines P=1 and P=0.5, and ball 2 passing through P=1, you will find that sometimes both balls make it through, even though both balls can't be red at the same time, and they can't communicate about passing through the P=0.5 machine (you can repeat the experiment with the balls being taken arbitrarily far away before passing through the filters).