Faster-than-light communication

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The Colonial Fleet does not appear to possess the ability to communicate faster than light, other than by sending a message on a ship making an FTL jump.

The Cylons however, indicate a possible capability of FTL/instantaneous communication without sending a ship to carry the message.

When a humanoid Cylon body is killed, the mind of the Cylon downloads to a resurrection tank. For example, Boomer is shot on Galactica (Resistance), and downloads to Caprica, many light years distant ^{(TRS: "Downloaded")}. While it is possible that her conscious is transmitted to a nearby Resurrection Ship which then jumps to Caprica, this would require the Cylons to stay in the same star system as the Colonials. The resurrection of killed Cylon agents would take years if the signal had to cross interstellar space.
The Cylons have repeatedly tracked the Fleet from long distances. For example, the Olympic Carrier is able to signal the location of the Fleet to the Cylons very rapidly after a jump ^(TRS: "33"). This ceases one, rather than two jumps after the Olympic Carrier fails to jump with the Fleet. On the way to the Ionian nebula, the Fleet is fellowed by the Cylons who stay several jump points behind ^{(TRS: "Crossroads, Part I")}.
When D'Anna Biers completes her documentary, she is unable to transmit it, but is able to signal for a Cylon Raider to appear to receive transmission of the video, which is then relayed to the following Fleet. As both Raiders are destroyed, one doesn't escape with the recorded footage, but instead seems to transmit it in real-time ^{(TRS: "Final Cut")}.
On several occasions, it is indicated that Cylon basestars communicate with one another over very long distances, however this could be done by sending message probes with FTL jump capability, or a Raider, provided they keep aware of the location of the target of any message-ship.

Notes[edit]

It is possible that all these instances of seemingly fast-than-light communication are just uses of FTL-capable ships like Raiders as relays. But that would still require the Cylons to stay relatively close to the Colonial Fleet in order to pick up is transmissions, bound by the speed of light, within a reasonable time. The exact nature of these communications is not established on screen.
In contemporary physics, FTL communication is inconsistent with causality, as is FTL propulsion (however the FTL jumps used in Battlestar Galactica are only apparently faster than light as travel is instantaneous).