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So we've arguably found that information can travel faster than the speed of light, using quantum entanglement. This can theoretically be used to create an ansible, where two devices are connected via quantum entanglement and thus changing the state of one changes the state of the other, allowing for instantaneous communication. Now, what if we just had a really, really long stick. One long enough that it takes less time to push it one centimeter (or any arbitrary length) lengthwise than for light to travel its length. Would this not create a crude ansible of sorts? Lets assume the stick is made of something very strong, and maybe very light (not sure how important that one is). Would the stick somehow compress so that light reaches the receiver before the end of the stick does? I know this is a rather absurd question, but it's been bugging me for a while now so I decided to ask. Thanks in advance for any responses! (I hope this is the right place to ask)

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Information cannot be transmitted by entanglement.

There is instantaneous collapse, but you cannot control what states the particles will collapse into, and you can’t tell after the fact if what you just observed was entangled or not. Plus, entanglement breaks on observation, so if you have to repeatedly send bits, you need to send new entangled particles, which happens slower-than-light (along timelike curves).

So…

we've arguably found that information can travel faster than the speed of light, using quantum entanglement

is a false premise.

Theoretically, a stick of infinite rigidity would react only at the speed of light. The speed of light isn’t just the speed of photons, but also causality. If I sit on the rod at position $x$ looking at you, and you push the rod at time $t$, I won’t see you push it - nor will I feel the physical effects of you pushing it - until $t+\frac{x}{c}$, in flat spacetime.

Physical effects cannot travel FTL in flat spacetime because doing so would involve moving along spacelike curves. Doing so would allow that effect to access its own past - something flagrantly-destructive to causality. As such, information and forces can’t move FTL in flat spacetime.

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