
#55
Oct310, 11:11 PM

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#56
Oct310, 11:20 PM

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#57
Oct410, 01:28 AM

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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. 



#58
Oct410, 02:04 AM

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#59
Oct410, 02:50 AM

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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 timeincrement 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 selfconsistent histories that obeyed the same local laws at each point? If so, suppose each selfconsistent simulated history was so finegrained 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 selfconsistent 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? 



#60
Oct410, 05:16 AM

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#61
Oct410, 05:57 PM

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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". 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". 



#62
Oct410, 05:59 PM

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#63
Oct410, 07:01 PM

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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. 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 itthere 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 speciallyselected subset of a much larger set of videos where the dooropenings were usually successful, we needn't find these "coincidences" too surprising! 



#64
Oct410, 07:30 PM

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#65
Oct410, 07:33 PM

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#66
Oct410, 09:14 PM

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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/Dymat00Tech.pdf 



#67
Oct410, 09:48 PM

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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". 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 ) 



#68
Oct410, 11:32 PM

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#69
Oct2010, 07:04 PM

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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 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. 


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