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Absolute reference frame

  1. Mar 2, 2007 #1
    Hi

    I know that the following can never be done in the real world, but in theory, if the vectors of all particles, antiparticles, photons etc. in the universe could be summed, would that qualify as an absolute reference frame for that instant in time?

    Clearly each instant would have a different vector sum, but if these sums were traced over a long period of time, it's possible that they would be confined to a sphere somewhere in the universe with a radius that was many orders of magnitude smaller than the universe itself.

    Not sure what practical uses such a reference frame would have, but if it is possible, at least theoretically, then it might lead to some interesting ideas.
     
    Last edited: Mar 2, 2007
  2. jcsd
  3. Mar 3, 2007 #2
    The universe does have a preferred frame of reference; you're describing something along the lines of the hubble flow, or being stationary compared to the cosmic microwave background radiation. But the laws of physics seem to behave the same regardless of your relative velocity..
     
  4. Mar 3, 2007 #3

    jtbell

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    In what sense, then, can one call the CMBR a "preferred reference frame?"
     
  5. Mar 3, 2007 #4

    Garth

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    It is an identifiable reference frame, in the sense that at any location any arbitrary observer, moving at any arbitrary velocity relative to another, can measure the CMB dipole and correct for their peculiar velocity relative to the Surface of Last Scattering. Every observer would then identify the same corrected frame of reference.

    Is this result that which is to be expected from the basic principles of GR?

    Garth
     
  6. Mar 3, 2007 #5

    pervect

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    While such a frame, if it could be defined, would be interesting, it would not qualify as an absolute frame. An absolute frame is generally understood to imply that no other object is used to construct it. In this case, you are using many objects to construct your frame. So it's just an interesting relative frame.

    There is an additional complication. In special relativity, what you describe would work as you think it should, but in general relativity the idea of adding momenta (what you call 'vectors') together to get a 'system momentum' is not well defined in the general case

    While there are some important special cases where total momentum can be defined the process is a little more involved than addition. One has to take into account the local metric coefficients as well as the mass and the momenta ('vectors') of the particle.
     
  7. Mar 3, 2007 #6
    shouldn't the sum be zero. or else it would be like the universe is moving somewhere.
     
  8. Mar 3, 2007 #7
    vectors of what, of forces acting on them, of their displacements,of their velocities, of what exactly?
     
  9. Mar 3, 2007 #8

    HallsofIvy

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    What do you mean by "the vectors" (that's really loop quantum gravity's question). All relevent vectors: force, acceleration, velocity, momentum, are only defined relative to some frame of reference. Starting from a different frame of reference would give different vectors and so a different result for the "sum of all vectors".
     
  10. Mar 3, 2007 #9
    Well here you have it, obviously: magical frame would be where the sum is 0, i.e. all things together do not move anywhere.
     
  11. Mar 3, 2007 #10

    jtbell

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    But what would be "magical" about that frame? Suppose we set up a laboratory which is at rest in that (inertial) reference frame, with no windows so we can't "look outside," and nothing from outside can get in. What experiments would work differently inside that laboratory than inside another laboratory which is at rest in a different inertial reference frame (i.e. moving at constant velocity with respect to the first frame)?
     
    Last edited: Mar 3, 2007
  12. Mar 3, 2007 #11

    ZapperZ

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    You are making speculative conjecture here.

    Ignoring the fact that you haven't answered loop quantum gravity's question, let's try something and then you can tell us where such a thing will apply.

    I have a mass at the origin of some coordinate system. At t=0, it explodes into 2 pieces, A and B, going in opposite direction. A and B do not have the same mass, and do not have the same speed.

    Now clearly, we know where the "origin" is, and where the "preferred" frame is simply by using the original starting frame. Using this example, can you show us ALL of the so-called vectors that you plan on adding that you conjectured to sum up to zero in this "preferred" frame? Because if you can't show this for this very simple and obvious scenario, what hope can there be for something more complicated like..... oh, I don't know... the universe?

    Zz.
     
  13. Mar 3, 2007 #12
    Jeez, and what on Earth we will do now? I guess we're screwed, right. Did someone mentioned an impulse? No? Just my imagination then.
     
  14. Mar 3, 2007 #13

    ZapperZ

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    No, I only gave a very simple scenario and asked you to apply on where exactly is this "magical frame" in which the "sum be zero". Are you saying that in this that very simple universe consisting of just 2 end masses, you cannot show such a thing?

    Zz.
     
  15. Mar 3, 2007 #14

    pervect

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    Some of the technical points regarding vectors in GR are rather,well, technical. I will give a source that points out that you can't add them together in GR the way you do in SR rather than talk about the details myself. See Baez's

    The Meaning of Einstein's Equation

    which also talks a little bit about "relative" vs "absolute" velocities. The following quote is from that URL.

    The only way I could make sense out of the OP (original post) was assuming that the OP meant "momentum" when it said "vectors". It's possible I misunderstood, of course. Regardless, all vectors (as the term is used in GR) have the properties that Baez describes regarding one's inability to add or even compare them unless they are at the same location.

    This is one reason why the closest thing the universe has to a frame that is "at rest", the CMB frame, is not an inertial frame, but a series of different frames that are all moving away from one another.

    It's probably also important to note that standard cosmological models assume the universe is infinite (or very very large, and that we are not near the edge). Of course the part we can actually observe (the observable universe) is finite.
     
    Last edited: Mar 3, 2007
  16. Mar 3, 2007 #15
    I'm sure there are all sorts of complications I'm not thinking of, but if the vector sums did remain within a sphere somewhere in the universe, the center of that sphere wouldn't move relative to any observer.

    I was thinking that it would be sort of like a brownian plot of a particle. The universe seems clumpy to a certain extent (as evidenced by CMBR pictures) so the vector sums would wander around a bit. It may be smooth enough however that the wandering sums stay within a defined and fairly small sphere (in relation to the total universe).

    If you could define the sphere, then the center of that sphere could be said to be stationary relative to every other point in the universe. Any apparent motion of that point across the sky could be interpreted as the observer's motion relative to this point rather than the other way around.

    Displacements for given time.

    I was starting with the premise that at any given time, the universe has a state that exists regardless of our ability to measure it.

    For example: If astronomers were lucky enough to record the birth of a sun-like star, the exact instant when it's nuclear fires ignited, and if after performing spectral analysis, they determined that the star was 4 billion light years away, it would be reasonable to assume that the star still exists. The star would actually be 4 billion years old, not days or weeks.

    So from this, we could say that the universe has a non-relativistic state. We can't measure that state, but we might be able to come up with a rough extrapolation by projecting known physical laws forward in time from the point of observation.

    Thanks for the link

    Interesting. I hadn't hread that.


    After chewing on that for awhile...

    If you define a set of points on a circle with a large radius from your frame (say, 5 billion light years). Select whatever particles are closest to these points to use as the origin. Sum all vectors from these points and due to the fact that some of these origin points are bound to be closer to the "edge" of the universe than others, over time, the sums from each point should display a definite bias.

    Points closer to the "edge" of the universe would display a bias in the direction of the geometric center as the shortened vectors from the edge side would be overpowered by the longer vectors from the rest of the universe.

    Comparing the bias for each of the origin points should indicate roughly where the geometric center of the universe is and where the edge is. If you could find the center then it could be used as "the mother of all reference frames" for all distance and time measurements.
     
    Last edited: Mar 3, 2007
  17. Mar 3, 2007 #16

    pervect

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    The problem is that there actually isn't any such vector sum mathematically defined, as I mentioned and my link mentioned.
     
  18. Mar 5, 2007 #17
    I am saying that if you could add impulses instead of velocities, you would successfully figure out "the magic frame".
     
  19. Mar 5, 2007 #18

    ZapperZ

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    Then show me using that very simple scenario that I've just described.

    Zz.
     
  20. Mar 5, 2007 #19
    If a mass was at rest before explosion, we're already in that frame due to this magical equation. If not, we should switch to frame of obserer co-moving with your mass. What you want me to show here? p(A) = -p(B)?
     
  21. Mar 5, 2007 #20

    ZapperZ

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    So then you would use ONLY the momentum conservation to pick out your "magic frame" in this simple universe?

    Zz.
     
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