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Concerns about ontological interpetations of Theory of Relativity

  1. Jan 30, 2006 #1
    First of all, browsing this forum, I feel that the level of competence regarding theory of relativity is higher than on average science forums. It may not be much to say, but the only reason I want to post here is because I believe criticism and comments might actually come from people who KNOW what they are talking about. In other words, People who usually do most of the arguing regarding theory of relativity, seem to be the ones who have very vague idea about what the theory actually means and describes. This includes both pro and anti-relativists, and I don't wish to be associated with either group :)
    --

    I find that ontological interpetations of Einstein's theory of relativity are incredibly sparse, while the mathemathical expressions are abound. As always, the ontological nature of the theory does not readily reveal itself from mathematical expressions. Incidentally, I find that the collective understanding of such key concepts as the relativity of simultaneity is very poor.

    This could be suprising, being that Einstein himself made it very clear how important the relativity of simultaneity is in making the theory actually work. But then, surely Einstein's incredibly poor choice of words in his famous thought experiment involving railway embankment and a moving train have contributed to this misconception:

    About Relativity Of Simultaneity by Einstein - See section 9

    Einstein makes it sound as if he is simply talking about how the lighting flashes are not SEEN simultaneously due to their limited propagation speed. Had the text not been written by Einstein, I'd claim writer didn't understand the relativity of simultaneity.

    I mean;
    "...he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A"

    Sound rather much like someone is describing an emitter theory. While the above IS what happens from the point of view of the embankment, it is very easy to get the wrong impression.

    Incidentally, this idea about how different things are SEEN at different times I find to be to most common misconception about the relativity of simultaneity. I have even seen TV-documentaries that convey this same erroneous idea about how "special relativity talks about how things visually appear".

    It should not be such a difficult idea to communicate, that the "very own speed of light" of every moving observer necessitates that a single beam of light could not begin its journey at the same moment for every observer. This would have been easier for everyone to see in a version of the train thought experiment, where the beams of light, the standing observer and the moving observer all meet in the midpoint simultaneously. Once you puzzle it out, the fact that in Einstein's version the moving observer moves away from the midpoint while the rays of light are propagating has NOTHING to do with the relativity of simultaneity, contrary to what most people would pick from Einstein's most confusing choice of words.

    Anyhow, since it has been established that the isotropy of speed of light requires that the actual moments when beams of light begin their journey undergo a transformation, which must occur in an actual time dimension which holds in itself all the events of the world, this seems to imply some things I never hear people discuss about anywhere. Yet they are perhaps the most important things to grasp about Special Relativity. At least in an ontological sense. (Of course ontology doesn't mean anything to mathemathicians, but it should to the physicists, and it definitely does to all the rest of us :)

    And since I don't really hear anyone talk about these things, I must wonder if there exists better interpetations (if so, haven't heard of those either). In other words, these are the ontological implications I've simply come to realize myself.

    Determinism in Special Relativity:
    Since the relativity of simultaneity is a key element in SR, then accepting SR also means we are accepting that the events that lie in our future, have already happened from the point of view of other objects. Namely, objects that are moving towards us fast enough and/or are distant enough. And thus every event in our future must be pre-determined. Rather problematic, but not an impossible idea. (Actually I expect determinism even without SR, but that's another issue and is not due to future already having happened from some perspective)

    Things moving back in time routinely:
    People usually have some sort of grasp about time slowing down in theory of relativity, but when you mention things moving routinely forwards and backwards in time, you often get an outcry; "Theory of relativity claims no such thing!". But of course it does, since simultaneity is relative.

    Let there be two observers "at rest", RED and BLUE.

    Blue shoots a beam of light towards Red.

    While the light is on its way, Red will change direction away from Blue.

    Pic01
    (Vertical axis is time, horizontal is location. The planes of simultaneity are black/grey, light is faint yellow -> speed of light is in 45 degree angle)

    The POV of RED:
    Even though the beam of light was well on its way BEFORE Red changed its direction, AFTER changing direction the light suddenly had not even began its journey.

    Pic02

    While this is a bit problematic philosophically (especially since there is no actual mechanic to explain it in the theory, rather it is derived as a necessity to the 2nd postulate), I guess there's no reason to think it is impossible. After all, there is nothing with which we could have ever directly see/experience this effect. But this does lead me to a worrying observation about SR, which doesn't really reveal itself in the math expressions.

    In the above example the Red did, in a sense, "hasten away from the beam of light". Even if the beam of light was just 2 seconds away from hitting the Red at the moment of acceleration, after the acceleration it can take a lot longer than 2 seconds for the beam of light to arrive. In this particular example, the two seconds would become about 5 seconds as measured by the Red itself (and about 7 from the POV of blue). But even then we can say that the SPEED of the beam stayed constant, since we assert that the moment when the light began its journey changed. This is basically what Lorentz-transformation does in SR, it adjusts moments of events in such manner that we can always interpetate the speed of light as C relative to ourself.

    So superficially, the Red could either decide he was indeed hasting away from the light, or he could decide to use the constant C to derive the actual moment of shooting and thus conclude the shooting took place much later than what the Blue is claiming. (Of course we should expect differences in details between different theories, yet the above should be understood about the nature of Lorentz-transformation)

    On top of the above, there are still issues I haven't been able to interpetate ontologically at all, nor have I found anyone even mentioning such scenarios. I wish to present these problems here, in case someone knows some solutions outright:

    Two rotating wheels on shared axis.
    I believe it has been established that the circumference of a rotating wheel, and thus the whole wheel, does in fact Lorentz contract in SR, when observed from the center:
    History of rotating wheels in Special Relativity

    This is problematic in the case when there are two wheels that are rotating in separate directions on a shared axis. According to SR, both the POV of either wheel, the other should be smaller. In other words, both wheels could push sticks from their circumference so that the sticks completely encircle the other. This does not seem logically possible in any kind of interpetation of SR that I can conceive.

    Obviously this is NOT the same case as two trains passing each others, in which case it is quite trivial to demonstrate how "both of the trains are shorter than the other", due to the relativity of simultaneity. As oppose to the passing trains, in the case of two wheels there is nothing passing anything in the direction of radius; there in fact exists no point in time when any outermost element of the circumference of either wheel actually exists within or outside the radius of the other wheel. In other words, we cannot really choose any moment in time when one wheel could be smaller than the other. So I'm at total loss here.

    Co-accelerating spaceships
    In my opinion, this displays particularly well my struggling with the second postulate of SR:

    Two identical spaceships which are at rest, perform identical acceleration events to identical direction, beginning simultaneously, as seen below:

    Pic03
    (Red ones are the space ships. Right one will be called the ship in front (since ships will be moving in line to the right). Blue one is an observer who stays at rest. The acceleration event is instantaneous here, but we will add real-world acceleration into the pile soon)

    From the POV of FRONT SHIP:
    As the front ship changes its direction, so does the rear ship. However immediately after changing direction, the ship on the rear MUST have gone back in time and not begin its acceleration in a while. (As is seen from the plane of simultaneity, in black)

    From the POV of the REAR SHIP:
    Vice versa happens. Immediately after the acceleration, the front ship MUST jump forward in time, and now "has been moving" for a while already.

    Due to this, while the distance between the ships stays constant from the POV of the blue observer (as he would expect since the ships go through identical acceleration procedure), from the POV of the ships the distance should increase:

    Pic04

    Even though they did go through the same acceleration procedure, after the fact these procedures exist in different moments in time.

    But we should arrive at the same conclusion even if there is a steel rod between the ships. Thus making it appear that we should expect any fast-moving object to be Lorentz-contracted ONLY if it is the observer itself has changed direction from "rest". If an external object accelerates, then we should expect it to experience stretching by the same mechanic that usually causes contraction, and thus remain at constant length from the POV of the observer.

    Very confusing, but that's not even the real bastard problem yet.

    The acceleration occurs instantly in the diagram, but if you will, please imagine little curves there in the place of the sharp corners, as would actually be the case. This doesn't actually remove the above problem, as you can surely imagine, but rather it reveals the whole magnitude of the problem;

    When the front ship begins it's acceleration, the rear ship begins identical acceleration. Since the acceleration event is identical, the ships should basically preserve their mutual conception of simultaneity at all times (since they would be co-moving at all times). In other words the ships & the rod should keep their length from their own perspective, and contract from the perspective of the blue observer.

    But the second postulate also very concretely requires that, for example, the rear ship must move backwards in time from the POV of the front ship during acceleration. If we assert it doesn't go back in time, then it becomes very trivial to demonstrate that light didn't move at the speed C relative to the observer by sending light signals from one ship to the other just before launch.

    So from the POV of the front ship, the rear ship would need to meet two mutually contradicting requirements; stay in the same inertial coordination system with the front ship (co-accelerate), and stay at "launch pad" longer than the front ship.

    And vice versa for the ship on the rear.

    I hope someone is able to point out a solution because this is driving me stark raving mad :rofl:
     
  2. jcsd
  3. Jan 30, 2006 #2

    JesseM

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    In a lot of these cases you are talking about how things look from the point of view of a non-inertial observer. But as you point out early in the post, asking how things "look from a given observer's point of view" is not really a question about how they see things using light-signals, its a question about when and where things happen in the coordinate system where they are at rest. But when you talk about an accelerating observer, there is no "standard" way to construct a coordinate system where that observer is at rest, unlike with inertial observers. Thus it isn't really right to say things move back in time from the point of view of an observer who changes velocity, for example; it's true that if you look at series of inertial reference frames where the accelerating observer is instantaneously at rest, then events which had already happened in an earlier frame in the series may have yet to happen in a later frame in the series, but this just shows that you have problems constructing a single well-behaved non-inertial coordinate system for the accelerating observer such that his definition of simultaneity at any given moment will agree with that of his instantaneous inertial rest frame at that moment.

    I talked a little more about the problems I saw with defining a coordinate system for a non-inertial observer in post #18 on this thread. I think it is possible to adapt SR to non-inertial coordinate systems using tensor mathematics, although you'd have to ask someone else to elaborate on this; but again, unlike with inertial observers there isn't a single "standard" agreed-upon way to define the coordinate system of an accelerating observer, you'd have a choice of different coordinate systems which would give different answers to questions involving simultaneity and so forth. And certainly you couldn't assume that the usual rules of SR (stated without tensor mathematics) would apply in such coordinate systems, like the rule that light must always have a coordinate velocity of c or the rule that time dilation and lorentz-contraction are based solely on coordinate velocity. So unlike with inertial observers, there will be no standard answer to what a non-inertial observer "observes" in a given situation, where "observes" is taken to mean what is true in the observer's rest frame as opposed to what he actually sees using light signals.
     
    Last edited: Jan 30, 2006
  4. Jan 30, 2006 #3

    robphy

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    [I fear that with such a long first post (with many issues and questions) this thread will be quickly convoluted... unfortunately. It may have been better to ask a single succinct and well-posed question... then proceed from there... possibly to related questions in other threads.]

    Just a comment concerning "Blue shoots a beam of light towards Red"... Red, of course, did not react to Blue's shooting... In other words, events "Blue Fires" and "Red Turns" are spacelike-related (i.e. causally-disconnected).

    On that website, you have some interesting graphics and animations of spacetime diagrams. Unfortunately, I need a translation and more explanatory text. The spacetime diagrams will help to discuss and hopefully resolve the issues you raise. Loosely or poorly defined words won't help. I suggest adopting operational definitions of various concepts.

    My $0.01
     
  5. Jan 30, 2006 #4

    pervect

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    I have to agree, it's difficult to tell where to start with such a long post.

    The first point that I want to make is that one needs to disentangle the notions of causality with the issues of assigning coordinates.

    Coordinates are a purely human invention, like a map of a territory. The specific assignment of coordinate values to events in space-time has no physical significance whatsoever (the map is not the territory).

    Causality is something that's physically significant. When a light signal is emitted at event A, and is received at event B, A and B are causally related. A is in B's past (I think this is sometimes called past domain of dependency).

    If two events are space-like separated, so that light cannot reach from A to B, then there is no causal relationship between them. Sticking different coordinate lables on them does not change this physical fact.

    The OP in this thread seems to be attaching too much physical and philosophical significance to human choices - the choice of a particular coordinate system. The fact that A has a lower time coordinate than B is not enough to establish a causual relationship (as can be seen by the definition using light cones).

    For instance, the two space-ships that accelerate "at the same time" in the two spaceship diagram are spacelike separted. This general paradox is called "Bell's spaceship paradox", and it's discussed somewhat in the sci.physics.faq, though not all the questions that the OP asks are answered there.

    http://math.ucr.edu/home/baez/physics/Relativity/SR/spaceship_puzzle.html

    There is no "unique" coordinate system associated with an accelerated obsesrver, since all coordinate systems are arbitrary. The choice of Fermi-Walker transport to define a local coordinate system is a very popular choice though, and is discussed at length in some textbooks such as MTW's "Gravitation".

    The mathematical defintion of this might help. The graph on pg 173 of MTW's gravitation would be even better (FIgure 6.4) - this graph can be construced by plotting the following equations which are easier to communicate than the graph itself is:

    If we let [itex]\tau, \chi[/itex] be the coordinates of the accelerated observer with a constant acceleration g, we can map them into inertial coordinates with the following equations:

    [tex]
    t = (1/g + \chi) \mathrm{sinh}(g \tau)
    [/tex]
    [tex]
    x = (1/g + \chi) \mathrm{cosh}(g \tau)
    [/tex]

    Plotting lines of simultaneity (constant [itex]\tau[/itex]) will reveal that they are all straight lines, with different slopes.

    Plotting the lines of constant [itex]\chi[/itex] will reveal that they are hyperbolas.

    The "grid" of lines of constant [itex]\tau[/itex] and constant [itex]\chi[/itex] form the "grid" of a local coordinate system (the Fermi-Walker coordinate system of the accelerated observer) - just as the grid of lines of constant t and lines of constant x form the "grid" of the cartesian inertial coordinate system.

    They define a coordinate system because a unique point is given by the intersection of a line of a specific [itex]\tau[/itex] and a line of specific[itex]\chi[/itex], just as a unique point is given by a specific line of constant t and a specific line of constant x.

    Actually, there is a "gotcha" here.

    The lines of simultaneity cross at the origin of the graph. This indicates that the coordinate system described does not cover all of space-time, because the coordinate lines are not allowed to cross in such a manner. A single point is not allowed to have more than one set of coordinates.

    For more on this, see my previous post
    https://www.physicsforums.com/showpost.php?p=887032&postcount=91

    The graph of [itex]\chi=0[/itex] will be the graph of the worldline of the accelerated obsever.
     
    Last edited: Jan 30, 2006
  6. Jan 30, 2006 #5
    Dear AnssiH,

    Einstein also explained in his book "Relativity: The Special and General Theory" Chapter 16 :

    "According to this theory there is no such thing as a “specially favoured” (unique) co-ordinate system to occasion the introduction of the æther-idea, and hence there can be no æther-drift, nor any experiment with which to demonstrate it. Here the contraction of moving bodies follows from the two fundamental principles of the theory without the introduction of particular hypotheses; and as the prime factor involved in this contraction we find, not the motion in itself, to which we cannot attach any meaning, but the motion with respect to the body of reference chosen in the particular case in point. Thus for a co-ordinate system moving with the earth the mirror system of Michelson and Morley is not shortened, but it is shortened for a co-ordinate system which is at rest relatively to the sun."

    Einstein was genius enough to understand that Physics is about physical information. It is not about ontology.

    Physics does not provide a knowledge of physical reality. Physics provides information about physical reality. Therefore, for the science of Physics a singular physical term, like a specific co-ordinate system in an experiment, "is shortened" and "is not shortened" at the same time. This is not a statement conflicting with itself, because the "is" and the "is not" refer to the physical information that the physical reality provides to different observers. The science of Physics does not provide the absolute knowledge of physical reality. It only provides relational information about physical objects of physical reality.

    In this context, Einstein made clear in the above passage that: "we find, not the motion in itself, to which we cannot attach any meaning, but the motion with respect to the body of reference chosen in the particular case in point".

    By the moment that we realize that "we can not find the meaning of the motion in itself, but we can find the meaning of motion with respect to the body of reference chosen in the particular case in point", we can realize Einstein's scientific perspective of finding physical information "with respect to...chosen reference".

    So, Einstein did not produced an ontology, but he invented/defined new mathematical/physical relations by which he was able to express in a scientific way the physical information of ratio between "space" and "time".


    "Simultaneity" is a term that, before Einstein, was used as a physical term that was defined by "time". Einstein made clear, in his work, that (Chapter 17) : "The four-dimensional mode of consideration of the “world” is natural on the theory of relativity, since according to this theory time is robbed of its independence". In this context, the term "simultaneity" according to Einstein's work is also “robbed of its independence”, defined after his work by four dimension of "time-space" - not just by the dimension of time.

    Having said that, we should also read carefully the following words of Einstein (Chapter 17): "It must be clear even to the non-mathematician that, as a consequence of this purely formal addition to our knowledge, the theory perforce gained clearness in no mean measure."

    Einstein does provide a mathematical analysis of the four dimensional world at the Appendix 2, where he writes: "From a “happening” in three-dimensional space, physics becomes, as it were, an “existence” in the four-dimensional “world.” "

    You can find a very nice VIDEO, about "Simultaneity" provided by "National Science Foundation" . In this video you can visualize the example of train, that Einstein used. Check also another video on "Time Dilation"

    Leandros
     
    Last edited: Jan 31, 2006
  7. Jan 30, 2006 #6

    Hurkyl

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    Bleh, I hate the word "ontology" -- I can never figure out what it means. :tongue2: But I'll take a shot at responding.


    A crucial feature of Special Relativity is that it asserts that space-time is a (3+1)-dimensional Minowski space.

    (Similarly, a crucial feature of classical mechanics is that it asserts space is a 3-dimensional Euclidean space)

    I would suppose that this completely characterizes the ontology of SR -- everything about which one might wish to speak can be expressed geometrically, and thus has its meaning reduced to the above statement.
     
  8. Jan 31, 2006 #7
    I was intending to describe what is happening from the point of view of an observer. If something gave the impression that I was describing what something looks like to an observer, it probably needs some clarification, so please point such cases out :)

    Ok, I see. I remember hearing the same thing, that there are difficulties in SR with non-inertial frames. You said in the other thread:
    At each moment along the object's worldline, should its definition of simultaneity match that of the inertial frame where it's at rest at that moment? If you try to do it this way, you can have problems with planes of simultaneity at different points along the wordline intersecting each other, so that the same event is sometimes assigned multiple time coordinates, and distant clocks can run backwards as coordinate time runs forwards.

    Don't the planes of simultaneity criss cross anyway after the acceleration, when the object is back at rest? Because of this, and because relativity of simultaneity is a key requirement, it seems to me that we cannot discard anything as false just because clocks need to run forwards and backwards routinely. It seems to me that they necessarily must do this in SR.

    So, regardless of how we treat the notion of simultaneity while changing direction, AFTER changing direction there necessarily exists events in your future that had already happened before you changed direction.
     
  9. Jan 31, 2006 #8
    True... Well, the point of the first part of the post was mostly to make sure I have grasped the correct idea of SR. It seems to me that just about all the paradoxes I've heard revolve around not grasping the relativity of simultaneity concretely. But then I'm at total loss with probelms that seem to arise BECAUSE of relativity of simultaneity.

    But if the first part seems about right, then I wish to concentrate only on the two actual problems; the spinning wheels, and two spaceships & a rod.

    Yes, this is very well understood. The point is just to discuss how the world actually operates according to SR. So in the above case the red could just be pre-timed to change direction, and the point of interest is the fact that the light actually cannot be on its way after the change of direction has happened.
     
  10. Jan 31, 2006 #9
    Yes, sounds like me :) Although I would like to argue about the "too much", because the philosophical aspect is the part which sparks my interest; how do things actually work. It's not the math, it's the actual interpetation of the math.

    But let it be said that I attach SO much philosophical significance to SR, for instance, that I am ready to accept that clocks can just do swoosh forwards and backwards. I just see no other choice. Basically I stand where Hurkyl appears to stand in his comment. Everything reduces to the statement about spacetime, or even further; to the postulates. That is, if you accept that the speed of information is in reality isotropic, then you also accept the full impact this has on the reality, as described by SR. There's no pick and choose here, you HAVE to accept it all.

    Of course that is not to say there couldn't ever come a better description of reality than the theory of relativity, but then such a description also necessarily has different postulates, and also comes as a full package that must be accepted as a whole.

    Thank you very much for the link about the two spaceships, I'll take a look at a better time...

    Is not? Why so? And if not, how do we maintain the idea of isotropic speed of information propagation, since the simultaneity lines of two inertial coordinates can cross too (like they do in the spacetime diagrams in the opening post) This is interesting since this is something that should have a direct impact on our notion of reality.
     
  11. Jan 31, 2006 #10
    Well, I would argue that the mechanic with which the physical information propagates IS part of reality. So the SR description of this does come with all its features attached.

    What Einstein meant with the relativity of simultaneity is well understood at this end, and surely Einstein also did understand perfectly well what a profound impact SR has on the actual reality of the universe. It is not just a mathematical construct, if its postulates are real.
     
  12. Jan 31, 2006 #11
    The trouble is that we use a lot of time-based words like before, after, is. In SR people tend to use these based on the time coordinate of a given inertial frame. I think that it's better to use them to reflect the structure of SR, so that before means 'in the past light cone of' and after means in the 'future light cone of', and the spacelike hypersurface called now has no significance whatsoever.
     
    Last edited: Jan 31, 2006
  13. Jan 31, 2006 #12
    Einstein said, in one of his lectures:

    “At this point an enigma presents itself which in all ages has agitated inquiring minds. How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality ? Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things ?

    In my opinion the answer to this question is, briefly, this: as far as the proposition of mathematics refer to reality, they are not certain; as far as they are certain, they do not refer to reality. It seems to me that complete clarity as to this state of things became common property only through that trend in mathematics which is known by the name of “axiomatics”. The progress achieved by axiomatics consists in its having neatly separated the logical-formal from its objective or intuitive content; according to axiomatics the logical-formal alone forms the subject matter of the mathematics, which is not concerned with the intuitive or other content associated with the logical-formal.”

    “Geometry and experience”, lecture by Albert Einstein before the Prussian Academy of Science, January 27, 1921.
     
  14. Jan 31, 2006 #13

    JesseM

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    Even if an observer starts out moving inertially and later returns to moving inertially, you can't just take the two different inertial frames and say that this is how things happen from that observer's point of view, because having a "point of view" that covers two different parts of a path demands having a single coordinate system which covers both parts. If this observer was travelling alongside an inertial observer A before accelerating, then after accelerating was travelling alongside another inertial observer B, he could say that an event that was in A's past before acceleration was in B's future after accelerating, but that wouldn't mean he could say an event that was in his own past before accelerating was in his own future after accelerating. If we are using "past" and "future" to refer to coordinate time, a statement like this can only make sense if the observer has his own coordinate system which covers both the time before he accelerated and the time after he accelerated.

    As chronon said, though, another way to talk about a given observer's past and future is using light cones instead of coordinate time, and in this case you can talk in an absolute way about which events are in the past and which are in the future and which are "elsewhere" for any observer, even an accelerating one, at any point on his path.
     
    Last edited: Jan 31, 2006
  15. Jan 31, 2006 #14

    pervect

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    My position is that it's not clocks that swoosh forwards and backwards. It's coordinates (things without any real physical significance) that can jump around.

    An actual clock will always tick in one direction - forwards.

    I would say that causality in alive and well in SR, and that it is handled mathematically by the idea of globally hyperbolic space-times (Minkowski space-times are always globally hyperbolic).

    This is additional structure "on top of" Minkowski space-time. I suspect that Hurkyl can define the extra structure more clearly using less words than I can :-).

    Things do get more complex in GR - it is possible to construct space-times that are not globally hyperbolic. These space-times are generally not regarded as being physically significant, however.

    The simultaneity lines of a single inertial observer never cross in the flat space-time of SR. They are parallel lines.

    It is only when an observer accelerates that the lines of simultaneity can cross. The crossing of these lines results in ill-behaved coordinate systems (where a single point has more than one coordinate), which results in a llimitation on the size of the coordinate system of an accelerated observer.

    The "Fermi-Walker" approach to defining the coordinate system of an accelerated observer basically means that the accelerating observer uses as his defintion of simultaneity the same defintion that an instantaneously co-moving observer uses.

    This is a very useful and practical coordinate system, but it does inherently have a limitation on its size, so it only works "nearby" the accelerating observer, because of the "line crossing" problem.
     
  16. Jan 31, 2006 #15
    I seem to be missing something here... Aren't the lines of two different inertial coordinates always crossing at far enough distance? I mean, you can replace the instantaneous acceleration with a curve here:
    http://www.saunalahti.fi/anshyy/PhysicsForums/Simultaneity01.jpg
    ...and you still get the lines crossing each others. How should that be solved?

    As for the rest of the responses;
    Is it your message to me that the notion of relativity planes is not an attempt to describe what happens in reality, but instead is a description of some sort of meta-reality, from which reality manifestates? In which case, aren't we completely missing a description of what happens in reality?

    I mean, I believe there is such a thing as reality which operates by certain simple laws. As a system builder, I am perfectly capable of thinking about how certain mechanics manifestate certain things, and as for the SR, I find it easier to just purge everything I THINK I know about reality, such as that time always flows forwards and everything can only happen once all that, and then lay down the mechanics of SR on a clean table.

    It becomes much much easier to see how information propagates in SR and how it all really operates, if I dream up a kind of "virtual" environment from scratch, where the speed of light is, say, 10 m/s.

    Suddenly stuff like you see in:
    http://www.saunalahti.fi/anshyy/PhysicsForums/Simultaneity01.jpg
    becomes up-close and intimate, and the reality of it all slaps you in the face (well, slaps ME in the face anyway :)

    So now if I actually implement the mechanic of SR, it will mean that a beam of light which is approaching an observer, CAN move backwards in time and back "into" the lightsource if the observer moves away. And while the learn operates in such a "backward" manner", observer will still learn of reality just like we do, and should find it quite impossible that time could flow backwards.

    So, it would seem the reality of the second postulate demands this, OR then we should treat the second postulate as a description of some sort of meta-reality, from which the "actual reality" arises, whatever that means.

    In any case, the ontological significance of SR cannot be stripped just if it sounds crazy, as long as its mechanic would produce a world just like we experience this one.

    Oh, and btw, the explanation of the twin paradox problem also relies on the factual nature of the relativity of simultaneity. If we accept that the clocks on earth could just jump years and years forward during a turning phase which could take just few moments, it should not be too hard to also accept that the clocks could factually move backwards?

    I mean, I am kind of sensing a collective reluctance to really think of these issues, perhaps they are not too interesting to anyone but me? :) But hey!

    Anyway, thanks for all the responses so far. Anyone has any clue as for how to solve the two wheel spinning problem? I would feel much more confident in my understanding of SR if I knew how that is solved...
     
  17. Jan 31, 2006 #16

    JesseM

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    It's just a description of different coordinate systems for describing the same spacetime. The question of whether any coordinate system's definition of simultaneity is more "correct" than any other is akin to the question of whether any placement of the origin of your coordinate axes is any more correct than any other.
    Not if you stick to a single inertial coordinate system it won't. This sort of thing only happens if you attempt to construct a coordinate system in which an observer who accelerates is always at rest, and you try to construct it in such a way that this coordinate system's definition of simultaneity always matches that of the inertial reference frame in which he is instantaneously at rest. But the theory of relativity does not demand that you define a non-inertial coordinate system in this way, that's just an arbitrary choice that you are making.
    You are still failing to understand that the second postulate is only meant to apply to inertial coordinate systems. The second postulate will be false in many (all?) non-inertial coordinate systems, because light beams will not in fact have a coordinate velocity of c at all times in these systems. The second postulate was never meant to say anything about what things should look like from the point of view of an observer who accelerates at any point on his worldline, simply because there is no standard agreed-upon way to construct a coordinate system for such an observer. And keep in mind the the "standard" definition of the coordinate system of an inertial observer is also just a matter of convention--but it so happens that the laws of physics have the property that they will obey the same equations when written in these different inertial coordinate systems, a property known as "lorentz-invariance", so it makes things more simple and elegant if you define the coordinate systems of inertial observers in this way.
    You're correct insofar as you're free to use just about any crazy coordinate system you want to describe the same spacetime and the same laws of nature. Which coordinate system you prefer to use is a matter of aesthetics, not physics. However, a coordinate system which assigns the same event multiple coordinates would probably not be considered "well-behaved", and I'm not sure it would be possible to write equations for the laws of physics in this coordinate system which would make all the same predictions as the laws of physics stated in well-behaved coordinate systems--you might get multiple possible solutions to the equations, or mathematical singularities, issues like that.
    The usual explanation of the twin paradox doesn't say anything about clocks jumping forward, it just points out that when you analyze the problem from the point of view of any one inertial frame, you conclude the accelerated twin will have elapsed less time. You can also point out that in the inertial frame where the travelling twin is at rest during the return voyage, the clocks immediately after the acceleration are far ahead of what they read immediately before acceleration in the inertial frame where the travelling twin was at rest during the outward voyage, but this is not equivalent to saying that the clocks "jumped forward from the travelling twin's point of view" or anything like that, it's just a comparison of two separate inertial frames. If you want to define a coordinate system where the travelling twin is at rest at all times, you have to define a non-inertial coordinate system, and again, the choice of how simultaneity will be defined in this coordinate system (and thus what the earth clock will be doing during the accelerating phase) is basically a purely aesthetic one. Presumably you could come up with a wide range of non-inertial coordinate systems which would all give different answers about how the earth-clock behaves throughout the voyage, including weird ones where, say, the earth clocks run slow until the travelling twin is 3/4 of the way home and then begin running fast. There is no physical reason to say that any non-inertial coordinate system's opinion on simultaneity is any more valid in an "ontological" sense than any other's.
    The usual way to analyze any problem in SR is to pick an inertial frame and apply the standard equations of SR in that frame. But you ask us in your description of the problem to take the POV of one of the wheels, and there is no single standard definition of what the POV of a non-inertial object should be in SR. You'd have to specify what coordinate system you want the wheel to use in order for your problem to have any well-defined answer.
     
    Last edited: Jan 31, 2006
  18. Jan 31, 2006 #17

    robphy

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    Yes, but this would also happen in non-relativistic Galilean spacetime. Your diagram could be interpreted as an ordinary distance vs time graph. One would simply say that "Blue missed". Of course, in the Galilean case, "Blue Fires" and "Red Turns" are causally-related...specifically, "Red Turns" is in the Galilean-causal-future of "Blue Fires".
     
  19. Jan 31, 2006 #18

    pervect

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    If you change inertial frames of reference, you always have the problem at some distance. But there is no problem for an inertial observer who does not accelerate (change frames of reference).

    Infinite accelerations (as in your diagram) are very unphysical, and cause problems anwhere were x < 0 (for acceleration in the x direction).

    Finite accelrations have the overlap occur at x < -c^2/g (again for accelerations in the x dirction).

    All I am saying is that coordinates are not reality - they are just labels that we stick on events. We can change a coordinate in a blink of an eye - this has no impact on reality, which is limited to lightspeed.

    I can go a bit further, putting on my philosphical hat, and say that the notion of "now", because it is observer dependent, is not a part of "reality" when "reality" is defined to contain only events that are observer independent.

    Philosophical notions vary so widely that perhaps other people view things differently, perhaps including observer dependent events as part of "reality".

    Explaining my point further, our brains, for instance, synthesizes the notion of things that are happening "now" by sorting various signals that travel at velocities a lot lower than that of light. It can get confused and put events in the wrong order.

    If two events are 1 foot apart, there is no ultimate resolution of what "now" means that is sharper than a nanosecond. Causality is caused by light speed signals, and if two events are 1 foot apart, it will take light 1 ns to travel between them. When events are space-like separated - i.e. so far apart that light cannot travel between them - there is no notion of causality, no unique "now", no preferred coordinate system.

    Two events happen, and we cannot unambiguously say which came "first", and which came second.

    It is not necessary to believe that clocks can jump years forwards and backwards during a turning phase - it is only needed to believe that coordinates can change that quickly.

    For the accelerated observer, a careful analysis shows that clocks only run forward in the region in which the coordinate system of the accelerated observer is valid. The region below the Rindler horizion (at -c^2/g) is not a region in which the coordinate system of the accelerated observer is valid.

    I'd suggest starting another thread for that question, this one is long enough already. I will mention that my favorite reference on the spinning disk is by Tartaglia, and can be downloaded from arxiv. If you start another thread I'll give you the exact reference.
     
  20. Feb 1, 2006 #19
    Yes, this is very good stuff. This is just the kind of things I wanted to discuss about. But it's not as simple as stating that the moments of times are different for two different observers and that while an observer is accelerating we don't really know how we should handle the math of planes of simultaneity.

    This is a response for JesseM as well; here's about the simplest way I can present my concern;
    ----
    Assuming:
    - Every event happens at some actual moment
    - We can figure out the moment by knowing our distance to the event when it happened and the speed of light
    - The notion of time is the same for every co-moving observer, regardless of the history if their world lines.
    - Special Relativity holds true

    Thought experiment:
    - Speed of light is 1 meter per second for every observer (it is slow just to make it easier to comprehend the situation. It makes no difference to SR; 1 m/s becomes the speed limit)
    - There is a stationary red clock.
    - There is a blue observer who is initially at rest with the red clock, 5 meters away from it.

    Blue observer knows the clock sends a light signal every day at a precise moment of 0s; he knows to expect to see it at 5s if he doesn't move from his location.

    Let there be also a purple clock standing right next to the observer, which has been synchronized to show the actual time of the red clock. So despite the information delay from the red clock, the blue observer knows what the red clock is ACTUALLY showing. The BLUE clock has also been synchronized to show the same time initially.

    PIC01

    Timeline:

    (BLUE) 0s - The blue observer knows the signal has been sent.
    (BLUE) 2s - The blue observer knows the signal is is only 3 meters = 3 seconds away from him. He decides to start running away from the clock. He will have no actual proof of the signal really having been sent at 0s, but there can be other observers who will tell him later that the light signal was indeed sent at 0s, as usual.

    We completely ignore what exactly happens to planes of simultaneity while he is accelerating. The acceleration period is marked in transparent since it makes no difference to us. Let's say the blue accelerates for 1 second. When the acceleration ends, and the blue observer is back in an inertial coordinate system; the second postulate of SR should hold true exactly again.

    PIC02

    (BLUE) 8s - The signal reaches the blue observer. (=At about 10s in the inertial coordinate system of the red clock)

    Now the blue observer has to make a CHOICE concerning reality. He knows the light signal was sent when the purple clock showed 0s. And he knows the light signal was only 3 seconds away from him before he started running, yet while he was receding from the clock in uniform motion, it still took about 5 seconds for the light to reach him.

    He must either:
    1. Conclude that because of receding from the clock, the light was approaching him with speeds less than C.
    Or
    2. Conclude that the light was approaching him at the speed C even while he was receding from the clock. It immediately follows, that the light must have begun its journey at the moment that is marked in the diagram with "Signal sent again?"; when blue clock was at about 4s, not 0s (This is the moment the light started its journey for ALL the observer that are now co-moving with the blue observer)

    The first option obviously violates the second postulate of SR.

    The second option means accepting SR, and accepting that there exist two REAL moments in the world line of the blue observer, in which he simply KNOWS the signal must have been actually sent, so to obey the rules of SR. 0s, and 4s. He can also verify this later from the other observers, who will tell him that yes, the light signal was indeed sent at BOTH moments he suspects must have been the case in his world line.

    PIC03

    Any other options? All the other options I can think of include ideas of meta reality and strange things about events not actually occuring unless there is someone to see and every observer living their own reality in which everyone else claims non-true things about the propagation of light. So there is a concern here in understanding what happens in reality when we are not there to see. The only logically sound assertion is that time does flow backwards when you are not there to see (albeit this is totally unintuitive).

    Does that sound strange?

    Ok, I'll do that in few days. (JesseM, to answer your question, I would like to know how the situation looks from the point of view of either wheel, as if there was an eye in the CENTER of the wheel. Which is co-rotating with the wheel. I am not sure if it makes no difference in SR whether both wheels are actually rotating in separate directions, or whether one is stationary and other one is spinning. In any case, the premise of SR should imply, that both wheels could push sticks from their circumference, that would completely encircle the other wheel)
     
  21. Feb 1, 2006 #20
    Do you understand that you can not use the same space/time frame for both clocks ? You have to use two different sheets for your diagrams, one for every clock. You can not use just one sheet of paper with the same orthogonal scale for both clocks. If you want to use a single "sheet" of paper for both clocks you have to use a curviformed sheet of paper; you must use a 3D surface, not a 2D surface.

    Leandros
     
    Last edited: Feb 1, 2006
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