Causality violation from FTL signaling within the same reference frame only?

[blincoln]

I apologize if this has been asked before. I searched numerous times and couldn't find any discussion on this specific topic.

Every description I've read of the impossibility of FTL signaling uses some variation of this diagram:

http://www.theculture.org/rich/sharpblue/archives/000089.html

(if the link ends up not working at some point, it's the thought experiment involving two pairs of spacecraft , with each pair sharing a reference frame between its members, but the two pairs having different reference frames, and the result being that communication to the past is allowed)

That makes sense to me, but after thinking it over for awhile, it seems to me that the specific paradox described there only rules out FTL signaling which can be used between observers in different reference frames*. That is, it rules out the faster-than-light equivalent of broadcast radio.

Is there also a paradox that arises in a hypothetical scenario where the communication mechanism only physically works if the sending and receiving party are in the same reference frame?

If I modify the standard thought experiment at the previous link with that limitation in mind, Carol sends her FTL signal to Dave at event Q, but in order to "close the loop" back to Alice, Dave would have to match reference frames with her (or use conventional, non-FTL signaling), and (unless I'm missing something, which is certainly possible) would therefore no longer be sending a signal into the past.

Again, sorry if this has come up before and I just couldn't find it.

* Obviously this assumes that communication to the past is impossible. For purposes of my question, let's assume that the laws of physics do not allow a mechanism by which causality can be violated, such as communication backwards in time.

 

[Fredrik]

Hi blincoln. Welcome to Physics Forums. I don't think there are any causality violations in that scenario*. The principle of relativity is violated instead, since physics in the inertial frame in which a stationary transmitter can send a superluminal message isn't the same as physics in other inertial frames.

*) It's obvious that no messages can be sent to an earlier point on the transmitter's world line, so there's nothing to prove unless you have a more sophisticated definition of "causality violation" than "messages can be sent into the past".

 

[blincoln]

Thanks Fredrik.

I'm mostly just trying to wrap my head around the implications of relativity and that specific paradox. Here's the thought experiment I had in mind:

Assume that it's possible to build a device which can communicate on a point-to-point basis with another similar device at faster-than-light speeds, but only if the two devices are stationary relative to each other. Then assume that there exists an arbitrarily large mesh or hub/spoke network of these devices, and that the network is accessible via conventional radio. That is, it's sort of an interstate highway for FTL communication - anyone can send a message to the closest node via radio, the network will relay it via FTL to the node closest to the intended recipient, where it will make the final hop via radio again.

In a modified version of the four-parties scenario where this hypothetical network exists, my assumption was what you state to be the case - the devices can't send a message into their own past. But does a paradox still arise in some more convoluted way (e.g. a single pair of the devices can't send a message into their own past, but Carol's radio signal to the FTL network is received by the network before Alice sends her radio signal to the network because three pairs of devices end up being involved)?

Regarding your second statement, is relativity actually violated? My (limited) understanding is that relativity forbids scenarios in which a particular viewpoint can be used to deduce which of two (or more) parties in relative motion is "really" in motion versus being at rest. But if this hypothetical signaling mechanism works equally well as long as the users are stationary relative to each other, that isn't the case - at most, all that will be revealed is that to Carol and Dave, Alice and Bob are known to be stationary relative to each other, but whether the Alice/Bob pair is in motion relative to a stationary Carol/Dave pair (or vice-versa, or both, of course) is still up for debate.

 

[Fredrik]

But does a paradox still arise in some more convoluted way (e.g. a single pair of the devices can't send a message into their own past, but Carol's radio signal to the FTL network is received by the network before Alice sends her radio signal to the network because three pairs of devices end up being involved)?

The only thing weird that can happen, as far as I can tell, is that if Alice sends a FTL message to Carol, there are inertial frames in which the message is going in the opposite direction. That would be pretty strange, but it doesn't appear to lead to any logical contradictions.

Regarding your second statement, is relativity actually violated?

Yes. Suppose e.g. that you gently accelerate the FTL message device to a different speed and let it go. By your assumption, it's no longer working properly. You could perhaps blame this on the device being "broken" by the acceleration, but that doesn't explain why it would start working again if you then accelerate it to its original velocity.

An even stronger argument is to consider two observers in two labratories with different velocities. Suppose that they build identical devices according to identical instructions. Why does only one of them work properly if physics is the same in all inertial frames?

 

[blincoln]

The only thing weird that can happen, as far as I can tell, is that if Alice sends a FTL message to Carol, there are inertial frames in which the message is going in the opposite direction. That would be pretty strange, but it doesn't appear to lead to any logical contradictions.

OK, thank you. That's what I thought, but since I'm no expert in the area, I wanted to make sure I wasn't missing anything.

An even stronger argument is to consider two observers in two labratories with different velocities. Suppose that they build identical devices according to identical instructions. Why does only one of them work properly if physics is the same in all inertial frames?

I think I phrased part of my description poorly, but it may also help for me to explain the reason I got into this line of thinking as well.

If it helps, consider instead that what I've been describing as a "pair" of devices is really just one mechanism that has a whole lot of mostly-empty space in between two parts (or three, really, which I'll get to in a moment). So if your two observers build identical mechanisms in their own inertial frame, those mechanisms will work for both of them, but they won't be able to communicate with each other using them (unless they match frames).

(Begin tangent)

The reason I started thinking about this - and I don't want to go off on too much of a tangent here, especially since it would belong more in the QM forum if anywhere, but I think it may help clarify things - is that like a lot of non-experts, I read about the delayed-choice quantum eraser and imagined something kind of like John Cramer's "retrocausality" experiment but without the ability to send a signal into the past. I didn't know about Professor Cramer until I did some web searching to see what sort of discussions there were on the subject, and found numerous examples here and on other sites (although a lot of them refer to Dopfer's earlier experiment as opposed to Cramer).

Since I just have a hobby interest in physics, my assumption was that the device I imagined was the sort of impossible object that would be the equivalent of a newcomer to computer science imagining a device that violates the halting problem (something that involved a logical contradiction), or at least explicitly violates accepted theory. IE I wanted to understand the subject better by finding out why it wouldn't work. So not only was I a little surprised that an actual physicist was working on an experiment to test something a lot like it, but also that all of the descriptions of "why it wouldn't work" relied on the ability of observers in different reference frames to communicate with each other using it. I'm a big fan of precise descriptions, and so that seemed to me like a significant loophole that wasn't discussed anywhere that I could find.

The idea that effect can actually precede cause (as opposed to an observer *perceiving* the effect occurring before the cause) isn't one I'm fond of, so unless an actual physicist proves otherwise I'm happy to accept that the standard four-parties scenario is a paradox and therefore illustrates why FTL communication between observers in different reference frames is impossible. But it still seems to me as though a system which was by its nature physically limited to communicating within one reference frame is not explicitly disallowed by relativity.

(End tangent)

OK, enough of that tangent. I'm struggling to come up with a really good analogy here, but what I have in mind (whether it works like Cramer's experiment or in a completely different way - I leave the design specifics as an exercise for the reader is a device which is physically (or even logically) limited to communication within a reference frame. Not something where the same device built in two different frames would behave differently. Sort of the opposite of how in an electric generator or microphone, the two parts *must* be moving relative to each other for anything to be transmitted, except that in this hypothetical device, relative motion would destroy/cancel out/prevent the effect rather than create it.

To take that comparison a little further, if your two observers build magnetic coils, they can generate electricity as long as they occupy different reference frames from each other. But as soon as they match velocities, the effect disappears. The same laws of physics still apply, but the ability of the equipment to generate electricity depends on their relative motion.

Note that (and this is one reason why the analogy isn't excellent) I'm not describing a mechanism which violates conservation of energy. Energy would most definitely need to be expended to run it. But the effect it was based on would depend on a lack of relative motion in a way similar to how a generator depends on relative motion.

Obviously, even if relativity doesn't explicitly forbid such a device, there may not be a physical effect that works in such a way, so it would still end up being impossible to create one (but for a very different reason). I'm just trying to figure out if it *is* forbidden in the first place, and if so, why (since this will help expand my understanding of the subject).

Sorry if I'm being dense and missing something obvious.

 

[Fredrik]

So if your two observers build identical mechanisms in their own inertial frame, those mechanisms will work for both of them, but they won't be able to communicate with each other using them (unless they match frames).

But they will be able to use them to communicate, because one of the things these devices do is to produce a "non-FTL" version of the message it has received. If they don't, they're useless to all observers. So if you're on a spaceship moving away from Earth, I can send a message to a device that you're about to pass, and you can simply read that message when you're passing it. (Just take a picture of the display if you can't read that fast). Then you can send a reply to a device that's moving with your velocity and is about to pass Earth, and I can read your reply when its passing me. Note that by the standard argument (which you seem to be familiar with...otherwise see this), I can read your reply before I sent the original message, assuming that you're moving fast enough and the FTL communication is fast enough.

 

[blincoln]

OK, after a lot of thought I believe I'm finally starting to understand.

Part of the reason I was confused was that I'd misread the diagram of the paradox. The "third leg" isn't superluminal communication - as you say, it may as well be that Dave drops a stone tablet with the message inscribed on it for Alice to find before she transmits the original copy. All that "leg" is showing is that Alice already has the message by the time she transmits the original copy.

Furthermore, the two steps which do involve FTL signaling *already* have the two parties being stationary relative to each other, so that part of my thought experiment wasn't adding anything new to the equation.

Even if the communication from Dave to Alice must take place using non-FTL means, because Alice is traveling slower than lightspeed she will receive it (doppler-shifted) before she sends the original copy.

Am I still misunderstanding anything?

Thanks again Fredrik.