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Help understand FTL causality implication

  1. Oct 29, 2012 #1
    First of all, I am fairly new to relativity, but not clueless. I am not saying that FTL is possible. I am not denying relativity principles. I am stating that FTL may be plausible.

    Relativity gives flexibility to how you can synchronize clocks and that does not affect outcomes of most equations and measurements. However, I believe that there are two ways to understand Maximum/Unlimited "faster than light speed" with causality and simultaneity in mind, which depends on which "synchronization method" will be used.

    For the sake of clarity, I will not involve moving objects, so all speeds and distances will involve distances and times between objects that don't move wrt themselves.

    If we were to look at a distant (or any) object, we will be receiving a delayed image of it. Arbitrary clock synchronization methods would allow us to perceive that the delayed image is in fact a target of our maximum velocity (that is FTL) so that sending something at maximum velocity to "now" at that location would be traveling to impose that something over that received image at t+1 observer's time. In that case, indeed FTL would mean that we would go back in time at which we could send signals to the past of what we consider the "present". Basically if we consider Einstein's definition of spacetime (where no observers agree on simultaneity of events and where definition of simultaneity is somewhere arbitrary, to become a definition of the universe) we determine maximum speed to be distance traveled (constant) over time the trip took time (~0) and allow the time at target to be anywhere in the range of 2t length of a time period - where t is defined to be the half of the time it takes for light to go from source to target and come back.

    If we were to define "present" to be a time that is synchronized per Einstein's synchronization, then FTL shouldn't necessarily imply paradoxes. If we define that present to be t0 at A = t0 at B where t0 is the clock reading on Einstein's synchronized clocks then the "maximum speed" would be defined as v=dt where d is the distance between the objects, t is the time it takes for the event to travel (~0) but the target's time at the arrival of the superluminal event is actually defined!

    Even in this case FTL does lead to some bizarre things, but I believe none lead to "traveling to the past".

    For example, if some observers were to observe a near-instantaneous superluminal travel from earth to Centauri:

    - On earth:
    An observer would observe the maximum-velocity superluminal traveller just leave earth and continue to approach Centauri over a course of 4 years.

    - On Centauri:
    An observer would see the traveller appear instantly before them, but there would appear to be three copies of the traveller:
    1) One that is the image of him at "now" living his normal life on Centauri.
    2) Another with him traveling BACK to Earth, that the observer would observe over a period of 4 years.
    3) Another with him drinking his coffee on earth or whatever during a course of 4 years with the final event of that image joining #2 at his apparent time of takeoff from earth.

    - On a space station forming a 4-ly equilateral triangle with Centauri and earth:
    An observer would not actually see anything interesting until about midway through the 4th year. Most of the time he would see the traveler living his normal life on Earth.
    Starting mid-4th year, he would see additional two images of the traveler splitting from the mid-point between Centauri and Earth. One image would be approaching earth and another Centauri. The "show" would end at the end of the 4th year with near-simultaneous launch of the travel from Eaarh and arrival on Centauri, at which point both split-images would join up with the events.

    I don't see any logical issues with the thought experiment here besides bizzareness of the events. If we "replace" the traveler with "superluminal message" or even "a conversation", I still don't see any logical flaws that produce causality problems. Can someone help iron this out?
     
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  3. Oct 29, 2012 #2

    PeterDonis

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    This is only true if you insist on privileging one particular simultaneity; that is, FTL travel can only be "instantaneous" to one particular privileged family of inertial observers. In your thought experiment where someone travels FTL from Earth to Alpha Centauri, you can only rule out paradoxes if the travel is always instantaneous as seen from the frame in which Earth and Alpha Centauri are at rest, regardless of the motion of the "source". (We are assuming that the Earth and Alpha Centauri are at rest relative to each other, even though in reality they aren't, since this is just a thought experiment.) If the travel is instantaneous as seen from the frame of the source, then you can't rule out paradoxes.

    For example, suppose that the FTL traveler didn't launch from Earth, but instead launched from a rocket ship flying past Earth, in the direction away from Alpha Centauri at a significant fraction of the speed of light. Suppose that FTL travel appears instantaneous in the rest frame of the source. Then, as seen in the Earth/Alpha Centauri frame, this FTL travel will go backwards in time (if the Earth time of departure is t = 0, then the Earth/Alpha Centauri time of arrival will be negative). Now the traveler, when he arrives at Alpha Centauri, comes to rest relative to Alpha Centauri/Earth; then he launches FTL again from Alpha Centauri back to Earth. This FTL travel will (by hypothesis) appear instantaneous in the rest frame of Earth/Alpha Centauri, and that means the traveler will arrive back at Earth *before* he launched, forming a closed causal loop, i.e., a potential paradox.

    I don't see any problem with your descriptions. However, the fact that those descriptions are consistent is not sufficient to rule out paradoxes. See above.
     
  4. Oct 29, 2012 #3
    Please define "appears instantaneous". If you define "instantaneous" to be "observer in the rocket ship sees traveler arriving at target instantly", then that is traveling back in time and not instantaneous and not defined as "instantaneous" in the way I described it in my example. Please take the time to read, if you didn't read carefully. I apologize if I didn't make the point clear.

    Also please refrain form using moving frames, if at all possible. I specified in the original post that I was trying to constrict the example to source and target not moving wrt each other. For moving frames, I'd have to understand time synchronization between them.
     
    Last edited: Oct 29, 2012
  5. Oct 29, 2012 #4

    PAllen

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    Suppose there are a pair of rockets, each traveling .8c in the same direction per earth (along the earth - alpha cent. line). One rocket is near earth, the other near alpha cent. Suppose the rockets (at rest relative to each other) have synchronized clocks. Suppose earth rocket sends instant signal to alpha rocket. Then, per earth, this signal has gone back in time. Further, if the alpha slow moving satellite near alpha rocket is 'passed' this message, and sends a response back to earth FTL (now earth - alpha rest, and clock synch), then earth will receive this answer before sending the original message.
     
  6. Oct 29, 2012 #5
    Moving clocks again... Sorry, but I don't understand. Rockets are moving.

    I also don't understand why you say "Then, per earth, this signal has gone back in time.". It has not. It arrives at October 29 2012 per Synchronized-clock time", which earth will see arriving with telescopes only 4 years later (in 2016).

    Edit: if the signal was INSTEAD sent by speed of light, it would arrive at Centauri in 2016 and earth would see the arrival of the signal in 2020. the signal would show recording of the Centauri clock showing 2016.

    Isn't that the common misconception about FTL travel that I mentioned?
     
    Last edited: Oct 29, 2012
  7. Oct 29, 2012 #6

    PAllen

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    You say: " I am not denying relativity principles" . If you also say "Rockets are moving" even though they are inertial and at rest relative to each other, you not only deny all of relativity but all of Newtonian and Galilean physics. Sorry, you can't have it both ways. Either it is ok to talk about rockets at rest with respect to each other with their own synchronization, or you set physics back literally thousands of years.

    As for the rest of your post, it shows you don't even know the computational aspects of Lorentz transform. A rocket moving at .8c in the the E(arth)-A(lpha) line,near A, sending an instant signal to another rocket at rest relative to it in near E, and simultaneous with the A rocket per the rockets doing simultaneity the same way E-A planets do - will arrive at near earth way before earth sent the initial signal. (By doing simultaneity the same way, I mean synchronizing clocks - between the rockets at relative rest - using Einstein synchronization convention).

    Exercise for you: until you can at lease compute this (irrespective of what you think of it) you actually understand nothing of SR. Sorry.

    [if you really can't work it out yourself, here is a link: http://en.wikipedia.org/wiki/Tachyonic_antitelephone ]
     
    Last edited: Oct 29, 2012
  8. Oct 29, 2012 #7

    PeterDonis

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    In the Earth/Alpha Centauri rest frame, the time of arrival is the same as the time of departure.

    For any FTL travel, there will be *some* frame in which it appears instantaneous in the above sense. I was assuming that the Earth/Alpha Centauri frame was that frame for simplicity, but it's your scenario; if you want to specify that the travel appears instantaneous in some other frame, go ahead. But there will always be some such frame, and that fact by itself is enough to ground the conclusions I drew.

    If you exclude moving frames then you exclude the possibility of paradoxes. But the universe doesn't exclude moving frames, so if you want to explore whether paradoxes are possible with FTL travel, you have to consider moving frames.
     
  9. Oct 29, 2012 #8
    I saw the actual link and that's what prompted me to post this. Relativity is great at measuring light and delayed events, but not so good at establishing simultaneity or the actual universe (under the covers of EM), and I suspect that Lorentz transformation is susceptible to his flaw too. If there is something int he transformation that would make the A or E rocket receive that superluminal message at other than 2012, then you are correct - I don't agree with the principles.


    If at time of "instantaneous" broadcast transmission of the message anyone's clock showed anything other than October 29 2012 at send and arrival time for all four components of the system then the method of clock synchronization is wrong, and I don't know yet how to perform it. Using any formulas to account for FTL is in no relativity books, because FTL i snot defined anyways.

    I know that non-relativistic universal time synchronization sounds Newtonian, but it's the way I feel that the universe is - and no theory or formula can prove otherwise. If you can, then feel free to do so. But if you do, understand that:
    1) If any observes OBSERVES another's clock to be showing exact timestamp as their own then one of the clocks is wrong.
    2) Any observer must observe other clocks to be delayed.
    3) Any observer can only predict where another object is, but never know exactly where the object is or see any events until the light reaches it. (Like a blind bat hearing the lightning 300m away 1 second later, or needing 2 seconds to use sonar to determine position of a 300m away object). Observers can only predict simultaneity or make conclusions after the fact.
    4) Any non-inertial observer can estimate "time now" quite precisely if they pick up the nearest clock from an army of infinite number slowly transported clocks distributed across the universe.

    No statement above contradicts with anything SR-based measurements performed to date did measure, so I am only enhancing it and refining some confusing terms. In some cases, input and result may just have to be interpreted correctly.

    I don't think it's fair to ask a Software Engineer to learn SR form cover to cover in order to pose a philosophical question. If you were on a software forum claiming that there's a bug in Windows, I wouldn't ask you to understand Windows source code to claim that you are experiencing a bug.

    So then explain to me what's wrong with the rocket's understating of simultaneity, and why are they wrong in the calculation. Don't try to attack me for my lack of SR knowledge.
     
  10. Oct 29, 2012 #9

    PeterDonis

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    In other words, you don't understand how moving frames work, yet you are making assertions that depend on understanding how moving frames work.

    Einstein clock synchronization is actually very simple; you can do it in a "moving" frame ("moving" relative to the Earth/Alpha Centauri, which we appear to be taking as the "stationary" frame for this discussion) just as easily as in the "stationary" frame. The key point is that any two observers that want to synchronize their clocks using Einstein clock synchronization must be at rest relative to *each other*. They don't have to be at rest relative to anything else.
     
  11. Oct 29, 2012 #10

    PAllen

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    The issue is what is 2012. Both 2012 per earth and alpha is different than both 2012 per comoving rockets nearby each.

    It is much worse than Newtonian. Newton and Galileo accepted that two comoving rockets were in every way physically indistinguishable from earth - alpha.


    I am actually a database performance expert, by profession, and have no formal degree in anything. Almost all I know about physics and math is self taught. There are a number of people here who have significant mastery of SR and GR from systematically reading textbooks on their own. Note, I have not read a college textbook on quantum field theory. Therefore, I would never conceive of going the quantum theory forum and claiming 'Feynman is all wrong and makes no sense; the world can't work this way with stupid entanglement and virtual particle following all possible paths; here is my better understanding, that I have without mastering the established knowledge'.
    There is nothing wrong with the rocket's understanding of simultaneity. The issue is simply if you accept that:

    - two rockets at rest with each other see the same physical laws and can use the same methods as two planets at rest
    - specifically, that Maxwells equations for EM hold identically for both

    then it follows necessarily that if each is allowed to sent an FTL signal (as perceived by each mutually at rest pair), then together they can arrange to have earth get a response to message before sending it.

    I will post more details in a succeeding post, since you seem unwilling to do work on your own.
     
    Last edited: Oct 29, 2012
  12. Oct 29, 2012 #11

    PeterDonis

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    Just for the record, I am one of these (at least, for some value of "significant level of mastery" :wink:). I have degrees in Nuclear Engineering, but none of my formal studies involved GR and they involved only the very basics of SR (what was needed to understand nuclear reactions in which some of the particles attain relativistic velocities). Everything I post about here on PF is based on my own self-education.
     
  13. Oct 29, 2012 #12
    But it should not be. Both rockets should be picking up local broadcasts of timestamps from local systems which should state Oct 29 2012, hence they should both be having the same readings.

    If they send data instantly to each other, those should arrive at time locally read Oct 29 2012. Any other date than that, and we messed up. I believe that they will differently measure the distance between the stars and themselves and each other, but that is fine.

    I mean you can't use formula for light to calculate where to send superluminal signal to, the same way you shouldn't use speed of sound to calculate where to send the light signal, as you wouldn't be using some light-based transport mechanism that would use means used in Relativity, but warp drive and.or some form of entanglement which are not conventional means of transport.



    So what is the problem then? If they are near earth/alpha at time of sending signals so their date is Oct 29 2012.
    Something to aspire to :)

    Yeah, and you you quite confidently explained to me how events don't take infinite time to escape micro black holes because geodesics change over time (time changing over time or something like that) :D
     
  14. Oct 29, 2012 #13

    PAllen

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    How do you propose:

    1) Earth and Alpha synchronize their clocks
    2) Co-moving rockets synchronize their clocks

    I am assuming each uses Einstein's convention.

    If you assume that they do something different (please explain, as clearly as you can), then at least one of them will see Maxwell's laws violated (which include the fact that light propagates at c, independent of source velocity). That is, if they agree on simultaneity, they cannot agree on the laws of physics.

    [Edit: Note, I am not writing up any calcutations of a tachyon anti-telephone scenario until the above is resolved because I see it would be rejected out of hand by you if we don't have agreement on the above issues. In particular, we must have agreement that all laws of physics are the same in all inertial frames, including the laws governing FTL signals.]
     
    Last edited: Oct 30, 2012
  15. Oct 29, 2012 #14

    PeterDonis

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    I explained to you that *signals* (not events) can escape from *evaporating* black holes (not "micro" black holes--a BH of any size can evaporate), which are quantum objects, as opposed to standard classical GR black holes, which aren't. This is because an evaporating BH is not static--it doesn't stay the same for all time--unlike a standard classical GR BH, which is and does. None of this requires formal studies in GR to understand.
     
  16. Oct 30, 2012 #15
    SR defines Length/time very specifically, this "ties" into the metric of spacetime. (along with...everything else)

    Discussions about FTL spoils this concept of spacetime. I would be interested to know how you would measure (define) length/time with this new maximum speed in mind.

    I am unsure how the statement "FTL is plausible" floats in the context of relativity principles.

    My perspective is that relativity principles imply that FTL is not only impossible, but illogical.

    I suppose to say it differently how would an observer measure FTL, where the continuum is a constant & c, intervals are invariant ect ect.

    The only case I am aware of with this kind of observation is where there is literally an increase in distance/spacetime in addition to the maximum interval (c).
     
    Last edited: Oct 30, 2012
  17. Oct 30, 2012 #16
    That _IS_ the problem that needs solving.

    Using just elativity between two individual actors in the system would be too simplistic for this problem. I don't think that GPS problem, for example, was as simple as that to solve. On the wikipedia page it says

    So to answer your question, the method would have to yield results that would be matching the results of the method that I described above:
    Each can estimate "time now" quite precisely if they pick up the nearest clock from an army of infinite number slowly transported clocks distributed across the universe. Let's say that clocks are set to "SMT" - Sun Mean Time. So for example, I am in a rocket and I want to know what time it is, I get my hand out the window and pick up a slowly transported clock :) Now you could make the problem a bit more complex and have the rockets seed the clocks and the whole system uses RMT (Rocket Mean Time) as reference, and per relativity, it should be a valid scenario and I personally don't see a problem with it . In that case the seeded slowly transported clocks would be constantly colliding with earth and earth-based clocks would have to be adjusted to run slower.

    If we take the SMT scenario, it means that for co-moving rockets, they would have to carry an additional clock that changes clock rates to account for time dilation by calculating distance from SMT "main clock" at any given time (or use a better method). Only then we can talk about simultaneity wrt earth/alpha.

    And of course there would be a problem with some GR principles if we took them as-is. But we could say the same way that GPS satellites measure speed of light to be different than C because their clocks are built to tick at a different rate. In any case, what I am trying to say, I guess, is that I believe that Tachyonic Antitelephone example is looking at relativity and simultaneity form the same shallow perspective, or I have some fatal error in my logic.
     
  18. Oct 30, 2012 #17
    I've just shown with a thought experiment that in static frames FTL doesn't cause any causality or logic problems. "Plausible" is probably overdoing it - say "compatible" . Does the described experiment in my post sound illogical to you?
     
  19. Oct 30, 2012 #18

    PeterDonis

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    What you are calling the "GPS problem" is a *different* problem than the problem of Einstein clock synchronization. For GPS signals to be useful to us, the timestamps encoded in them have to be based on a common standard of simultaneity with the ground-based receivers that use them. That means the timestamps encoded in GPS signals use a *different* standard of simultaneity (and a different clock rate) than the "natural" standard of simultaneity and clock rate of the satellites. Einstein clock synchronization is about how to synchronize spatially separated clocks that are at rest relative to each other, when *all* you have is the "natural" standard of simultaneity and clock rate of each clock by itself; i.e., you have *no* external information like the GPS satellite clocks have.

    Btw, the Wikipedia page is incorrect when it says that the adjustments on the satellites make them "run differently than earth-based clock". The adjustments are made to give the satellite a time reference that is the *same* as an earth-based clock. That's the whole point.

    This will give the "time now" according to the global reference frame defined by the times shown by the army of clocks and their spatial positions. It will *not* tell you anything about the proper time recorded by clocks moving relative to that global reference frame. Basically you are once again ignoring moving frames, which eliminates the entire issue you are trying to investigate. (I see that you do mention "Rocket Mean Time" later on--see below.)

    This is not to say that such a global network of clocks reading "Sun Mean Time" (or "Galactic Mean Time" or anything else) would not be a useful thing to have. It would, just as GPS is. But it wouldn't have anything to do with Einstein clock synchronization for clocks moving relative to the global network.

    I don't think this scenario is quite that simple, but it may not be worth going into it in more detail.

    You don't need an additional clock to do this; you just need information on your velocity relative to Earth/Alpha, which is easy to get by measuring the Doppler effect on light signals coming from both places.

    Which ones? I don't see any problem with GR in anything you've said.

    Only with an incorrect definition of "speed of light". If you set up an actual measurement of the speed of light aboard a GPS satellite, the measurement will yield a result of c.

    Yes, you do. I suggest that you draw a spacetime diagram of your FTL scenario; I think it will help to clarify things.
     
  20. Oct 30, 2012 #19

    PAllen

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    At best, you've shown that if the laws of physics are not the same in all reference frames, then FTL need not lead to causality issues. This just shows that if SR is false, FTL without causality issues may be possible. So what?

    You haven't shown anything assuming SR, because your claims about simultaneity violate it. I note you have not answered any of the questions in my post #13, which would help you understand this.

    Note that there are developed theories of FTL compatible with SR. They have the feature that if the relativity principle applies to FTL signals as for all other laws, then signals can go back in time. There are various interpretations to make this more acceptable (e.g. it is always possible to interpret such a scenario in a block universe such that there is no causal paradox; but there is still an answer to a question received before the the question was sent; the causality is modified such that the received answer is what triggered the question, for example).
     
  21. Oct 30, 2012 #20

    PAllen

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    I didn't see #16 and #18 when I wrote #19.

    Peter has answered most issues.

    I'll add a slant on one set of issues. Suppose you set up in the rockets two sets of clocks, and follow two different systems of position/length measurement. System A is constructed to yield identical results for each time and position as the Earth-Alpha frame. System B is constructed per Einstein conventions between the co-moving rockets. Then any tests of laws of physics (including speed of light) will agree whichever you use; if you mix them, of course they won't. This equivalence is another way of stating the consequences of SR, and is experimentally verifiable, all within the rockets.

    Now it seems OP's idea is that FTL operates directly according to Earth-Alpha frame only. The statement that there is no back in time message applies only with System A measurements; using System B, there is a back in time message. Thus, as I said in #19, you must make one of two choices:

    - System A and System B do not always agree on physical laws (e.g. FTL behavior); System B is objectively inferior because it can self identify as the system in which backward time messages are possible (assuming they never occur per special system A).

    - Or, if FTL follows the same laws in both, then an anti-telephone is possible in either frame.

    So, basically OP is, in fact, saying if the principle of relativity is wrong, then: then FTL is possible without causality issues (and the unique, preferred frame of the universe is physically identifiable by the behavior of FTL signals). But this is non-controversial, and well known. Also well known is the converse: that if the principle of relativity holds for all phenomena, including FTL signals, then any observer can experience the tachyon anti-telephone, in cooperation with another relatively moving observer.
     
  22. Oct 30, 2012 #21
    Laws of physics will be the same whether you or I want them or not want them to be. I've shown nothing new. I've shown that in frames that don't move wrt each other simultaneity can be established globally - aka universal simultaneity.

    Look at this diagram:
    http://upload.wikimedia.org/wikipedia/commons/c/ce/Twin_Paradox_Minkowski_Diagram.svg
    Now explain to me what physically occurred when twin turned around and all of the sudden different laws took place and different simultaneity took place? I'll give you the answer - nothing. The twin just turned around but he is simultaneously in he same place at Alpha and at same time as Alpha. The shift between the slope of the red and blue lines mean that:
    If the traveling twin resumes going in this direction, then the events from the earth twin will be received offset in time by this much because of the light delay. You can just use blind bats example where bats can't see but only hear delayed by speed of sound and you can draw same diagrams for two bats where one is moving away from another. If bats could "see" then they would draw horizontal lines (Answer to PeterDonis's question). The same equivalence applies to "simultaneity", which you can consider to be a dimension/universe a level higher than spacetime.

    Just imagine a scenario where you see a relativistic alien kinetic projectile approaching mars

    It tells us nothing about the actual/true simultaneity. If we were to draw Horizontal lines, they should be the true simultaneity and universally equal, and I've somewhat shown it herewhen we grilled the twin paradox for the millionth time.


    Feel free to find a case that satisfies the 4 simultaneity rules that I've explained in the previous posts. I will repeat again - velocity is time * distance. Depending on what you consider simultaneous, then time and/or interpreted distance will vary. Minkowski and Einstein are saying "well it depends and it's relative". It is simply a fiction of the formula. By saying that simultaneity is relative you are not claiming or proving anything. If your supervisor comes to you with a life of death question should we evacuate earth because Alpha is about to go supernova, you can't just play a scientist and say "well it's relative, i'll just draw a Minkowski diagram and prove to you that it may or may have not exploded depending on who examines the events or whether we instantly accelerate in this or that direction".
     
  23. Oct 30, 2012 #22

    Nugatory

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    The commonly used terms "the frame of X" and "X's frame" are both verbal shortcuts for the more precise "the frame in which X is at rest". If the two frames aren't moving with respect to each other... Then they're the same frame, and of course you can establish global simultaneity within that frame, using the Einstein synchronization procedure or equivalent.
     
  24. Oct 30, 2012 #23

    PeterDonis

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    Well, of course. Nobody is disputing that, as I said before, if you ignore "moving" frames, you eliminate the problem. But you can't ignore moving frames if you want to deal with reality. See below.

    Um, the twin turned around?

    The twin's turning around doesn't change the physical laws.

    Maybe this is the root of your problem. Try looking at it this way: simultaneity is a *convention*. It doesn't correspond to anything "physically real". When the twin turns around, the most natural simultaneity *convention* for him to adopt changes, but that's just a convention. Nothing physically real changes about any of the possible "lines of simultaneity" he could adopt; all that changes is which of those lines is most natural for him to adopt.

    It's worth noting that there is one other thing that does change when the twin turns around: the Doppler shift he observes in light signals coming from Earth changes (from redshift to blueshift). If you're looking for *something* "physically real" that happens when the twin turns around (besides the twin feeling acceleration), this will do just fine.

    There is a sense in which I actually agree with this (see above). However, it doesn't seem to be the sense in which you mean it.

    If he turns around at Alpha (I assume this is what you mean), then yes, at the turnaround event he is obviously "in the same place" as Alpha. This is true in all frames because the twin's and Alpha's worldlines intersect at the turnaround event.

    Only in the sense that the twin could choose to reset his clock to match "Alpha time" at the turnaround event; since he is *at* Alpha at that event, there is no light speed time delay involved if he wants to look at the reading on Alpha's clock. But as soon as he starts moving away from Alpha, back towards Earth, his clock (if he lets it run at its "natural" rate) will get out of sync with Alpha's clock again.

    That's true regardless of the slope of the lines. For example, at the turnaround event, the light speed time delay for signals coming from Earth is the same for the twin coming in (i.e., with the blue lines as simultaneity planes), for Alpha (i.e., with horizontal lines as simultaneity lines), and for the twin going out (i.e., with the red lines as simultaneity lines).

    No, they would draw lines (on a spacetime diagram) with a 45-degree slope (corresponding to the velocity of light) instead of with a much steeper slope (corresponding to a much slower velocity for sound).

    In any case, this is irrelevant. The relativity of simultaneity, and relativistic time dilation and length contraction, are not effects that arise from light speed time delay. They are effects that remain *after* you have compensated for light speed time delay.

    Because there is no such thing as "the actual/true simultaneity".

    The "natural" simultaneity convention to adopt, and therefore time and distance, will vary only if two observers are moving relative to each other. But if they are moving relative to each other, then velocity will vary as well. So what's the problem?

    Your "scientist" is a straw man. If Alpha goes supernova "right now", then it will take 4.3 years (Earth time) for the wave of radiation from the supernova to get to Earth. If you, hearing the news, get on a fast rocket and fly in the direction opposite to Alpha, then it will take longer for the wave to get to you. These things are true regardless of who draws the spacetime diagram or what simultaneity convention they use. And these things are what people actually care about; nobody cares about whether the supernova has or has not happened "right now" according to whether or not you are moving relative to Earth. (Except that you appear to care, I'm not sure why.)

    You appear to have missed the key point about relativity; it's not really about what's relative. It's about what's invariant, i.e., about what *doesn't* change when you change reference frames or states of motion. It's about invariant relationships between events, not about what particular coordinate grid we overlay on spacetime to put numbers to events. (To be fair, this is not a hard mistake to make since the theory is called the theory of relativity instead of the theory of invariants, as Edwin Taylor says it ought to be.)
     
    Last edited: Oct 30, 2012
  25. Oct 30, 2012 #24

    Nugatory

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    Let's try an equivalent variant, one in which the traveling twin doesn't turn around, he just continues his outbound journey. However, there's a second ship, traveling at the same speed (relative to earth) as the traveling twin but in the opposite direction. This ship passes the outbound traveling twin at the point where the turnaround would have happened, and therefore continues on the same path that the traveler would have taken on his return journey.

    But this ship will be using the red planes of simultaneity all along, both before and after the crossing point. Likewise, the traveling twin, no longer turning around, will be using the blue planes of simultaneity all along, both before and after the crossing point.

    So the answer to your question is that nothing physical occurred at the crossing point. There were two points of view all along, both before and after the crossing.

    And then let's try another variant: In this one, the traveling twin jumps from his outbound spaceship to the incoming ship as they pass each other at the crossing point. This is for all practical purposes the original twin paradox problem, but it's more clear that there were two coexisting points of view all along. The crews of the two ships have been using the red lines (left-moving ship) and the blue lines (right-moving ship) all along, and there's no discontinuity at the crossing point. All that's happened is that the traveling twin, if he jumps, switches from one point of view to another.
     
  26. Oct 30, 2012 #25

    Nugatory

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    Staff: Mentor

    PeterDonis has already responded to this, but I'd like to add two additional comments.

    First, this particular aspect of relativity of simultaneity is already being intensively discussed in another live thread: https://www.physicsforums.com/showthread.php?t=647831; if you haven;t been following that one you may want to.

    Second, this misconception that relativity of simultaneity is an illusion created by light travel time and it would go away if we could just properly correct for the light travel time.... It's very common.

    I think it's so common because most explanations of relativity of simultaneity start with light beams transmitted to a central observer as in the classic train example. that in turn tempts the naive (like me, some decades ago) to think that the frame-dependence of simultaneity is caused by the light travel times, that there is some sort of underlying reality which is being complicated by all the light beams bouncing around and confusing our sense of when things "really" happened.

    However, you don't have to approach the relativity of simultaneity from that direction. Instead, you can start with the invariance of the speed of light, do some algebra with that, and derive the Lorentz transformations, and let the relativity of simultaneity follow from the Lorentz transforms without further ado. In this approach, the light-travel-time based thought experiments aren't used to prove relativity of simultaneity; they're used to demonstrate that the physics implied by the Lorentz transforms, although bizarre and counter-intuitive, is complete internally consistent and coherent.
     
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