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Does SR imply determinism

  1. Jan 17, 2005 #1
    Came across an article of interest claiming SR implies the future is predetermined. The salient argument is summarized below:

    We start with the notion that we cannot attribute reality to the future since it is yet to be determined. Nor can we claim that what we see is real in the present because, if we are looking at distant light sources, we only see them as they were in the past. One definition of reality would be: “all that exists, now, here and elsewhere” This avoids things that do not exist anymore and things that do not yet exist.

    Consider a Minkowski diagram having space as abscissae and time in ordinates. At time t = 0 an observer J located at the origin of an inertial system S would regard as objectively real all events that lie on the X axis (i.e., simultaneous with the presence of J at the origin at t = 0). But if another inertial frame S1 is considered that is in uniform motion v wrt to S, an observer J1 at rest in S1 must attribute reality to all events happening at his present time t1 = 0. These events are different from those constituting the reality of J. Given the complete symmetry demanded by SR, if the reality line of J1 passes through the origin 0, all the events on the X1 axis whose equation is t1 = 0 with inclination determined by the relative velocity v can be considered equally real as those on the X axis.. In other words J1 will attribute reality to events in J’s future which are not part of his present reality.

    To make it more meaningful, consider other observers P1 and P2 at different points along the positive X axis. These are all equivalent in their description of their present reality since the time t = 0 is the same for all of them. It is seen that the reality line of J1 will be intersected by the personal future(s) of P1 and P2 (you will need to draw the point X1 above X and a line from the origin through X1 with p1 and p2 somewhere spaced somewhere along the positive x axis, then dotted lines up from p1 and p2 to intersect the 0-X1 axis ...sorry the drawing gets scrambled when I copy it from the clipboard).

    Since there can be an infinite number of reality lines corresponding to different velocity frames that all pass through the origin - each representing the present for some legitimate inertial observer - is the future fixed in every detail?'''''''

    ct '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' X1
    !
    !
    !____________________________________ X
    0 ...........p1 ....................p2
     
    Last edited: Jan 17, 2005
  2. jcsd
  3. Jan 18, 2005 #2

    Hurkyl

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    Implication of determinism isn't peculiar to SR; the same can be said about classical mechanics, GR, and even QM (when phrased properly).

    Such arguments come with the implicit assumption that there is a deterministic description of some piece of space-time, and then use time evolution formulae to extend that determinism to other parts of space-time (possibly all). While the various theories admit such a case, none require it.

    P.S. I didn't really follow the particular argument you were trying to make.
     
  4. Jan 18, 2005 #3
    yogi
    P1 and P2 can only obeserve the past of others including each other.
    With the one time exception of when they are in the same place.

    P1 only sees P2's past within the common ref frame unless P2 comes by for a visit in the current place and time.
    Same applies to other ref frame members. In fact all ref frames has a part of it visiting P1's current place and time. All other part only share thier past with P1. As P1 does the same for them.
     
  5. Jan 18, 2005 #4

    ohwilleke

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    My intuition is that there is a unit of measurement flaw in the determinism argument for SR. In otherwords, the time scales aren't well calibrated and that apples and oranges in different calibrations are being compared.

    Also, while all classical theories are deterministic, it doesn't necessarily follow that the SR piece of the classical theory is the lynchpin that creates the determinism.

    Finally, I've never heard any coherent argument that QM is deterministic. Indeed, one of the best arguments for non-determinism is that QM is inherently stochastic and that the notion of "chaos" (i.e. sensistivity to initial conditions in certain non-linear systems) makes it possible for the stochastic underpinnings of QM to make themselves felt at the macroscopic level.
     
  6. Jan 18, 2005 #5
    The diagram is confusing because it gets corrupted when I paste to the forum. Anyway - to clarify (maybe) just consider the X axis as coincident with the "now" line of J and ct orthogonal to the X axis - we can consider J to be at the origin ct = 0 and X = 0. Another frame in which J1 is at rest also passes through the same origin - but this frame has a velocity v wrt to J. So we can represent the "now" line of J1 as a sloped line connecting the origin with X1. Since according to SR, this is equally real from the standpoint of J1 as are the events that lie along the X axis are real to J. As time progresses the observers p1 and later p2 will intersect the line from 0 to X1 - when they do they will be arriving at a spacetime point that was a "now" event for J1 at an earlier time. Does that clarify or confuse?
     
  7. Jan 18, 2005 #6

    Hurkyl

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    Wrap your diagram in code tags. e.g.

    [ code ]
    /
    /
    /
    /
    /
    [ /code ]

    becomes

    Code (Text):

        /
       /
      /
     /
    /
     
     
  8. Jan 19, 2005 #7
    The argument goes as follows: Suppose that event B is in the future of event A. Then there is an event C which is spacelike separated both from A and from B. Thus a suitably moving observer at A would see C as 'now' and a suitably moving observer at C would see B as 'now'. If we assume that what is happening 'now' is already determined, then B should be already determined at A.

    I would argue against this as follows: suppose we assume that freewill exists - I make a decision after A which changes what happens at B. Is there anything it the above argument which contradicts this? No there isn't. I would say that the problem is believing in some special significance to 'now' at distant locations - I think of all events which have spacelike separation from me as having the same significance.
     
  9. Jan 19, 2005 #8

    Aether

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    There is a special significance to 'now' at distant locations, chronon (e.g., cosmological time). SR does not strictly apply anywhere in the real world, it is a local approximation to GR, which isn't rock-solid itself.

    SR is only valid in the limit as the space-time volume under scrutiny goes to zero, so you can't extrapolate SR "to all events which have a spacelike separation from me" and still be talking about the real world. For example, in flat space-time, satellites do not orbit planets, planets do not orbit stars, etc..
     
    Last edited: Jan 19, 2005
  10. Jan 19, 2005 #9
    Dosn't "Spacelike seperated" mean there is no moving obeserver that is able to could see now as common between A & C or B & C.

    If they could by definition they couldn't be "Spacelike seperated" could they?

    RB
     
  11. Jan 19, 2005 #10

    Hurkyl

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    Not in GR.
     
  12. Jan 19, 2005 #11

    Aether

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    Care to elaborate, Hurkyl? Here is an example of where I am coming from:

     
  13. Jan 20, 2005 #12
    General relativity actually allows a wide choice of coordinate systems (and most of the mathematics of GR consists of converting between them). Cosmologists choose a coordinate system where the time is given by the proper time of an object moving with the expansion. This emphasises the homogeneity and isotropy of the universe, but I would still see it as a choice rather than as having physical significance. I've written more about this on my website, especially at http://www.chronon.org/Articles/milne_cosmology.html.

    I would note that if you do believe in a preferred time coordinate, then the SR argument for determinism no longer applies.
     
  14. Jan 20, 2005 #13

    Hurkyl

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    It's merely a choice of coordinate chart -- they have picked a (family of) coordinate charts that are convenient for explaining the large scale structure of the universe. It's no different than picking a frame in SR that is convenient for analyzing an SR problem.

    It's important to note that physical clocks cannot agree with the time coordinate of such a chart -- in an extreme case, it would have to pass through a black hole and come out! Even in the mild case, it would have its rate of time altered by local gravitational fields. Actually, I don't think it's even possible to locally work out in which direction it's supposed to be travelling, as it is buffeted by local gravitational fields.
     
  15. Jan 20, 2005 #14

    Aether

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    The WMAP team's estimate for the age of the universe at 13.4Gyr, based on the CMB monopole, is one example of a real cosmological clock. This is a physical clock, and it is easy to work out locally, using the CMB dipole anisotropy, in which direction it is supposed to be traveling. By "locally", do you mean to restrict the clock from receiving signals from outside itself?

    So, are you saying that the CMB monopole does not have the same value at the same cosmological time regardless of spatial coordinates (within our universe)?

    Do you agree that the CMB monopole is simultaneously observable at any given cosmological time t, and will be seen to have the same value, at all spatial locations, for any arbitrary inertial frame, and for any local gravitational conditions within our universe?
     
    Last edited: Jan 20, 2005
  16. Jan 20, 2005 #15

    russ_watters

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    I'm not sure what you are saying is correct, but assuming it is, why should we care? What's so great about that particular frame of reference? Seems to me it is only relevant to cosmologists (and then still not for many things). I can't think of anyone else who would use it over a heliocentric or geocentric frame. Since we live in the geocentric frame, its virtually always the most important.
     
    Last edited: Jan 20, 2005
  17. Jan 20, 2005 #16

    Chronos

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    I think there is a difference between an absolute [preferred] reference frame and a convenient reference frame. If you strictly apply the rules of SR, it's apparent [at least to me] the CMB is merely a convenient reference frame, not absolute. The rules apply in exactly the same way as they do in any other reference frame. I find the term 'cosmological time' unsettling because I have seen it used in a way that implies it is a somehow superior way to keep time. I object to that notion. It may be conceptually simpler, but it is mathematically indistinguishable from any other clock.
     
  18. Jan 20, 2005 #17

    Aether

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    Most of what I said in my last post was in the form of three questions, and that is because I am not sure that it is all correct myself; but it is to the best of my understanding at this time. I hope that it is OK with you if, as I am studying GR and cosmology on my own, that I can continue to ask such questions here.

    Isn't it enough to say that it is relevant to cosmologists? When a scientist attempts to extrapolate SR principles across vast distances, then they have stepped into the realm of cosmology. When chronon, for example, says that:

    then he has clearly entered into the realm of cosmology, and the cosmological principle applies. I have not objected, so far, to anyone's use of heliocentric or geocentric frames when the scope of their observations haven't expanded to encompass the entire universe (and beyond).
     
    Last edited: Jan 20, 2005
  19. Jan 20, 2005 #18

    Aether

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    I also find the term cosmological time unsettling, and that is why I keep bringing it up. I was unaware of the concept myself until about three or four months ago.

    Why do you say that a cosmological clock is mathematically indistinguishable from any other clock? A proper time clock runs slower with increased velocity, but a cosmological clock does not (as I understand it). The 13.4Gyr estimate for the age of the universe, based on the CMB monopole temperature, does not depend on the velocity of the observer; the CMB dipole anisotropy does, but that is easily compensated for.
     
    Last edited: Jan 20, 2005
  20. Jan 20, 2005 #19

    russ_watters

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    I asked the question because you seem to be implying that the CMB constitutes a Universal reference frame, ie one contrary to Special Relativity. If such a frame existed, it would be important to everyone, not just cosmologists.

    My understanding of this is a little thin, but it sounds like "cosmological time" is just earth time corrected for our motion through the CMB (and gravity?). Yes, certainly, then any clock that is corrected for its motion through the CMB (and gravity?) would tick at the same rate, but that does not imply cosmological time has any special significance. In fact, its an empty assertion, logically identical to saying that any clock corrected to show earth time will show earth time. True, but useless.
     
    Last edited: Jan 20, 2005
  21. Jan 20, 2005 #20

    Aether

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    OK, so a cosmological clock based on the CMB monopole gives the same output as a Universal Clock should, but the step of extracting the CMB dipole anisotropy somehow profoundly distinguishes between the two types of clock? Can you explain the nature of this distinction in greater detail, or give a link to where such an explanation is posted?
     
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