Does instantaneous communication implies a preferrred Lorentz frame?

[Demystifier]

Nonlocal entanglement of quantum mechanics suggests the existence of instantaneous communication between distant particles. Related to this, one often hears the following argument:

Argument 1:
"If the communication is instantaneous in one Lorentz frame, then it is not instantaneous in any other Lorentz frame. Therefore, there is a preferred Lorentz frame with respect to which the communication is instantaneous. Consequently, the principle of relativity is violated."

However, such reasoning is completely incorrect. The simplest way to see this is to consider the following reasoning about classical relativistic mechanics where all massive particles move slower than light:

Argument 2:
"If a particle moves slower than light, then there is a Lorentz frame in which it is at rest. Therefore, there is a preferred Lorentz frame with respect to which the particle is at rest. Consequently, the principle of relativity is violated."

Of course, Argument 2 is erroneous. But my point is that Argument 2 is completely analogous to Argument 1. In other words, Argument 1 is erroneous for the same trivial reason as Argument 2. In both cases, a "special" Lorentz frame does NOT need to refer to ALL particles, but at each time each particle may have another its own "special" Lorentz frame. In other words, the "special" Lorentz frame is not special at all.

An explicit realization of instantaneous communication without a preferred Lorentz frame is provided by Lorentz-covariant Bohmian mechanics:
http://xxx.lanl.gov/abs/0811.1905 [Int. J. Quantum Inf. 7 (2009) 595]
Whatever you may think on Bohmian mechanics in general, this paper provides an explicit counterexample to the frequent claim that superluminal communication necessarily violates the principle of relativity. Perhaps it violates something else (like some versions of the causality principle), but not the principle of relativity.

What do you think?

 

[dx]

The principle of relativity applies to the laws of motion, not the motions themselves. Obviously, the spacetime motion of an electron or an EM field is not lorentz invariant, i.e. it does not look the same in all frames. What does look the same is the law of motion, i.e. Maxwell's theory. Instantaneous action, by definition, has to refer to a special hyperplane of simultaneity, and therefore the laws of this action, whatever they are, cannot be lorentz invariant.

Superluminal communication is not ruled out by relativity. Tachyons have Lorentz invariant dispersion relations, and therefore obey relativity. But comminication with tachyons has some peculiar features, such as receiving a reply before the message is sent, etc. So there are some difficulties with causality, but this is not strictly a requirement of relativity.

 

[Fredrik]

The principle of relativity doesn't rule out the possibility that "messages" emitted by a particle are instantaneous in that particle's rest frame, or instantaneous in some other frame that can be calculated from information about all the particles involved in the interaction. It's ruled out by the paradoxes that it leads to.

So if you want to allow this type of messages, you have to assume that the particles involved in this interaction have some pretty peculiar properties that eliminate the paradoxes. For example, the time it takes to emit or detect a single bit of information could grow rapidly with distance. You need something like that to make sure that it isn't possible to receive an answer before you ask the question.

 

[f95toli]

Nonlocal entanglement of quantum mechanics suggests the existence of instantaneous communication between distant particles.

Not necessarily. One just as well say that entangled "particles" are not really separate entities, i.e. that the classical concept of a particle is never valid. Or one could just use a non-realist non-local interpretation of QM.

Moreover, even IF there was some form of instantaneous interaction we would never be able to detect it, at least if SR is correct. This means as far as the physics of QM is concerned the idea is on the same footing as the flying spaghetti monster.
Effects that can not be detected even in principle are the realm of philosophy and religion, not physics.

 

[zonde]

Argument 1:
"If the communication is instantaneous in one Lorentz frame, then it is not instantaneous in any other Lorentz frame. Therefore, there is a preferred Lorentz frame with respect to which the communication is instantaneous. Consequently, the principle of relativity is violated."

However, such reasoning is completely incorrect.

Reasoning is a bit short in argument 1 but is not incorrect.

This is almost correct:
"If the communication is instantaneous in one Lorentz frame, then it is not instantaneous in any other Lorentz frame."
But I would add that there are Lorentz frames where this communication will have finite speed but it can be forward in time or backward in time.
So in order to avoid causality loops you should abandon relativity and allow instantaneous communication only in one "preferred" frame.

 

[zenith8]

So in order to avoid causality loops you should abandon relativity and allow instantaneous communication only in one "preferred" frame.

Well, 'abandon relativity' is a bit strong. You mean 'abandon the Einstein-Minkowski interpretation of relativity'. You just want the neo-Lorentzian interpretation of relativity - which is perfectly in agreement with experiment.. As Bell said:

I think it's a deep dilemma, and the resolution of it will not be trivial; it will require a substantial change in the way we look at things. But I would say that the cheapest resolution is something like going back to relativity as it was before Einstein, when people like Lorentz and Poincare thought that there was an aether - a preferred frame of reference - but that our measuring instruments were distorted by motion in such a way that we could not detect motion through the aether. ... that is certainly the cheapest solution. Behind the apparent Lorentz invariance of the phenomena, there is a deeper level which is not Lorentz invariant. ... what is not sufficiently emphasized in textbooks, in my opinion, is that the pre-Einstein position of Lorentz and Poincare, Larmor and Fitzgerald was perfectly coherent, and is not inconsistent with relativity theory. The idea that there is an aether, and these Fitzgerald contractions and Larmor dilations occur, and that as a result the instruments do not detect motion through the aether - that is a perfectly coherent point of view. ... The reason I want to go back to the idea of an aether here is because in these EPR experiments there is the suggestion that behind the scenes something is going faster than light. Now if all Lorentz frames are equivalent, that also means that things can go backwards in time. ... [this] introduces great problems, paradoxes of causality, and so on. And so it is precisely to avoid these that I want to say there is a real causal sequence which is defined in the aether.

So as Zonde says, superluminal signalling violates causality only if one assumes a locally Minkowski structure for spacetime, and not with Lorentz. Historically, Minkowski structure was developed for a local physics. If Nature turns out to be nonlocal, then we might consider revising that structure.

 

[Demystifier]

The principle of relativity applies to the laws of motion, not the motions themselves. Obviously, the spacetime motion of an electron or an EM field is not lorentz invariant, i.e. it does not look the same in all frames. What does look the same is the law of motion, i.e. Maxwell's theory.

I fully agree.

Instantaneous action, by definition, has to refer to a special hyperplane of simultaneity, and therefore the laws of this action, whatever they are, cannot be lorentz invariant.

No, instantaneous action does not need to refer to a SPECIAL hyperplane of simultaneity. The law of motion with instantaneous influences may look the same in all frames. The explicit example is provided in the paper mentioned in the first post above.

Superluminal communication is not ruled out by relativity. Tachyons have Lorentz invariant dispersion relations, and therefore obey relativity. But comminication with tachyons has some peculiar features, such as receiving a reply before the message is sent, etc. So there are some difficulties with causality, but this is not strictly a requirement of relativity.

With that I agree again.

 

[Demystifier]

It's ruled out by the paradoxes that it leads to.

I don't think that it leads to paradoxes. At least not if "free will" does not exist, except as an illusion.

You need something like that to make sure that it isn't possible to receive an answer before you ask the question.

I don't think there is any problem with receiving an answer before asking the question, provided that "free will" does not exist, except as an illusion.

 

[Demystifier]

So as Zonde says, superluminal signalling violates causality only if one assumes a locally Minkowski structure for spacetime, and not with Lorentz. Historically, Minkowski structure was developed for a local physics. If Nature turns out to be nonlocal, then might consider revising that structure.

What I push forward is the idea that it is causality (i.e., the principle that events can be ordered into "causes" and "consequences") that should be abandoned. If so, then both nonlocality and Minkowski structure can be retained.

 

[Demystifier]

So in order to avoid causality loops you should abandon relativity and allow instantaneous communication only in one "preferred" frame.

That is true, but one of my points is that there is no need to avoid causality loops.

 

[Demystifier]

Let me organize my line of thoughts in the following way:

Step 1: Take the laws of physics seriously!
It means that the laws of physics (whatever they are) describe EVERYTHING. Clearly, free will is not described by the laws of physics (as we currently understand them), which implies that I don't take the existence of free will seriously (except as an illusion).
Without free will, grandfather-like paradoxes are no longer paradoxes.

Step 2: Take Minkowski spacetime seriously!
It means there is no big difference between time and space (except in the sign of the metric). Therefore, there is no flow of time (because there is no flow of space), except as an illusion (due to the fact that we happen to live in a universe in which entropy increases in some direction).
Without a flow of time, the spacetime is best viewed as a static 4-dimensional structure (block universe). Consequently, there is no causality (i.e., no "causes" and "consequences"), except as an illusion.

 

[Demystifier]

Moreover, even IF there was some form of instantaneous interaction we would never be able to detect it, at least if SR is correct.

Can you explain WHY do you think so?

 

[Fredrik]

I don't think that it leads to paradoxes. At least not if "free will" does not exist, except as an illusion.
...
I don't think there is any problem with receiving an answer before asking the question, provided that "free will" does not exist, except as an illusion.

If the reply you get is "the message you sent hit your daughter in the head and killed her", and you're still unable to stop yourself from sending the message, you don't even have the illusion of free will.

 

[Demystifier]

If the reply you get is "the message you sent hit your daughter in the head and killed her", and you're still unable to stop yourself from sending the message, you don't even have the illusion of free will.

Sure, but I don't see any paradox or inconsistency with it. The paradox/inconsistency would appear, e.g., if my daughter was both alive and dead at the same time, but I see nothing like this in the scenario above.

Additional comment: If I receive such a message in real life, I will not interpret it as a true reply. Instead, I will interpret it as someones joke. If I don't have any other evidence that my daughter is already dead, I will send the message to her anyway, and I will feel that I am doing it freely (even though the free will is only an illusion).

 

[Fredrik]

Sure, but I don't see any paradox or inconsistency with it. The paradox/inconsistency would appear, e.g., if my daughter was both alive and dead at the same time, but I see nothing like this in the scenario above.

Edit: I didn't like my first reply to this, so I'm replacing it. See my next post for a paradox of that sort. Let's recap the discussion so far:

F: Superluminal communication leads to paradoxes (or long emission/detection times).
H: Not if free will is only an illusion.
F: If you can't stop yourself from sending a message (which is necessary to avoid the paradox), you don't even have the illusion of free will.
H: OK, but I still don't see a paradox.

I find that last reply (the one I quoted here) pretty confusing. Here's what I think you meant: You're saying "sure" to my observation that it's not enough to say that free will is an illusion (if we want to eliminate the paradoxes), and then you're saying that there's nothing internally inconsistent about a special relativistic universe with tachyons that can be detected in zero time, if it doesn't even have the illusion of free will. I agree that there are no internal inconsistencies there. The problem is that we do have the illusion of free will in our universe, so I don't see how your argument is relevant. If you think we don't have the illusion of free will, I have to ask you to define what you mean by "illusion of free will".

Additional comment: If I receive such a message in real life, I will not interpret it as a true reply. Instead, I will interpret it as someones joke. If I don't have any other evidence that my daughter is already dead, I will send the message to her anyway, and I will feel that I am doing it freely (even though the free will is only an illusion).

There are ways to make sure that the reply can be trusted, at least to such a degree that you would feel that sending the message would be to gamble with your daughters life with nothing substantial to gain. You can e.g. use encryption and digital signatures, and put someone you trust at the other end. That someone doesn't even have to be a person. It could be a computer that you programmed yourself, and rigged to explode if tampered with.

 

[thehangedman]

I would agree. I think this issue demonstrates how easy it is to get confused between two separate systems and one connected one. You can't think of this as two separate systems communicating, but one system just changing state. As long as the fields are "entangled" they have to be treated as a single system.

 

[Fredrik]

Consider the following scenario: (You probably have the spacetime diagram in your head already, so I won't describe everything in detail).

A computer that's hooked up to a tachyon transmitter is running a program that tells it to send a 1-bit message at t=1 that contains the NOT of the 1-bit message it received at t=0. (If we receive 1, send 0. If we receive 0, send 1). The computer at the other end is set up the same way, except that it's running a program that tells it to send the same 1-bit message that it has received, immediately after it has received it. This scenario contains a paradox:

Receive 1 → send 0 → receive 0
Receive 0 → send 1 → receive 1

You're suggesting that a way out of this is to say that free will exists only as an illusion. How does that help? Do you mean that computers running these two programs can't be built? Do you think they can't be hooked up to tachyon emitters or tachyon detectors? What do you think happens if I try? Do I get hit by a meteor? What if we all try? More meteors?

Do you think we would be unable to choose to try? I have two problems with that option. First of all, that doesn't just eliminate free will, but also the illusion of free will. How can we resolve a paradox by assuming that something we know is true (that we have the illusion of free will) is false? Second, if our brains are just physical systems that gather and utilize information, then we're not very different from the computers mentioned above. So why would it be more likely that the event that prevents the paradox happens in my brain than in the computer?

 

[RUTA]

Consider the following scenario: (You probably have the spacetime diagram in your head already, so I won't describe everything in detail).

A computer that's hooked up to a tachyon transmitter is running a program that tells it to send a 1-bit message at t=1 that contains the NOT of the 1-bit message it received at t=0. (If we receive 1, send 0. If we receive 0, send 1). The computer at the other end is set up the same way, except that it's running a program that tells it to send the same 1-bit message that it has received, immediately after it has received it. This scenario contains a paradox:

Receive 1 → send 0 → receive 0
Receive 0 → send 1 → receive 1

I'm trying to understand this spacetime pic. There are two computers at rest wrt each other. The computer on the left, say, is programmed to emit the opposite signal it receives while the one on the right is programmed to emit the same signal it receives. The signals' worldlines are superluminal. At t = 0 (in computer rest frame), L receives 0 from R (event 2), emitted at t < 0 (event 1). At t =1, L emits 1 (event 3), received at t > 1 by R (event 4). In the computer frame, the order of events is 1, 2, 3, 4. In some other frame, the order of events becomes 2, 1, 4, 3. In this second frame, it appears that R receives 0 and emits 1, in contradiction to its program. Do I have this correct or have I missed the point?

 

[DrChinese]

Consider the following scenario: (You probably have the spacetime diagram in your head already, so I won't describe everything in detail).

A computer that's hooked up to a tachyon transmitter is running a program that tells it to send a 1-bit message at t=1 that contains the NOT of the 1-bit message it received at t=0. (If we receive 1, send 0. If we receive 0, send 1). The computer at the other end is set up the same way, except that it's running a program that tells it to send the same 1-bit message that it has received, immediately after it has received it. This scenario contains a paradox:

Receive 1 → send 0 → receive 0
Receive 0 → send 1 → receive 1

You're suggesting that a way out of this is to say that free will exists only as an illusion. How does that help? Do you mean that computers running these two programs can't be built? Do you think they can't be hooked up to tachyon emitters or tachyon detectors? What do you think happens if I try? Do I get hit by a meteor? What if we all try? More meteors?

Do you think we would be unable to choose to try? I have two problems with that option. First of all, that doesn't just eliminate free will, but also the illusion of free will. How can we resolve a paradox by assuming that something we know is true (that we have the illusion of free will) is false? Second, if our brains are just physical systems that gather and utilize information, then we're not very different from the computers mentioned above. So why would it be more likely that the event that prevents the paradox happens in my brain than in the computer?

Fredrik, I didn't follow your example of the contradiction.

I assumed that if there were instanteous transmissions, everyone could agree (synchronize their clock) on what T=0 is. Once that happens, the example above doesn't seem valid because you don't send messages to the past, just to the same absolute time frame. I get that each observer's frame may evolve differently (so my T=1 clock may be different than someone else's T=1 clock if we are in different inertial frames) but that could be fixed simply by refreshing our agreed synchronization (say from an agreed upon 3rd party).

Obviously I have trouble understanding WHY and HOW instantaneous transmission (or preferred frames) lead to causal loops. Can you or Demystifier explain in more detail for me?

 

[zonde]

There are two computers at rest wrt each other.

Not at rest but in inertial motion toward each other.
Because they are in different reference frames they have different simultaneity and what is instantaneous (simultaneous) in one reference frame is backward in time in other frame.

EDIT: Sorry, not toward each other but away from each other.

 

[zonde]

Well, 'abandon relativity' is a bit strong. You mean 'abandon the Einstein-Minkowski interpretation of relativity'. You just want the neo-Lorentzian interpretation of relativity - which is perfectly in agreement with experiment.

Well, of course not abandon completely because it is undeniably useful but kind of abandon in this context. And speaking about neo-Lorentzian interpretation I prefer aether interpretation over no aether interpretation because as I see aether interpretation is more universal and much more rational.

 

[DrChinese]

Not at rest but in inertial motion toward each other.
Because they are in different reference frames they have different simultaneity and what is instantaneous (simultaneous) in one reference frame is backward in time in other frame.

As I said before, I don't follow this. If you have the advantage of instantaneous communication to help you synchronize clocks, the typical example of the 2 lightning strikes (or similar) wouldn't matter. I mean, if all the communication is done instantaneously, I don't see how that happens as our notions of the present remain the same.

 

[zonde]

As I said before, I don't follow this. If you have the advantage of instantaneous communication to help you synchronize clocks, the typical example of the 2 lightning strikes (or similar) wouldn't matter. I mean, if all the communication is done instantaneously, I don't see how that happens as our notions of the present remain the same.

You imply preferred frame for your instantaneous communication. That way you already have deviated from relativity. You will not have the same equations describing instantaneous communication in all Lorentzian reference frames.

 

[Fredrik]

I'm trying to understand this spacetime pic. There are two computers at rest wrt each other. The computer on the left, say, is programmed to emit the opposite signal it receives while the one on the right is programmed to emit the same signal it receives. The signals' worldlines are superluminal. At t = 0 (in computer rest frame), L receives 0 from R (event 2), emitted at t < 0 (event 1).

What you call event 1 is supposed to be later than event 2. This is the message that's sent into the past. I'll elaborate below.

I assumed that if there were instanteous transmissions, everyone could agree (synchronize their clock) on what T=0 is.

Zonde got it right. What you're saying here is right if we're assuming that the instantaneous messages are instantaneous in every frame. If you instead consider messages that are instantaneous in the emitter's rest frame, and only in that frame, those messages will be described as superluminal messages into the future in some frames, and as superluminal messages into the past in some frames.

Note that this doesn't give us a preferred way to synchronize clocks. It gives us infinitely many inequivalent ways to do that.

Obviously I have trouble understanding WHY and HOW instantaneous transmission (or preferred frames) lead to causal loops. Can you or Demystifier explain in more detail for me?

OK, I'll elaborate. Let's use the standard terminology by calling the first computer I mentioned "Alice", and the second one "Bob". I'll be describing things using Alice's rest frame, so Alice's world line coincides with the time axis. For simplicity, we will consider 1-bit messages that are instantaneous in the emitter's frame. (This is just for simplicity. We would end up with the same type of paradox even if the speed of a message in the emitter's frame is just slightly higher than c. It would just be more difficult for me to describe the experiment). Bob's world line is a line with slope 10 (i.e. velocity 1/10) through the point (1,10). That event is simultaneous in Bob's frame with (0,0) in Alice's frame (because if the slope of his world line is 1/v, the slope of his simultaneity lines is v). So if Bob sends an instantaneous message to Alice at (1,10), it will reach her at (0,0).

Alice is programmed to reply at the event (1,0). The program says that the reply must be 0 if the message received at (0,0) was 1, and vice versa. (The reply is the logical NOT of the message she received). The message that Alice sends at (1,0) is received by Bob at (1,10). Bob is programmed to reply immediately with the same bit that he received.

Now suppose that Alice receives 1. She replies by sending 0. Bob receives the message and replies by sending 0. Alice receives 0.

 

[Fredrik]

Now let's talk about ways to avoid the paradox:

1. The standard answer: No tachyons exist.

2. Long emission/detection times: Note that if it takes Bob more than 1 unit of time to detect the tachyon, he won't be able to reply in time to cause the paradox. Note also that if Bob had been 20 units of distance away instead of 10, detection must take him at least 2 units of time for the paradox to be avoided. So detection times must grow at least linearly with distance, which is pretty weird.

3. No free will: This experiment is impossible to perform in a universe where spacetime can be approximated by Minkowski space on the scales represented by the triangle we draw in the spacetime diagram. I just don't see what part could possibly fail as long as we have the illusion of free will. I think it's incorrect to describe this option as "no free will". It should be described as "no illusion of free will". And since we do have the illusion of free will in the real world, I think this option can be ruled out.

 

[Demystifier]

This scenario contains a paradox:

Receive 1 → send 0 → receive 0
Receive 0 → send 1 → receive 1

Do you mean that computers running these two programs can't be built?

Yes, that's what I mean.

What do you think happens if I try?

The point is - you will not try. (You don't have free will to try.)

Do you think we would be unable to choose to try?

Exactly.

I have two problems with that option. First of all, that doesn't just eliminate free will, but also the illusion of free will.

It doesn't elliminate the illusion of free will. You may think that it was your choice to not to try. Or you may think that your free will is not asolute. (You may think that you can choose to do the possible, but that you cannot choose to do the impossible. For example, you cannot choose to levitate.)

Second, if our brains are just physical systems that gather and utilize information, then we're not very different from the computers mentioned above. So why would it be more likely that the event that prevents the paradox happens in my brain than in the computer?

I agree that we are not much different from the computers. The point is that such (inconsistent) computers cannot exist. The event that prevents them does not necessarily happen in the brain.

 

[Demystifier]

3. No free will: This experiment is impossible to perform in a universe where spacetime can be approximated by Minkowski space on the scales represented by the triangle we draw in the spacetime diagram. I just don't see what part could possibly fail as long as we have the illusion of free will. I think it's incorrect to describe this option as "no free will". It should be described as "no illusion of free will". And since we do have the illusion of free will in the real world, I think this option can be ruled out.

As I explained above, it is not in contradiction with the illusion of free will. Whatever you do, you may A POSTERIORI interpret your action as being due to your choice to do that.

You cannot choose to do inconsistent stuff. For example, you cannot chose to turn to the left and to the right at the same time. If you ask what happens if you try, the answer is that you never try to do such inconsistent stuff. You try only one of this two options at a given time, and whatever it is, you think that it is because you have chosen to.

 

[zonde]

Demystifier,
can you explain what you understand as a "free will"?
Can you agree with my understanding of "free will"? - As I understand any action has to have some reason. So in that sense there is no actions free from reason. But if you can not predict outcome of some action (future) then it's as good as some other action with unknown outcome. And that (impossibility to predict future) is "free will" in practical sense.

 

[Demystifier]

Zonde, your view of free will does not coincide with mine. In your view, a random event also appears as a free will event, which does not in my view. In my view, a free will event is an event that is not controlled by any fixed physical laws, either deterministic or probabilistic. Clearly, if physical laws as we currently know them describe EVERYTHING, then free will does not exist.

 

[Fredrik]

Can you agree with my understanding of "free will"? - As I understand any action has to have some reason. So in that sense there is no actions free from reason. But if you can not predict outcome of some action (future) then it's as good as some other action with unknown outcome. And that (impossibility to predict future) is "free will" in practical sense.

That seems like an odd definition, especially considering that we're talking about a mathematical model of the universe that's just a 4-dimensional manifold with a bunch of curves in it. Cause and effect are just words that identify the direction of increasing entropy in the subset of the manifold that we're considering. (Drop a glass bowl so that it shatters against the floor. The only reason to say that the drop caused the shattering and not the other way round is that entropy is increasing in that direction).

I would say that free will implies a lot more. The mind would have to be something more than just a bunch of physical interactions in the brain, and whatever it is, it would have to be able to change the outcome of some of those interactions. That sounds like paranormal nonsense to me, and even those who disagree with that would have to agree that there's no good evidence for this kind of free will. The illusion of free will is more interesting. I don't know the best way to define it, but I certainly feel like I have it when I press the "submit reply" button to post this.

 

[Demystifier]

Illusion of free will is like doing stuff after hypnosis.
When people after hypnosis do stuff as they were commanded during the hypnosis, they do not think that they do it because they have no choice. They think that they do it because they want to. Thus, they have an illusion of free will. Nevertheless, they do what they was commanded to, so their actions are not really free will actions.

 

[Fredrik]

You cannot choose to do inconsistent stuff. For example, you cannot chose to turn to the left and to the right at the same time. If you ask what happens if you try, the answer is that you never try to do such inconsistent stuff. You try only one of this two options at a given time, and whatever it is, you think that it is because you have chose to.

I agree with this of course. But I strongly disagree with your conclusion. Turning left and right at the same time doesn't even make sense. To build a computer that replies with the NOT of what it receives isn't inconsistent. To build a computer that replies with the same message it receives isn't inconsistent. To put the second computer on a spaceship traveling at c/10 isn't inconsistent. None of the details in the scenario I suggested is inconsistent by itself, and we only get a paradox if we succeed to do all of them. So I can certainly choose to do any of them, but according to you I won't choose to do all of them. I can tell you right now that I would need a very good reason not to do all of them. And if I choose to quit without a good reason, it's not going to seem like free will to anyone, least of all me.

And if I do get a good reason, something like a series of quantum tunneling accidents involving my floor so that I keep losing pieces of my legs, it would make me feel even more strongly that the illusion of free will is gone.

To preserve the illusion of free will, I think the event that prevents the paradox must happen a long time before I even start to think about these things. For example, I might not get born at all. I don't think it's enough that I don't get my hands on a spaceship, because if the technology ever exists, it will sooner or later be in the hands of someone with similar ideas. I think the most reasonable option by far is that nothing that even resembles intelligent life will evolve in a special relativistic universe with tachyons that can in principle be detected in a short time.

As you can see, I can't prove that I'm right, at least not right now. But I feel very strongly that your view can't be correct, and I suspect that I would be able to come up with a much stronger argument if I had a good definition of what "illusion of free will" means.

Edit: What about the scenario I described earlier, where the experiment puts you in a position that gives you a good reason to believe that choosing the action that prevents the paradox will kill your child? There's nothing inconsistent about this scenario. Would you choose to kill your child, and still consider the illusion of free will to be intact?

I'm choosing to go to sleep now. I'll read the replies when I wake up.

 

[RUTA]

OK, I'll elaborate. Let's use the standard terminology by calling the first computer I mentioned "Alice", and the second one "Bob". I'll be describing things using Alice's rest frame, so Alice's world line coincides with the time axis. For simplicity, we will consider 1-bit messages that are instantaneous in the emitter's frame. (This is just for simplicity. We would end up with the same type of paradox even if the speed of a message in the emitter's frame is just slightly higher than c. It would just be more difficult for me to describe the experiment). Bob's world line is a line with slope 10 (i.e. velocity 1/10) through the point (1,10). That event is simultaneous in Bob's frame with (0,0) in Alice's frame (because if the slope of his world line is 1/v, the slope of his simultaneity lines is v). So if Bob sends an instantaneous message to Alice at (1,10), it will reach her at (0,0).

Alice is programmed to reply at the event (1,0). The program says that the reply must be 0 if the message received at (0,0) was 1, and vice versa. (The reply is the logical NOT of the message she received). The message that Alice sends at (1,0) is received by Bob at (1,10). Bob is programmed to reply immediately with the same bit that he received.

Now suppose that Alice receives 1. She replies by sending 0. Bob receives the message and replies by sending 0. Alice receives 0.

Bob is moving at v = 1/10 relative to Alice and his worldline passes through (1,10), so it also passes through (0,0). We're using Alice's coordinates so she is always at x = 0. [Note: Bob's worldline passes through (0,0), not the relevant sfc of simultaneity.] A hypersfc of simultaneity for Bob passing through (1,10) has slope 1/10 so it passes through (0,9.9), which precedes (1,10) by t = 0.1 in Alice's frame. Bob sends a signal (ONE) to Alice along this sfc of simultaneity, so Alice receives ONE at t = 9.9 and sends a signal (ZERO) to Bob alg a t = 9.9 sfc of simultaneity in her frame (slope of 0). This sfc of simultaneity intersects Bob's worldline before he sent his ONE at t = 10. The exact values of time for Bob don't matter and the signal itself (ONE or ZERO) that he sends doesn't matter. Whatever Bob sends at t = 10 is inverted at t = 9.9 and returned to him in his past (t = 9.9), so he can't possibly send the same thing he receives. Thanks for the explanation, Fredrik!

 

[RUTA]

I agree with this of course. But I strongly disagree with your conclusion. Turning left and right at the same time doesn't even make sense. To build a computer that replies with the NOT of what it receives isn't inconsistent. To build a computer that replies with the same message it receives isn't inconsistent. To put the second computer on a spaceship traveling at c/10 isn't inconsistent. None of the details in the scenario I suggested is inconsistent by itself, and we only get a paradox if we succeed to do all of them. So I can certainly choose to do any of them, but according to you I won't choose to do all of them. I can tell you right now that I would need a very good reason not to do all of them.

I agree with Fredrik. IMO, if it is possible, there has to be something in physics to make it work -- a physical mechanism bearing on brain states and/or computer electronics. This appears to require new physics. If it isn't possible, then we need something in physics to rule it out, which again seems to require new physics because there's nothing in SR per se that forbids superluminal worldlines.

 

[tetis]

Well, 'abandon relativity' is a bit strong. You mean 'abandon the Einstein-Minkowski interpretation of relativity'. You just want the neo-Lorentzian interpretation of relativity - which is perfectly in agreement with experiment.. As Bell said:

I think it's a deep dilemma, and the resolution of it will not be trivial; it will require a substantial change in the way we look at things. But I would say that the cheapest resolution is something like going back to relativity as it was before Einstein, when people like Lorentz and Poincare thought that there was an aether - a preferred frame of reference - but that our measuring instruments were distorted by motion in such a way that we could not detect motion through the aether. ... that is certainly the cheapest solution. Behind the apparent Lorentz invariance of the phenomena, there is a deeper level which is not Lorentz invariant. ... what is not sufficiently emphasized in textbooks, in my opinion, is that the pre-Einstein position of Lorentz and Poincare, Larmor and Fitzgerald was perfectly coherent, and is not inconsistent with relativity theory. The idea that there is an aether, and these Fitzgerald contractions and Larmor dilations occur, and that as a result the instruments do not detect motion through the aether - that is a perfectly coherent point of view. ... The reason I want to go back to the idea of an aether here is because in these EPR experiments there is the suggestion that behind the scenes something is going faster than light. Now if all Lorentz frames are equivalent, that also means that things can go backwards in time. ... [this] introduces great problems, paradoxes of causality, and so on. And so it is precisely to avoid these that I want to say there is a real causal sequence which is defined in the aether.

So as Zonde says, superluminal signalling violates causality only if one assumes a locally Minkowski structure for spacetime, and not with Lorentz. Historically, Minkowski structure was developed for a local physics. If Nature turns out to be nonlocal, then we might consider revising that structure.

Aniway I think isn't so simple go back to Lorentz Poincaré Larmor Fitzgerald aether after then Einstein go forward to general relativity. A consistent general aether theory includind gravitation could pretend probabilly an entirily new formulation of physic's laws. Actually quantum gravity could be a candidate to realize these new laws, but in that case doesn't need to go back to aether, the local quantum field theory, without requiring, in nosense, a violation of the causal principle, require that vacuum breaks full Lorentz symmetry for massless sector of the theoy [1] and on the other side Einstein's equation solution require to specify some degree of freedom for the metric [2], Einstein considered this circumstance just like a relict of the old aether, but in a general covariant version, and without any need to restaurate an absolute sincronization [3]. Extension of Einstein equations are considered nowday [4] which admit new fields, sometimes these fields resemble to the true time vector of the old Lorentz Poincaré Larmor Fitzgerlad theory, that is removed in general relativity.

[1] Haag: "Local quantum physics"
[2] Wheeler Misner Thorpe: "Gravitation"
[3] Abraham Pais "Subtle is the Lord"
[4] Bekenstein: "Relativistic gravitation theory for the modified Newtonian dynamic paradigm",
http://prola.aps.org/abstract/PRD/v70/i8/e083509

So i think there are a lot of reason in order to think to an objective simultaneous section arising from local field quantum theory, from observational data, but no one is conclusive and the arguments pointed out from the OP are in fact wrong arguments. None the quantum field theory requires a violation of causality arising from EPR effect, none classical tachyons are required in order to threat the EPR effect, none the conventional character of simultaneity in relativity require to drop out the causality in order to have the EPR. Aniway a Bohmian formulation should be coherent with extension of general relativity and not necessarily with full general relativistic local quantum field theories.