So I was reading about wave function collapse and quantum decoherence of separated entangled pairs of photons and a paradox was mentioned. Namely that measuring one of a pair determines the state of the other.

Scenario:

A pair of entangled photons are fired to the left and the right of the source. Of these two photons, one is 0° polarized and the other 90° polarized.

We have two observers on the left and right side of the source.

So let's say the observer on the right side measures the polarity of the photon and it turns out to be 90°. So the other photon is the 0° photon.

Yet, it has been proven that the photons are not determined to be 90° and 0° until the right observer measured it.

Once the right observer knows the photon is 90°, the left photon is now 0° with probability 1.

The two observers now collude beforehand, they set a time at which the measurement is to be taken. The right hand side observer will then measure the photon slightly before or slightly after that time. The left hand side observer will perform their measurement/tests exactly on the dot.

The time difference between the right and left side will be small enough that the two observers are outside each other's light cones.

So my question is:

Is it possible for the left observer to know (over a large number of measurements), if the photon they are looking at has already decohered before their measurement? (ie. did the right side observer already measure it?)

If this is possible, the left side observer could run the test across some large number of photons to determine, faster than light, whether the right side observer measured their photon(s) before or after the agreed time...

## Wave Function Collapse and information

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### Wave Function Collapse and information

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### Re: Wave Function Collapse and information

jseah wrote:So my question is:

Is it possible for the left observer to know (over a large number of measurements), if the photon they are looking at has already decohered before their measurement? (ie. did the right side observer already measure it?)

Short answer: No

Relevant cartoon (note the mouse-over text) and slightly longer answer: The no-communication theorem rules out the transfer of information (at any speed) via the mechanism that you posit.

"The age of the universe is 100 billion, if the units are dog years." - Sean Carroll

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### Re: Wave Function Collapse and information

Whether or not your partner has already measured his half of the pair, you will find that half the time you observe 0 polarization and the other half 90. You will always get the opposite result your partner does, but that doesn't help you send any information. All I know by getting a 0 is that my partner got (or will get) a 1, and all my partner knows by getting a 1 is that I got (or will get) a 0. I don't know whether it has already been measured.

- Soupspoon
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### Re: Wave Function Collapse and information

It's very much like the lighthouse beam. The beam (or lack of it) sweeps outwards from its source at SoL, yet beyond a certain distance the circumferential path of the beam (rotation*radius) is faster than light itzelf could ever be around that path, and beyond another limit is faster even than the chord-path between to such radial points, even the 2r diameter between antipodes. So imagine all the ways you can get two such distant recipients to communicate by using someone's clever alternation of beam on/off to have the beam (or lack) that passes across them to interact with how the beam/lack lands on the other (say that you know it will be on for exactly half the circular trip and off for the other half, but not where in the cycle/in which half the opposing observers lie, just that they will be in opposite phases).

And then realise that there's nothing transmitted (superluminally) between observers. They may get the state of the rotating lantern at the centre (after an exactly lightspeed-slow transmission of photons, that indicate the status of the lantern some time ago, has arrived, observed from above as a spiral of 'light landing' potentiality, expanding out into the void) and deduce the experience of the counterpart, but no unprearranged information ("If I'm lit, I'm going to <foo>!" is something that would not break causality to arrange by 'normal' means in advance, and does not even guarantee that it ever happens), but until the regular/reflected light crawls across the divide (assuming the counterpart was even still there to be potentially illuminated) you're still not getting any real information from that distance.

And then realise that there's nothing transmitted (superluminally) between observers. They may get the state of the rotating lantern at the centre (after an exactly lightspeed-slow transmission of photons, that indicate the status of the lantern some time ago, has arrived, observed from above as a spiral of 'light landing' potentiality, expanding out into the void) and deduce the experience of the counterpart, but no unprearranged information ("If I'm lit, I'm going to <foo>!" is something that would not break causality to arrange by 'normal' means in advance, and does not even guarantee that it ever happens), but until the regular/reflected light crawls across the divide (assuming the counterpart was even still there to be potentially illuminated) you're still not getting any real information from that distance.

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