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Twin Paradox Simplified

  1. Oct 16, 2007 #1

    rqr

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    Primary Goals of Thread:
    (1) Eliminate all unnecessary concepts
    (2) Focus solely on the physics

    Tom and Bill are floating in space (that is, they are
    moving inertially). Let Bill meet Tom as they pass
    each other. They notice that they are both about
    the same age. After Bill and Tom have separated, Bill
    turns around and again passes Tom. However, during
    this second meeting, they notice that Bill is much
    older than Tom.

    No clocks = no definition of simultaneity
    No rulers = no definition of measurement
    No need to mention coordinate systems

    The only physical difference between the two
    people (Tom and Bill) are Bill's accelerations
    during his turnaround.

    However, this is a difference without a
    distinction because accelerations have no
    effect upon either aging or clock rhythms.

    [Reference:
    http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html
    (sighted words from cited site:
    "... it has been verified experimentally up
    to extraordinarily high accelerations, as
    much as 10^18 g in fact ....")]

    Therefore, current physics has no absolutely
    no physical explanation for the age difference.

    But there is a very good reason for this major
    sin of omission, namely, the simple fact that
    current theory incredibly denies all meaning to
    the notion of motion through space, and yet such
    motion is the only possible cause of the given
    age difference.

    I said "incredibly" because there has always
    existed a simple and effective absolute frame
    in the form of any light ray.

    Despite the utter failure of the Michelson-Morley
    experiment, the fact remains that all light rays
    always move at the known speed c through space.
    And all that is required of an absolute frame is
    for it to have a constant and known speed through
    space.
    Why, then was the Michelson-Morley experiment utterly
    unable to utilize the given absolute frame? The answer
    is simple, and Lorentz gave it long ago - one ruler
    contracted during the experiment. And if a clock is
    added, then it will physically run slow during the
    experiment. Given distorted instruments, one must
    obtain a distorted result, namely, a null result,
    despite the given absolute reference frame.

    Had Michelson & Morley used an uncontracted ruler
    (and/or an unslowed clock), then they would have
    obtained a positive result.

    Even though we have no means of finding an unslowed
    clock or an unshrunken ruler, we need not despair
    because we still have the one-way experiment.

    As of today, no one has yet performed the one-way
    version of the Michelson-Morley experiment. That
    is, no one has measured light's speed between two
    fixed points, despite special relativity theory's
    strong-but-wrong implication that the result should
    or would or could be null.

    I said "implication" because, surprisingly to most,
    special relativity does not scientifically predict
    what will happen if we measure light's one-way
    speed between two fixed clocks. ("Fixed" means
    nonrotated and nontransported.)

    This is because special relativity does not believe
    in absolute simultaneity (absolute synchronization).

    But not believing in something does not prove that
    it cannot exist.

    And given correctly related clocks (or absolutely
    synchronous clocks), and given our absolute frame
    (aka light), we must obtain a nonnull or positive
    result in the one-way light speed case.

    rqr
     
  2. jcsd
  3. Oct 16, 2007 #2

    JesseM

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    Sorry, but saying "accelerations have no effect upon either aging or clock rhythms" is a statement that is only meant to apply within the context of the coordinate systems which you want to do away with...the page is pointing out that the instantaneous rate a clock ticks in a given coordinate system is solely a function of its instantaneous velocity in that system. Accelerations certainly do affect the amount a clock ticks over an extended period, as the page explains:
    The explanation is that one accelerated. Your attempt to deny this is nothing more than a word-game, conflating two quite different meanings of the phrase "accelerations have no effect".
    Yes it does, it just says it will depend on what physical process you use to synchronize the clocks. If you use the Einstein synchronization convention, then the one-way speed will be c (this is almost a tautology, since the Einstein synchronization convention is based on the assumption that clocks a distance of x apart as measured by rulers in their rest frame should be synchronized in such a way that a light signal takes a time of x/c to pass from one to the other). If you use some different convention, the measured speed can be different (although everyone should agree the two-way speed is c since this only requires a single clock so synchronization is not an issue)--this doesn't contradict relativity.
    Relativity makes predictions about any well-defined physical scenario. If you can't define a physical procedure for synchronizing two clocks so that they read the same time "simultaneously" according to absolute simultaneity, then you don't have a well-defined physical scenario--absolute simultaneity would be a purely metaphysical postulate with no relevance to the outcome of any specific experiment, and we'd have absolutely no way of testing whether two clocks were in fact "synchronized" in the absolute sense.
     
    Last edited: Oct 16, 2007
  4. Oct 16, 2007 #3

    Dale

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    There is no experimental difference between Lorentz's theory and Einstein's special relativity. If you like the Lorentz story better than the Einstein one that is fine by me, but the ending is the same regardless of which one you choose.
     
  5. Oct 16, 2007 #4

    pervect

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    I think the simplest approach is to accept, as a fundamental fact, the principle of maximal aging.

    From the above link:

    For most purposes, one can replace "extremum" with "maximum" (at least in SR), hence "principle of maximal aging".

    This principle directly says that the "natural motion" (i.e. with no acceleration) of a body is the motion that maximizes the proper time - so if you fly in some roundabout path with a spaceship, you'll have a lower age than the maximal age you'll get by travelling along "a natural straight line". Which is the "twin paradox" in a nutshell.

    The one bit of fine print needed in GR: you can have multiple extremal paths between two points in a general curved space-time. (This is not an issue in the flat space-time of SR). Only one of these multiple paths is a true maximum. This is the main technical reason for using the more general "extremal" than the more specific "maximal". I believe you'll see Taylor et al using the principle of maximal aging in other works where they talk about only SR and do not include GR.

    The simplest approach (though not necessarily the most elementary approach) is to recognize the principle of maximal aging as a given, and to explore the consequences for physics. The approach is simple conceptually and philosophically, but requires knowledge of the calculus of variations, which is why it is not the most elementary.
     
    Last edited: Oct 16, 2007
  6. Oct 17, 2007 #5

    rqr

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    JesseM, you misread the cited site.
    It said that only speed affects clock rates,
    not accelerations. This is readily apparent
    from the following single sentence from the cite:

    "(The clock rate won't be affected by circular motion
    at constant speed.)"

    (This is constant acceleration with no speed change.)

    And a good little hint was the part about the 10^18 g's; why
    mention that if acceleration in fact does affect clock rates?

    Sure, a _change_ in acceleration will change a clock's
    rate, but this is because of the different speed, not
    the acceleration per se.

    Also, take a look at this from Tom Roberts:

    -------
    NewsGroup: sci.physics.relativity
    Thread: Acceleration should cause Time Dilation
    Date: October 15, 2007

    gu...@hotmail.com wrote:
    > A person pulling Hi G's in a plane can barely move,
    > likewise a clock should also have a hard time moving,
    > which would cause time dilation?

    The decay of muons is a clock that is unaffected
    by an acceleration of 10^18 g -- vastly larger
    than any pilot could sustain.

    > Yet none of the airplane time dilation tests seem to
    > have taken this into account.

    There is no such effect to take into account.

    > As well Gravity generates a time dilation,

    It is not "gravitational force" or "gravitational
    acceleration" that is associated with gravitational
    time dilation, it is a difference in gravitational
    potential. Loosely speaking, that is a difference
    in energy, not an acceleration.

    Tom Roberts
    -------

    JesseM wrote:
    "The explanation is that one accelerated."

    No, accelerations do not affect clock rates;
    therefore, current theory has no physical
    explanation for the age difference.

    The only possible physical cause is different
    speeds through space or different absolute
    speeds.

    -------

    Going back to the one-way light speed experiment,
    you must cope with the fact that no one has
    ever used two (fixed) clocks to experimentally
    measure light's one-way speed.

    In other words, the one-way Michelson-Morley
    experiment has never been performed.

    JesseM said:
    "If you use some different convention, the measured
    [one-way light] speed can be different ... --this
    doesn't contradict relativity."

    Wrong, relativity theory would certainly be contradicted
    by a non-c measurement of light's speed.

    JesseM said:
    "Relativity makes predictions about any well-defined
    physical scenario."

    As I said, relativity theory makes no prediction in
    the only open and the only post-SR case, the one-way
    light speed case. To assume that clocks must be set
    to get c is not a prediction of an experimental
    result.

    But you seemed to stretch relativity theory into
    predicting an experimental outcome based upon the
    use of that which the theory flatly denies, namely,
    absolutely synchronous clocks.

    Let's assume (and rightly so, because it's true) that
    I have a specific method for absolutely synchronizing
    two fixed clocks; if we then ask, as you apparently
    did, What is relativity theory's prediction in the
    case of using such synchronous clocks to actually
    experimentally measure light's one-way speed?

    I notice that your answer was 50% wrong and 50% right,
    i.e., you said that the result would not be c, but
    that this would not conflict with relativity.

    If relativity's prediction is non-c, then it is
    conflicting with itself by admitting that there is
    certainly a way to detect absolute motion, and that
    is by simply using absolutely synchronous clocks to
    measure light's one-way speed.

    This is also admitting that light is an absolute frame,
    in contrast with relativity theory's constant claim
    that no such frame exists.

    Something is rotten in Denmark.

    rqr
     
  7. Oct 17, 2007 #6

    Hurkyl

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    rqr: do you recognize that there is a difference between

    . the time dilation of an accelerating clock, as measured by an inertial frame
    . the time dilation of an inertial clock, as measured by a noninertial frame

    ?



    Incidentally..
    You have that backwards. Bill is younger than Tom.
     
  8. Oct 17, 2007 #7

    jtbell

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  9. Oct 17, 2007 #8

    JesseM

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    You ignore my point that the statement is only meant to apply to instantaneous "clock rates" and "speed" as measured in any given inertial frame. And of course, all acceleration results in a change in speed, so if you want to calculate the elapsed time on a clock over an extended period as opposed to just finding its instantaneous clock rate, you have to integrate the instantaneous clock rate over the whole period, so any changes in speed have an effect on this total time elapsed. It is possible to prove using calculations than in any given frame, if one traveler goes from one point in spacetime to another at constant speed, while another traveler goes between the same two points in spacetime at a non-constant speed, then the one with the non-constant speed will always have aged less.

    If you want to drop all notions of "reference frames" from your scenario, and you want to talk about the elapsed time on the clock over an extended period as opposed to just its instantaneous rate of ticking at a single moment, then the statement "only speed affects clock rates" cannot be taken to imply that it's irrelevant which one accelerated--that is definitely not what the page you quoted was saying. Again, it had a specific meaning in terms of the instantaneous rate of ticking depending only on instantaneous speed in a particular frame, with the total time elapsed depending on integrating the instantaneous speed.
    Yes, in the particular inertial frame in which the clock is moving in a circle at constant speed, since its instantaneous speed is always the same its instantaneous rate of ticking will always be the same, that's what they mean by "the clock rate won't be affected". But the fact remains that if you have an object moving in a straight line which intersects the circle at two points, and the speeds are such that the object moving in a circle passes right next to the object moving in a straight line at both those points, then the object moving in the circle will have elapsed less time on its clock, and the reason for this is that it is accelerating. There is no contradiction between the two notions, it is only your word-games that make you think that since the instantaneous rate of ticking is affected only by the instantaneous speed, this somehow prevents us from explaining the fact that the total time on the clock moving in a circle is shorter in terms of the fact that it was accelerating.
    Acceleration doesn't affect instantaneous clock rates.
    Sure, I agree (although any comments about 'clock rate' and 'speed' only make sense relative to inertial coordinate systems, so your idea that we can dispense with coordinate systems and somehow still make sense of the statement 'clock rate only depends on speed' is nonsense). But like I said, it's possible to prove that if you have two paths between the same two points in spacetime, and one involves changing speed while the other involves constant speed, the clock with changing speed will always have less elapsed time.
    Once again, you're just playing word-games. Acceleration does not affect instantaneous clock rate at any given moment, but since the total time elapsed over an extended period depends on integrating the instantaneous clock rate, this is quite compatible with the notion that a path between two points with constant speed (and thus constant instaneour rate of ticking) will always have a greater elapsed time between a pathe between the same two points with non-constant speed (and thus non-constant instaneous rate of ticking).

    It would really help if you looked at the geometric analogy I offered on a previous thread, which you never addressed there:
    To spell out the analogy:

    1. a given set of xy axes on the paper = a given inertial coordinate system in SR

    2. y-coordinate on xy axes = time-coordinate in inertial coordinate system

    3. two paths on paper = two worldlines in SR

    4. "partial path length" of a given path as a function of y = elapsed time on clock moving along a given worldline as a function of time-coordinate in inertial coordinate system

    5. the fact that the rate at which the partial path length is growing at a given y-coordinate depends only on the slope of the line at that y-coordinate = the fact that the rate a clock's elapsed time is growing (i.e. its instantaneous rate of ticking) as a function of the coordinate's system time-coordinate depends only on its speed in that coordinate system

    6. The fact that the length of a path between two points that has a non-constant slope will always end up being greater than the length of a path between the same two points with a constant slope = the fact that the elapsed time on a clock that goes between two points in space time with a non-constant speed will always end up being less than the the elapsed time on a clock that goes between the same two points with a constant speed

    7. The fact that the statement about geometry (6) can be restated without reference to a particular set of xy axes, and without reference any notion of "slope" or "instantaneous rate that partial path length is growing" in that coordinate system, just by saying "a straight line is always the shortest path between two points" = the fact that the statement about SR in (6) can be restated without reference to a particular inertial frame, and without reference to any notion of "speed" or "instantaneous rate that a clock is ticking" in that frame, just by saying "an inertial worldline always gives the greatest elapsed time between two points".

    So, do you think that since (5) says the rate at which partial path length is increasing at a given y-coordinate depends only on the slope, not the rate the slope is changing, this is incompatible with the statement in (7) that a straight path (with no change in slope) is always the shortest distance between two points? If not, then why should the statement in (5) that the instantaneous rate a clock accumulates time at a given t-coordinate depends only on its speed, not the rate the speed is changing, be incompatible with the statement in (7) that a clock moving between two points in spacetime with constant speed will always have the maximum time?
    Do you fail to understand that the very nature of the Einstein synchronization convention guarantees that the one-way speed is c? You're using a light signal between two clocks to "synchronize" them using the assumption that the one-way speed must be c, so of course any subsequent measurement of a light beam using the same two clocks will give a speed of c.
    Nonsense, relativity only says that the one-way speed is c when measured by clocks that are "synchronized" in their inertial rest frame, using Einstein's synchronization convention. Of course if you are allowed to define "synchronization" any way you want you can get pretty much any value for distance/time...for example, I could set a clock at the right end of my hallway to read a date of midnight, Jan. 1, 2000, while a clock at the left end of my hallway was set to read a date of midnight. Jan. 1, 1850 (say that in the clocks' relativistic inertial rest frame, these two readings are simultaneous). In this case a light beam moving from left to right will be measured to take over 150 years to complete the journey according to these clocks, even if my hallway is just a few meters long! Does this somehow invalidate relativity?
    You don't have to set them to get c...for example, you could use relativity to predict the times on the two clocks in my above example as the light passes them, using an inertial frame where the two clocks are 150 years out-of-sync. In this case relativity would give an accurate answer.
    Relativity does not say there cannot be something like "absolute simultaneity" in a metaphysical sense, it just says that the measured laws of physics look the same in all the inertial rest frames defined by relativity, which means it's impossible to find any actual experimental evidence of absolute simultaneity, or any experimental procedure for synchronizing clocks in an absolute sense.
    This is the part that's incompatible with relativity. If relativity is true, then even if there is a single "correct" definition of simultaneity, it is unknowable by us, because any experiments we do will look the same in all the different inertial coordinate systems given by SR with all their different definitions of simultaneity. So, if SR is correct, the only way to ensure your clocks were synchronized in an absolute sense (assuming there is some truth about this question, which of course the philosophical view known as 'four-dimensionalism' or 'eternalism' would deny, as I explained on the previous thread) would be to obtain the knowledge in some "supernatural" way, like praying to God to give you the answer.
    Relativity doesn't have a prediction about this, because if you have an experimental method for picking out a preferred definition of simultaneity, then relativity has already been falsified. But note that I mean "preferred" relative to the laws of physics, not relative to external physical landmarks like the galaxy or the CMBR...I'm talking about an experimental method that would allow different observers in closed windowless boxes in relative motion to all arrive at the same definition of simultaneity.
     
    Last edited: Oct 18, 2007
  10. Oct 17, 2007 #9

    robphy

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    Let me offer my approach
    www.phy.syr.edu/courses/modules/LIGHTCONE/LightClock/
    which, I feel, addresses your goals
    Once the light clock is established as a instrument measuring proper time along a worldline, the clock effect is demonstrated visually... essentially by following the paths of light rays in a light clock on a spacetime diagram.
     
  11. Oct 17, 2007 #10
    Based on the way the rqr framed the problem, and after correcting the error noted by Hurkyl as to who is older, the straightforward treatment given by pervect in post 4, IMO hits the nail on the head. The cited material is from Taylor's book on "Black Holes" ... I found chapters I and II complete - does anyone know if the rest of the book on line for free??
     
  12. Oct 17, 2007 #11

    JesseM

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    No, that's very wrong. Time dilation is for all physical clocks in SR, I'm not sure what it would even mean to say it's "for light" (unless you mean a light clock). I recommend reading the twin paradox page from John Baez's site.
     
  13. Oct 18, 2007 #12

    Even in the website u given for reference to twin paradox, both twins are using the light clocks to measure their times ...from this it is obvious that only the time in their light clocks changes but not their age...Biological clocks are different from light clocks..

    Moreover,can you give one real life evidence or proof for this twin paradox...
     
  14. Oct 18, 2007 #13

    JesseM

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    The light clock link was specifically about light clocks. But the twin paradox page doesn't say the twins use a light clock, it just says "Stella ages less than Terence between the departure and the reunion."
    No, they aren't. All the known fundamental laws of physics (which govern any type of physical clock) are Lorentz-symmetric, meaning they work the same in any inertial reference frame (and the first postulate of relativity says that all the laws of physics must work the same in any inertial reference frame, so if this wasn't true the theory of relativity would have to be thrown out). So, if a given type of physical clock runs at the same rate as a light clock that's at rest relative to it in one frame, then this must be true in all frames--any physical clock will run at the same rate as a light clock that's at rest relative to it.
    Sure, many types of physical processes have been found to obey the time dilation equation, like how the decay time of various particles in particle accelerators is slowed down by just the right amount when they are traveling at relativistic speeds (see here), or how atomic clocks placed on the space shuttle, which were initially synchronized with atomic clocks on Earth, are slightly behind clocks on Earth when they return, by just the amount predicted by relativity (see the last paragraph of this article).
     
  15. Oct 18, 2007 #14

    Hurkyl

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    Last edited: Oct 18, 2007
  16. Oct 18, 2007 #15
    There can also be effects of gravitational field which could have caused the minimal time difference... SR is applicable for only inertial frames...What are the two inertial frames in that experiment...
     
  17. Oct 18, 2007 #16

    russ_watters

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    Please be advised that you are now looking clear evidence in the face and refusing to accept it. That is an unscientific posture and one that we do not accept here. That experiment (and there are others, such as GPS clocks, which perform the experiment continuously and at several orders of magnitude better accuracy) does test what it is intended to test. Look at the numbers! What is the SR effect? What is the GR effect? What is the accuracy of the clock?
     
    Last edited: Oct 18, 2007
  18. Oct 18, 2007 #17

    jtbell

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    Set up a light-clock that "ticks" once every second, when it is stationary. Find a person whose heart beats once every second. Synchronize the light-clock so that it "ticks" at the same time as the person's heart, when they are standing right next to each other. Connect the light-clock and the person to a coincidence detector that prints a mark on a piece of paper if and only if the light-clock and the person's heart "tick" simultaneously. In the inertial reference frame in which the light-clock and the person are stationary, marks appear on the paper at the rate of one per second.

    Clearly all inertial observers must agree on the presence or absence of marks on the paper. Therefore, in another inertial reference frame, in which the same light-clock, the person and the coincidence detector are moving, marks must also be printed on the paper, although at a slower rate because of time dilation.

    There are indeed effects due to gravity which are taken into account in the analysis of the experiment. Similarly, the GPS system must take into account (with greater precision) the effects of both gravity and speed on the orbiting satellite clocks.
     
    Last edited: Oct 18, 2007
  19. Oct 18, 2007 #18

    rqr

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    2 jessem

    JesseM concluded his analogy with the following:
    "... I'd say there's no single true answer to the question of which twin is accumulating proper time faster (or 'aging faster') before they reunite at a single point in space."

    Absolutely synchronous clocks could tell us the truth
    about time in any multiple-event case. (See more about
    such clocks below.)

    rqr wrote:
    Wrong, relativity theory would certainly be
    contradicted by a non-c measurement of light's
    speed.

    JesseM replied:
    "Nonsense, relativity only says that the one-way speed is c when measured by clocks that are 'synchronized' in their inertial rest frame, using Einstein's synchronization convention. Of course if you are allowed to define 'synchronization' any way you want you can get pretty much any value for distance/time...for example, I could set a clock at the right end of my hallway to read a date of midnight, Jan. 1, 2000, while a clock at the left end of my hallway was set to read a date of midnight. Jan. 1, 1850 (say that in the clocks' relativistic inertial rest frame, these two readings are simultaneous). In this case a light beam moving from left to right will be measured to take over 150 years to complete the journey according to these clocks, even if my hallway is just a few meters long! Does this somehow invalidate relativity?"

    Of course not, because light's one-way speed
    still wouldn't vary with frame velocity.

    In other words, my above is not nonsense.
    I was saying simply that a non-invariant
    light speed would conflict with relativity.

    JesseM wrote:
    " Relativity does not say there cannot be something like 'absolute simultaneity' in a metaphysical sense, it just says that the measured laws of physics look the same in all the inertial rest frames defined by relativity, which means it's impossible to find any actual experimental evidence of absolute simultaneity, or any experimental procedure for synchronizing clocks in an absolute sense."

    The same-laws rule does not preclude absolute
    synchronization. For example, in the case of
    light's experimentally-measured one-way speed,
    the absolute synchronization result would be
    w = c±v, and since this law would have the
    same form in all frames, this would not be
    a violation of the principle of relativity.

    Further, since it is not possible to prove
    a negative, no rule, including the principle
    of relativity, could really say that it is
    impossible to absolutely synchronize clocks.

    JesseM wrote:
    "So, if SR is correct, the only way to ensure your clocks were synchronized in an absolute sense (assuming there is some truth about this question, which of course the philosophical view known as 'four-dimensionalism' or 'eternalism' would deny, as I explained on the previous thread) would be to obtain the knowledge in some 'supernatural' way, like praying to God to give you the answer."

    JesseM continued:
    "I'm talking about an experimental method that would allow different observers in closed windowless boxes in relative motion to all arrive at the same definition of simultaneity."

    That's precisely the method about which I am talking.
    My method must be and is a closed-lab method.
    It can also be independently verified.
    The key notion behind this method is the simple fact
    that we need not actually measure each clock-starting
    entity's speed, but we need only to assure that these
    speeds (relative to the clocks to be started) are equal.

    JesseM wrote:
    "... any comments about 'clock rate' and 'speed' only make sense relative to inertial coordinate systems, so your idea that we can dispense with coordinate systems and somehow still make sense of the statement 'clock rate only depends on speed' is nonsense)."

    It is not nonsense, but is based on the
    simple fact that no passing coordinate system
    can possibly physically affect anyone's aging
    process or any clocks atomic rate.

    Returning to the twins, let's put it another way,
    as follows:

    Suppose we let Bill's turnaround be a very small
    part of his overall trip. Then we cryogenically
    stop Bill's aging process during the turnaround.
    Then, if he and Bob have different ages when they
    meet the second time, no one can use or pretend
    to use, acceleration as the cause.

    rqr
     
  20. Oct 18, 2007 #19

    JesseM

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    Yes it would, if you define clocks as "synchronized" when they are actually out-of-sync in their SR rest frame. In the above example, the light would take a little over 150 years to travel from the left end of the hallway to the right, but it would take a little over -150 years (a trip back in time) to travel from right to left. To pick an example that doesn't involve time travel, suppose I take a hallway 5 light-seconds long, at the left end I put a clock that reads 0 seconds, at the right end end I put a clock that reads 2 seconds "simultaneously" in their mutual SR rest frame, but then I throw away the SR rest frame's definition of simultaneity and define simultaneity in terms of these two clocks (so an event that happens next to the left clock when it reads 3 seconds is defined to happen at the 'same time' as an event that happens next to the right clock when it reads 3 seconds, for example). If I send a light signal from left to right when the left clock reads 0 seconds, analyzed from the SR frame it takes 5 seconds to get to the right clock, but since the right clock clock was already 2 seconds ahead in the SR frame it'll read 7 seconds when the light reaches it. So, if I am defining these clocks as "synchronized", I'll say that the one-way speed of the beam=distance/time = 5 light-seconds/7 seconds = 0.71c. Now if I send a beam back to the right at 7 seconds, then in SR terms it again takes 5 seconds to travel back, but since the left clock is 2 seconds behind the right one in their SR frame, the left clock only reads 7+5-2=10 seconds when the beam reaches it. So, if I'm defining these clocks as "synchronized", the beam departed from the right clock at 7 seconds and arrived at the left one at 10 seconds, so speed = distance/time = 5 light-seconds/3 seconds = 1.67c. So clearly, because I have arbitrarily chosen to define these clocks as "synchronized" even though they are out-of-sync by 2 seconds in their SR rest frame, then the one-way speed of light will be different in different directions in any coordinate system where the two clocks actually are synchronized. Do you think this simple trick of setting clocks to be out-of-sync in their SR rest frame is a falsfication of relativity, even though I actually used the SR rest frame to calculate what the time would be on each clock as the light beam passed them?
    If their was some physical method for picking out a preferred definition of simultaneity for two clocks that did not necessarily agree with the definition of their SR rest frame, then using this alternate definition you could get different one-way speeds. But in this case the thing that contradicts relativity is the physically preferred definition of simultaneity, the fact that the one-way speed can vary is just a consequence of that. On the other hand, it's quite easy to arbitrarily define two clocks to be "synchronized" even when they're out-of-sync in their SR rest frame with no physical motivation for this altered definition of simultaneity, as I did in the above example, and in this case you'll also get a varying one-way-speed, but that doesn't contradict SR.
    Yes it would be, because each frame would have a different numerical value for v (which is presumably their velocity relative to a preferred frame whose SR definition of simultaneity is the "correct" one in absolute terms). Lorentz-invariance means the equations for all fundamental laws must be identical when written in the coordinate systems of different inertial frames, there can't even be a difference in numerical constants.
    But relativity doesn't "prove" that the first postulate is true, it postulates that as a fundamental principle. It's up to experimentalists to decide whether the real-world laws of physics respect this postulate. The point is that if experimentalists find that the laws of physics are not identical in every inertial frame in flat spacetime, then this proves that the theory of relativity itself is incorrect. My argument is just that absolute synchronization would be totally incompatible with the theory of relativity, not that I can "prove" that the theory of relativity is actually correct (although all evidence found by physicists so far suggests it is).
    Maybe instead of being mysterious about your new method you could give the details, so if there's a flaw in your reasoning we could point it out?
    Relativity simply says there is no coordinate-independent truth about one's "rate of aging", at least not one that can be experimentally tested (there could be an 'metaphysical' truth just like there could be an 'metaphysical' truth about simultaneity). Did you read my geometric analogy? Do you understand that in the block spacetime view, "rate of aging" (i.e. the rate that a clock's total time is increasing) is analogous to the notion of "the rate that the partial path length is increasing" for a path drawn on a piece of paper, which just depends on the slope of a line at a given point? Do you agree that by rotating our xy axes, we can change the slope of the same line at any given point? Would you argue that this is problematic since "no rotated coordinate system can possibly physically affect the slope of a physical line drawn on a piece of paper", or would you acknowledge that "slope" is itself a coordinate-dependent concept with no absolute physical reality, so this isn't a problem?

    Perhaps the difference between these situations is that "the rate partial path length increases" is defined relative to the y-coordinate, and you don't assume there is any such thing as an "absolute y-axis" on a piece of paper, whereas "the rate that a clock's elapsed time increases" is defined relative to a given frame's t-coordinate, and you assume there is such a thing as absolute time so that it makes sense to ask what rate a clock's elapsed time is increasing relative to absolute time. But unless you can come up with an experimental way of figuring out which SR frame's t-coordinate corresponds to absolute time, this is a purely metaphysical belief with no empirical basis, and I think the geometric analogy shows that there is nothing illogical about dispensing with the idea of absolute time altogether.
    First of all, relativity is talking about time passed in terms of fundamental physical processes, if the time elapsed for a given traveler is 40 years then this isn't changed by freezing him so he doesn't look 40 years older, an atomic clock placed next to him would still show that 40 years had passed and the number of oscillations in the atoms in his frozen body would still be the number that the laws of physics would predict for a 40-year period, and the same would go for any other 'clock' based on fundamental laws like the decay of isotopes in his body.

    Second, I don't understand why it was Bill who you imagined freezing, and why you specified that he only be frozen in the turnaround...I think you may still be confused about how the twin paradox works in SR. First of all, if Bill is the one who accelerates during the turnaround while Bob moves inertially, SR already less time will have elapsed for Bill, so freezing Bill won't make their ages equal, it'll just make him appear even younger when they meet...wouldn't it have made more sense to suggest freezing Bob? Second, relativity doesn't predict that anything special happens during the turnaround phase...you can make Bill's turnaround instantaneous and the time on his clocks will still be significantly less than Bob's when they reunite.
     
    Last edited: Oct 18, 2007
  21. Oct 18, 2007 #20

    Dale

    Staff: Mentor

    Hi Pervect, JesseM, et al.,

    I think it is pointless to debate people who insist that Lorentz was right and Einstein was wrong. Since special relativity is just a simpler way to derive the Lorentz transform the two theories are experimentally indistinguishable. Whenever you are talking with someone who thinks that they have actually said something meaningful by asserting Lorentz over Einstein then you know that you are not dealing with someone who is really interested in science.
     
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