The young post-doctoral fellow at the podium began her speech to the audience assembled in the lecture hall.
"We had discovered a ray that apparently traveled faster than light -- specifically at ten times the speed of light. Our experiment was motivated to verify the ray's existence and speed, and test the physical and logical consequences.
"We equipped an unmanned spacecraft with an emitter and a detector, and sent that spacecraft to the L2 Lagrange Point. We also equipped an unmanned high-speed spacecraft with identical emitter and detector, sent it out about a quarter light-year away, and accelerated it to four-fifths the speed of light back toward us.
"As the high-speed spacecraft passed by the L2 spacecraft, they synchronized their clocks, labeling that time and position the zero point. Each spacecraft, upon receiving an FTL signal replied with its own signal. If no signal was received or sent within a 24-hour period, the spacecraft sent a signal.
"Unfortunately, we never received signals from the high-speed spacecraft, and the L2 spacecraft sent signals every 24 hours for the next three months.
"This experiment was an unfortunate failure."
Having completed the experimental summary, she awaited questions from the audience. A middle-aged professor raised his hand as was acknowledged. "Did your L2 detector receive anomalous signals, different from an expected signal from the high-speed spacecraft?"
The speaker replied, "The detector received numerous noise signals, which were filtered out from genuine signals. One student noticed a set of signals with a distinct pattern. The first signal came at time ten hours and twelve minutes -- that's 10.2 hours -- and again every 10.2 hours following. The particular feature, in addition to the periodicity, was that the signal was sent towards the spacecraft instead of from the spacecraft. A further feature was that the detector *amplified* the signal, despite lacking design for such amplification."
The professor replied, "May I suggest that the experiment was not a complete failure. It would be interesting to consider what would have happened had L2 sent a reply to those signals, treating them as genuine, instead at the 24-hour intervals."
The speaker said, "Um, yeah, that would be interesting."
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Comments
Time Dilation?
Or the reversal of cause and effect?
Reversal
Reversal of cause and effect was what I had originally in mine. Actually, I was aiming for a paradox: if earth didn't receive a signal from the fast spacecraft before 24 hours, it sends the signal out then. Otherwise, not. So originally, earth sent the signal at 24h. Spacecraft receives it at the calculated time, and promptly replies using its own equipment. Earth receives the signal before 24h, and therefore doesn't send the signal at 24h. Spacecraft never replies, and therefore earth sends the 24h signal.
Since the reply signal goes backwards in time in the earth's frame, I realized that signal was going from earth to spacecraft. In the spacecraft's frame, the signal isn't completely interrupted by the earth's detector, but merely weakened. Therefore, the earth's frame had an incoming signal going toward the spacecraft, and the detector amplified the signal.
I could have reintroduced the paradox by having the detector system recognize those signals as based in the spacecraft, and consequently sent a reply. That would mean that the detector receives the spacecraft's reply even earlier, which means it sent the reply earlier, etc.
Wikipedia discussed a possible form of aneutronic nuclear fusion in this reaction: p + 7Li --> 8Be --> 2 4He. The article mentioned it as ultimately failing because of an alternate charge-exchange reaction: p + 7Li --> n + 7Be. A charged pion is exchanged between the nucleon and the nucleus. In one frame, the proton emits a positive pion to become a neutron, and the nucleus absorbs the pion to become beryllium. In another frame, the lithium nucleus emits a negative pion, and the proton absorbs it to become a neutron.
In the center of mass frame, it's impossible to say which is which. All we can say is that a charged pion was exchanged.
-- Daphne Xu