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Physical basis for DSR

  1. Jun 6, 2009 #1


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    As I recall, Rovelli never published anything about DSR until August 2008, when he posted "A note on DSR" on arxiv (0808.3505). And he never took part in the discussion of whether GLAST spacecraft (now called Fermi) might or might not observe that high-energy photons are delayed.

    It appears that he had a speculative note suggesting a possible physical mechanism which might cause DSR to appear (as an approximation to reality) in the limit. And this note circulated privately for some time before he posted it in 2008. I can appreciate the caution in dealing with a speculative risky idea that one isn't sure about.

    However this risky idea is interesting, I think. You might like to consider it. Keep in mind that from the standpoint of a relativist special rel is not fundamental. SR only arises as an approximation in a certain flat limit where G -> 0, or where matter is negligible.

    What is fundamental is the dynamic geometry of GR, which is the cause of any flat approximate geometry that one might find applicable in particular situations. Or more precisely it is the sought-after quantum version of geometry that is fundamental--the quantum GR.

    So one can imagine taking limits from that theory, as hbar -> 0 or/and as G -> 0.
    What one gets depends on how one takes the limit, and will determine for which application the approximation is appropriate.

    Rovelli asks, what if we take limits as hbar and G both go to zero but the ratio hbar/G stays constant?

    Well hbar/G is the square of the Planck mass. So that amounts to keeping the Planck mass constant while one lets G -> 0 (the flat empty space limit) and hbar -> 0 (the non-quantum classical largescale limit).

    Curiously, it looks like he gets something like DSR when he does this.
    The point is that there is some physics which does not depend on hbar separately or on G separately, but which depends on the ratio hbar/G. And this carries over into the limit.

    So if you take the limit in a clumsy way where you first let hbar -> 0 and then you let G -> 0, then you miss seeing these effects. You have to take the two limits simultaneously, keeping the ratio constant, and then you see the effects.

    The paper is only 6 pages, and comparatively simple writing, so you can see for yourself
    how it works out. Better than if I try to repeat every step of the argument.

    Just a comment: there is a curious epistemological point that comes out which is that since points in space or spacetime have no objective reality you cannot define a reference frame without designating some particle or particles of matter. So it is philosophically necessary that a reference frame must have a mass associated with it. This is quite strange. At least to me it never occurred to think this before.
  2. jcsd
  3. Jun 6, 2009 #2


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    There are a couple of typos in equation (3) but I've figured out what the correction should be and will write it out here as time permits. Have to be off the computer for a few minutes but will get back to this. Equation (3) is basic to the argument.

    Note that Rovelli is setting c = 1. That is why the planck area = Ghbar, and why the square of the planck mass = hbar/G.

    In (3) he is finding the ratio that relates the Minkowski proper time (of special rel) to the real proper time (of gen rel).

    The particle (defining the frame) has mass m
    and so the characteristic length, the Compton, is naturally hbar/m

    And the potential depth of the particle in Newton approximation is Gm/(Compton) = Gm/(hbar/m) = Gm2/hbar.

    Now I almost don't have to spell out how to correct the typos in (3).
    If you are interested in this and are looking at Rovelli's short note, then you can see how to fix it. Will get back to this later.

    OK, I'm back.

    Now the ratio between the square of the Minkowski proper time and the square of the correct GR proper time is (1 - 2(potential depth)) =
    (1 - 2Gm/Compton).

    But we noticed that Gm/(Compton) = Gm2/hbar,
    and hbar/G = MP2, so therefore
    Gm/(Compton) = Gm2/hbar = m2/MP2.
    I will stop writing this dumb subscript P for "planck" and just write M for planck mass.

    The ratio between the squares of the proper times is now (1 -2m2/M2)

    So you have a correction which depends on how the mass of your ref frame compares with the Planck mass.

    Or more exactly how the mass of the point particle you chose as origin of your frame compares to planck. There are no objectively real points except what can be designated using a point particle (like Einstein said, points by themselves have no objective physical reality) and so you must designate a point particle, and this defines a mass.
    You cannot jump to a "center of mass" of an extended body because to determine a center of mass already requires a frame. So to have a point you must tag a particle. :biggrin: I like this, hope you do too.

    So in effect Rovelli is pointing out that time goes slow in reference frames which have large mass (a large fraction of planck).
    And when we learned special rel and were working in Minkowski space we just did not notice this because all our frames that we were using had such tiny tiny mass that it could be neglected, and we could neglect differences in time resulting from the mass of the frame.

    Note that mass-of-frame effects depend not on G or on hbar alone but on hbar/G, the ratio. So we can start with a basic theory and let hbar -> 0 and G -> 0 but these effects will carry over, the physics is preserved in the DSR limit. DSR is talking about something real. Although it is just an approximation to the basic theory.

    What we really should have been doing when we studied Minkowski special rel was use a different symmetry group. This is the group of symmetries between all frames of the same mass.

    So you add a coordinate that gives the mass of the frame. Now you are 5D, and you have this "fifth wheel" tacked on. And you transform in SO(1,4) and you restrict to those transformations which keep the x4 coordinate invariant.

    What happens to x0 thru x3 is similar to what you expect from the Lorentz group SO(1,3) more or less. But you also have to keep the mass of the frame unchanged. So Rovelli is nudging you in the direction of looking at a different group, always a welcome suggestion.

    And the upshot is that there seems to emerge a version of DSR that was presented in December 2004 by Florian Girelli and Etera Livine, who both, I think, in former times were Rovelli PhD students http://arxiv.org/abs/gr-qc/0412079
    so although this note came out in 2008, it could have been brewing for some time.
    Last edited: Jun 6, 2009
  4. Jun 6, 2009 #3


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    In case anyone is interested in this, like I am, I want to mention some relevant details. Yesterday was the main day of talks at the Abhayfest. The 60th birthday party conference for Abhay Ashtekar. The program is significant. I gave the program link here:

    ==And here is a little excerpt==
    Friday June 5 is the big day of the Abhayfest, with talks followed by a banquet in the evening. Friday's talks include:
    9:30 AM - 10:15 AM Carlo Rovelli What is a Particle?
    10:15 AM - 11:00 AM Robert Wald The Formulation of Quantum Field Theory in Curved Spacetime
    2:00 PM - 2:30 PM Laurent Freidel Quantum Geometry from Spin Foam
    2:30 PM - 3:00 PM Jerzy Lewandowski Spin Foams from Quantum Geometry
    3:00 PM - 3:30 PM Lee Smolin Unimodular Gravity and the Cosmological Constant Problem
    5:00 PM - 5:30 PM Rodolfo Gambini The Issue of Time in Generally Covariant Theories and Quantum Gravity


    Quantum Geometry is a name used for LQG within the research community itself and is how Ashtekar refers to LQG, which will help you interpret some of the titles.

    What I am thinking about is the title of Rovelli's talk. The talk may be somewhat relevant to this note about DSR. Because of the idea of a point particle. When one quantizes geometry---then the minimal structure that can contain all the quantum numbers is the spin network. It represents the measurable or observable geometric relations. The areas the volumes etc that one can measure. There is a standard way to represent fields on a spin network, by labeling the links and nodes. Fields exist OK. But what about point particles? What are they? Maybe there are questions. Maybe Rovelli has thought of something that isn't obvious. Could it have to do with frames? Could a massive point particle exist only in so much as a corresponding frame is definable? What about the center of a black hole? In the spin network representation that corresponds to a node from which many many many links are branching out. Is this in some sense a particle? But yet no frame can be defined with it as the origin! To have a frame, the mass must be less than Planck. And so on. I am thinking that Rovelli's abhayfest talk of yesterday (Friday 5 June) could have had something to do with this note on DSR.


    In any case the point of DSR is that different versions have empirical consequences.

    Strictly speaking DSR is not Lorentz violation, it is Lorentz modification. Violation connotes the appearance of a preferred frame, which does not happen in DSR. But DSR gets discussed by phenomenologists "in the same breath" as Lorentz violation. And it happened that just a couple of days ago an expert on this, Stefano Liberati, posted a review paper on tests of LV and DSR.
    This review paper was prepared for publication in the Annual Review of Nuclear and Particle Science.

    "...We hope that this review has convinced even the most skeptical reader that it is now possible to strongly constrain Planck-suppressed effects motivated by QG scenarios. The above discussion makes clear that this can be achieved because even tiny violations of a fundamental symmetry such as Lorentz invariance can lead to detectable effects at energies well below the Planck scale... "

    "...As we discussed at the beginning of this review, LV is not the only possible low energy QG signature. Nonetheless, it is encouraging that it was possible to gather such strong constraints on this phenomenology in only a few years. This should motivate researchers to further explore this possibility as well as to look even harder for new QG induced phenomena that will be amenable to observational tests. This will not be an easy task, but the data so far obtained prove that the Planck scale is not so untestable after all."
    Last edited: Jun 6, 2009
  5. Jun 6, 2009 #4


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    Thanks Marcus. Two comments regarding DSR:
    - it is definitly NOT Lorentz violation but non-linear implementation or deformation
    - some physical effects may be similar, but as there is still NO preferred frame of reference, one MUST NOT confuse breaking with deformation
  6. Jun 7, 2009 #5
    That phrasing bothers me. One could argue that the essence of special relativity is lorentz symmetry (which doesn't contain the gallilean symmetry of Newtonian mechanics). The simplest case is to consider this a global symmetry (special relativity), but it is retained exactly as a local symmetry in general relativity.

    Lorentz symmetry is exact in GR. DSR destroys this (or if you prefer, "deforms" this ... for there is still no preferred frame).

    I don't see how the dynamics are important at all in this discussion (nor what you even mean by "what is fundemental is the dynamic geometry"). It seems more appropriate to say what is fundemental in this discussion is "the local symmetry of the theory".
  7. Jun 7, 2009 #6
    Marcus, Is there some relation between Rovelli's DSR ideas an smolin unimodular view. I hope so because i taught smolin's article in physicsworld is really interesting !!..
  8. Jun 7, 2009 #7


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    From my personal view what you highlight here makes great sense to me from a conceptual point of view, since I think that the measurement frame, and the observers frame, necessarily is encoded in the observer, physically, and is thus constraint by the complexity or mass of this observer.

    I think it's great insight, and a step in the right direction. I think it has the great power than you can consider the limit of this frame complexity/mass -> 0. And during that scaling I would expect unification, which would also correspond to the "high energy limit".

    I think of this somehow as the two scales meeting. The miniminum resolution and the maximum perspective. If the reference mass is small relative to the minimum scale, the continuum models are I think bound to fail for understanding the actions. The actions must be formulated discrectly by permutations of discrete possibilities. Then ideally all the interactions including coupling constants we konw should emerge in a large frame mass limit.

    So, how does the laws of physics scale, as the frame mass scales? Would it not be very reasonable to expect that as the mass scale -> 0, the set of POSSIBLY distinguishable physical laws (relative to the frame) would be strongly constrained - possibly even unique?

    But it's always easier to reduce complexity than to selforganise chaos. So I think the biggest problem is to understand how the complex frames emerge, and self-stabilise. What "PHYSICAL FRAMES" ie. particles populate this universe and why?

  9. Jun 7, 2009 #8


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    Maybe Paul Wesson has something to say about this physical basis?


    Consequences of Kaluza-Klein Covariance
    Authors: Paul S. Wesson
    (Submitted on 1 May 2009)

    Abstract: The group of coordinate transformations for 5D noncompact Kaluza-Klein theory is broader than the 4D group for Einstein's general relativity. Therefore, a 4D quantity can take on different forms depending on the choice for the 5D coordinates. We illustrate this by deriving the physical consequences for several forms of the canonical metric, where the fifth coordinate is altered by a translation, an inversion and a change from spacelike to timelike. These cause, respectively, the 4D cosmological 'constant' to become dependent on the fifth coordinate, the rest mass of a test particle to become measured by its Compton wavelength, and the dynamics to become wave-mechanical with a small mass quantum. These consequendes of 5D covariance -- whether viewed as positive or negative -- help to determine the viability of current attempts to unify gravity with the interactions of particles.

    The Equivalence Principle as a Probe for Higher Dimensions
    Authors: Paul S. Wesson
    (Submitted on 17 Jan 2006)

    Abstract: Higher-dimensional theories of the kind which may unify gravitation with particle physics can lead to significant modifications of general relativity. In five dimensions, the vacuum becomes non-standard, and the Weak Equivalence Principle becomes a geometrical symmetry which can be broken, perhaps at a level detectable by new tests in space.


    Five dimensional relativity and two times

    Authors: Paul S. Wesson
    (Submitted on 28 May 2002)

    Abstract: It is possible that null paths in 5D appear as the timelike paths of massive particles in 4D, where there is an oscillation in the fifth dimension around the hypersurface we call spacetime. A particle in 5D may be regarded as multiply imaged in 4D, and the 4D weak equivalence principle may be regarded as a symmetry of the 5D metric.


    On Higher-Dimensional Dynamics
    Authors: Paul S. Wesson
    (Submitted on 17 May 2001)

    Abstract: Technical results are presented on motion in N(>4)D manifolds to clarify the physics of Kaluza-Klein theory, brane theory and string theory. The so-called canonical or warp metric in 5D effectively converts the manifold from a coordinate space to a momentum space, resulting in a new force (per unit mass) parallel to the 4D velocity. The form of this extra force is actually independent of the form of the metric, but for an unbound particle is tiny because it is set by the energy density of the vacuum or cosmological constant. It can be related to a small change in the rest mass of a particle, and can be evaluated in two convenient gauges relevant to gravitational and quantum systems. In the quantum gauge, the extra force leads to Heisenberg's relation between increments in the position and momenta. If the 4D action is quantized then so is the higher-dimensional part, implying that particle mass is quantized, though only at a level of 10^{-65} gm or less which is unobservably small. It is noted that massive particles which move on timeline paths in 4D can move on null paths in 5D. This agrees with the view from inflationary quantum field theory, that particles acquire mass dynamically in 4D but are intrinsically massless. A general prescription for dynamics is outlined, wherein particles move on null paths in an N(>4)D manifold which may be flat, but have masses set by an embedded 4D manifold which is curved.

    Quantization in Spacetime from Null Paths in Higher Dimensions
    Authors: Paul S. Wesson
    (Submitted on 11 Dec 2008 (v1), last revised 25 Jan 2009 (this version, v2))

    Abstract: Massive particles on timelike paths in spacetime can be viewed as moving on null paths in a higher-dimensional manifold. This and other consequences follow from the use of Campbell's theorem to embed 4D general relativity in non-compactified 5D Kaluza-Klein theory. We now show that it is possible in principle to obtain the standard rule for quantization in 4D from the canonical metric with null paths in 5D. Particle mass can be wavelike, as suggested originally by Dirac, and other 4D/5D consequences are outlined.
    Last edited: Jun 7, 2009
  10. Jun 7, 2009 #9


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    Paul Wesson supports this web page:

    http://astro.uwaterloo.ca/~wesson/ [Broken]

    The 5D space-time consortium


    We are a loosely bound group of physicists and astronomers with a common interest in pursuing Einstein's dream: the unification of what he called the "low-grade wood" of matter and energy with the "fine marble" of geometry. Our approach follows one originally due to Kaluza and Klein, but with important differences. Like Kaluza, we write down Einstein's field equations in more than four spacetime dimensions, with no explicit higher-dimensional source terms. Unlike Klein and many others since, we avoid overly restrictive assumptions about the scale or topology of the extra coordinates. Dimensional reduction then leaves us with the usual field equations of gravity in four dimensions, plus extra terms. We identify these extra terms with matter and energy in the four-dimensional world.

    Space-Time-Matter (STM) theory has important features in common with other higher-dimensional unified-field theories including supergravity, superstrings, string/M-theory and brane cosmology. It is consistent with the classical tests of general relativity in the solar system, as well as cosmological and other experimental data. It also contains a candidate for dark matter in the form of higher-dimensional analogs of black holes known as solitons.

    Please use the table of Contents at upper left to learn more about the members of the STM Consortium and their publications.
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  11. Jun 9, 2009 #10


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    I'm wondering how do massless fields fit into all this?
    (The stuff about "mass ratios" becomes ill-defined in that limit.)

    If ordinary DSR basically just boils down to Poincare + Dilation, then
    incorporating massless fields suggests that the larger conformal algebra
    should emerge somehow (Poincare + Dilations + Transversions).
    But in that case, a 5D representation is not big enough.
  12. Jun 9, 2009 #11


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    I guess to define a frame you need at least one massive point particle. A frame has to have a location. And it has to be moving at less than c, relative other frames.
    But as I say, I'm just guessing. I think your question is interesting, strangerep.

    Correct me if I am wrong, strangerep, but I see no need to define frames attached to particles which cannot be at rest (in any frame) because they have no rest mass.
  13. Jun 9, 2009 #12


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    In this thread we are talking about Rovelli's paper "Physical basis for DSR" and space-time has the usual 4D dimensionality. This is not about 5D spacetime or KaluzaKlein stuff :biggrin:

    Strangerep, getting back to your post, maybe I didn't understand your questions.
    The new thing is that a frame has a mass. This can lead to the 4D spacetime metric being energy-dependent. (Something a lot of people have played around with.) Here is what I think is the key point:
    This was the point at which your post came in, right?
    I don't see how massless particles would relate here.
    BTW the relevant Einstein quote sounds great in German:
    ==quote from biographical source material==
    ... he again wrote about general covariance that
    thereby time and space lose the last vestige of physical reality” (“Dadurch verlieren Zeit & Raum den letzter Rest von physikalischer Realität.” Einstein to Moritz Schlick, 14 December 1915).
    ... see page 43 of this pdf at a University of Minnesota website
    and also

    I think this means that to operationally specify a location you need some mass (if this isn't true then please enlighten me!) and therefore a reference frame must have mass. It seems so obvious. And yet we seem to have been neglecting to specify the masses of our reference frames all this time. Puzzling.
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  14. Jun 11, 2009 #13


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    Hi Marcus,

    [I needed to think more about this before replying...]

    Part of the problem I was having is the fast and loose way
    that the concept of "mass" is being used. In one place
    (section II) it seems to start off as Newtonian mass to
    arrive at eq(2), then a sleight of hand ("rest mass") allows
    a change to "SR mass", and then one finds that a particle's
    self-gravitational corrections (in a "DSR" limit) implies
    that this "SR mass" is "relative".

    But all this is hardly surprising, because "SR mass"
    is not been defined as a Casimir of SO(4,1), nor has
    "GR mass"[itex]:= g^{\mu\nu} p_\mu p_\nu}[/itex]
    been used carefully throughout.

    So when you wrote:

    I wondered what "mass" definition you meant -- the GR mass
    or the SR mass. (I'm guessing you meant SR mass?) But
    studying "the group of symmetries between all frames of the
    same mass" should encompass the massless case. I suppose one
    could argue that the practical "reference frames" we use for
    measurements always involve a non-zero mass somewhere, even
    if one strictly uses only the radar method (bouncing light
    signals) to relate other events to one's own local rest frame.

    IMHO, we seem to have been neglecting to specify the scales
    of our reference frames, from which the relative SR-mass thing
    follows as a consequence.

    (BTW, I also wonder whether instrinsic spin also needs to be
    included in the parameters characterizing a "local frame",
    requring a "group of symmetries between all frames of the
    same mass and spin". Rovelli's paper doesn't address this,
  15. Jun 11, 2009 #14


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    He meant GR mass. And try to extend of that definition to something deeper than GR.
    Last edited: Jun 11, 2009
  16. Jun 12, 2009 #15


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    Regarding strangereps questioning of definition of mass.

    I fully agree on this.

    But I still think that the way rovelli uses the term mass in that paper is not final. So I also think that we still need a better understanding/definition/abstraction of "mass". The current "definitions" of mass, coming from present theories, which we are now attacking, clearly must be modified too, that's what I think.

    But I try to see the paper to it's best favour. I personally think that the main point is pretty much what Marcus points out.

    All measurements, need a references, and this reference unavoidably needs a physical basis, and thus mass.

    I think of that as a first "soft" insight. Then harder problem is still have to clothe this in new mathematics.

    Personally I do not start with current definitions, I think the meaning of mass in the context above is more like (due to my informational angle) simply is a form of complexity or information capacity. IE. some number, of how many distinguishable states (of ANYTHING) a given observer can physically ENCODE. This I think will correlated to the mass. But it still remains to define the relation exactly, and how the old definitions of mass emerge in some limit. If one is too seriously disturbed by the lack or preciseness here I think progress will be hard. I see this as an idea, a fuzzy idea, but a good one. That is motivation for working on the preciseness.

    Some terms are poorly defined here, but I think that's due to the nature of this problem, and it's indeed part of the problem.

    About massless fields, there is still the question of how the complexity disitnguishes between restmass, and energy, if we think that conceptually mass is just "constrained energy". "Massless" systems still have energy, and the question is if there really are unconstrained systems in nature? It seems at minimum they are constrained to the size of universe. So from my point of view, I think the problem of energy vs mass, is the one of constraining degrees of freedom to space, and space is just an index... and i think we need to understand how this common index we call space emerges as these "massive frames" are interacting.

    I think it will be quite difficult, but it will possibly be a little easier if one at least can identify the direction where to make effort.

    In that prespective I think the message that reference frames must have mass, is interesting; even given that it is not precisely defined. It probably won't be precisely defined until we have the answer.

  17. Jun 13, 2009 #16
    Here's a question about the physical basis for DSR that I've been led to via this interesting thread -- thanks, Marcus. I'm taking a liberty in asking contributers to this thread to alleviate my ignorance about this arcane twig of theory.

    AMELINO-CAMELIA and MAJID were led to propose (in their 1999 Arxiv paper
    hep-th/9907110 on WAVES ON NONCOMMUTATIVE SPACETIME AND GAMMA-RAY BURSTS) that a consequence of DSR would be the dispersion of photons, manifesting itself as a delayed arrival here, relative to optical signals, of high-energy gamma rays from remote gamma-ray bursts. This seems to have not yet been convincingly established, though.

    Would this suggestion of theirs not also have implications for models of the early universe?

    Black-body radiation in a FLRW model universe --- for example the CMB radiation --- consists of photons in thermal equilibrium with whatever else constitutes the model. As one traces the history of the expanding universe backwards, the peak intensity of such radiation gets shifted towards higher energies (Wien's Law). When one thinks back into the inflationary era, this shift is extreme, to put it mildly. Any high-energy-temperature DSR dispersive effects should then manifest themselves, should they not?

    For instance, if photons were used to set up coordinates, as in the protocols of SR, would this not result in confusion --- or even make the whole scheme of quantifying the dimensions of space and time meaningless?

    A physicist considering this dilemma might just conclude that time is slowed to a halt as inflation is imagined to regress. The question of the universe's origin could then be relegated to a past eternity.

    Wouldn't that solve a problem? Viva DSR, Viva.
  18. Jun 13, 2009 #17


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    Interesting thoughts. We need to keep in mind that c is constant in DSR, the same for all observers. But c is not the speed of "average" light. It is the speed of low-energy light. More exactly the low-energy limit.

    In the DSR schemes we are thinking about here, very high energy photons somehow get slowed down. So another way of describing c is as the upper bound speed of light. The fastest that a photon can go. It seems to me this remains well-defined in the early universe, at least as much as anything else.

    In our experience, it goes without saying, all light is low energy relative to Planck and it all goes at the max, or indistinguishably close the maximum speed.

    But that having been said, I think it's fair to raise issues about how observers would operate in the very early. And we want our definitions to be operational. So some definitions might break down because of a failure of Gedankenexperiment practicality. It is even possible that the idea of distance would break down. It's a novel idea. I can't respond, or can only respond in a very partial way at this point.
  19. Jun 14, 2009 #18


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    Fwiw, my personal view of the question of the origin of the universe in the context of associating a mass to an observer frame is like this:

    First the "question of the universes origin" can be read in two ways, either as

    a) question of the UNIVERSES ORIGIN
    - realist emphasis; with this I mean that the question is supposed meaningful and not questioned; the focus on on the actual univere origin, not the operational meaning of it

    b) QUESTION of the universes ORIGIN
    - this this I mean that the question of origin is imaginary SCALED back to what an inside observer AT the origin would phrase. So the question is interpreted as something like the "origin of question" in the sense of "origin of observers"

    If all measurements, relating to a frame, has mass, then this mass is scaled down, the complexity of what measurements(and questions) that are possible to ask is reduced. This is one possible view of the origin problem; ie. the scaling of the BASIS of the question itself.

    Ie. when the physical basis of measurements and questions scales down, the some questions disappear; it's a true state space reduction.

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