Reconcile time travel paradox using entanglement

Question

Imagine a crazy nut with exceptional intelligence managed to sent radiowave signals across multiple timelines, 10 years into the past and the future. That messages contained a blueprint of a time travel device that prepares and creates entanglement state of the mind between users, in short the machine will entangle the minds of the user which is separated by decades apart. But the problem is how can I sent message containing the blueprint of the machine across time before it was invented, I'm wondering how can I reconcile this paradox or I should leave this chicken and egg problem in limbo since it makes better plot point?

Since I had 2 entangled states in 2 different time, I can formulate messages and send them to and fro so no violation of causality or have I?

Answer 1

Strictly speaking, entanglement cannot be used for communication

let’s say that Alice is in Alpha Centurai while Bob is in Copenhagen. We produce these particles and send one to Alice and one to Bob. Now, when Alice measures the spin on her particle, she finds it to be up. This means that Bob must measure spin down for the total spin to be zero.

When Alice collapsed the entangled wavefunction by measuring her particle, what happened to Bob’s particle? It seems as if information is instantly transmitted across light years from Alice to Bob, telling his particle’s spin to point downwards.

Perhaps this phenomenon could be exploited to allow for faster-than-light communication

Faster-than-light communication, if it were possible, would wreak havoc with the laws of physics. Special relativity sets light-speed as the ultimate speed limit for information transmission in the Universe – and with good reason.

Without this, causality – the sequence of cause and effect – is ruined. If faster-than-light communication is possible, some observers in certain reference frames will see the signal travel back in time – and perhaps arrive at its destination before it is sent. Such a phenomenon, that would effectively allow for time-travel of signals, would present all kinds of knotty paradoxes that physics would struggle to resolve.

Luckily, it turns out that there are several reasons that this system cannot be used for faster than light communication – and laboratory tests, as well as a massive multiplayer video game have thoroughly examined various loopholes that might allow you to imagine using quantum entanglement to communicate some substantive information.

The first thing to understand is that the outcome of Alice’s measurement makes no immediate difference to Bob. Even if his particle is collapsed into a particular state, he has no way of knowing this without making a measurement. The process of measuring an entangled particle that has already collapsed into a definite state, and the process of measuring an entangled particle that has not yet collapsed are identical.

So if Bob sees that his particle is spin-down, he has no way of knowing whether this is because Alice already measured hers to be spin-up, or if he has collapsed the entangled wavefunction himself. The second measurement still appears random. Communicating information about the first measurement from Alice to Bob will be limited by light speed.

What if Alice and Bob agree in advance on who will measure their particles first, and when the particles will be measured? Again, this is no good for faster-than-light communication: Alice has no control over the outcome of the first measurement, which is still a 50-50 chance. She cannot intentionally use it to transmit a bit of data, a zero or a one, a yes or a no to Bob. Instead, regardless of what Alice does, Bob’s perception of his measurement and situation will be the same.

So, no, you can't use entanglement to send messages.

Answer 2

Consider which timeline owns the message as it transits

When does the "message I'm sending to the past" become a "message I received from the future"? Until someone actually does this we'll never know, but my hypothesis until someone proves otherwise: when you link two things across time such that they can communicate, the behavior of the message in transit is what determines paradox resolution.

Basically, it's one of four cases:

Atomic.
Ownership cleany switches as it transits

"Digital" and owned by some other timeline while in transit
(A 3rd timeline, so speak).

"Analogue". Ownership is a spectrum
A message in transit morphs ownership from sender to destination.

(Or - no ownership transfer. This is a possibility, it means that anything arriving from the future is owned by the future timeline in the present, and since it's existence changes the future, destroying the sending timeline, no message from the future can exist in the present. I'm ignoring this possibility as it means past messaging isn't possible, but we're assuming this is possible as part of the question.)

When the message arrives back 10 years ago, the receiver starts modifying their actions, creating a new timeline that may not result in the message being sent 10 years later, in which case, any evidence of the messages existence is immediately wiped from the now non-existent timeline. This results in one of 3 cases:

Atomic. The message appears to of been created out of thin air. (The thought just pops into your head randomly, you have no idea where it came from):

Digital. The message comes out of the medium it would've been put into. (A thought pops into your head that you know came from the future):

Analogue. The message morphs into existence like the timey wimey wibbly wobbly stuff it is. (The thought slowly forms in your head, and like a dream is hard to grasp and remember unless written down immediately)

All 3 of these result in past you being able to build a time-sending machine 10 years earlier, despite the sender no longer existing to send the message.

We don't know how the signal is sent between timelines, but I don't think the medium actually matters here. The message has to change which "time" it's in - regardless of the method of sending information back in time: If you're putting letters in a magic mailbox, or sending packets over an ethernet cable dragged through a wormhole, or linking two minds neuron to neuron across time, or throwing a blood-stained letter through the stargate as it wraps around the sun while it's flairing, that message still changes which timeline its in, and that determines ownership of the message.