5 Light-Year long stick question

[Fredrik]

Whatever particles/fields/etc. are added, it's assumed there are some known Lorentz-invariant laws governing their behavior, laws which can be stated in local form like the differential form of Maxwell's equations. And if tachyons exist and don't have a preferred frame, one should be able to write down some local Lorentz-invariant laws governing their behavior too. So, can't you just impose the condition that the global collection of local facts about particles/fields at each point in spacetime must satisfy these same local laws at every point? This global condition on allowable "histories" of particles/fields throughout the entire 4D spacetime should guarantee that the Novikov self-consistency principle would hold.

I don't see how that's different from just stating that scenarios that contain contradictions are not allowed.

By the way, a minor change to the computer program in my thought experiment would eliminate the contradiction. Is the scenario where the computers run "safe" programs allowed by the laws of physics? If yes, then what exactly is preventing me from setting up that scenario, and then edit the computer program? Will I get hit by a meteor that's been heading my way for a billion years the moment before I save the changes? Will I change my mind for no apparent reason, and choose not to save the changes?

Why would either party think they are getting messages from the future,

See the post I linked to in #37.

Note that for the reply message to go into the past, it's necessary that the messages are instantaneous in the transmitter's rest frame. If they're all simultaneous in some specific inertial frame, then no messages are being sent to the past, but the principle of relativity is violated instead.

 

[JesseM]

I don't see how that's different from just stating that scenarios that contain contradictions are not allowed.

I don't see what it would even mean for a scenario to "contain a contradiction". Suppose we are given a complete set of facts about all local physical variables at every point in an infinite Minkowski spacetime--as long as we assume there is a single correct fact about the state of affairs at each point (i.e. we can't have two contradictory 'parallel' truths about what's happening at a single point in spacetime, like whether a given type of particle is present or absent at that point), then what would it mean for this list to contain a contradiction? Of course if we don't impose the rule that the same local laws of physics must apply at each point, then it might be possible for this complete set of facts to contain weird discontinuities, like a tachyon-receiving device that records having received a "1" at points on its worldline shortly after it received a tachyon message, but then at some point before sending a message it abruptly and for no lawlike reason changes to being in a state where it records having received a "0". But a discontinuity is not really a "contradiction", it's just a breakdown in the usual laws of physics at some point in the spacetime. And if we impose the rule that the only "complete set of facts" allowed are ones where the same local laws are obeyed at each point, then this sort of discontinuity won't happen, and the complete set of facts will necessarily be a globally self-consistent set of facts.

By the way, a minor change to the computer program in my thought experiment would eliminate the contradiction. Is the scenario where the computers run "safe" programs allowed by the laws of physics? If yes, then what exactly is preventing me from setting up that scenario, and then edit the computer program? Will I get hit by a meteor that's been heading my way for a billion years the moment before I save the changes? Will I change my mind for no apparent reason, and choose not to save the changes?

Yes, something like that would presumably have to happen in either an SR scenario with tachyons or a GR scenario with a traversable wormhole that allows you to travel into your own past--if at some point you decide to try to create a contradiction, events will "conspire" to stop you or at least change your mind.

This need not imply any "intelligence" on the part of the laws of physics, of course--with a sufficiently powerful computer we could use brute-force methods to generate a simulated universe which followed the same local laws at every point, which allowed "time travel", and which was guaranteed to be self-consistent in this way. To see this, consider a simpler analogy. Imagine you want to write a computer program to generate a possible chess game. One way is to start with the pieces in their starting configuration, then have the program generate each successive configuration on the next turn from the configuration on the previous turn, using only legal chess moves. But here's another, more elaborate way to do it. have the computer generate an entire series of configurations at once, completely randomly, so it just picks randomly which pieces to put in which positions on which turn. It is very unlikely that the resulting series will look like a legal chess game--a piece might randomly be on a particular square on one turn, but then the next turn randomly be on some totally different square that it shouldn't be able to get to in one move by the rules of chess. But suppose you have access to an idealized computer with nearly infinite speed and memory, and you have it generate a gigantic number of random series this way--if your number is large enough, chances are at least some of the series would just happen to satisfy the rules of a legal chess game. So you could specify that the computer should throw out all series which violate the rules of chess, and be left only with series that represent legal chess games. But since you are dealing with an entire series at once, you could also place other constraints on them, like "throw out all series where white wins", or "show me only series where the black rook checkmates the king in 25 moves", whatever you want. For sufficiently detailed conditions, it might be very hard to generate a chess game that matched them in the traditional way of starting from the beginning and basing each new configuration of pieces on the configuration of the previous turn, but using this brute-force method of generating a near-infinite number of entire histories, and throwing out all but the ones that satisfy your constraints, it's easy to get a game that satisfies any conditions you like without even having to think about it or plan the details of the game.

And suppose we want to come up with a game of "4D chess" which is similar to ordinary chess but with some extra rules that allow you to send pieces "back in time" to earlier time-increments in the game, but only in a self-consistent way where history is not changed. For example, suppose there are two squares labeled A and B on the middle of the board, such that if at any time-increment a piece is moved onto square A, then the rules say it is transported to square B four moves earlier (and say the player who controls the piece has to immediately move it when it appears on square B, and pieces can't move directly to square B by non-time-travel routes, to avoid the issue of multiple pieces occupying square B on a particular time-increment). It would be pretty hard to generate self-consistent games following these rules by the usual method of starting from some initial configuration and evolving it forward step-by-step, but if you just generate some astronomical number of random histories, the computer can algorithmically check any given randomly-generated history to see if it actually is a self-consistent 4D chess game that obeys the rules at every point, so with enough memory and computing power it should be able to find some valid games.

Similarly, suppose you were using this incredibly powerful computer to generate a simulation of an entire universe--instead of picking some initial conditions and then letting it evolve forward according to some set of laws of physics, you could again specify your "laws" in terms of constraints on entire histories, with the computer generating a huge number of random histories and then throwing out all the ones that don't satisfy the conditions. If the "laws of physics" you pick happen to allow time travel, then obviously any universe that respects the laws of physics locally at every point in spacetime must be globally self-consistent, and the computer will find some histories satisfying this condition. But the computer does not need to have any intelligence to do this, it's just randomly generating a huge number of possibilities until it finds one that satisfies the constraints. From the point of view of a simulated sentient being in this universe with access to a time machine, it might seem like the universe was cleverly finding ways to "outsmart" them and thwart their plans every time they tried to change history, but it would actually be the result of a fairly simple rule, just not a dynamical rule based on picking initial conditions and evolving them forward, as with normal computer simulations.

 

[JesseM]

I am not understanding this. Can you exlain more how causality fits in? I'm just thinking I can send signals as fast as I want, so I can set up absolute simultaneity between any two regions of space to any desired precision. Why would either party think they are getting messages from the future, each believing the other's messages were from the future? One would instead believe a common 'now' has been established to arbitrary precison over arbitrary distance.

Well, it's just a matter of the relativity of simultaneity--if there is some frame where the sending of the tachyon message happens at the same time as the receiving of the same message at a different location (i.e. the tachyon signal traveled instantaneously, with infinite speed, in that frame), then it's easy to show using the Lorentz transformation that there must be some other frame where the signal was actually received at an earlier time then it was sent, i.e. the tachyon signal went back in time in that frame! And if the first postulate of relativity is obeyed, then if tachyon signals are allowed to travel back in time in one inertial frame, they must be allowed to travel back in time in any other frame as well. You can only use tachyons to establish a preferred definition of simultaneity if there is some preferred frame such that tachyons can travel with arbitrarily large speed in that frame but they cannot travel backward in time in that frame (and if that were the case, tachyons could never be used to create true causality violations where information about some event E could be transmitted into E's own past light cone as in these diagrams, with a preferred frame it would still be true that tachyons moved back in time in other frames but the information they carried would always remain outside the past light cone of the event of the tachyons being sent)

 

[PAllen]

Well, it's just a matter of the relativity of simultaneity--if there is some frame where the sending of the tachyon message happens at the same time as the receiving of the same message at a different location (i.e. the tachyon signal traveled instantaneously, with infinite speed, in that frame), then it's easy to show using the Lorentz transformation that there must be some other frame where the signal was actually received at an earlier time then it was sent, i.e. the tachyon signal went back in time in that frame! And if the first postulate of relativity is obeyed, then if tachyon signals are allowed to travel back in time in one inertial frame, they must be allowed to travel back in time in any other frame as well. You can only use tachyons to establish a preferred definition of simultaneity if there is some preferred frame such that tachyons can travel with arbitrarily large speed in that frame but they cannot travel backward in time in that frame (and if that were the case, tachyons could never be used to create true causality violations where information about some event E could be transmitted into E's own past light cone as in these diagrams, with a preferred frame it would still be true that tachyons moved back in time in other frames but the information they carried would always remain outside the past light cone of the event of the tachyons being sent)

What I'm claiming is that if tachyon messages were really possible, one would conclude distant simultaneity is well defined and would never derive or believe the Lorentz transform. The whole basis for deriving or believing it would gone. Thus, one would be forced to develop some radical alternative to SR.

 

[JesseM]

What I'm claiming is that if tachyon messages were really possible, one would conclude distant simultaneity is well defined and would never derive or believe the Lorentz transform. The whole basis for deriving or believing it would gone. Thus, one would be forced to develop some radical alternative to SR.

Why do you say that? If tachyons could really travel backwards in time in any frame as well as FTL or instantaneously, then I don't see how they could be used to establish any absolute notion of simultaneity, and the laws governing tachyons could still be Lorentz-symmetric (i.e.e the same equations would accurately predict their behavior in the coordinates different frames related by the Lorentz transformation) just like the laws governing other particles. Fundamentally it is the Lorentz-symmetry of the laws of physics that makes people "believe" in SR, the addition of tachyons wouldn't change this any more than the subtraction of photons and other particles capable of moving at c (even if absolutely no particle in the universe could move at c, the laws of physics governing slower-than-c particles could still be Lorentz-symmetric)

 

[PAllen]

Why do you say that? If tachyons could really travel backwards in time in any frame as well as FTL or instantaneously, then I don't see how they could be used to establish any absolute notion of simultaneity,

Ah, I finally get it, this is the key. If I observed a tachyon message sent from my future, I could not independently know how to interpret the 'time sent' for any tachyon message I receive. Then the rest of this approach follows. Thanks for your patience explaining this.

 

[Fredrik]

I don't see what it would even mean for a scenario to "contain a contradiction".

I guess I could have phrased it better, but you know what I mean. The technique of proving an assumption wrong by deriving a contradiction is clearly just as valid here as in any other area of mathematics.

And if we impose the rule that the only "complete set of facts" allowed are ones where the same local laws are obeyed at each point, then this sort of discontinuity won't happen, and the complete set of facts will necessarily be a globally self-consistent set of facts.

I agree. We're really just talking about a bunch of curves in Minkowski spacetime (curves representing the motion of particles), so there can't be any inconsistency. The "local laws" must be statements about what the curves are doing.

Yes, something like that would presumably have to happen in either an SR scenario with tachyons or a GR scenario with a traversable wormhole that allows you to travel into your own past--if at some point you decide to try to create a contradiction, events will "conspire" to stop you or at least change your mind.

This is what I can't accept. The properties of tachyons and their interactions are such that all scientists would choose to murder their children rather than change a 0 to a 1 in a computer program? If I use a telescope to look for meteors before I make the change, I will die in a terrorist attack instead? If I lock myself away where I'm safe from terrorists, I have a heart attack instead? If I make sure that I'm in perfect health...I guess we're back to ninja turtles.

What I just described doesn't sound anything at all like the universe we live in, and I also don't think it can be justified by a rule that says that the same "local laws" are obeyed in each region of spacetime. If these "local laws" say that I can build a device that sends instantaneous messages (in the device's rest frame), and the same thing can't be done in another region of spacetime, then I would say that the laws in that region are different from the laws in the first region, or alternatively, that the laws are the same everywhere, but different from what we previously thought that they were. I know the principle explicitly said the there won't be any new physics, but now I think it contradicts itself on that point.

Even if we assume that there are such global laws (for both tachyons and normal matter), they don't seem to describe something that resembles the universe we live in, where people have an illusion of free will.

 

[swapnanil_s]

My friends and I are having an argument over this question:

"Someone 5 LY away on a planet is getting "poked" by a 5 LY long stick from here on earth"

Does it take five years (or more) from the time one end of the stick is pushed until the person right next to the other end is poked by it? Or does it happen in next to no time at all?
- I personally believe that it will take alteast five years.. since if the person being poked had a telescope and watched the person push the stick, it would take the light ("information") 5 years to reach him.. and he can't get poked by the stick if it hasn't been pushed?

Is that right to say?

*Ignoring the fact of obvious problems with the situation, like requiring a massive force to move the stick.

My friend, light is not instantaneous. Suppose your friend lives next door, around 10 metres away from yours.If you hold a 10 m long stick in your hand, and poke him, that surely will be instantaneous. The same happens with electrons in a conductor... Their speed is in picometres. Then how is it that immediately you put the switch on, your pc starts? This has got to do nothing with the speed of light... But u poke him today, he'll fell it just now, but u can see him feel that 5 years later!

 

[JesseM]

I guess I could have phrased it better, but you know what I mean. The technique of proving an assumption wrong by deriving a contradiction is clearly just as valid here as in any other area of mathematics.

But like I said before, I'm assuming that we have some complete set of facts about the conditions at every local point in the spacetime, as would be true in the computer simulation example where the computer generates entire histories. There can't be a contradiction in such a complete set of facts. But there could be a discontinuity, like one region of spacetime including me sending a 0 while a later region of spacetime has you receiving a 1...even if the local laws work correctly in each region there'd have to be a violation on the boundary between them somewhere, an unexplained flip from 0 to 1.

This is what I can't accept. The properties of tachyons and their interactions are such that all scientists would choose to murder their children rather than change a 0 to a 1 in a computer program? If I use a telescope to look for meteors before I make the change, I will die in a terrorist attack instead? If I lock myself away where I'm safe from terrorists, I have a heart attack instead? If I make sure that I'm in perfect health...I guess we're back to ninja turtles.

What I just described doesn't sound anything at all like the universe we live in, and I also don't think it can be justified by a rule that says that the same "local laws" are obeyed at each point. I don't think it's even consistent with such a rule. For example, if these "local laws" say that I can build a device that sends instantaneous messages (in the device's rest frame), and the same thing can't be done in another region of spacetime, then I would say that the local laws are different in the two regions of spacetime.

I never said anything about not being able to send instantaneous messages in every region. But to modify your argument a bit, it could be true that by self-consistency, the fact that I received a 1 in the past means that the sender at a later time is constrained so he can't send a 0 back in time, even if he knows I got a 1 and wants to create a contradiction, and even though another experimenter in a different part of spacetime could send a 0 with the same device because in her case doing so wouldn't create a contradiction. But then, even in a deterministic universe without time travel the conditions of one region of spacetime A may constrain the possibilities that lie in some other region B that lies in its future light cone, so certain events cannot happen in B that might happen in some other region of spacetime C with a different set of conditions in its past...that doesn't mean the local laws of physics are different in region B and C, it's just a matter of conditional probabilities! If you consider an ensemble of different spacetimes that all satisfy the local laws everywhere (like in the computer simulation argument where we imagine generating a huge number of random histories and then throwing out all the ones where the local laws aren't obeyed in each neighborhood, leaving us with an ensemble of possible histories that do obey these local laws everywhere) then any conditions that hold in region C in some members of the ensemble could be found in region B in other members of the ensemble, and vice versa. Same would be true for an ensemble of self-consistent histories, there'd be nothing that's consistently impossible in one region throughout the ensemble even though it's consistently possible in a different region.

Did you consider my computer simulation argument carefully? Suppose the underlying laws of physics in the simulation were something like lattice QCD or even a simple cellular automata type rule, where the law tells you what states are allowed in one "cell" given the states in surrounding cells, much the same way that in "4D chess" the piece that might be found on a square at one time-increment would depend on the positions of the pieces at other times (both past and future in 4D chess, just past in normal chess). Would you agree that for any such local laws governing a physical simulation, if we imagine a vast computer of the gods that has googleplexes and googleplexes of memory and can do googleplexes and googleplexes of calculations, then the computer could simply use the method of generating "random histories" where the state of each cell is decided in a completely random way and then the history looks at each and every cell at each time increment in the history to see if its relation with surrounding cells follows the correct local laws, throwing out the vast majority of random histories and only keeping the tiny tiny fraction that follow the correct local laws at each point? Would you agree that if the local laws allow for causality violation, the tiny fraction the computer didn't throw out would have self-consistent histories that obeyed the same local laws at each point? If so, suppose each self-consistent simulated history was so fine-grained and vast that over billions of simulated years you could observe the formation of stars, planets, and in some cases the evolution of life eventually leading to simulated sentient beings with brains as complex as ours...if some of those sentient beings tried to exploit the laws of physics in their simulated universe to send messages back in time and create paradoxes, wouldn't the mere fact that the computer had kept only the histories that were self-consistent and followed the same local laws everywhere, while throwing out all the histories that didn't satisfy this, mean that in any such history including sentient beings the beings would fail in their attempts to create paradoxes?

So we would at the very least have to talk about "global" laws about what the curves look like, and require that what we otherwise would have thought of as "local laws" are actually false, even though they work in all situations where no tachyons are involved. I know the principle explicitly said the there won't be any new physics, but now I think it contradicts itself on that point.

I disagree. Again, the mere fact that there is a single unique truth about what happens at each point in spacetime in any global "solution", and that the relation between what's happening at each point is constrained to relate in the same lawlike way to what's happening at nearby points, is enough to guarantee that everything is globally consistent. If you disagree, please think about my computer simulation analogy and tell me if you at least agree that this would be true in that case.

Even if we assume that there are such global laws (for both tachyons and normal matter), they don't seem to describe something that resembles the universe we live in, where people have an illusion of free will.

Well, we only have the illusion of free will because we haven't found any way to learn what choices we will make before we make them. I don't personally think that's ever likely to change but the simple fact that it hasn't happened yet doesn't prove it could never happen. And if we ever succeed in creating some type of artificial intelligence (for example, by mapping a human brain and simulating it in sufficient detail that the simulation behaved just like the original brain, an idea known as mind uploading) then the artificial intelligence could have experimental evidence it doesn't have free will, in the form of multiple parallel simulations of the mind in closed-off virtual environments running on deterministic computers with the same initial state, in which case each simulation should run in perfect lockstep. Of course this wouldn't be the same as knowing what you were going to do before you did it, but it would still be a demonstration that free will is an illusion, and it's the sort of thing I do expect to be possible in the real universe eventually if our civilization lasts long enough.

 

[dx]

Well, we only have the illusion of free will because we haven't found any way to learn what choices we will make before we make them...

Not sure what you guys are talking about since I didn't read the thread but..

Recognition of complementary relationship is not least required in psychology, where the conditions for the analysis and synthesis of experience exhibit striking analogy with the situation in atomic physics. In fact, the use of words like 'thoughts' and 'sentiments', equally indispensable to illustrate the diversity of psychical experience, pertain to mutually exclusive situations characterized by a different drawing of the line of separation between the observer and the observed. In particular, the place left for the feeling of volition is afforded by the very circumstance that situations where we experience freedom of will are incompatible with psychological situations where causal analysis is reasonably attempted. In other words, when we use the phrase 'I will', we renounce explanatory argumentation.

 

[Fredrik]

But like I said before, I'm assuming that we have some complete set of facts about the conditions at every local point in the spacetime, as would be true in the computer simulation example where the computer generates entire histories. There can't be a contradiction in such a complete set of facts.

I was talking about the method of proof by contradiction, and it can't be dismissed by saying that you are talking about a scenario without contradictions. It's certainly possible to make assumptions about matter that do lead to contradictions, and those contradictions would then prove the assumptions false.

I disagree.

I probably didn't express myself very clearly, since the things you said right after "I disagree" are all things I agree with. I meant e.g. that if the laws that we think describe the behavior of matter say that it's always possible for a computer hooked up to a transmitter to send "1", and "global consistency" says that it isn't, then the laws we started with were inconsistent to begin with! (Does the "principle" really add anything here? I don't think so. An inconsistent set of statements wouldn't be considered a theory, so we don't need a "principle" to eliminate it for us, at least not if we have a definition of "theory" that makes sense).

Let me be more specific. Maxwell's equations are consistent, but they can't tell us if a computer+transmitter is able to send a specific tachyonic message, because they don't say anything about tachyons. So we would need a theory of matter (in this context I consider all fields and particles to be "matter") in Minkowski spacetime that includes both electromagnetic fields and tachyons. If we think we have found such a theory, and we find that it says that the computer and transmitter can always be built and always do what they're programmed to do, then the conclusion must be that we were wrong to think that we had a consistent theory (since the axioms of the "theory" imply the contradiction I described in the other thread), and we would have to start looking for another one.

So when we consider the question "Are tachyons consistent with SR?", we need to be a lot more specific. Some candidate "theories" that seem like they might be an accurate description of tachyons and their interactions with normal matter will lead to contradictions, and some might not. The ones that do can of course be ruled out. The simplest theories (in particular the one that treats tachyons as classical particles that just happen to have spacelike world lines) do lead to contradictions, and they can't be saved by some "consistency principle".

Did you consider my computer simulation argument carefully?

I've read your arguments, but they are really just addressing aspects of this global consistency thing that I don't have a problem with.

it could be true that by self-consistency, the fact that I received a 1 in the past means that the sender at a later time is constrained so he can't send a 0 back in time, even if he knows I got a 1 and wants to create a contradiction,

I'm still not buying that a universe where every sender chooses to murder his children (or gets hit by a meteor) instead of sending the message can be anything like ours. I don't have a proof that it isn't (at least not yet), but I expect that one can be found.

There is however a (seemingly) less crazy scenario that I might be able to accept. Suppose that the (quantum) theory that describes tachyons and their interactions with normal matter predicts that executing the "send" command on the computer+transmitter will generate a tachyon pulse with some probability P<1 that goes to zero as the entire scenario "goes to a contradiction" in some sense. That sounds extremely weird, but not as weird as the meteor/murder option. I can't really decide if I consider this a reasonable possibility yet, or even if it really is less weird than "meteor/murder". I would at least have to think about what that "limit" really means before I can decide.

There's also the possibility that I suggested in the other thread: That the time it takes to emit/detect a tachyon grows faster than linearly as a function of the distance between the emitter and the detector.

I would say that neither of these "loopholes" in the original argument relies on a "consistency principle".

 

[Fredrik]

Not sure what you guys are talking about

We're talking about whether a "consistency principle" can be a reason to think that tachyons might exist. I still don't see how such a principle is actually saying something that isn't already a part of any reasonable definition of "theory".

 

[JesseM]

I was talking about the method of proof by contradiction, and it can't be dismissed by saying that you are talking about a scenario without contradictions. It's certainly possible to make assumptions about matter that do lead to contradictions, and those contradictions would then prove the assumptions false.

I'm talking about considering what would happen if you consider a very large ensemble (perhaps infinite) of "random histories" where each history consists of a set of facts about each local point in spacetime where the facts are assigned completely randomly, with no regard for any laws of physics whatsoever (aside from laws limiting what is possible at a single point, like laws which give allowable particle masses); then if we define "laws of physics" in terms of constraints on the relation between local facts at one point and local facts at other nearby points (or perhaps arbitrarily distant points if we allow FTL), then we can simply go through every history in the ensemble and throw out all the ones where the laws of physics don't hold at every point, then what we should be left with is a set of histories where the laws of physics do hold at every point.

Do you think there is something incoherent or impossible about the first part of this, considering a huge ensemble of "random histories"? If not, then by definition since each history gives only a single set of facts about what occurs at every point, then each history in the ensemble must be "noncontradictory", even if it shows complete disregard for any laws of physics. If you were arguing somehow that it would be impossible to find a single member of this ensemble that obeyed the laws of physics at every point (or that the laws of physics cannot be stated in a local form so that the notion of 'checking every point' in a history doesn't make sense) in the case where the laws of physics allowed for time travel, I suppose I could understand the argument even if I disagreed with it, but I don't understand how your claim of a "proof by contradiction" is supposed to apply to my argument, where by definition each member of the original random ensemble is a single noncontradictory history.

I probably didn't express myself very clearly, since the things you said right after "I disagree" are all things I agree with. I meant e.g. that if the laws that we think describe the behavior of matter say that it's always possible for a computer hooked up to a transmitter to send "1" and "global consistency" says that it isn't, then the laws we started with were inconsistent to begin with!

I still think you are failing to distinguish between conditional and unconditional possibilities. Even in a non-time-travel universe it's not "always possible" for a computer hooked up to a transmitter to send a 1 if we take into account conditions in the past or future light cone of the event of the computer sending a signal--for example if the laws of physics are deterministic then detailed knowledge of the transmitter's microstate in the past light cone may be sufficient to guarantee that the computer is going to send a 0 (even if its macrostate immediately before sending a signal is the same macrostate that has been observed for other transmitters that sent a 1), and likewise if we imagine an observer viewing the 4D spacetime from "outside" who can examine conditions in the future light cone before examining conditions when the signal was sent, that observer can see that if the future light cone includes the receiver getting a 0, then it's not possible for the transmitter to have sent a 1. Same in a universe with time travel, if you think in terms of unconditional probabilities then it is indeed "possible" for a transmitter of this type to send a 1, but if you already know some more facts about other regions of same history then the conditional probability of it sending a 1 given these other facts may be zero.

Let me be more specific. Maxwell's equations are consistent, but they can't tell us if a computer+transmitter is able to send a specific tachyonic message, because they don't say anything about tachyons. So we would need a theory of matter (in this context I consider all fields and particles to be "matter") in Minkowski spacetime that includes both electromagnetic fields and tachyons. If we think we have found such a theory, and we find that it says that the computer and transmitter can always be built and always do what they're programmed to do, then the conclusion must be that we were wrong to think that we had a consistent theory (since the axioms of the "theory" imply the contradiction I described in the other thread), and we would have to start looking for another one.

So when we consider the question "Are tachyons consistent with SR?", we need to be a lot more specific. Some candidate "theories" that seem like they might be an accurate description of tachyons and their interactions with normal matter will lead to contradictions, and some might not. The ones that do can of course be ruled out. The simplest theories (in particular the one that treats tachyons as classical particles that just happen to have spacelike world lines) do lead to contradictions, and they can't be saved by some "consistency principle".

Again, if our laws of physics give some set of possibilities for local conditions at each point in spacetime (or at each cell in a discrete cellular automata or something similar), then we can simply consider the ensemble of all possible ways of assigning local conditions to each point, the vast majority of which will be completely random and won't obey any laws, but which will at least each be noncontradictory. Then if we state "laws" in terms of mutual constraints on the relationships between conditions at different points (possibly differential equations dealing with infinitesimally nearby points) we can consider the question of whether there will be at least some members of the ensemble of random histories which obey these laws at each point, and since every member of the original ensemble was a noncontradictory history, the subset of law-obeying histories would each be noncontradictory too. Perhaps you are saying that your "proof by contradiction" is supposed to prove that there would be zero self-consistent histories of this type, but if not I don't understand how your argument is supposed to be a counter to mine. And if that is what your argument is supposed to prove, it seems much too handwavey, as it deals with complicated macroscopic devices as opposed to microphysics--there's no way we could actually build a device that would infallibly send a 0 when it received a 1, there's always some possibility of error or interference from external influences.

I'm still not buying that a universe where every sender chooses to murder his children (or gets hit by a meteor) instead of sending the message can be anything like ours. I don't have a proof that it isn't (at least not yet), but I expect that one can be found.

But remember, the whole point of the rule is that we generate a huge number of universes where anything can happen and then throw out the ones that don't meet the correct conditions. Some of these random histories might include sub-regions that obey the correct local laws and which include things like an experimenter getting a "1" from his partner outside the region (with memories that the partner was supposed to just transmit the same digit back by tachyonic signal) and later sending a "0" to his partner, but most random histories like this would get thrown out because the local laws failed to be obeyed at points outside the region (for example, if local laws were also obeyed in the region of the partner, and that region included the event of the partner getting a "0" and sending back a "0", then there would have to be some local along the points in spacetime that the tachyon's worldline passed through). By definition, the only ones that remain after the process of throwing out all those that are noncontradictory (because all the 'random histories' generated before any were thrown out were at least noncontradictory) and which have no discontinuities or other breakdowns in the local laws. Since this is just a tiny subset, any given region of spacetime where someone is trying to create a contradiction may be a lot more likely to contain "weird events" then if we consider the larger subset of random histories where just that region (but not necessarily the rest of the universe outside of it) obeyed the correct local laws throughout and contained someone trying to create a contradiction, but that's because we had to throw out all the ones where various coincidences didn't prevent someone from acting in a way that could be part of a single self-consistent global history that obeyed the correct laws everywhere.

Another analogy: suppose I show a series of videos of people approaching unlocked doors with intent to open them, pausing each video before they actually reach the door. You'd expect that most of them will reach the door and succeed in opening it, right? But suppose I tell you I am actually an immortal alien with a fetish for seeing humans fail to open doors, so I have been using tiny hidden cameras to make movies of every human that ever approached an unlocked door with intent to open it throughout history, and then I simply throw out all the boring ones where they succeed and keep the interesting ones where they don't for my collection. Then if you believe my story is correct, you naturally know that in all of the videos the person will fail to open it--there might be all sorts of weird "coincidental" reasons, for example some might show the person hearing someone in the opposite direction calling their name before reaching the door, some might show them slipping on the floor and being knocked unconscious, some might show them simply stopping and changing their mind for some reason, etc. Taken together this set of videos would seem extremely coincidental, but if we know it's just a specially-selected subset of a much larger set of videos where the door-openings were usually successful, we needn't find these "coincidences" too surprising!

 

[JesseM]

We're talking about whether a "consistency principle" can be a reason to think that tachyons might exist. I still don't see how such a principle is actually saying something that isn't already a part of any reasonable definition of "theory".

What do you mean by "reason to think that tachyons might exist"? I certainly don't think tachyons are likely to exist in the real world, or that a "consistency principle" increases the likelihood that they exist in the real world. It just shows that there doesn't need to be any logical contradiction in the notion of tachyons (or any other form of causality violation) that would allow us to rule them out a priori. I'm just saying that it's logically possible that that 1) the local laws of physics are Lorentz-invariant and allow tachyons, and 2) out of all possible "histories" which assign local states to each point in spacetime, it's logically possible that some small subset would obey the local laws specified by 1 at every single point. If 1 and 2 are correct, then any member of the subset described by 2 would necessarily be one that is globally self-consistent, so any attempts to create "time travel paradoxes" would fail in this subset.

 

[JesseM]

Not sure what you guys are talking about since I didn't read the thread but..

Well, if you want to understand this discussion between me and Fredrik it isn't actually necessary to read the whole thread, you can just start with Fredrik's post #37 and read subsequent posts by Fredrik and me after it.

 

[PAllen]

Back to (almost) the initial topic of this thread. Early on, someone proposed that hitting a 5 meter rod would push 'instantly' on the other end. This was roundly and validly criticized. It occurred to me that modern techniques should readily measure the small, finite time for the far end to respond. The link below describes a test method to determine the tensile strength of rigid ceramic rods of laboratory size precisely by measuring the propagation delay between hitting one end at arrival at the other. Sometimes this sort of concrete (or ceramic) response is better than a lot of theory.

http://www.mater.upm.es/fgalvez/PDF/Dymat00-Tech.pdf

 

[Fredrik]

I'm talking about considering what would happen if you consider a very large ensemble (perhaps infinite) of "random histories" where each history consists of a set of facts about each local point in spacetime where the facts are assigned completely randomly, with no regard for any laws of physics whatsoever (aside from laws limiting what is possible at a single point, like laws which give allowable particle masses); then if we define "laws of physics" in terms of constraints on the relation between local facts at one point and local facts at other nearby points (or perhaps arbitrarily distant points if we allow FTL), then we can simply go through every history in the ensemble and throw out all the ones where the laws of physics don't hold at every point, then what we should be left with is a set of histories where the laws of physics do hold at every point.

Do you think there is something incoherent or impossible about the first part of this, considering a huge ensemble of "random histories"?

I don't. That's why I said that your analogies are only addressing the things I don't have a problem with.

I would describe the things you just said (in this quote) a bit differently. Whatever theory we have for tachyons and their interactions, it includes some sort of "equation of motion". Let's say that the theory is a classical field theory. Then the solution is a field. The algorithm you're describing is simply generating fields randomly, and then checking if they solve the equation. A field solves the equation of motion if and only if, for each finite region of spacetime, the restriction of the field to that region is the solution to a boundary value problem for that region. (The boundary value problem is defined by the same equation and by the values of the field on the boundary). This is all fine, but it doesn't seem to have anything to do with some "principle of consistency".

If not, then by definition since each history gives only a single set of facts about what occurs at every point, then each history in the ensemble must be "noncontradictory", even if it shows complete disregard for any laws of physics.

Agreed. When the theory is a field theory, a random "history" is just a field that may or may not solve the field equation.

I don't understand how your claim of a "proof by contradiction" is supposed to apply to my argument, where by definition each member of the original random ensemble is a single noncontradictory history.

Exactly...so why did you use these arguments in response to something I said about proofs by contradiction? (Rhetorical question). We have clearly been talking past each other for a while.

Even in a non-time-travel universe it's not "always possible" for a computer hooked up to a transmitter to send a 1 if we take into account conditions in the past or future light cone of the event of the computer sending a signal

I was just showing you an example of how it's possible to make assumptions that lead to a contradiction. The assumption that the computer and tachyon transmitter can always do what they're supposed to do implies that there are no restrictions on the initial state.

What do you mean by "reason to think that tachyons might exist"?

The issue isn't whether tachyons can be ruled out, but whether the consistency principle prevents them from being ruled out. I still say that the principle adds absolutely nothing. Some sets of axioms for candidate theories of tachyons in Minkowski spacetime can be easily dismissed, as they are inconsistent (and wouldn't be if we just remove the tachyons), but that's really all we can say. This doesn't involve the principle in any way. The principle doesn't tell us anything (as far as I can tell) about which axioms define valid theories and which ones don't. It doesn't seem to say anything about anything.

It just shows that there doesn't need to be any logical contradiction in the notion of tachyons (or any other form of causality violation) that would allow us to rule them out a priori.

How does it do that? Any theory of matter and interactions in Minkowski spacetime (or any other spacetime) is consistent by definition of "theory", so we don't need a "principle" to tell us that a theory of tachyons is consistent. The principle also doesn't invalidate any proof that shows that a given set of axioms is inconsistent. So what exactly does it do?

Edit: I appreciate the efforts you have made trying to explain your views to me, but I don't think more analogies would help. (Just trying to save you some time )

 

[JesseM]

I don't. That's why I said that your analogies are only addressing the things I don't have a problem with.

I would describe the things you just said (in this quote) a bit differently. Whatever theory we have for tachyons and their interactions, it includes some sort of "equation of motion". Let's say that the theory is a classical field theory. Then the solution is a field. The algorithm you're describing is simply generating fields randomly, and then checking if they solve the equation. A field solves the equation of motion if and only if, for each finite region of spacetime, the restriction of the field to that region is the solution to a boundary value problem for that region. (The boundary value problem is defined by the same equation and by the values of the field on the boundary). This is all fine, but it doesn't seem to have anything to do with some "principle of consistency".

What do you mean? Do you agree that if the local laws are such that some valid solutions include causality violations (whether this is because the local laws involve time travel or because the local laws include the Einstein field equations along with matter fields that violate the energy conditions that need to be violated in order for a GR solution to allow for the creation of timelike curves), then if we generate a vast (perhaps infinite) set of "random spacetimes" with all the fields and curvature at each point set at random, then throw out all the ones that include any violations of the local laws leaving only spacetimes that respect them at every point, then these remaining spacetimes will all obey the principle of self-consistency? As the authors of the paper on the self-consistency principle said in the quote I brought up earlier, the "principle of consistency" is not a separate assumption from the idea that we live in a spacetime with a unique truth about the physical facts at each point and where the same local laws are respected in the neighborhood of each point, it's just a statement of one consequence of those assumptions for any situation involving causality violations. But you seemed to say that somehow the "principle of consistency" was actually inconsistent with the idea that the same local laws are respected at every point, in statements like this one from post #57:

This is what I can't accept. The properties of tachyons and their interactions are such that all scientists would choose to murder their children rather than change a 0 to a 1 in a computer program? If I use a telescope to look for meteors before I make the change, I will die in a terrorist attack instead? If I lock myself away where I'm safe from terrorists, I have a heart attack instead? If I make sure that I'm in perfect health...I guess we're back to ninja turtles.

What I just described doesn't sound anything at all like the universe we live in, and I also don't think it can be justified by a rule that says that the same "local laws" are obeyed in each region of spacetime. If these "local laws" say that I can build a device that sends instantaneous messages (in the device's rest frame), and the same thing can't be done in another region of spacetime, then I would say that the laws in that region are different from the laws in the first region, or alternatively, that the laws are the same everywhere, but different from what we previously thought that they were. I know the principle explicitly said the there won't be any new physics, but now I think it contradicts itself on that point.

So do you still think there is some contradiction? Obviously any theory involving tachyons would necessarily involve some new physics, but the principle was originally meant to apply in the GR case, so let's consider that one. If 1) we assume GR plus some local laws governing matter fields, and these laws allow for the violation of energy conditions needed for CTCs, and they are also rich enough to allow for the existence of things like sentient observers and computers, and 2) we imagine generating the infinite set of all possible pseudo-Riemann manifolds with arbitrary curvatures and arbitrary values for the matter fields at each point, and 3) we throw out all the ones that don't respect the Einstein field equations and the local laws governing matter fields, then 4) do you agree it's very plausible that at least some of the remaining lawful spacetimes will include sentient observers who have access to time travel and at some point have a desire to "change history"? If you do agree with 4), then do you agree that by just virtue of how this set of lawful spacetimes was generated, in every single member of the set all sentient observers must fail in attempts to change history, whether for simple reasons like changing their minds or very weird coincidences like dying in a terrorist attack or having a heart attack? (no need to answer this question if you don't agree with 4, obviously!) And if you do agree with that last bit, then would you also agree that the conclusion of such consistent failures 'can be justified by a rule that says that the same "local laws" are obeyed in each region of spacetime'? Please give me clear answers to these questions, because I'm really having trouble understanding what you're arguing.

I was just showing you an example of how it's possible to make assumptions that lead to a contradiction. The assumption that the computer and tachyon transmitter can always do what they're supposed to do implies that there are no restrictions on the initial state.

But I thought your earlier argument wasn't just that these assumptions lead to a contradiction, but that you think we actually have some very good reason to think these assumptions are valid, and thus that any universe in which events "conspired" to prevent people from creating paradoxes would be one wildly incompatible with facts we already know about the real universe. If so, I just don't see it--a universe with tachyons or wormhole time machines that sentient beings took a while to discover/create could well look a lot like ours until the time where some causality-violating device was actually built by them.

The issue isn't whether tachyons can be ruled out, but whether the consistency principle prevents them from being ruled out. I still say that the principle adds absolutely nothing.

But like I said, isn't that exactly what the authors of the paper on self-consistency were saying in that quote too? The self-consistency principle is not any sort of additional law beyond just the requirement that the same local laws apply everywhere, if the local laws allow time travel then it seems to just be a logical consequence.

Some sets of axioms for candidate theories of tachyons in Minkowski spacetime can be easily dismissed, as they are inconsistent (and wouldn't be if we just remove the tachyons), but that's really all we can say. This doesn't involve the principle in any way. The principle doesn't tell us anything (as far as I can tell) about which axioms define valid theories and which ones don't. It doesn't seem to say anything about anything.

Like the quote said, it's just a statement of the fact that no new laws come into play in regions containing CTCs than in other regions (and in GR CTC-containing regions may be cleanly divided from regions where none can occur by Cauchy horizons), the same local laws apply everywhere. If you have no problem with this, I don't see why you object so strenuously to the idea that events would "conspire" to thwart attempts by time travelers to change history, do you think it's not an obvious logical consequence of the assumptions of "local laws allow for solutions with causality violations" + "local laws apply at every point"?

The principle also doesn't invalidate any proof that shows that a given set of axioms is inconsistent.

Do you there is an inconsistency in the idea of the local laws allowing for causality violations plus the ideas that the local laws apply at every point and that they allow for things like computers and sentient observers who formulate plans to change history?

 

[Fredrik]

A short summary in case someone else wants to join in: There's a standard argument that attempts to show that FTL messages are inconsistent with special relativity. (See this post). It shows that the following assumptions lead to a contradiction:

• The assumptions of special relativity.
• We can program a computer to send the same bit it received, and make sure that it actually sends it after a delay specified by the program.
• We can program a computer to send the XOR ("opposite") of the bit it received, and make sure that it actually sends it after a delay specified by the program.
• It's possible to build a device that sends a message that travels at speed v>c relative to the device, when it's instructed to do so by a computer.

The counterargument that was brought up by JesseM in this thread, and by Demystifier in another one, goes roughly like this: It's undeniable that those assumptions lead to a contradiction, but that doesn't rule out FTL messages. The time evolution of the state of the matter in the universe is described by a solution to an equation of motion of some theory. A solution is by definition a single-valued function, and it would (at least) take a multi-valued function to describe a "contradiction" (if it makes sense to try to describe contradictions at all), so there can't be a solution that describes an experiment where the components mentioned above work properly. There might be solutions where one component part is malfunctioning, solutions where the experimenter decides not to push the start button, solutions where the experimenter decides to push the start button but gets hit by a meteor that's been heading his way for a billion years just as he tries to push it, solutions where an intelligent species discovers a way to blow up their solar system the year before they would have discovered how to send FTL messages...but no solutions where this whole thought experiment is actually carried out.

The question is, is this "consistency principle" a valid counterargument to the standard argument against FTL messages? Is it a reason to say that there might exist a theory that allows FTL messages and is consistent with special relativity? I'm still not sure. Something about this argument just feels very wrong, but I still can't put my finger on it.
[/summary]

It's interesting to try this counterargument on a "proof" that Newtonian gravity is inconsistent with SR. Consider two rockets that are held at fixed positions in some inertial frame S. The rockets are attracted to each other gravitationally, but they're held in place by a thin string that just barely can handle the force. Any additional force, and the strings would break. At some event on the world line of rocket A, its engine is turned on. It breaks the string that's holding it, and it starts accelerating towards rocket B. As the distance in S between the rockets decreases, the gravitational force that A exerts on B increases, so B's string must break too. But when? Newton's law of gravity says that the effect will be felt "immediately", but that means something different in each inertial frame, and SR says that all these inertial frames are equivalent. So the theory of Newtonian gravity+SR makes infinitely many different predictions about at what event B's string breaks.

The counterargument would be that the equation of motion of matter can't have a solution that describes this scenario. There might be a solution that describes a scenario that starts out the same, but where rocket A never moves. So we can't rule out that Newtonian gravity is consistent with SR. This is what makes things interesting: While using the "consistency principle" counterargument to save Newtonian gravity, we ruled out motion instead. Newtonian gravity is consistent with SR, but only if massive particles are constrained not to move. This means that the theory that saves Newtonian gravity makes predictions that are contradicted by all experiments. So the counterargument is useless here, and really doesn't save Newtonian gravity.

I don't have a similar argument for FTL messages, but that doesn't mean that one can't be found. So while I agree that the counterargument has shown that things aren't quite as simple as they seem at first, I'm still not convinced that it can save FTL messages. I also think it's misleading to call this counterargument a "consistency principle", because it's really just a reminder of what a solution is.