Tuesday, May 5, 2015

Instant Messaging

Advanced Communication Processes




In this essay, I am going to describe a method that seems to be capable of sending signals across spacial distances instantly, and also describe how this can then be used to send messages backwards through time.  Although sending messages instantaneously should be something that will be realized within our lifetimes, the engineering challenges involved in sending information back in time will likely take centuries to overcome.



Instantaneous Message Transmission


The method revolves around using entangled quantons (e.g., photons, electrons, protons, etc.) to transmit information.  Quantum entanglement refers to a situation where two quantons are in a state such that the properties of one depend on the properties of the other, and this dependency holds regardless of the spatial separation of the particles.

There is a common belief that quantum entanglement cannot be used to send information because it could, in principle, be used violate causality.  Basically, causality means that causes always precede their resulting effects.  If you can send information faster than the speed of light, then the special theory of relativity shows us that there are reference frames (ways of perceiving spacetime), in which the message was received before it was sent.  This would imply that there would be ways of perceiving the universe where causality is violated.

The usual explanation given in physics classes as to why it's impossible to use entanglement to send information is that knowing what a wave function collapsed to doesn't change the fact that it does so randomly, and thus cannot transmit information [No Communication Theorem].

My understanding of the theorem is this.  If A and B are entangled quantons, and you measure A, this collapses A's wavefunction.  Because B is entangled with A, B's wavefunction also collapses.  However, B's wavefunction does so in a way that is indistinguishable whether A is being measured or not.

The thing I do not understand is why not use the fact that the state has collapsed at all, not what it has collapsed to, as the means to send information?

To be specific on how this would work, I'll link a YouTube video explaining the quantum eraser experiment.  You only need to watch the first minute and a half to understand what I am talking about:  Quantum Eraser Experiment.  If you would like more details, see the Wikipedia article: More Information on Quantum Eraser Experiment.

I will describe how instantaneous transmission of information is possible using the experimental set up in the video.  A person at M1 could send information via Morse code to another person at M2.  Specifically, have switching M1 on and off play the role of the on-off tone for Morse code, and send information that way (fringes vs no fringes).



To clearly distinguish between the on and off distributions, it can be mutually agreed upon that the particles will be sent in packets of N (where N is a number high enough to resolve which distribution is being formed).  This way, the slate is wiped clean every N particles and there is no serious confusion as to whether M1 is sending an on or off tone.  We will call a series of such packets of quantons a quanton message packet for the sake of discussion.  As an example, a quanton message packet can be used to encode messages of the form {On, Off, On On On, Off} by having the first N quantons in collapsed states, the next N in uncollapsed states, the next 3N quantons in collapsed states, and the last N quantons in uncollapsed states.  The On state would correspond to a dot (or a 0), and the On On On state would correspond to a dash (or a 1).

This would allow for information to be sent at a rate that is nearly instantaneous, primarily only being limited by the rate at which the Morse code representation of the information can be encoded/decoded.  However, if one can send information faster than the speed of light, then causality no longer applies; effects can be perceived which precede their causes.




Sending Messages Back in Time


Although a little tricky, in principle the instant communication process can be used to propagate information back in time.

To understand how this works, you will need to have a pretty good grip on is what simultaneous events look like in spacetime diagrams.  In case you need a refresher / would like an introduction to this topic, here is a link to the basics of special relativity and another for the video in the series specifically on the  relativity of simultaneity.  The important point to take away is that events that are simultaneous in reference frame A are not simultaneous in reference frame B, if B is moving relative to A.  As a coupled wavefunction (presumably) collapses instantaneously with respect to the reference frame making the measurement, these events need not be simultaneous in other reference frames.  This is what we are going to use to bounce a message backwards through time.

Consider the spacetime diagram presented below for a situation where there are two observers, O1 and O2, and the quanton emitter is placed slightly closer to O2 than O1.  On this diagram, time and space are measured in the same units, so light rays are represented as lines making a 45 degree angle with the axes.  Packets of coupled quantons will be denoted by green lines making (almost) a 45 degree angle with the axes.  Although this would be technologically very difficult to accomplish (almost 45 degree angles mean the quantons are moving at relativistic speeds; which is only easy to do for photons), it is still physically possible.


Note that although the wave function collapse is instantaneous, it still takes a finite additional amount of time for the collapsed quantons to reach the receiver.  However, this additional amount of time can be made arbitrarily small by having the emitter located arbitrarily close to the midpoint between the two observers.  This is what is meant to be conveyed by the red text.  In the limit that the emitter is as close as is possible to the center of the two while still being closer to one than the other, it effectively transmits information instantaneously.

Setting up a pair of systems, one with the emitter slightly closer to O1 and another with the emitter slightly closer to O2 would then allow O1 and O2 to communicate instantaneously with each other, we will call such a system an IMS (Instant Messaging System) for the sake of discussion.

To send messages back in time, we will also need apparatuses that will call observer stations.  An observer station is basically just a long room with an observer at each end.  This room has an IMS system so the two observers can instantly communicate with each other, but also has two windows (labelled 'a' and 'b') that can accept quantum message packets from the outside.






Consider the spacetime diagram below of a purple observer station (of length L) and a blue observer station (of length 2L) that are moving relative to one another.  The purple observer station is identical to the one pictured above, where the two lines on the spacetime diagram correspond to the observers in the station.  The situational set up for the blue observer station is analogous.  To be clear, getting macroscopic objects, such as observer stations, up to relativistic speeds is very far outside of our current technological capability.  Still, this is situational set up is physically possible in principle.  All of the smaller dots in the diagram represent the spacetime location of the events described below.




Now, for how this can be used to send information back in time.  Consider the following set of events, that allow for a generic message, that we'll refer to as X, to be sent back in time with respect to the reference frame that initially sends it.

a)  Coupled quanton packet "a" is sent out

b)  Coupled quanton packet "b" is sent out

1)  O1 collapses packet b to encode message X.

Following the purple line from (1,b) to (b,2), we reach

2)  O3 receives message X from collapsed packet b

Following the blue line from 2 to 3,

3)  O3 instantly transmists X to O4 using the station's IMS.

Following the blue line from 3 to 4,

4)  O4 collapses packet a to encode message X.

Following the blue line from 4 to 5,

5)  Wave packet a collapses and contains X simultaneous with (4) in O4's reference frame.

Following the thin blue line from 5 to 6,

6)  Packet a with X reaches O2.

Following the purple line between 6 and 7,

7)  O2 instantly transmits X to O1 using the station's IMS.

Following this chain of events, O1 recieves X at a point in its timeline before the message was sent; this information was sent back in time.

It would require technology we will probably never see in our lifetimes, but I do not see any reason why it wouldn't work.  That said, I am not well versed in relativistic quantum mechanics (just special relativity and quantum mechanics separately), and I feel I may be missing something.

The reason I feel a sense of doubt is because of the following issue.  Assume that X can take on the values 0 or 1.  If O1 receives X=0 at event 7, then what would prevent it from sending X=1 at event 1?

I cannot think of anything, but this is not logically consistent with respect to the model that gave an explanation as to why X=0 was received (namely, because it was the message sent out at event 1).

By "logically consistent" I mean that it does not produce both statements of the form "Z is true" and "Z is not true".  In the framework of a logically consistent system, only one of those statements can be true.  However, in our case, we would have that X=0 was sent at event 1 inferrable to O1 from the fact that it was received at event 7, but O1 can choose to send X=1 at event 1 instead.  However, if O1 chooses to sent X=1 instead at event 1, then O1 has direct observational evidence of this.  This then leads to a situation where O1 can infer that both X=0 at event 1 is a true statement and X=1 at event 1 (i.e. "X=0 at event 1" is not true) is also a true statement.  This is not consistent.

However, this logical inconsistency within a given timeline can be avoided if what we normally consider to be the universe (i.e. the set of all physically accessible spacetime points) is just one instantiation of a greater multiverse (i.e. the set of all possible universes).  In this case, the timeline/universe of O1 that sends X=0 at event 1 would not be the same timeline/universe as the case where O1 sends X=1 at event 1; the universe where X=0 is a true statement is not the same universe where it is a false statement [THIS NEEDS MORE FLESHING OUT].





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