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Is there an implied spherical shell mass external to the universe

  1. Aug 20, 2015 #1
    consider two concentric spheres, where inner radius is r and outer radius is r+delta. Assume space between the two spheres is mass of an amount to be solved for. Given the metric inside the sphere, assumed to be varying as implied by the Cosmic Background Radiation anisotropy (CBRa), can the mass and thickness of the annular sphere be deduced?

    Now if it can, then use the varying metric for our universe g_mu_nu, assume it is anisotropic as implied by the CBRa, and set r=13.7B light years. Calculate M and delta.

    Can this be done or does this just make no sense? asks an experimental particle physicist who just does not know GR :)

    in other words, can the real world metric (g_mu_nu?) that exists in our universe imply a particular spherical mass shell external to the universe, and if so what's the mass and effective if not real thickness?

    As an outsider to GR, I do not know the connection between the recently measured Cosmic Background Radiation anisotropy (CBRa) and g_mu_nu in GR. What I mean by saying above "Given the metric inside the sphere" I am assuming that the CBRa implies a varying g_mu_nu metric but maybe this is wrong. I am seeking GR experts to educate me on the relation between the CBRa and g_mu_nu. If there isn't one I apologize that my ignorance on this topic makes the question nonsensical
  2. jcsd
  3. Aug 20, 2015 #2
    a first comment to the first part above by PAllen was (brought over from a private thread on another topic)

    You should really post this in the relativity subforum. However, first issue is that the metric inside the inner sphere will be flat Minkowski metric. This is the GR analog of Newton's shell theorem. Also, the metric outside will nowhere be the flat Minkowski metric. So both ends of your problem description are counter-factual. Also, on cosmological scales, our actual universe is no-where Minkowski - it is approximately the FLRW metric on large scales.
  4. Aug 20, 2015 #3


    Staff: Mentor

    What do you mean by "inside the sphere"? Do you mean "between the two spheres"? Or do you mean "inside the inner sphere"? If it's the latter (inside the inner sphere), the metric will not be varying; it will be that of flat Minkowski spacetime, by the shell theorem.

    This is due to fluctuations in the density of the universe when the CMBR was emitted (which in turn were caused by quantum fluctuations during the inflation era, magnified by inflation and causing anisotropies in the density of the hot, dense matter and radiation that was produced by reheating at the end of inflation). It has nothing at all to do with any "external" mass; as noted above, any spherical distribution of matter has no effect on the metric of an empty region inside the sphere.

    No. It's due to the matter and energy within our universe. See above.

    It implies a varying density of radiation. At the present time, the effect of this on the metric of the universe is negligible, because the density of radiation is so small, compared to the density of matter.

    When the CMBR was emitted, however, the density of radiation was comparable to the density of matter, and the fluctuations in both produced the fluctuations we currently observe in the CMBR. Those fluctuations, at that time, produced significant fluctuations in the metric as well. However, those fluctuations were random, so they had no effect on the overall dynamics of the universe; that's why they're usually left out when cosmologists describe the metric of the universe.
  5. Aug 20, 2015 #4
    Thank you PAllen for the Newton Shell Theorem point. I see from point 2 of the Wikipedia page on this Newton Shell Theorem that:

    If the body is a spherically symmetric shell (i.e., a hollow ball), no net gravitational force is exerted by the shell on any object inside, regardless of the object's location within the shell.

    which renders my initial question non-sensical (for which I do apologize)

    Therefore, my modified GR question is whether the CBRa implies anything about g_mu_nu for our real space inside the universe? I suppose I really just do not really know what g_mu_nu really is and whether it has any connection to the matter clumps or CBRa in the universe. Seems to me the CBRa has to imply something and can't we use that fundamental structure to imply something about what is outside the universe?
  6. Aug 20, 2015 #5
    Thank you Peter. I meant inside the inner sphere, assuming that there is simply mass between the two spheres across the thickness delta and I did not wonder what the metric was in that mass region (though that could be asked I suppose). Now I get the shell theorem which I didn't before, thank you for pointing that out
  7. Aug 20, 2015 #6


    Staff: Mentor

    Btw, why are you interested particularly in the metric?
  8. Aug 20, 2015 #7
    Peter, on your second point. Ok if a spherically uniform mass distribution in the annular sphere implies nothing for the metric inside, then can the CMBRa imply a specific non-uniformity of that mass distribution? in other words, can the CMBRa imply a specific and unique non-uniformity? is it consistent with any mass distribution, if not specific and unique then some general distribution?

    Reason for asking is not to suggest this non-uniform mass distribution as cause for the CMBRa but rather just that it is equivalent to one in the sense that in GR gravity in a reference frame at rest is equivalent to acceleration of the reference frame. Equivalence may be powerful if it exists but if there is no connection between CMBRa and g_mu_nu then there cannot be any such equivalence at all and so the model is non-sensical after all
    Last edited: Aug 20, 2015
  9. Aug 20, 2015 #8
    Thanks PAllen for the FLRW metric point. Can the FLRW metric itself be used to imply any sort of specific non-uniformity in the mass distribution of an assumed spherical mass shell external to our universe?
  10. Aug 20, 2015 #9
    The reason I propose the model is because I want to know if the CMBRa measurements can be used to imply anything about what is external to our universe. The recent measurements of the CMBRa represent a very precise measurement of a very real property of the space-time in our universe so if they do imply anything about what lies outside the universe I wonder what those implications are.

    I assumed that the CMBRa would be related to g_mu_nu and that from there (or the FLRW metric) implications might be derivable about what is external to our universe. If the metric is just irrelevant but the CMBRa can be used by itself, then I suppose this topic no longer needs to be concerned about the metric, but rather just how could the CMBRa be used to imply anything about what lies outside the universe.

    This simple toy model external spherical mass shell would appear to be a vast simplification compared to the recent model proposed by Niayesh Afshordi, Robert B. Mann and Razieh Pourhasan (published in Scientific American article) which states that a 4D star supernova'ed and its 3D event horizon remnant is our universe. Could the CMBRa imply anything about this model and in particular does it rule it out or in?

    I guess if the CMBRa could imply anything about the external mass shell outside our universe it would do so differently at different times. The state of that mass shell today would be described by the CMBRa as it is now, and the way it used to be at prior times would describe that 4D supernova at those earlier times too. Then would the time when matter and radiation densities were the same imply anything specifically different from now? etc...

    I originally thought of this simple toy model years ago when I first heard about the missing energy and matter called Dark Energy and Dark Matter. I thought if there really is missing matter, maybe it exists as an external mass shell outside the universe, and not as a bunch of odd property elementary particles for which modern day particle physics experiments routinely search (minting new PhDs in the various null results).

    Now that this 4D supernova model has been proposed, the simple toy model seems to relate to it possibly if there exists a CMBRa implied non-uniform mass distribution external to our universe, an effective one if not a literal one
    Last edited: Aug 20, 2015
  11. Aug 20, 2015 #10


    Staff: Mentor

    Mass distribution or metric? The CMBRa is a non-uniformity of the mass distribution (more precisely, of the radiation energy distribution, but mass and energy are equivalent). It's just that, as I said before, this non-uniformity at present is insignificant because the density of radiation energy is so much smaller than the density of energy due to matter.

    This is not the way the equivalence principle is normally phrased. Normally it is phrased as: being at rest in a gravitational field is equivalent to being accelerated (with the same proper acceleration--i.e., the same felt force) in empty space with no gravity present. There is nothing about reference frames.

    Huh? Why not? The equivalence principle does not say anything about how the "gravitational field" is produced, nor does it say anything about the metric. It is a purely local statement, and the whole point is that locally, you can't tell, just from the acceleration you feel, whether you are in a flat metric (accelerating in empty space with no gravity present) or a curved metric (at rest in a gravitational field due to a body like the Earth).
  12. Aug 20, 2015 #11


    Staff: Mentor

    No, they can't. That's the whole point of the shell theorem. See below.

    Do you have a link to the actual paper on arxiv? The SciAm article is a pop science treatment and is not a good source of information about what the model actually says. (That's a good general rule anyway--always look for the actual scientific paper, never trust pop science treatments if you're actually trying to learn about the science.)

    In any case, if I'm understanding the basics of this model (and your "toy model") correctly, you are proposing that our universe is in the interior of a spherically symmetric "external" mass distribution. If that is true, there is no way for us, inside, to tell by measurements we make inside, because of the shell theorem. So nothing about the CMBRa, or any other measurements we make here, can tell us whether such a model is true.
  13. Aug 20, 2015 #12
    I thought the whole point of the Shell Theorem was that a uniform mass distribution has no impact on the interior. That's why I modified my query to be about the precise non-uniformity of the mass distribution "implied by" the CMBRa (or variablility of g_mu_nu). I thought the shell theorem therefore implies that if the mass distribution is non-uniform then it actually does have impact interior to the sphere because all of the symmetric cancellations of the uniformity no longer exist and the Shell Theorem conditions are violated.
    Last edited: Aug 20, 2015
  14. Aug 20, 2015 #13
    Yes, I do. I contacted Niayesh Afshordi who responded 9/8/2014 thus:

    Thank you for your interest. The published paper (which is open access) can be found here: http://iopscience.iop.org/1475-7516/2014/04/005/

    which is pretty similar to our preprint from a year ago: http://arxiv.org/abs/1309.1487
    Last edited: Aug 20, 2015
  15. Aug 20, 2015 #14
    so now consider it is not spherically symmetric. Let's drop that condition. Let's assume it has some non-uniformity which is related in some actually time-dependent way to the CMBRa

    does GR provide for a calculation method to start from the CMBRa data and go either through the LFRW (or some other GR) metric or perhaps not through the metric but just directly, to the mass distribution between r and r+delta where now delta is itself a function of polar and azimuthal angle (theta and phi in polar coordinates, or whatever other angular coordinates for space-time GR models use)?

    In this sense, the time-dependent external mass distribution could actually describe the ejected mass from a 4D stellar collapse? Could the CMBRa data be used to verify or deny the 4D stellar collapse model?
  16. Aug 20, 2015 #15


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    This paper is very interesting, but it has nothing to do, really, with classical GR. It would be better discussed in the "Beyond Standard Model" subforum (which here means beyond GR+standard particle physics). It is certainly outside my expertise to intelligently comment on.
  17. Aug 20, 2015 #16

    Does the CMBRa imply a non-uniformity in both the mass distribution of the toy model and the metric?

    If there is no relation between the CMBRa and the metric then we can forget about the metric.

    The question then becomes can the CMBRa provide the information needed to use GR to deduce the mass distribution M(r,theta,phi) and the angular function delta(theta,phi)? with or without the metric?

    Like I said at the beginning, I do not know GR so maybe this connection is non-sensical still. That didn't stop me from wondering this. :)
  18. Aug 20, 2015 #17
    Just found this on a phys.org article on this:

    While the model does explain why the universe has nearly uniform temperature (the 4-D universe preceding it would have existed it for much longer), a European Space Agency telescope called Planck recently mapped small temperature variations in the cosmic microwave background, which is believed to be leftovers of the universe's beginnings.

    The new model differs from these CMB readings by about four percent, so the researchers are looking to refine the model. They still feel the model has worth, however. Planck shows that inflation is happening, but doesn't show why the inflation is happening.​
  19. Aug 21, 2015 #18


    Staff: Mentor

    Actually, Cosmology would be the most applicable, since this is really an alternate theory about the origin of the universe. Thread has been moved.
  20. Aug 21, 2015 #19


    Staff: Mentor

    It implies a non-uniformity in the mass distribution (and therefore the metric, since that is determined by the mass distribution) at the time the CMBR was emitted. What it implies further back than that depends on your model. I am not familiar enough with the "4D stellar model" to know whether they predict a linkage between the CMBRa and the mass distribution in the very early universe in their model.

    In principle I suppose it could, but as above, I don't know enough about the model to comment on that.
  21. Aug 21, 2015 #20


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    The paper does not seem to have interested other researchers. It was posted on arxiv just about 2 years ago, and there have been no citations so far, in other research.
    Here is the arxiv listing:
    Out of the White Hole: A Holographic Origin for the Big Bang
    Razieh Pourhasan, Niayesh Afshordi, Robert B. Mann
    (Submitted on 5 Sep 2013)
    While most of the singularities of General Relativity are expected to be safely hidden behind event horizons by the cosmic censorship conjecture, we happen to live in the causal future of the classical big bang singularity, whose resolution constitutes the active field of early universe cosmology. Could the big bang be also hidden behind a causal horizon, making us immune to the decadent impacts of a naked singularity? We describe a braneworld description of cosmology with both 4d induced and 5d bulk gravity (otherwise known as Dvali-Gabadadze-Porati, or DGP model), which exhibits this feature: The universe emerges as a spherical 3-brane out of the formation of a 5d Schwarzschild black hole. In particular, we show that a pressure singularity of the holographic fluid, discovered earlier, happens inside the white hole horizon, and thus need not be real or imply any pathology. Furthermore, we outline a novel mechanism through which any thermal atmosphere for the brane, with comoving temperature of 20% of the 5D Planck mass can induce scale-invariant primordial curvature perturbations on the brane, circumventing the need for a separate process (such as cosmic inflation) to explain current cosmological observations. Finally, we note that 5D space-time is asymptotically flat, and thus potentially allows an S-matrix or (after minor modifications) AdS/CFT description of the cosmological big bang.
    16 pages, 3 figures
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