Q: How does instantaneous communication violate causality?

Physicist: You may have heard that if a technique can be found that allows you to send a signal faster than light, then you can send a signal back in time.  The very short answer for why is that relativity causes some problems when you try to define “instant”, and those problems can be used to send signals back in time.

The speed of light is crazy fast, but on large enough distances it’s agonizingly slow.  Talking to people on the Moon involves a net 2 second delay, which is a little annoying.  If you send a signal to a robot on Mars it’ll take between 8 and 40 minutes to get a response, depending on where Mars and Earth are in their orbits, which is crippling (this is a big part of why the rovers were made to be fairly independent).  So why not just create some kind of sub-space, tachyon, ultrawave relay, thingy that allows you to send FTL (faster than light) or even instantaneous signals?

Any physically realizable communication always involves some delay (left), instantaneous communication doesn’t seem to cause any problems (right), but it totally does.  In all of these pictures time moves from the bottom to the top.

Relativity does more than just place a cap on the speed that signals and objects can move.  It also muddles this question in particular, by complicating what’s meant by “instantaneous”.  One of the unfortunate results of relativity is what’s happening “now” depends on how fast (and in which direction) you’re moving.  That is, if one person sees that two events are happening at the same time (“right now”), then someone traveling at a different speed will see the two events not happening at the same time.

In particular, if you send an instantaneous signal to somewhere else, then the sending and arriving both happen “now”, but to someone else (moving relative to you) one happens before the other.

Two objects, as well as a couple moments from each of their perspectives.  (left) The red object is stationary.  (right) The blue object is stationary.  Notice that the “nows” of the two objects are skewed with respect to each other.

The details of why can be found here, but for now just keep in mind that when something passes by, the set of things that are happening “right now” for that thing happen later for you in the direction of motion.  So, if something passes left to right in front of you, then its now will, for you, happen in a moment and to the right as well as a moment ago and to the left (whens and wheres get mixed up a bit in relativity).  It takes a little pondering (done in the link above), but this result actually falls out of the whole “speed of light is the same to everyone” thing pretty quickly.

By the way, that shouldn’t make any intuitive sense, and should be difficult to keep track of, so don’t stress.

So, “instantaneous communication” isn’t as easy to define as one might think.  But, if you accept the basic tenet of relativity, that everything no matter how it’s moving is on equal footing, then one person’s instantaneous signal is merely traveling very fast to someone else, or even slightly backward in time to another someone else.  So, say you have two objects sending instantaneous (from each of their perspectives) messages back and forth.  Because of how they’re moving, while the sender perceives the message being sent and received instantly, the recipient perceives the message arriving a little after or even a little before it was sent.

Since differently moving things have different notions of now, instantaneous signals can zig-zag backwards or forwards in time.

Getting a message after it was sent is no biggie.  I mean; write yourself a letter if you want to see that in action.  But getting a message before it was sent causes issues (see for example; practically every sci-fi franchise).  What those issues are exactly depends on how time travel works (e.g., “Timecop” or “Back to the Future” rules?), and that’s wide open to debate.

There is a “cure” for faster-than-light communication causing causality violations.  There isn’t really a problem with signals going back in time, if they only go back in time somewhere else.  For example,imagine there was a magic post office in the year 1500 that sent letters from Rome (Rome) to Tenochtitlan (Mexico City) and one week back in time.  Since it took 5 weeks to cross the Atlantic, there’s no risk of paradoxes and causality violations (“Dear Ahuitzotl, in a week Giovanni Borgia is going to be killed.  Nothing you can do about it, just thought you’d like to know.”).  The real problems crop up when you can send instantaneous messages in two or more reference frames.  That allows you to bounce signals back and forth, and thus send a message to yourself in the past.  So, the fix is to have only one frame with instant communication (magic post offices only send letters in one direction).

But this cure; picking a special reference frame (a special speed) in which communication can be instantaneous, isn’t really in keeping with the spirit of relativity or observational evidence; that all speeds are equivalent.

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23 Responses to Q: How does instantaneous communication violate causality?

  1. Locutus says:

    What if it is space as the thing that is moving?

    Love Long and Prosper

  2. Gaurav Bhattacharjee says:

    Now, after looking at the word ” space as a thing that moves”,I would like to put forward a question related to Godel’s theory of a rotating universe. According to his theory, we would be able to move back in time, as we move back in space. Why would this happen?Will you please be kind enough to give me an answer to the question?

  3. The Physicist The Physicist says:

    Unfortunately, I’ve never gotten around to looking into Godel’s physics stuff. Specifically, I don’t know what he meant by “rotating space”. Since movement in general is described with respect to a fixed frame, what is meant by “rotating frame” is a probably a bit abstract.

  4. James says:

    It might just be the engineer in me trying to find ways to abuse the rules and get the universe to do what I want it to. But before different now frames, time dilation and Lorentz contraction where explained to me at the same time, when I heard an explanation about just one of them I would have thoughts like ‘well if now frames can be adjusted with just acceleration why don’t we use an accelerating telescope to get a fast time video of how a distant galaxy formed over billions of years’. Then I read an explanation of the three effects at the same time and while there may not be as many fun exploits when they all apply together it make a whole lot more sense.

    http://www.askamathematician.com/2011/01/q-why-does-relativistic-length-contraction-lorentz-contraction-happen/

  5. Locutus says:

    If instant communication violates relativity and so on, would it be possible for FTL to not be instant? I say this since a photon, from its own point of view, leaves, flies, and arrives at the same time.

  6. The Physicist The Physicist says:

    The post here is a little careful about what an “instantaneous signal” is. Clearly the time of something should be zero. But while the time light experiences getting from place to place is zero, for everyone else time passes. So, to stick to what is more intuitively meant by an instant signal, an instant signal is defined as being sent and received simultaneously from the point of view of one particular reference frame (one particular relative speed). In fact, a straight “FTL path” is only instantaneous to one frame of reference, which is what gives rise to the whole “in some frames the signal is going back in time” thing.
    There’s another old post that looks at this from another angle.

  7. Kirov says:

    I remember reading about entangled particles separated by large distances being used for FTL communication. As soon as you know the spin of one, you know the spin of the other, regardless of how far away it is. Since this allows for FTL communication, I must have something wrong. Could you explain this sometime, or link to where it’s already been explained?

  8. The Physicist The Physicist says:

    This talks about it, but you’re right; there should be a dedicated post.

  9. Alan McDougall says:

    I think consciousness must come into the equation an entangled particle will instantaneously interact with its twin , but an observer could never see this effect, because he or she are stuck in linear time; thus cause and effect can never be violated in our universe.

    Alan

  10. Kelvin says:

    Hi, talking about FTL communication, I have a simple thought experiment, suppose we can find an object say a rod made out of very hard and rigid materials (like diamons), the rod may not have to be very long, let’s say 1 meter in length, one end of the rod is attached to a button and the other end is my finger pushing the rod, when the rod is pushed, the other end should move “at the same time” and hence pressed the button. Now, since nothing travels faster than light, even at 1 meter range, if I replaced the apparatus with a torch light 1 meter away from the light sensor, it would still take about 3.33 x 10^-9 sec for light to reach the sensor. So the diamon rod seems to be able to “transmit” information faster than light since both end of the rod should travels “at the same time”?

    Well, 1 meter may be too “expensive”, but any arbitrary length the results will be still the same. The question is, and I know it’s not possible, why not? Thanks.

  11. The Physicist The Physicist says:

    There’s an old post about exactly that!

  12. Darren says:

    If every thing in the universe is rotating around some axis,planets suns solar systems -etc,and some say the universe it self rotates,?-Then the big question that science has ducked and weaved around,is still not answered and yet is taught to children in schools as a absoulute given ,-that there is no out side of the known universe.
    If the universe indeed rotates then a medium must exsist out side our universe to allow this.
    What is truth,?

  13. Alasdair says:

    Darren,
    A couple of things:
    1) Why does the Earth’s rotation have anything to do with what may or may not be “outside” the universe? I don’t follow your train of thought from one to the other.
    2) The universe is rotating, is it? Relative to what? How do you know? How COULD you know?
    3) Science has “ducked and weaved around” very little. Your very question is one that theoretical physicists around the world have pondered. They have as many guesses as there are people working on it, and we may never be able to test any of these hypotheses anyway. Unless you know of a way to get out of our universe and have a look!
    4) “Outside our universe” is a tricky concept to talk about with laymen. While there very probably is something out there, the confusing part is that no matter how far you travel in any direction, you’ll never find the edge of the universe. There isn’t one. Not from the inside, anyway! That, I think, is what you have misunderstood as “there is nothing outside the universe”.
    5) Do you think this should be taught to our kids before or after quantum mechanics? That’s taught to kids, right?

  14. Murdakah says:

    This is a bit more in the direction of travel, but the same principle applies I think.
    Say we have 2 planets, for arguments sake lets say they are 2 lightyears appart. Now from planet A and B are both stationary. A spaceship travels between the two, at 0.99c, so the time it takes to reach B is a bit more than 2 years, no problem there, still within the speed barrier. A second craft with FTL capabilities woud traverse that same distance at 2c (purely hypothetical of course), and thus halve the time the clocks on the planets measures its time between departure and arrival. So the time it takes to reach planet B from A, from either planet’s clock’s perspective is only 1 year, and would arrice there before a beam of light. The craft returns to planet A and thus the total time away from planet A should read 2 years. This violates the “speed barrier” but not really causality since the craft still arrived after it departed. So how exactly does exceeding the speed of light violate causality? I’m aware of the donkey-car and the bicycle analogy, but even then, if you would technically collide with the car before the light of you reach it, you become infinitely close, and you constantly radiate light before actually colliding. So technically the light and yourself should reach itself at the same instant, think of the (sinx)/x as x tends to 0 = 1 kind of thing. I’m sorry if this seems uninformed but i’ve been reading a shit-tonne and I can’t get my head around this.

  15. EinsteinWasRight says:

    Faster-than-light communication for sending signals instantaneously or back in time seems to be possible based on GR (general relativity):

    1. GR seems to allow faster-than-light spaceship travel, aka “Star Trek warp drives”, in theory: http://en.wikipedia.org/wiki/Alcubierre_drive

    NASA is looking into it, but there are a lot of problems of course.

    2. GR also permits wormholes and time loops, but the theoretical problems there remain scary.

    3. Distant objects in the universe move apart at speeds exceeding light due to the expansion of the universe. This effect, known as Hubble’s Law, is apparently not an inherent law of physics but rather the effects of a kind of “momentum” imparted on most space that causes it to expand. This also suggests that manipulating spacetime using GR can be used to reach superluminal speeds.

    Quantum entanglement doesn’t seem to be a useful mechanism for communicating faster than light due to the apparent randomness involved. There is also the problem that after decades of experimentation, no one has been able to prove that non-local entanglement actually exists – google “loopholes in Bell test experiments” and you will see. Einstein’s “local realism” is still compatible with all experiments up-to-date.

  16. Dan says:

    Murdakah’s question is valid and should be answered first. But let me also pose a separate, but related comment.
    Frankly, I don’t believe instantaneous communication can violate causality. First of all, a more useful definition of the term “instantaneous communication” would be information that is received at the same moment it is sent in ALL frames of reference (perhaps not observed at the same moment, but occur at the same moment, like how we know the cosmic microwave background was emitted billions of years ago as opposed to when we observe it). Let me clarify, the sender would, of course, know that the message is received immediately, regardless of the distance separating them. Additionally, the receiver, knowing that the message is transmitted instantaneously, would know that it was sent exactly when he receives it. Now, to the sender, he would observe the message being received when light from the receiver reaches him (probably well after he gets a reply, but I’ll get to that later); the receiver observes the message being sent when light from the sender reaches him. Essentially, this is where I believe most physicists get confused (and I’m a cosmologist, so I know the usual thought process). Both people “know” when sending and receiving take place, regardless of what they observe. If the receiver sends a reply instantaneously, causality is not violated for him because he got a message and replied; a linear time process. The sender doesn’t violate his causality because he necessarily receives the reply after he sent the original message. The confusing part is this: to an outside observer that is not part of the conversation, it is possible to WITNESS the receiver get a message and reply before the sender sends it. While many physicists claim this is still fine and dandy, they often obfuscate the problem based on this idea such that you could convince yourself a problem arises.
    However, remember how I noted that the sender and receiver observe that the message and its reply are sent after they receive them? And we were fine with that? Good. In fact, that is the entire situation. Regardless of velocity, both general and special relativity state that all events that happen in the same location in a given reference frame are causally linked. Meaning, that to the sender, he can never receive a reply before he sends the message; they send it, they know the other side receives it right away, then (again, regardless of reference frame) a small amount of time passes while the other side makes the reply, then the reply is sent and the sender receives it necessarily after sending the initial; in all reference frames). The fact that it is possible to be in a frame where it would seem like the reply is sent before the message is irrelevant.
    Let me give an example, the speed of sound is fixed for given atmospheric temperature and pressure. We know the speed of light is faster. Imagine you had a device that made a loud bang when you turned it on and it emitted a radio signal at the same time that turned on another similar device that you know (you know!) could only be turned on by the first device. In theory, you could be in a reference frame where you hear the bang of the second device before the bang of the first. Does this mean the second one turned on before it was told to? No, that’s just silly because we know the radio signal travels faster. The observer is just hearing the irrelevant bangs, where the radio information is what should be focused on. In essence, our situation is the same (I know the relativistic differences, but the underlying point of the metaphor remains valid). For any communication, FTL or instantaneous, it is impossible for the sender to receive a reply before sending the initial message (and I challenge anyone to give me an example contradicting that statement that is both understandable to the layman and does not rely on any other posts (it’s easy to cite another post and avoid giving the logical consideration that this requires)); that is, it is impossible unless you were to disregard a fundamental concept of relativity – an event that occurs in the same location as another but at a later time in one inertial reference frame, occurs at a later time in all inertial reference frames.

    To sum up the main point: in order for instantaneous communication to violate causality, you can boil it down to the scenario where a recipient of an initial message must send a reply BEFORE he receives the message, and it must be true for an observer in the recipient’s inertial frame. An observer in any other frame is essentially just hearing the bangs but missing the information (refer to my example above).

  17. Murdakah says:

    @Dan: I agree completely with you. And your interpretation is almost exactly what my thought process was. Again this has to do with the fact that the actual time between the messages, recieved and sent, no matter how small, won’t violate causality. It seems to me (I’m probably wong, and please correct me if I am!) like the when it seems if it violates causality is from the difference in ship-time, since the time on one space ship will move faster, and consequently will receive a message at a ship-time of say 13:00 and the the message has in fact been sent a few after from the other space ship, say at 17:00 ship time. The messagges are time stamped to make this easier to keep track of (You need to assume a third observer for this to work)

  18. Alasdair says:

    Murdakah,
    In your first comment, you imagined that the ships were taking off from two stationary planets. I would say it’s pretty much impossible for two planets to be stationary relative to each other, especially if they’re that far apart. But as to talking about the ship’s travel time, my memory of the Lorentz equations is a bit rusty, and I don’t have time to sit down and work with them just now, but I’m sure that would help here. Give me a day and I’ll get back to you.
    In your second comment, where you went wrong is in saying one ship’s clock is faster than the other. What actually happens is that each ship’s occupants see the other ship as being slow. And they’re both right. Click through this link from the article (under the second diagram: “The details of why can be found”) to read about that, but in a nutshell our old friends Alice and Bob are moving away from each other. After a while, if you ask Bob the time, he’ll tell you “it’s t=7 here, which means it’s only t=5 for Alice right now.” Hop in your Tardis to see Alice, and sure enough it’s only t=5 there. But she’ll point out that it’s only t=3 for Bob. Tardis back to Bob, and yep, t=3. Say hi to your past self while you’re there.

    Dan,
    The problem with instantaneous communication is that there’s no such thing as instantaneous, because there’s no grand, universal now. Time is a localized phenomenon, so there’s only “here-and-now,” never “there-and-now.” This isn’t just physicists getting confused because it takes time for the light to travel from an event to our eyes (I’d like to think we’re a little smarter than that), this is (to quote that article I linked) “literal and physically real.”

  19. Dan says:

    @Alasdair, You’re right, I was being overly simplistic. Physicists are much smarter than that. However, while it is true that to any observer, the concept of now is an entirely local phenomenon, one can still have something that is instantaneous the way I defined it. Let me offer 2 separate reasons.
    First (and I think this is the more understandable reason), the concept of a “local now” is entirely based on the principle that the fastest possible speed at which information can travel is light; not because of our ability to observe something, but because of the relativistic and causal effects that apply when sending information at or near the speed of light. If you pay close attention to the original progression of logical thought surrounding relativity, you see that the idea that events outside each other’s light-cones cannot be causally linked spawns from this principle AND it (the part involving the word “causality”) is only applicable to scenarios where information does not travel faster. Thus, if we start with that principle as one of our premises, it’s not surprising that we find instantaneous communication to be meaningless and FTL communication to be impossible. It is a case of “let f(x) be valid over [0,A]; determine validity of f(B>A); function is invalid”. And before you say “physicists are smarter than that”, no they aren’t. There are MANY examples in the history of science where blatant logic has been ignored (a recent, but slightly poor example is believing in the existence of magnetic monopoles, which heavily relies on div(curl(vector_potential)) != 0, which is opposite a mathematical identity).
    In fact, the concept of “now” being localized is a special case of a more generalized idea. Whatever the fastest possible speed that information can be sent at, the now for anything outside of this cone cannot be determined. If you receive a message and you know (hypothetically) that it was sent instantaneously, then you CAN deduce that wherever the sender is and whatever time his watch says, at that very instant, his finger is on the send button (I will elaborate on why his now is your now in reason 2). This is, in a way, true for any speed of information.
    Aside: Yes, it is true that for non-instantaneous messages, when you receive the message, it is impossible to determine what the sender’s watch might say, even if a time-stamp is included (excepting cases where you can predict their trajectory), but you can always be sure that at some point in your and his proper pasts, his finger was on the send button (which necessarily preserves causality).
    Thus, you can have instantaneous communication because the localization of “now” updates with the fastest speed of information transfer.
    Aside: Yes, I know relativistic effects still apply. And as long as an observer induces velocity through the EM force OR is in part composed of EM fields when moving, they will continue to experience relativistic effects near the speed of light. But for the record, that has no significant effect on communication if the information is not bounded by c.

    Reason 2: This may be a little ill-presented, but I appreciate the patience you’re giving it. Instantaneous communication is independent of what both parties’ “now” is. I’ll begin with some meaningless tautologies. Everything that exists in the universe exists in the universe. The exact state of each thing that exists in the universe (knowable/unknowable/entangled/etc.) at any arbitrary instant of time, for a specific observer, must exist exactly at that instant of time (otherwise the thing doesn’t exist). From these tautologies alone, I can conclude that regardless of what our separate “nows” might be, if you exist in the universe (even if I cannot possible know of your existence), then at my “now” (which I define as an exact instant of time, not an infinitesimal time step), you must exist in some form and as an exact state (which I might never be able to determine) simply because you exist, and a time-step of 0 is Lorentz and many other kinds of invariant. I can call the state you exist in at my now, “your now” because I know that regardless how time plays out after or before that point, at that point it is your present (i.e. now). Thus, there is, in fact, a “There-and-now”; it’s just that “now” can only refer to my now, which I can artificially impose on you.
    Now, because I can impose my now on any arbitrary existing location (by virtue of its existence), had I means of sending information instantaneously, I would be able to send it to said location at my imposed “now”, which for all intents and purposes, the receiver would consider their “now” (even if it is different). Furthermore, if you subscribe to the idea that the proper time of anything can only progress forward (a necessary criterion when developing all cosmologies), then we have essentially linked the progression of time and causality of the two locations. While time may still progress at different rates, it must now inevitably progress in the same direction. Thus, a response might not be received instantaneously, but since your time and my time must move in the same direction, I can no longer receive a response before I send my initial message; thus, preserving causality and allowing me to say “There and now”.

    If you review the procedure for defining events as space-like (the kind where “now” becomes blurry), you can observe that the “now” of two locations is impossible to determine because of the lack of a causal link between them, and there is no causal link because of the limitations imposed by the speed of light (the effects of relativity only build upon those limitations). Thus, in a hypothetical universe where I managed to send information instantaneously, the definitions describing where now is broaden enough to allow me to say that the exact moment I send the message and you receive it represents a “now” that we were lucky enough to share.

    If you happen to have a counter-point, I’d love to read it. I’m finding this to be quite fun (in an educational way).

    PS, your example was flawed. With Alice and Bob, your key word was that each “sees” the other ship’s clock as moving slower, but that’s as much an effect of light itself as relativity. The clocks might “seem” to say one thing, but in reality, at a given instant, they would both show times that are non-paradoxical (probably the same thing if they both underwent the same acceleration ala general relativity).

  20. Murdakah says:

    @Alasdair: I see what you mean but for the sake of the experiment, just assume the planets are stationary. Secondly, what about the effects of time dilation? An atom clock in the ship moving faster would literally count slower, and the one moving slower will “tick” faster. Every thing that I’ve read seems to indicate that time dilation is a litteral effect, rather than an illusion. At least, that is what everyone believes.

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  22. kk says:

    People keep getting something confused: The speed of light is the fastest possible speed BECAUSE of special relatavistic effects, not the other way around.

    What it boils down to is this: physicists were solving an equation to use fundamental constants to determine the speed of light relative to an arbitrary frame of reference … and the relative velocity of the arbitrary frame of reference cancelled out. The equation that defined the speed was solely dependent on constants. So reference and velocity don’t change it.

    That means that if I hold a flashlight in one hand the photons will travel away from me at c. But if I aim a gun in the same direction and fire … from the perspective of the bullet the photons will STILL be travelling away from it at c.

    Let’s say it was a super special magical bullet that travelled at 200,792,456.2 m/s
    This does not mean that the photons would travel 99,000,456.2 relative to the bullet … instead the bullet would observe the bullets to be travelling away;

  23. mak says:

    there is no violation between them. As relativity said no object with Mass can exceed the speed of light. It never say there is ways u can transmit information faster than the speed of light as in quantum entanglement. In fact quantum entanglement can be used to proof the validity of relativity theory eg time dilation,

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