On Causality
In this essay, I am going to describe a method that should be capable of sending signals backwards through time. It is not a method that will be technologically feasible any time soon, but I don't see any reason why it theoretically wouldn't work.
The method revolves around using entangled quantons (e.g., photons, electrons, protons, etc.) to transmit information. Since it is commonly believed this is impossible, I will explain why I do not hold this belief.
How to Use Entanglement to Send Information Instantaneously
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.
The basic idea behind entanglement can be illustrated by a coin flip. Say you flip a coin and catch it in mid-air. Then, you immediately place it with one side down and with the coin still covered up. When you uncover the coin, as soon as you see which side is up, you know which side is down. The faces are "entangled" in a way analogous to the way entangled quantons are; as soon as you know the property of one (i.e. it face up) you immediately know a property of the other (i.e. it is face down). The difference between coins and quantons is that you can separate quantons in some cases, and this property will still hold. The same is not true if you split a coin in half and separate the faces.
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, so it cannot be used to transmit information. A slightly more specific explanation comes from the No Communication Theorem.
To get an understanding of what is going on with the No Communication Theorem, say A and B are entangled quantons, and take it for granted that wavefunctions describe all allowable states of a particle (the latter is just a basic assumption that always applies in quantum physics). If you measure quanton A, the measurement will collapse A's wavefunction to a random allowable state. Because B is entangled with A, B's wavefunction also collapses. The reason that it is supposedly impossible to send information using entangled state collapse is that if you measure the state B has collapsed to right after A's state has collapsed, then the results of the measurement on B will be the same whether A's state has been collapsed or not.
I am saying "supposedly" because it assumes you are trying to send information using collapsed states. This is not the only approach to sending information using entanglement. Specifically, you can send information using whether or not the states have been collapsed.
To be explicit on how this would work, you will need to watch the first minute and a half of this YouTube video on the quantum eraser experiment: YouTube Video on Quantum Eraser Experiment. I'll include a few more links on the quantum eraser experiment, because it seems to validate that the approach I describe below would in fact work: YouTube Video Going Over the Experiment, Article Discussing Details of the Experiment, Wikipedia Article: More Information on Quantum Eraser Experiment,
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).
As you can see, these two distributions corresponding to "on" and "off" still have the same mean, namely the point dead between the two slits. Still, the resulting distributions are completely different and clearly distinguishable; they can be used to send signals.
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.
How to Send a Message Back in Time
Although a little tricky, in principle this instant messaging method can even 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, whenever 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 the 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 (at most) a 45 degree angle with the axes. Although achieving a 45 degree angle 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.
In this scenario, O2 is going to send a message to O1 using collapsed quanton packets.
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 IM (Instant Messaging) system for the sake of discussion.
To send messages back in time, we will also need apparatuses that we will call observer stations. An observer station is basically just a long room with an observer at each end. This room has a double IM system (one with an emitter closer to O1 and the other with an emitter closer to O2) so the two observers can instantly communicate with each other. This station is also equipped with two windows (labelled 'a' and 'b') that can accept quantum message packets from the outside IM systems.
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 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 IM system.
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 IM system.
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 in principle. 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 as to this working in practice 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 "not logically consistent" I mean that we have a case where both "Z is true" and "Z is not true" seem to follow from our assumptions. 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 inferable 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 can infer that both X=0 is a true statement and X=1 (i.e. "X=0" is not true) is also a true statement.
However, this logical inconsistency within a given timeline might 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 such a case, the timeline/universe of O1 that sends X=0 at event 1 may 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.
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Inconsistency With Free Will
The reason I feel a sense of doubt as to this working in practice 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 "not logically consistent" I mean that we have a case where both "Z is true" and "Z is not true" seem to follow from our assumptions. 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 inferable 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 can infer that both X=0 is a true statement and X=1 (i.e. "X=0" is not true) is also a true statement.
However, this logical inconsistency within a given timeline might 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 such a case, the timeline/universe of O1 that sends X=0 at event 1 may 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.
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