My layperson understanding is it's like someone giving you a penny and they keep a penny. One is heads and the other is tails.
When you eventually peak at your penny you know what the other is.
When you eventually peak at your penny you know what the other is.
Take two entangled photons. Measuring both polarizations with horizontal/vertical polarizers, you find that horizontal polarization (h) of the first means vertical polarization (v) of the second. So far, everything is classical and analogous to the coin example. The source could just produce the pairs h/v and v/h each 50% of the time.
But now note that both h- and v-photons pass through a diagonal polarizer 50% of the time. So if you measure with diagonal polarizers you‘d classically expect no correlation. But in fact, if the first photon passes through a diagonal polarizer, the second will never pass the same diagonal polarizer, and always pass through a perpendicular-diagonal polarizer. This is impossible with just classical randomness.
Bell‘s inequality describes how strong the correlations between polarizations could be with any classical model, and in reality we measure them to be stronger than that.
how would we ever know the difference?
Quantum mechanics allows you to measure the projection of the arrow along any one axis, and you'll always get +1 or -1. If the two people with entangled particles measure along the same axis, they will always get opposite results. But they are also free to measure along different axes.
The statistics of what results the two experimenters get when they measure their particles arrows along random axes in repeated trials are not the same as what you would get if the arrows had a predetermined direction all along.
Google "Bell inequality" for details.
Imagine two dice. There's no sense in which one die has a number until you throw it and one side lands upwards.
With entanglement, you have two dice but they're correlated. For example they may always land opposite sides up.
So if you see the value of one, you also know the value of the other. No matter where it is.
The hard questions are:
1. How does one dice/particle know the other has landed/been measured? This is really just a special case of the unsolved measurement problem, but over larger than usual distances.
2. Where does the entanglement information live? If you look at a single die/particle it has no physical property that shows it's entangled. Individually, entangled and unentangled particles are absolutely identical. So you have a correlation that can't be explained by the structure of each die/particle.
IANAQP but to me this suggests that you're looking at a 4D spacetime projection of an object which exists in some higher and/or more abstract space. So there's a single object in a hypothetical Quantum Space and we're seeing two views of it in our 4D spacetime. Entanglement somehow fixes the projection in a certain orientation.
We can transmit that same information synthetically without entanglement, but it's not the same methods.
I imagine entanglement being the hardware implimented version, and current methods the generic C implimentation.
Nope. Bell Inequality: a more complex lab experiment shows that they don't hold their state, they were not "that way" before measurement.
That's the reason behind the rants about spooky action at a distance, superdeterminism, MWI, etc.
Before someone starts yelling "You can't prove that, you can't peek the quantum states, you cheater!" I'd like to point out that it's reality showing its weird face and no human-made proofs were in use.