Does instantaneous communication implies a preferrred Lorentz frame?

[DrChinese]

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!

I'm sorry I am so dumb, but I just don't follow.

Alice's clock is always moving forward and Bob's clock is always moving forward. But they may not be moving forward at the same rate. Instantaneous Communication (IC) implies that there could be another party, let's say Chris. Chris sends out the time to Alice and Bob via IC. Regardless of their frame relative to Chris, they will always receive timestamps that are moving forward, even if they are different than their own. They will at least agree that at any point, they can see the delta between their own time clock and Chris'.

Now, how does the hypersurface of either Alice or Bob matter? A relativistic hypersurface won't come into play because all communication is by IC. You have a preferred frame because of Chris I guess, how does a causal loop problem appear?

According to Chris's clock (which both Alice and Bob are aware of) which is initially sync'd to both Alice and Bob:

a. Alice at t=0 (per her and Chris' clock) sends a 1.
b. Bob receives a 1 at t=0 (per his and Chris' clock).
c. Bob sends a 0 after some very short delay, let's say it reads t=1 per Chris' clock but t=2 per Bob's clock.
d. Alice receives a 0 at t=1 per Chris' clock but it is t=20 per her clock.
e. Alice sends at 0 to Bob at t=2 per Chris' clock but it is t=21 per her clock.
f. Bob receives a 0 at t=2 per Chris' clock but it is t=2.1 per Bob's clock.

So I guess it seems to me that everyone's clocks are advancing. Of course I do not believe that IC is possible. I am simply saying that IF there were such, how does the paradox arise? I know I should probably understand this, but I don't. HELP!

 

[RUTA]

I am simply saying that IF there were such, how does the paradox arise? I know I should probably understand this, but I don't. HELP!

Draw an X-Y graph. Y is Alice's time coordinate (t) and X is Alice's spatial coordinate (x). Alice's worldline is the t axis, i.e., x = 0 for all t. Bob is moving to the right at v = 0.1. His worldline (slope 10) passes through the origin (0,0) and through the point (x = 1,t = 10). Spatial slices for Alice (t = constant) are horizontal lines, slope = 0. Spatial slices for Bob are NOT horizontal lines, they're lines of slope 0.1. That's how everyone can measure the same speed of light even when they're in relative motion, i.e., they disagree on spatial length and temporal duration because they don't agree on which events are simultaneous (to measure the length of an object, you need to know where its ends are at the same time). So, the point on the t axis simultaneous with (1,10) according to Alice is (0,10). But for Bob, the point on the t axis simultaneous with (1,10) is (0,9.9), i.e., a line of slope 0.1 at (1,10) passes through (0,9.9). So, when Bob sends an "instantaneous signal" in his frame towards Alice from (1,10), that signal gets to Alice at (0,9.9). Now when Alice sends an "instantaneous signal" in her frame towards Bob from (0,9.9), that signal gets to Bob at (0.99, 9.9). Those three points make a triangle -- event 1 at (1,10) to event 2 at (0,9.9) to event 3 at (0.99, 9.9) back to event 1 at (1,10).

Now let's follow the sequence of events. Bob sends a signal from event 1 to Alice at event 2. She sends the inverse signal from event 2 to Bob at event 3. Thus, no matter what Bob sends from event 1, he receives the opposite signal at event 3, which is BEFORE event 1. Therefore, he cannot send the same signal he receives, but he receives a signal from Alice before he sends his, so what prevents him from sending the same signal?

 

[Fredrik]

Bob is moving at v = 1/10 relative to Alice and his worldline passes through (1,10), so it also passes through (0,0).

No, I meant that Bob is at x=10 at t=1. The slope of his world line in the spacetime diagram (with time in the "up" direction) is 1/v=10, not v, so his world line (if he's been moving at constant velocity for a long time) intersects Alices world line at t=-99.

The line that goes through (1,10) and (0,0) is a simultaneity line for Bob. It's Minkowski orthogonal to his world line. Its slope is dt/dx=(1-0)/(10-0)=1/10=v.

I didn't read the rest of your post since the first sentence got it wrong...or maybe you're just drawing the time axis to the right in your spacetime diagrams? The conventional way to draw them is to have time increasing in the "up" direction.

 

[Fredrik]

Now, how does the hypersurface of either Alice or Bob matter? A relativistic hypersurface won't come into play because all communication is by IC.

You still seem to be making the mistake of defining an IC to be instantaneous in all frames. In the scenario I'm describing, Alice is sending a message that reaches the destination at the same time it was sent (or very shortly thereafter) in her rest frame. This sort of message is what we mean by an IC in this scenario. The world line of the message will coincide with one of her simultaneity lines, because an IC message is defined as a message that follows one of her simultaneity lines. That's what it has to do to be instantaneous to her in a universe where special relativity is a good theory (which btw implies that the preferred method of clock synchronization is by light signals). Maybe it should be called an I_AliceC message instead.

The IC message that Bob sends follows one of his simultaneity lines. This is what IC means here, so maybe I should call it I_BobC.

Also note that we're not trying to use these messages to find out what mathematical model of space and time we should be using. We're assuming that this is happening in a universe where spacetime can be approximated by Minkowski space, at least on the time and distance scales that we draw in our diagrams.

I know I should probably understand this, but I don't. HELP!

I think that if you go back and read my description (in #24) again, and keep in mind that the world lines and simultaneity lines we're talking about are in Minkowski space (where simultaneity for an inertial observer is well-defined), and that "instantaneous" in this context is defined as "following a simultaneity line of the emitter", you won't have any difficulties understanding it.

 

[RUTA]

No, I meant that Bob is at x=10 at t=1. The slope of his world line in the spacetime diagram (with time in the "up" direction) is 1/v=10, not v, so his world line (if he's been moving at constant velocity for a long time) intersects Alices world line at t=-99.

The line that goes through (1,10) and (0,0) is a simultaneity line for Bob. It's Minkowski orthogonal to his world line. Its slope is dt/dx=(1-0)/(10-0)=1/10=v.

I didn't read the rest of your post since the first sentence got it wrong...or maybe you're just drawing the time axis to the right in your spacetime diagrams? The conventional way to draw them is to have time increasing in the "up" direction.

You had written, "Bob's world line is a line with slope 10 (i.e. velocity 1/10) through the point (1,10)," and "That event is simultaneous in Bob's frame with (0,0) in Alice's frame," so one of those two statements had to be corrected. I chose to correct the point of simultaneity, i.e., (0,9.9) instead of (0,0). With that one change your story makes the point, as I explained to Dr. Chinese in post #37.

 

[Fredrik]

You had written, "Bob's world line is a line with slope 10 (i.e. velocity 1/10) through the point (1,10)," and "That event is simultaneous in Bob's frame with (0,0) in Alice's frame," so one of those two statements had to be corrected.

The second statement is equivalent to the first, so no correction is necessary. A line through (1,10) with slope 10 goes trough (0,-99), not (0,0). And the corresponding simultaneity lines have slope 1/10 (because a simultaneity line is Minkowski orthogonal to the world line), so the simultaneity line through (1,10) goes through (0,0).

Edit: RUTA found a mistake here. The (0,-99) above should be (-99,0). Bob's world line intersects the time axis (where x=0) at t=-99, as I said in #38.

 

[DrChinese]

You still seem to be making the mistake of defining an IC to be instantaneous in all frames. In the scenario I'm describing, Alice is sending a message that reaches the destination at the same time (or very shortly thereafter) in her rest frame. This sort of message is what we mean by an IC in this scenario. The world line of the message will coincide with one of her simultaneity lines, because an IC message is defined as a message that follows one of her simultaneity lines. That's what it has to do to be instantaneous to her in a universe where special relativity is a good theory (which btw implies that the preferred method of clock synchronization is by light signals). Maybe it should be called an I_AliceC message instead.

You are correct, and I can see the idea of what you are saying. But it seems to me to miss the idea of IC with a preferred frame (which I thought was the central question in the thread - if you assume that there are only worldlines like we currently believe, then you don't have a preferred frame). I would imagine that would require us to have the following:

a) the speed of light is observed to be the same in all reference frames.
b) some method of IC not involving light.
c) possibly leading to a preferred reference frame (although I understand that may or may not be a strict consequence of assuming b).

So I imagine IC by some channel - obviously I don't actually believe this - in which light is not the medium. Maybe it is instead some undiscovered mechanism. I picture a type of spacetime in which the distance from "here" to "there" in one dimension is much shorter than in the other (traditional) directions.

We don't have to devote any more time to me, I understand now what everyone else is assuming in the example that I did not. Thanks!

 

[RUTA]

The second statement is equivalent to the first, so no correction is necessary. A line through (1,10) with slope 10 goes trough (0,-99), not (0,0). And the corresponding simultaneity lines have slope 1/10 (because a simultaneity line is Minkowski orthogonal to the world line), so the simultaneity line through (1,10) goes through (0,0).

Slope = (Y_final-Y_initial)/(X_final-X_initial). Your final point is (1,10) and your initial point is (0,0). Slope = (10-0)/(1-0) = 10. His worldline goes through (0,0) and (1,10). You're right about the simultaneity lines having slope 0.1 (= v), which means the simultaneity line of slope 0.1 through (1,10) goes through (0,9.9).

Your numbers give (10- -99)/(1-0) = 109 for the slope of Bob's worldline. I think you want the final point to be (10,1) instead of (1,10), then your other points work as you say.

 

[Fredrik]

Slope = (Y_final-Y_initial)/(X_final-X_initial). Your final point is (1,10) and your initial point is (0,0). Slope = (10-0)/(1-0) = 10.

The conventional way to draw a spacetime diagram is to have time increasing in the "up" direction, and most people (including me) would say that a horizontal line has slope 0, not infinity. The slope of a line in a spacetime diagram is therefore dt/dx, which for the line through (0,0) and (1,10) is 1/10=v. This is a simultaneity line for an inertial observer moving with velocity v, because it's Minkowski orthogonal to a line that represents inertial motion with velocity v.

His worldline goes through (0,0) and (1,10).

The conventional intepretation of that statement would be that his speed is ten times the speed of light. (He has moved 10 light-years in 1 year). I'm not sure what you're doing, but it's either very wrong or very unconventional.

 

[Neo_Anderson]

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.

But I thought that there was nothing that can't say the effect can precede the cause. It's possible to have an effect come before a cause, provided that both occur, no? I know it's an odd thing to think about, but there's nothing physically impossible with it, isn't there?

 

[Fredrik]

But I thought that there was nothing that can't say the effect can precede the cause. It's possible to have an effect come before a cause, provided that both occur, no? I know it's an odd thing to think about, but there's nothing physically impossible with it, isn't there?

See post #30 for some comments about what you're asking.

The problems associated with receiving a reply before the message was sent are much more severe than just "effect preceding cause". See #17 and the clarifications in #24.

 

[zonde]

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.

Physical laws are developed based on observations and experiments. If physical law poorly describes physical reality then it's useless or simply wrong. So assuming that there is something like free will physical law either should incorporate it (that is not allowed by your definition) or be discarded and the phenomenon considered random (that too is not allowed by your definition).
So it seems to me that your view states impossibility and is useless. Can you show it otherwise?

 

[zonde]

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.

But why do you identify cause and effect with increasing entropy? Cause and effect is related to time and we have common piece of equipment called "clock" to make measurements of time. How do you measure increase in entropy?

(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).

Sequence of events is the reason to say that the drop caused the shattering (by definition).

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.

I think that this 4-dimensional mathematical model of the universe creates illusion that you can foresee the future. That is not so. Deterministic laws are good for accumulating information about the past because for the past you can retrospectively sort information in more relevant and less relevant. And you have to do things like that because there is limited amount of information you can keep.
But you can not with certainty predict what information will be relevant in the future.
Now if you can not predict with certainty the future how can you know what changes certain action can possibly make? You can only try and see. And that is your free will what you will try and what you will not.
For example you can try rational things that will lead to highly predictable outcome and you can try irrational things that can lead to quite unpredictable outcome.

 

[Demystifier]

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.

Exactly. The idea is that nature works globally.

So I can certainly choose to do any of them, but according to you I won't choose to do all of them.

I am saying that you cannot choose to do all of them, because nature works globally.

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.

The reason nature quits is because nature wants to avoid inconsistencies. The reason is of a global nature. However, our subjective consciousness is used to interpret nature in terms of LOCAL reasons. On the other hand, in this case local reasons do not exist. So, how our subjective consciousness will interpret it? My idea (which I cannot prove because I don't completely understand how consciousness works) is the following: As consciousness is unable to see the global reasons, consciousness will interpret it as happening without a reason. That is, it will interpret it either as a local random event, or an event caused by local free will. Nevertheless, the true nature of the event is neither random nor free. Instead, it is determined by the principle of global self-consistency.

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 don't know how exactly my brain will behave in this situation (except that I know that its behavior will be consistent with all other circumstances). Perhaps I will feel as a schizophrenic person who feels that he must do something, despite of knowing that it is wrong. So yes, in this case my (illusion of) free will may be intact, in the same sense the (illusion of) free will of a mentally ill person may be intact.

Or perhaps I will feel that my hands are moved by some external force. In this case, I will feel that I don't want to kill my daughter, but something else moves my hands.

 

[Fredrik]

But why do you identify cause and effect with increasing entropy?

We're talking about a manifold with a bunch of curves in it. Cause and effect aren't really meaninful concepts in that context. I was just suggesting one way of giving those words meaning again. You suggested another by saying that the earlier event is the cause. I think mine is more natural because if you ever observe a series of events with decreasing entropy, e.g. thousands of tiny pieces of glass jumping up from the ground to form a glass bowl, would you really think of the earlier event as the cause? Or would you feel that the reason why they jumped in those exact directions was that the result would be a bowl? To use time ordering to define which event is the cause seems very arbitrary, especially since the dynamical laws in the model we're considering are perfectly symmetrical under time reversal. If you know all the positions and velocities at a given time, you can calculate them at any other time, both in the past and in the future. So why do you want to use time? Isn't it because entropy increases as time increases? What other difference is there between the two directions of time?

I think that this 4-dimensional mathematical model of the universe creates illusion that you can foresee the future. That is not so.

It would be so if this model had been an exact description of our universe. Of course, QM makes things a lot more interesting.

 

[Fredrik]

Nevertheless, the true nature of the event is neither random nor free. Instead, it is determined by the principle of global self-consistency.

I just want to say that I completely agree with statements like this. I just don't think global self-consistency in a special relativistic universe with tachyons is consistent with the illusion of free will, and I don't see why you think it is.

I don't know how exactly my brain will behave in this situation (except that I know that its behavior will be consistent with all other circumstances). Perhaps I will feel as a schizophrenic person who feels that he must do something, despite of knowing that it is wrong. So yes, in this case my (illusion of) free will may be intact, in the same sense the (illusion of) free will of a mentally ill person may be intact.

So from my point of view, you went insane enough to kill your own child while trying to set up an experiment that can't possibly be completed because of global self-consistency. That proves to me that you didn't actually have free will, and that's it for the illusion of free will as far as I'm concerned. What could we possibly mean by illusion of free will other than that there's nothing we can do to prove that we don't have actual free will? (I think this is the definition of "illusion of free will" that I've been saying we need).

You could argue that one experiment doesn't prove it conclusively, but if we repeat the experiment a thousand times with different people, and they all choose to kill their children over the alternative, which is to not press a button for a few seconds, I would say that we have proved it as conclusively as anything can be proved in a universe where quantum effects are sometimes relevant.

(Suppose e.g. that an alternative theory competing with QM predicts that an experiment must have result R with probability P(R). Such a theory isn't falsifiable in the absolute sense, but if we do the experiment over and over, and the fraction of results that have been R so far is getting closer and closer to P(R)/2, we would eventually consider the theory to have been "falsified", even though technically it never will be. A theory that only predicts probabilities 0 or 1 doesn't have this problem, since it can be falsified with a single experiment. A theory that predicts non-trivial probabilies is never strictly falsifiable. Instead they satisfy a weaker requirement that I think of as "statistical falsifiability". So we can never really prove that an alternative quantum theory is false. That's what I had in mind when I said that "we have proved it as conclusively as anything can be proved in a universe where quantum effects are sometimes relevant").

 

[zonde]

We're talking about a manifold with a bunch of curves in it. Cause and effect aren't really meaninful concepts in that context.

If you have past and future light cones in your manifold then cause and effect are meaningful.

I think mine is more natural because if you ever observe a series of events with decreasing entropy, e.g. thousands of tiny pieces of glass jumping up from the ground to form a glass bowl, would you really think of the earlier event as the cause?

Ok, if I will ever observe as tiny pieces of glass are jumping up from the ground to form a glass bowl I will agree that your view is more natural. But until then I will consider mine to be more natural. Is it ok?

What other difference is there between the two directions of time?

So for you future is only ever increasing entropy and nothing new? Then maybe we can make a deal - let's the past be for you and the future for me if it the same for you?

It would be so if this model had been an exact description of our universe. Of course, QM makes things a lot more interesting.

It would be nice to see would be model that can handle infinite amount of information.

 

[Demystifier]

I just don't think global self-consistency in a special relativistic universe with tachyons is consistent with the illusion of free will, and I don't see why you think it is.

So from my point of view, you went insane enough to kill your own child while trying to set up an experiment that can't possibly be completed because of global self-consistency. That proves to me that you didn't actually have free will, and that's it for the illusion of free will as far as I'm concerned.

Fredrik, it seems to me that we have just arrived at an agreement, or at least that we are very close to it.
Let me clarify. Assume that relativistic superluminal influences associated to nonlocality of quantum entanglement - exist. Then, due to decoherence at the macroscopic level, in MOST cases of everyday macroscopic life these superluminal influences are NEGLIGIBLE. Therefore, in most cases there is nothing that can destroy the illusion of free will, because the illusion of free will is an emergent phenomenon that appears only at the macroscopic level. That is why the illusion of free will is so effective in practice. Nevertheless, significant superluminal influences at the macroscopic level are possible, at least in principle. This means that, in principle, they can destroy the illusion of free will. But in practice, it does not happen due to decoherence. In this way, hypothetic relativistic superluminal influences (at the fundamental microscopic level) are compatible with the fact we feel the existence of free will (at the emergent macroscopic level).
This is similar to the fact that quantum mechanics at the fundamental microscopic level is compatible with classical mechanics at the emergent macroscopic level.

Do you agree now?

 

[Demystifier]

Let me summarize the final picture how is that possible to have both relativity without a preferred frame and instantaneous communication:

1. At the fundamental microscopic level we have
- Minkowski spacetime (where time and space are treated on an equal footing)
- quantum laws of motion
- both subluminal and superluminal influences
- no arrow of time
- no causality (i.e., no causes and consequences)
- no free will

2. At the emergent macroscopic level we have the illusions of
- Einstein (1905) relativistic space and time (where time and space are not treated on a completely equal footing)
- classical laws of motion
- only subluminal influences
- arrow of time
- causality (i.e., causes and consequences)
- free will

 

[zonde]

And is it scientific i.e. is it falsifiable?

 

[Demystifier]

And is it scientific i.e. is it falsifiable?

At the moment, I don't know.

But the point was to show that it is at least possible (to have both relativity and superluminal influences).
I think it is important to show that it is possible, because there are many "theorems" stating the opposite.

 

[RUTA]

The conventional way to draw a spacetime diagram is to have time increasing in the "up" direction, and most people (including me) would say that a horizontal line has slope 0, not infinity. The slope of a line in a spacetime diagram is therefore dt/dx, which for the line through (0,0) and (1,10) is 1/10=v. This is a simultaneity line for an inertial observer moving with velocity v, because it's Minkowski orthogonal to a line that represents inertial motion with velocity v.


The conventional intepretation of that statement would be that his speed is ten times the speed of light. (He has moved 10 light-years in 1 year). I'm not sure what you're doing, but it's either very wrong or very unconventional.

I do have time in the vertical direction and the slope of a horizontal line is zero. In the examples here it looks like you're writing (Y,X) instead of (X,Y) for your pairs, but that doesn't jive with your previous statement, "A line through (1,10) with slope 10 goes trough (0,-99), not (0,0)." If you're simply switching the X-Y order of the pairs, the slope of the line through (1,10) and (0,-99) would be (1-0)/(10- -99) = 1/109, not 10 as you claim. Again, all your math works if you simply change the (x,t) pair (1,10) to (10,1), since (1 - -99)/(10-0) = 10 is the slope of the worldline through pts (0,-99) and (10,1), and (1-0)/(10-0) = 0.1 for the slope of the sfc of simultaneity through pts (0,0) and (10,1).

 

[DrChinese]

Let me summarize the final picture how is that possible to have both relativity without a preferred frame and instantaneous communication...

So that is how you imagine there is no preferred frame. So what about having a preferred frame? Do you think that is possible? I know most of the Bohmian type theories have this attribute. Are those interpretations inevitably in conflict with relativity?

 

[Demystifier]

So that is how you imagine there is no preferred frame.

What you say that now you UNDERSTAND how is that possible? (If not, then I failed.)

So what about having a preferred frame? Do you think that is possible?

It is certainly possible.

I know most of the Bohmian type theories have this attribute. Are those interpretations inevitably in conflict with relativity?

They are in conflict with relativity at the fundamental microscopic level, but not at the emergent macroscopic level. Although it is consistent, I allways felt that it is somewhat cheap and inelegant, and that one can do better than this.

Now I have done this (relativity at the fundamental level) explicitly. Of course, I have not done it without a price. The price is that causality and free will are only emergent.

 

[DrChinese]

What you say that now you UNDERSTAND how is that possible? (If not, then I failed.)

Didn't mean to imply anything about the perspective itself. Just trying to see all of the alternatives as clearly as possible. My personal goal is to be able to evaluate interpretations based on new experimental and theoretical work which comes out almost daily.

 

[Demystifier]

Didn't mean to imply anything about the perspective itself. Just trying to see all of the alternatives as clearly as possible.

So, let me rephrase my question.
Would you say that now you see this alternative - clearly? (If not, then I failed.)

 

[DrChinese]

Yes, probably as clearly as I am capable.

 

[Demystifier]

Good! That's all I want, to make others understand how is that possible. (Not to convince others that this is how nature really works.)

 

[Fredrik]

In the examples here it looks like you're writing (Y,X) instead of (X,Y) for your pairs,

My pairs are of the form (t,x). That's seems to be the most common way (by far) to write them, probably because it ensures that time is always $x^0$ instead of being $x^4$ when we're considering 3+1-dimensional spacetime and $x^2$ when we're considering 1+1-dimensional spacetime. There's certainly nothing wrong with writing time as the last component, and I know that there are some authors who do that, but I never do. I like to write four-vectors as $(x^0,x^1,x^2,x^3)=(t,\vec x)$, and when I'm dealing with 1+1-dimensional spacetime I just drop the vector symbol from the right-hand side.

...but that doesn't jive with your previous statement, "A line through (1,10) with slope 10 goes trough (0,-99), not (0,0)." If you're simply switching the X-Y order of the pairs, the slope of the line through (1,10) and (0,-99) would be (1-0)/(10- -99) = 1/109, not 10 as you claim.

Oops, you're right about that. I got it wrong in that attempt to explain these things to you. Everything I said in #24 is correct, and as I said in #41, the two statements that you considered contradictory are actually equivalent. I also got it right in #38, where I said that Bob's world line intersects Alice's at t=-99, but the coordinates of that event are (-99,0), not (0,-99). So everything in #17, #24 and #38 still looks completely correct to me, but I finally made a blunder in #41 when I tried to say the same thing that I had already said in #38 in a different way, and accidentally wrote (0,-99) when I meant (-99,0).

I hope that clears it up.

 

[Fredrik]

If you have past and future light cones in your manifold then cause and effect are meaningful.

Ok, if I will ever observe as tiny pieces of glass are jumping up from the ground to form a glass bowl I will agree that your view is more natural. But until then I will consider mine to be more natural. Is it ok?

Your post doesn't contain any actual arguments. I at least tried to explain why I consider my view more natural. You haven't said anything about why you like yours better. Light cones do not give us a reason to prefer the statement "A caused B" over "B caused A".

So for you future is only ever increasing entropy and nothing new? Then maybe we can make a deal - let's the past be for you and the future for me if it the same for you?

It's not the same for me. I remember the past but not the future...because entropy is increasing towards the future. (We have chosen to define "future" as the direction of time in which entropy is increasing). At least that's how we would have to describe it using a classical theory like SR. It seems to me that QM doesn't invalidate this, but I could be wrong about that.

 

[Fredrik]

Fredrik, it seems to me that we have just arrived at an agreement, or at least that we are very close to it.
Let me clarify. Assume that relativistic superluminal influences associated to nonlocality of quantum entanglement - exist. Then, due to decoherence at the macroscopic level, in MOST cases of everyday macroscopic life these superluminal influences are NEGLIGIBLE. Therefore, in most cases there is nothing that can destroy the illusion of free will, because the illusion of free will is an emergent phenomenon that appears only at the macroscopic level. That is why the illusion of free will is so effective in practice. Nevertheless, significant superluminal influences at the macroscopic level are possible, at least in principle. This means that, in principle, they can destroy the illusion of free will. But in practice, it does not happen due to decoherence. In this way, hypothetic relativistic superluminal influences (at the fundamental microscopic level) are compatible with the fact we feel the existence of free will (at the emergent macroscopic level).
This is similar to the fact that quantum mechanics at the fundamental microscopic level is compatible with classical mechanics at the emergent macroscopic level.

Do you agree now?

I don't know. I don't think entanglement has a lot to do with what we've been dicussing, since entanglement can't be used to send superluminal messages. It seems to me that the only thing that can be a problem for the illusion of free will is the existence of easily detectable tachyons. Note that if we take the ensemble interpretation of QM as our starting point, we can't even conclude that there are superluminal influences in tests of entanglement over spacelike separations (since this interpretation assumes that QM isn't a description of what actually happens).

On the other hand, that assumption strongly suggests that there's an underlying theory that does describe what actually happens, and that the variables of that theory aren't observables. (If they were, I think we'd have problems with Bell inequalities and that sort of stuff). Since we have no idea what that theory is, it's hard to speculate about it, but I'll offer two thoughts about it anyway.

I don't see a reason to think that superluminal influences between unobservables would force us to behave in a certain way to avoid a violation of "global consistency" like the paradox described in #24. So such influences wouldn't necessarily be a problem for the illusion of free will, like easily detectable tachyons would.

It also seems to me that Minkowski spacetime may be the illusion here. Maybe concepts like "distance" or "spacelike separation" don't even enter into the description of entanglement in the fundamental model. Maybe the two entangled particles are just a single system there, and the separation between them is the illusion. I think that concepts such as "distance" are unavoidable in a falsifiable theory, because it must include a mathematical representation of operationally defined equivalence classes of measuring devices (i.e. an algebra of "observables"), and it's impossible to define anything operationally without mentioning space and time. But they do not have to be a part of a description of what actually happens in terms of unobservables.

Now let's take the MWI as the starting point instead. (I define the MWI as the assumption that the usual axioms about Hilbert space and the probability rule can be interpreted as a description of what actually happens). Decoherence can cause correlations in spacelike separated measurements, but does it make sense to describe those as "superluminal influences"? I don't know. I don't understand the MWI and decoherence well enough.

 

[dmtr]

Now let's take the MWI as the starting point instead. (I define the MWI as the assumption that the usual axioms about Hilbert space and the probability rule can be interpreted as a description of what actually happens). Decoherence can cause correlations in spacelike separated measurements, but does it make sense to describe those as "superluminal influences"? I don't know. I don't understand the MWI and decoherence well enough.

AFAIK all these causality-loop paradoxes simply go away under the MWI interpretation. In the example above 'Alice sending 0' would be from a different subjective history from the 'Alice sending 1'.

 

[Fredrik]

AFAIK all these causality-loop paradoxes simply go away under the MWI interpretation. In the example above 'Alice sending 0' would be from a different subjective history from the 'Alice sending 1'.

That may be true, but I suspect that it's not that simple. If it's true, then it should be easy enough to write down a QM description of the sequence of events I described in #24 that makes it obvious that what you said is correct. I expect that the result would be the opposite, i.e. that if we tried to prove this, we would end up proving that the same paradox is present in the MWI too. I haven't tried to do this yet. Maybe I'll give it a shot later.

 

[zonde]

Your post doesn't contain any actual arguments. I at least tried to explain why I consider my view more natural. You haven't said anything about why you like yours better. Light cones do not give us a reason to prefer the statement "A caused B" over "B caused A".

But Frederik, you are unjust. I gave my argument previously you just dismissed it.
I said that time can be measured directly with clock while entropy do not have means of direct measurement.
And there is straight forward motivation for that argument. Because while mathematical model hangs in the air it is useless but to make some relation to physical world you are facing conversion process where you are using measurement equipment. And the more straight forward is this conversion process the less (interpretation) error prone it is.
To be more direct - how can you state that entropy is increasing if you can not measure it? How can you state that system is closed? And as to closed systems I think there are no closed systems in physical world and so there is no physically meaningful way to define change in entropy. Consider for example a possibility that fields can be carriers of disorder - can you shield any system from fields?

And if you need a reason why one direction in time is preffered over the other - the reason is that we do not care about changing the past but we care about changing the future (we care about our survival in the future).

 

[zonde]

Demystifier,
before you make conclusion I propose to consider another scenario.
Take Frederik's example with two computers communicating "1" and "0". But modify it so that it becomes non contradicting i.e. computers are just storing the value they get and then transmit it back to the past of other computer.
As I understand you allow possibility of such scenario.
In that case we can have this causality loop in two states:
1. first computer have stored "0"; it transmits "0" to second computer; second computer have stored "0"; it transmits "0" back to first computer.
2. first computer have stored "1"; it transmits "1" to second computer; second computer have stored "1"; it transmits "1" back to first computer.
Separately each of two computer do not have free will but the whole causality loop has free will to be in one of two states. The state at any point is not random and is not caused by any physical law outside this causality loop.

What you can say about this scenario? Do you see any inconsistency in my reasoning?