Tachyons & Photons: Time & Speed of Light

[Magic Man]

When tachyons became all the rage, why was the automatic assumption made that, because they seemed to travel faster than light then they must travel backwards in time?

Why wasn't it just the case that perhaps here is a particle that is just faster than light, we should update our current understanding to be that nothing can travel faster than a tachyon from now on. Why is time seen as so interwoven with the speed of light (apart from the obvious fact of the way me measure time) which is, afterall, just the speed of a particular particle - why it that particle seen as so special?

Please, I'm genuinely interested here, I'm not trying to be awkward as some may think. I don't have a background in physics so forgive my bumbling, I'm just questioning things from a laymans point of view.

Thanks.

 

[JesseM]

When tachyons became all the rage, why was the automatic assumption made that, because they seemed to travel faster than light then they must travel backwards in time?

Why wasn't it just the case that perhaps here is a particle that is just faster than light, we should update our current understanding to be that nothing can travel faster than a tachyon from now on. Why is time seen as so interwoven with the speed of light (apart from the obvious fact of the way me measure time) which is, afterall, just the speed of a particular particle - why it that particle seen as so special?

Please, I'm genuinely interested here, I'm not trying to be awkward as some may think. I don't have a background in physics so forgive my bumbling, I'm just questioning things from a laymans point of view.

Thanks.

It has to do with the relativity of simultaneity which says that different reference frames in relativity can disagree about whether events at different points in space happened at the "same time" or "different times", as well as the first of the two postulates of relativity which says the laws of physics should work the same way in every reference frame. Take a look at The equivalence of time travel and faster-than-light travel from the wikipedia time travel article and see if that helps, then you can come back here with any questions you have.

Why wasn't it just the case that perhaps here is a particle that is just faster than light, we should update our current understanding to be that nothing can travel faster than a tachyon from now on. Why is time seen as so interwoven with the speed of light (apart from the obvious fact of the way me measure time) which is, afterall, just the speed of a particular particle - why it that particle seen as so special?

Basically because it was a postulate of relativity that if every observer assumed the speed of light was the same relative to them, and that they each constructed their own coordinate systems based on this assumption, then they would each observe the same laws of physics in these coordinate systems (meaning the laws of physics have a property called 'Lorentz-symmetry', since the different coordinate systems constructed in this way are related by the Lorentz transformation), and all investigation of other laws of physics has shown that all the most fundamental laws we know about do satisfy this postulate.

 

[jcsd]

When tachyons became all the rage, why was the automatic assumption made that, because they seemed to travel faster than light then they must travel backwards in time?

Why wasn't it just the case that perhaps here is a particle that is just faster than light, we should update our current understanding to be that nothing can travel faster than a tachyon from now on. Why is time seen as so interwoven with the speed of light (apart from the obvious fact of the way me measure time) which is, afterall, just the speed of a particular particle - why it that particle seen as so special?

Please, I'm genuinely interested here, I'm not trying to be awkward as some may think. I don't have a background in physics so forgive my bumbling, I'm just questioning things from a laymans point of view.

Thanks.

Tachyon is just the name for any (hypothetical) particle that travel faster than c. There is pretty much zero evidnece to suggest that tachyons exist and plenty of reasons to believe that they don't.

c is the most important speed in the universe, it's like a speed limit. All massless particles travel at c, photons are massless.

Tachyon's violatate casuality, it is pretty easy to show in special relativity that you could use tachyon's to send messages back in time.

 

[yuiop]

Hi Magic man,

In another thread related to tachyons https://www.physicsforums.com/showthread.php?t=211093 someone posted this link http://www.theculture.org/rich/sharpblue/archives/000089.html that claims to demostrate that communication using tachyons would violate causalty.

Basically they claim the answer to the question sent by P to Q returns to P before P sent the question. See if you work out why the demonstration in that link is flawed and show that the answer actually arrives at the time the question was sent. In that demonstration they are assuming that tachyons travel infinitely faster than light and messages are sent instantaneously.

 

[yuiop]

Another thought:

Imagine there was a particle with negative gravitational mass. That particle would fall upward. It could be claimed that the particle actually falls downwards like normal matter but appers to fall upwards because it is moving backward in time (like reversing a film of a falling object). The backward time interpretation is just a mathematical trick.

 

[JesseM]

Hi Magic man,

In another thread related to tachyons https://www.physicsforums.com/showthread.php?t=211093 someone posted this link http://www.theculture.org/rich/sharpblue/archives/000089.html that claims to demostrate that communication using tachyons would violate causalty.

It only demonstrates that if tachyons obey the postulate that says they should behave the same way in every reference frame, they must violate causality. One could imagine that tachyons violated this postulate, and therefore couldn't be used to violate causality in this way.

Basically they claim the answer to the question sent by P to Q returns to P before P sent the question. See if you work out why the demonstration in that link is flawed and show that the answer actually arrives at the time the question was sent. In that demonstration they are assuming that tachyons travel infinitely faster than light and messages are sent instantaneously.

Because of the way the coordinates of different frames relate, if something travels even a little faster than light in one frame--say, 1.0000000000001c--there will be some other frame where it travels "instantaneously", i.e. any two points on its path will have the same time-coordinate in this frame.

 

[JesseM]

Imagine there was a particle with negative gravitational mass. That particle would fall upward.

No, actually it would fall downward in both Newtonian gravity and general relativity. In Newtonian gravity this isn't too hard to see--if the object's mass is m and the planet's mass is M, then the gravitational force on the object is equal to its mass m times its acceleration a, so we have ma = GmM/r^2, and you can see that m just cancels out so its acceleration a = GM/r^2 would be the same as any other massive object. The effect of the object's own negative gravitational mass is that it would repel other objects gravitationally--if you could form a planet with negative gravitational mass (which would be difficult, since the bits of the planet would repel one another rather than attract one another), then objects placed near the planet would fall upward.

It could be claimed that the particle actually falls downwards like normal matter but appers to fall upwards because it is moving backward in time (like reversing a film of a falling object).

As far as I can tell it is meaningless to say an object is "moving forwards in time" or "moving backwards in time". This was also discussed on the Tachyons travel backward in time? thread, starting in post #15.

 

[Magic Man]

Thanks very much for the replies.

So there are a few assumptions. I.e. we must take c as the absolute limit assuming, from current evidence, that photons have no mass (or at least no current measurable mass?). If, at a later date we somehow manage to measure some mass in a photon (since I assume we cannot categorically 100% state they have absolutely no mass) the theories and postulates would need to be changed?

If we assume tachyons obey our current understanding based on c then our current understanding could explain how they would travel back in time. If they don't obey the postulate or there is some other error in the postulate then they take the speed crown from c and therefore we don't have to explain any travel back in time?

 

[JesseM]

So there are a few assumptions. I.e. we must take c as the absolute limit assuming, from current evidence, that photons have no mass (or at least no current measurable mass?). If, at a later date we somehow manage to measure some mass in a photon (since I assume we cannot categorically 100% state they have absolutely no mass) the theories and postulates would need to be changed?

c is a physical constant built into all current theories, finding that photons had mass would just mean that photons move at a speed slightly less than c in our reference frame.

If we assume tachyons obey our current understanding based on c then our current understanding could explain how they would travel back in time. If they don't obey the postulate or there is some other error in the postulate then they take the speed crown from c and therefore we don't have to explain any travel back in time?

If you're saying that the existence of tachyons would disprove relativity, that's incorrect. Relativity is compatible with the notion of particles which always move faster than c, so "taking the speed crown from c" would not in itself disprove relativity. But if tachyons exist and can be used to transmit information faster than c, but cannot be used to send information backwards in time, that would mean they can't behave the same way in all reference frames, so that would disprove relativity.

 

[GDogg]

Tachyon's violatate casuality, it is pretty easy to show in special relativity that you could use tachyon's to send messages back in time.

If you're saying that the existence of tachyons would disprove relativity, that's incorrect. Relativity is compatible with the notion of particles which always move faster than c, so "taking the speed crown from c" would not in itself disprove relativity. But if tachyons exist and can be used to transmit information faster than c, but cannot be used to send information backwards in time, that would mean they can't behave the same way in all reference frames, so that would disprove relativity.

Are you sure of this? It was my understanding that a tachyon sending information back in time can always be reinterpreted as an antitachyon sending information forward in time because of the impossibility to distinguish between creation and annihilation of tachyons. This reinterpretaion done by Feinberg would preserve causality.

 

[JesseM]

Are you sure of this? It was my understanding that a tachyon sending information back in time can always be reinterpreted as an antitachyon sending information forward in time because of the impossibility to distinguish between creation and annihilation of tachyons. This reinterpretaion done by Feinberg would preserve causality.

If tachyons can be used to transmit information FTL in any frame, then there must be frames where the receiver learns the information before the sender sent it (even if the information concerned some event which had just happened in the sender's own local region), regardless of what you consider the tachyon to have been doing in between; so again, if we adopt the principle of relativity, it must be true in every frame that it is possible to send messages such that they are received before they are sent, which means that two observers moving at different speeds can transmit a message and a reply such that the first sender receives the reply before he sends the original message, a clear violation of causality.

The idea you are thinking of is not about tachyons, but about the rules for summing "Feynman diagrams" involving virtual particles in quantum field theory--you can read more about this in the virtual particles FAQ here. Basically, the idea is that in order to make predictions in quantum field theory, one must do a sum in which each term can be represented as a diagram showing some possible pattern of emission and absorption events for "virtual particles" (which come in the same types as regular measured particles--virtual photons, virtual electrons, and so forth), and these diagrams are known as Feynman diagrams. There is apparently a sort of mathematical trick in performing this sum, where if the diagram involves something like the emission of a virtual positron (the antimatter version of an electron) and its absorption at a later time, one can treat this as a virtual electron which is absorbed at an earlier time then it was emitted, which could be described as a virtual electron "going backward in time". Something like this is discussed for the case of a virtual photon (which is its own antiparticle) in this section of the FAQ:

Now, consider a virtual photon that comes from the particle on the right and is absorbed by the particle on the left. Actually calculating the photon's wave function is a little hairy; I have to consider the possibility that the photon was emitted by the other particle at any prior time. (However, I can save myself a little effort later by automatically including the possibility that the photon actually comes from the particle on the left and is absorbed by the particle on the right, with the recoil nudging the left particle: all I have to do is include situations in which the photon is "emitted on the right" in the future and goes "backward in time," and take its momentum to be minus what it really is! As long as I remember what's really going on, this trick is formally OK and saves a lot of trouble; it was introduced by Richard Feynman.)

As I said, I think this is really just sort of a mathematical trick in performing the sum, sort of like the difference between performing an integral from $$\int_{t_0}^{t_1}$$ and performing it in the opposite direction from $$\int_{t_1}^{t_0}$$. So we should be cautious about being too literal about its physical significance, especially since the virtual particles which appear in Feynman diagrams can never really be observed, so they can never be used to transmit information the way a real tachyon might (the sum over Feynman diagrams also apparently includes diagrams where virtual particles move faster than light, but it is not possible to exploit quantum field theory to transmit information FTL; this is discussed in the section of the FAQ titled 'Do they go faster than light? Do virtual particles contradict relativity or causality?')

 

[GDogg]

If tachyons can be used to transmit information FTL in any frame, then there must be frames where the receiver learns the information before the sender sent it (even if the information concerned some event which had just happened in the sender's own local region), regardless of what you consider the tachyon to have been doing in between; so again, if we adopt the principle of relativity, it must be true in every frame that it is possible to send messages such that they are received before they are sent, which means that two observers moving at different speeds can transmit a message and a reply such that the first sender receives the reply before he sends the original message, a clear violation of causality.

But using this reinterpretation they can't be used to transmit information. A detector of tachyons from the future would actually emit tachyons instead of detecting them.

I didn't invent this. It was actually published by Nature, American Journal of Physics and Physical Review. http://wildcard.ph.utexas.edu/~sudarshan/pub/1969_003.pdf".

 

[JesseM]

But using this reinterpretation they couldn't be used to transmit information. A detector of tachyons from the future would actually emit tachyons instead of detecting them.

I didn't invent this. It was actually published in 1969 in Nature. http://wildcard.ph.utexas.edu/~sudarshan/pub/1969_003.pdf"'s the article and it includes a reference to Feinberg's original article published in Physical Review and the relation to the Feynman-Stückelberg interpretation of antiparticles in Feynman diagrams that you mention.

Ah, sorry, I didn't realize you were talking about a theory where tachyons couldn't be used to transmit any information at all. Now that I think of it, I remember something like this being mentioned at the end of the tachyon article on [URL='https://www.physicsforums.com/insights/author/john-baez/']John Baez's site[/url]--apparently if you try to analyze tachyons in quantum field theory, you find either that disturbances in the field that are supposed to represent the tachyon don't actually travel faster than light in the first place, or that it is impossible to localize a tachyon to any particular region. But it doesn't seem like the article you link to is talking about the same sort of thing, since it doesn't really seem to based on quantum field theory at all (it just briefly mentions Feynman's idea about antiparticles in one paragraph after the main argument), it just seems to be reinterpreting the the tachyon's path so that the emission is always understood to be the event that happened first in whatever frame you use. I don't see how this reinterpretation alone would prevent the transmission of information faster than light though. If I have a source producing localized, FTL particles but I place an obstacle in their path to you, then I remove it as soon as I observe a certain event such as a radioactive atom decaying, then when you receive the particles you'll be able to figure out the time that this event occurred in my region, even if we pick a weird "interpretation" where the tachyons started to be emitted by you at just the right time so that they would come in and hit my source as soon as I removed the obstacle (in this interpretation I guess the tachyons would display a 'precognition' of sorts, beginning to be emitted by your detector in anticipation of when I will remove the obstacle).

 

[GDogg]

Ah, sorry, I didn't realize you were talking about a theory where tachyons couldn't be used to transmit any information at all. Now that I think of it, I remember something like this being mentioned at the end of the tachyon article on [URL='https://www.physicsforums.com/insights/author/john-baez/']John Baez's site[/url]--apparently if you try to analyze tachyons in quantum field theory, you find either that disturbances in the field that are supposed to represent the tachyon don't actually travel faster than light in the first place, or that it is impossible to localize a tachyon to any particular region. But it doesn't seem like the article you link to is talking about the same sort of thing, since it doesn't really seem to based on quantum field theory at all (it just briefly mentions Feynman's idea about antiparticles in one paragraph after the main argument), it just seems to be reinterpreting the the tachyon's path so that the emission is always understood to be the event that happened first in whatever frame you use. I don't see how this reinterpretation alone would prevent the transmission of information faster than light though.

They used the same interpretation when they were quantized in http://wildcard.ph.utexas.edu/~sudarshan/pub/1968_005.pdf".

 

[JesseM]

They used the same interpretation when they were quantized in http://wildcard.ph.utexas.edu/~sudarshan/pub/1968_005.pdf".

I just skimmed it, but I didn't see that paper addressing the question of whether tachyons could be used to transmit signals FTL either.

 

[GDogg]

I just skimmed it, but I didn't see that paper addressing the question of whether tachyons could be used to transmit signals FTL either.

Actually, I still don't see the problem if tachyons were to transmit signals FTL. The whole point of banning FTL communication is that in some reference frames the causal order would be inverted. If this reinterpretation prevents that from happening, and observers would only disagree on the direction in which the particles traveled, then what's the problem?

 

[JesseM]

Actually, I still don't see the problem if tachyons were to transmit signals FTL. The whole point of banning FTL communication is that in some reference frames the causal order would be inverted. If this reinterpretation prevents that from happening, and observers would only disagree on the direction in which the particles traveled, then what's the problem?

If it's possible to transmit information FTL, then it must be possible in some frames for an individual to get information about events that haven't happened yet, and by the principle of relativity this must be true in all frames, so that observers can get information about events which lie in their own future light cone, which I think would ordinarily be defined as a causality violation. Flipping the definition of which event is the "transmission" and which is the "reception" won't change this, it'll just mean that in some frame, my receiving a signal from you FTL can be reinterpreted as my receiver spontaneously sending a signal to you, but the event of my receiver "sending" that signal still gives me the same information about events in your vicinity immediately before you "received" it (and in this frame those events lie in the future of the time my transmitter sent the signal). That's what I meant when I said:

If I have a source producing localized, FTL particles but I place an obstacle in their path to you, then I remove it as soon as I observe a certain event such as a radioactive atom decaying, then when you receive the particles you'll be able to figure out the time that this event occurred in my region, even if we pick a weird "interpretation" where the tachyons started to be emitted by you at just the right time so that they would come in and hit my source as soon as I removed the obstacle (in this interpretation I guess the tachyons would display a 'precognition' of sorts, beginning to be emitted by your detector in anticipation of when I will remove the obstacle).

 

[GDogg]

If it's possible to transmit information FTL, then it must be possible in some frames for an individual to get information about events that haven't happened yet, and by the principle of relativity this must be true in all frames, so that observers can get information about events which lie in their own future light cone, which I think would ordinarily be defined as a causality violation. Flipping the definition of which event is the "transmission" and which is the "reception" won't change this, it'll just mean that in some frame, my receiving a signal from you FTL can be reinterpreted as my receiver spontaneously sending a signal to you, but the event of my receiver "sending" that signal still gives me the same information about events in your vicinity immediately before you "received" it (and in this frame those events lie in the future of the time my transmitter sent the signal). That's what I meant when I said:

If I have a source producing localized, FTL particles but I place an obstacle in their path to you, then I remove it as soon as I observe a certain event such as a radioactive atom decaying, then when you receive the particles you'll be able to figure out the time that this event occurred in my region, even if we pick a weird "interpretation" where the tachyons started to be emitted by you at just the right time so that they would come in and hit my source as soon as I removed the obstacle (in this interpretation I guess the tachyons would display a 'precognition' of sorts, beginning to be emitted by your detector in anticipation of when I will remove the obstacle).

I don't think that's a violation of causality because there's no causal loop. Yes, I will know about my own future, but I'd be unable to alter it. If I tried to send an FTL signal back to you (so it arrives before the atom decays and you can prevent it from happening) the obstacle would block it and you'd never find out. Unless there's a free will principle in physics, everything seems to be alright.

But now suppose there is no obstacle, and you emit a signal A when you see the radioactive decay in your region. Then I get your signal A and try to prevent the decay by sending you another FTL signal B which you will get before the decay. The end result: you will be the actual emitter of the signal B I tried to get you to absorb and this signal B will trigger the original signal A you sent when the decay happened. So even if you manage to prevent the decay, I'll still get signal A and I won't be sure if the decay actually occurs or not.

This is a variation of Ehler's Paradox, which is solved http://wildcard.ph.utexas.edu/~sudarshan/pub/1970_008.pdf" (page 144).

 

[JesseM]

I don't think that's a violation of causality because there's no causal loop. Yes, I will know about my own future, but I'd be unable to alter it.

I think physicists usually define causality violations in terms of events in the future being able to "cause" events in the past, not in terms of "changing" the past. For example, I think physicists would agree that if closed timelike curves are possible using wormholes, then this is a violation of causality, even if something like the Novikov self-consistency principle holds and it's impossible for a time traveler to actually change anything in the past.

If I tried to send an FTL signal back to you (so it arrives before the atom decays and you can prevent it from happening) the obstacle would block it and you'd never find out.

Wait, didn't you just agree people could learn about events within their own future light cone? There should be no reason you can't send a signal back to me which travels FTL in your frame and which arrives before it was sent in my frame, unless the laws of physics don't work exactly the same in every frame. There's no reason the obstacle couldn't have a tachyon detector on the front, for example (its only purpose is to block tachyons which in my frame are being emitted by my source), and in any case you don't have to send your reply back on precisely the same path (you could send your reply to a location 1 mile to the left of me, and there'd be plenty of time for an observer at that location to relay the message via an ordinary radio signal before my radioactive atom decays).

But now suppose there is no obstacle, and you emit a signal A when you see the radioactive decay in your region. Then I get your signal A and try to prevent the decay by sending you another FTL signal B which you will get before the decay. The end result: you will be the actual emitter of the signal B I tried to get you to absorb and this signal B will trigger the original signal A you sent when the decay happened.

Why would the signal B "trigger" the original signal A? And note that even if we choose an interpretation in which I "sent" signal B, the tachyons were still spontaneously emitted from my detector B in such a way as to give me a message from you about when the atom would decay. If something like the Novikov self-consistency principle held, I couldn't choose not to send that later signal A when it actually did decay, but my sending the signal wasn't really "triggered" by the signal B, it was triggered by seeing the decay.

So even if you manage to prevent the decay, I'll still get signal A and I won't be sure if the decay actually occurs or not.

Why would I send the signal A if not because of the decay? I suppose I could be lying, but that would be true in a case involving conventional radio signals as well. I don't really understand your logic here...

This is a variation of Ehler's Paradox, which is solved http://wildcard.ph.utexas.edu/~sudarshan/pub/1970_008.pdf" (page 144).

Their attempt to resolve Ehler's paradox also is just based on definitions of which event is a tachyon emission and which is a tachyon detection, but it does not address the point that a spontaneous tachyon "emission" from a detector can convey a message about the future to the person next to it. This must be true if tachyon signals can ever convey information, since for any case where an observer receives a tachyon signal and gains some new information in brain mind from it, there must be some frame in which the tachyon signal was actually emitted by her detector, but different frames can't disagree on localized physical facts like what the observer experienced in her brain, the different frames would just be differing on their "interpretation" of whether the tachyons were being emitted or received by the same detector.

 

[GDogg]

I think physicists usually define causality violations in terms of events in the future being able to "cause" events in the past, not in terms of "changing" the past. For example, I think physicists would agree that if closed timelike curves are possible using wormholes, then this is a violation of causality, even if something like the Novikov self-consistency principle holds and it's impossible for a time traveler to actually change anything in the past.

Yes, I see your point. Knowing about the future would violate causality because the cause of the emission would be in the future. And if there were a single emission I'd know about the future.

But in the article I cited, a single event triggered an emission in a range of tachyon momenta. So, couldn't it be that your attempt to send me information of a specific event in time triggered an emission of several tachyons and I'd be unable to get information about the decay? I think this is what is meant in the http://en.wikipedia.org/wiki/Tachyon#Modern_interpretation:_Quantum_field_theory_and_causality" where it says "any incoming tachyonic message would be lost against the tachyon background noise, which is an inevitable accompaniment of the uncontrollable emission".

Wait, didn't you just agree people could learn about events within their own future light cone? There should be no reason you can't send a signal back to me which travels FTL in your frame and which arrives before it was sent in my frame, unless the laws of physics don't work exactly the same in every frame. There's no reason the obstacle couldn't have a tachyon detector on the front, for example (its only purpose is to block tachyons which in my frame are being emitted by my source), and in any case you don't have to send your reply back on precisely the same path (you could send your reply to a location 1 mile to the left of me, and there'd be plenty of time for an observer at that location to relay the message via an ordinary radio signal before my radioactive atom decays).

I addressed this when I assumed there was no obstacle.

Why would the signal B "trigger" the original signal A? And note that even if we choose an interpretation in which I "sent" signal B, the tachyons were still spontaneously emitted from my detector B in such a way as to give me a message from you about when the atom would decay. If something like the Novikov self-consistency principle held, I couldn't choose not to send that later signal A when it actually did decay, but my sending the signal wasn't really "triggered" by the signal B, it was triggered by seeing the decay.

Why would I send the signal A if not because of the decay? I suppose I could be lying, but that would be true in a case involving conventional radio signals as well. I don't really understand your logic here...

It's not MY logic. The source I linked to says that your emission of signal B initiated other events at A. I'm not exactly sure why, though. I haven't read the whole thing. Isn't it stated somewhere in the article?

 

[gel]

hmm, although I don't agree with GDogg here (he seems to be giving up on free will in order to allow tachyons), I think tachyons could possibly exist as long as any FTL or backwards-time information transmitted is not immediately usable. Similar to the way information is seemingly instantaneously transmitted in some quantum experiments.

Don't think they really do, but it did get me thinking about how tachyons could exist in simple "toy" models. Seems rather long to post here, but I added it to my blog.

 

[JesseM]

Yes, I see your point. Knowing about the future would violate causality because the cause of the emission would be in the future. And if there were a single emission I'd know about the future.

But in the article I cited, a single event triggered an emission in a range of tachyon momenta. So, couldn't it be that your attempt to send me information of a specific event in time triggered an emission of several tachyons and I'd be unable to get information about the decay? I think this is what is meant in the http://en.wikipedia.org/wiki/Tachyon#Modern_interpretation:_Quantum_field_theory_and_causality" where it says "any incoming tachyonic message would be lost against the tachyon background noise, which is an inevitable accompaniment of the uncontrollable emission".

But why would it inevitably be lost? Take the perspective of a frame where the you send a tachyon signal and I receive it at a later time. Different frames can't disagree about whether I get the message, so if your message is inevitably lost in the frame where my detector actually emits the tachyons, it must be lost in this frame where you send me the message too. But why couldn't you send a really powerful burst of tachyons at me, enough so that I could distinguish them from the background noise, whatever the level of that noise?

It's not MY logic. The source I linked to says that your emission of signal B initiated other events at A. I'm not exactly sure why, though. I haven't read the whole thing. Isn't it stated somewhere in the article?

In that section, they have two events on S1's worldline A and E, and two events on S2's worldline B and D (they also have event C on S2's worldline, but that's just the event of S2 accelerating away from S1). E happens before A on S1's worldline, and B happens before D on S2's worldline. In S1's frame, A is the event of S1 sending a tachyon signal to S2, which hits S2 at event B. In S2's frame, D is the event of S2 sending a tachyon reply back to S1, which hits S1 at E (before A). In their discussion, they don't actually say that event E on the worldline of S1 "causes" the later event A, although they do say that E "affects" A (which would be true if S1 already knew what signal he was going to send at A because he had seen the reply at E), and they also say the event B on the worldline of S2 "causes" event D (which it should, since D is supposed to be a reply to the signal S2 received at B). Here's their wording:

Two possibilities are there. S1 could have seen a tachyon emission at E which is absorbed at D. He could have E also affecting A at which point a tachyon signal is sent to B and in turn causing C and D. In this case there is no causal anomaly.

But then they do later say that in S1's frame the event E "initiated other events at A", which may suggest they're saying that E actually caused the sending of the signal at A. But the wording is sort of unclear, "initiated other events" could just mean it affected the state of S1 at A (in particular, gave S1 knowledge in advance about what signal he'd send at A) but wasn't necessarily the primary cause of the tachyon emission at A. In any case, even if they do think that E somehow caused A, they don't explain why in this section.