[yetihehe]

If the other changed, you could ue those changes to send information by varying time between changes (pulse width modulation). Instead when you measure one you go from "not knowing which one is red or blue" to "knowing color of both".

[Tomminn]

No, just because something changes doesn't mean it can be used to send information. You need changes you can control.

The thing about the change of "colour" in this analogy is you don't know in which direction it changes. So let's say you observe you "marble" through a "purple filter", which gives has:

- a 50% chance of being transparent to your marble (corresponding to a red-blue superposition marble collapsing to a purple marble)

- a 50% chance of being opaque to your marble (corresponding to red-blue superposition marble collapsing to a green marble).

The issue is that when you learn your marble is purple, while you know with 100% certainty the marble in australia is green, there is no way you can send information to Australia using that. This is because the other 50% of the time, your marble will be green, and the marble in Australia is purple.

So if I'm sitting in Australia, when I measure the marbles in my envelopes with purple filters, all I see is purple marbles 50% of the time and green marbles 50% of the time no matter what measurements you are performing at your end. So you can't send me messages by performing measurements at your end because you can't change the statistics of those measurements.

But you'll know the answer to every measurement I performed, if you've measured the other marble with a purple filter too.

[yetihehe]

So, how "it changes from state we don't know to a different state after measurement" differs from "we don't know what state it is, but after measurement we know"? How do you know state changes after measurement when you don't know which state it is before measurement? Does it really change, or do our knowledge of that state changes? That's why I say that state doesn't change, we only know what state it is after measurement.

[liminvorous]

I think you can only tell if it’s changed by measuring the thing and comparing the results with the other person.

[yetihehe]

AFAIK you don't need to compare. It's like random number generator, but you have two complementary generators. When one generates 1, the other generates 0. You don't know what you will get next, but you know what was last and you know that other person got opposite number.

[Dylan16807]

Only if the measurements align. If they do you get perfectly correlated numbers. If the angles are 90 degrees apart you get completely unrelated numbers.

The problem comes in when the angle between your two measurements is anything else. The chance that the measurements match is based on the cosine of that angle. There's no way for this to happen if the measurements are independent.

If you try to write two equations, where the first equation takes the secret particle state and first angle and gives you 1 or 0, and the second equation takes the secret particle state and second angle and gives you 1 or 0, you won't be able to reproduce the odds you get in the real world. Only equations that know both angles will work.

[throwaway_pdp09]

You can't.

[yetihehe]

Exactly. Because they don't change. If you detect one color, it stays the same.