Those kind of mechanisms can't create the kind of correlations that are observed in real particles, so we know that something else is going on.

You can play around with this by trying to design the pair of devices that were described in my second link (https://news.ycombinator.com/item?id=35905284).

To recap, you want to design a pair of devices that each have 3 buttons labeled A, B, and C, a red LED, a green LED, and a counter. The counter starts at 1000. When you press any one of the buttons one of the LEDs flashes and the counter decrements. When the counter reaches 0 the device stops responding.

You should also specify a way that if the devices are brought together the pair of them can be reset.

You can specify any kind of non-quantum hardware you want in the devices. As much computing as you need, as much RAM and ROM and disk as you want, and physical sensors. Include clocks if you need to. You can include true random number generators. It doesn't have to be limited to current technology--it just has to be limited to known physics and not use quantum entanglement.

What are need to achieve with that hardware and whatever algorithms you specify is:

1. Suppose someone has used one of the devices, and recorded the results of a very large number of interactions.

Suppose that a statistician is given a list of 5-tuples (P, F, n, R, t) of those interactions with one of the devices, where P is which button was pressed, F is which LED flashed, n is the value on the counter when the button was pressed, and R is how many times the device has been reset (i.e., R = 0 the first 1000 times the device is used, then when it and the other device are reset R = 1 for the next 1000 uses and so on), and finally t is the time at which the button was pressed.

It should not be possible using any known statistical test on that list of 5-tuples for the statistician to distinguish the device from a device whose algorithm is simply:

if any_button_pressed():
r = uniform_true_random_from_0_to_1()
if r < 0.5:
flash(GREEN)
else:
flash(RED)

2. If the lists of 5-tuples from both devices matched up by n and R we should find that (1) if the same button was pressed on both, the same color LED flashed on both, (2) if B was pressed on one and A or C on the other, then 85.355% of the time the same color flashed on both, and (3) if A was pressed on one and C on the other than 50% of the time the same color flashed.

A couple things to note.

1. The above has to hold even if the users take the devices very far apart from each other before they start pressing buttons.

In particular the users might choose to take the devices so far apart before they start pressing buttons that each has finished their run of 1000 before any possible communications from their device could reach the other.

2. The users might wait a long time before starting a run of 1000, and they might wait a long time between presses within a run.

3. The users are determining when to press independently so you can't count on them alternating. You can't even count on them overlapping: one might do all 1000 presses before user the other starts.

4. The users might use a true random number generator to determine which buttons to press.