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GR. Mach and cosmic redshift

  1. Jul 24, 2010 #1
    .............This is just a concept I have been playing with for awhile...........

    As my knowledge of GR is limited and my knowledge of Mach's principle is limited to its application to inertia I am going to use my own generalizations from them both.

    If my understanding or interpretation of either is wrong I will be glad to learn it .

    ..........GR which I will call Local.................MACH.which I will call global........................

    .....Local to global ....................................................Global to local.........................

    ......ABsolute.........................................................Relational (relative)..................

    ,,,From the bottom up...........................................From the top down.......................

    ,,,,From the center to the periphery.....................from the periphery inwards.............

    Local------, gravity is viewed as an independant local phenomena , building up from the concentrations of mass through increasing scales and distances to minimum.
    The global is the sum of all the local interactions

    Global ------The local effects are more dependant on the global distribution of matter.

    Regarding the G factor and dilation

    Local -----scale starts at the maximum with the largest masses , black holes, and works upward with diminishing values for decreasing masses and greater distances to reach a minmum in the reaches of intergalactic space

    Global---- starts out with a minimum base factor in the voids of space due to the overall mass distribution and proceeds down through decreasing localizations through galactic clusters, galaxies ,and finally stars and planets with these various masse distributions acting as fluctuations on the minimum base value.

    It would appear that these views might not be incompateble or simply two perspectives on the same thing.

    But also suggests the possibility that there could be significant difference.

    That there might be a greater minimum value in the global system.

    But this idea faces the dilemma of all relative perspectives: How could this possibly be measured. From what possible frame.

    For those that think, if it cant be measured, it is not real or existent, this would make the question moot.

    But the perspective may still have value. For example:

    Newtonian gravity, Keplers Laws regarding the relationship of orbital radii to angular velocity and GR were all derived from observations within a system where the overwhelming majority of the total mass was to be found in the center.
    Center based direct calculations work fine. As Newton said you can practically disregard all the mass behind you , relative to the center.

    But does this neccessarily apply to a system like a globular or spiral galaxy where the mass distribution is considerably more diffuse??

    Could perhaps the anomalous angular velocities observed in these systems be explained from the perspective of the global distribution of matter instead of assuming dark matter or huge masses in the center ?

    ANother possible application:
    Our current cosmic view is; the light coming from the boundary of out perceptual universe is reaching us from a time period approx.14 billion years ago.
    From a time when we conceive of the universe as being more condensed by a huge factor.

    What if we assume that this much greater density would mean a much higher base value for G and dilation compared to our contemporary locale?

    We can still imagine that early scientists would get the same local readings.
    As both electron emitance frequencies and absorbtion frequencies would be equally lower the visable spectrum might appear exactly as it does to us. The vacuum speed of light might be lower but measurements would be taken with dilated clocks so there is no reason to neccessarily expect a different reading.

    But light which was not absorbed and traveled through free space would be relatively lower in frequency compared to the electron resonances here today.

    WHich suggests the possibility that at least part of the observed redshift could be due to emitter dilation rather than relative velocity or spatial expansion.

    There is also the possibility that light speed has actually increased due to the decreasing G factor from reduced overall density.

    That in transit through space it would also be translating through time, passing through zones of later, less dense spacetime.
    but it can not neccessarily be measured as being different
    as clocks in any zone are now running faster than the early universe.

    Taking this idea further it seems to imply that the overall time base of the universe might be speeding up, even as it is slowing down locally through condensation ,relative to that base.

    In any case I would be interested to hear other ideas regarding this.

  2. jcsd
  3. Jul 24, 2010 #2

    Jonathan Scott

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    I like your way of thinking and I personally feel that the failure to comply with Mach's Principle (especially when it comes to linear frame dragging, which would otherwise neatly explain inertia) is GR's most obvious weakness. There are books about Mach's Principle and plenty of online resources with other speculation, much of it unfortunately of not very high quality.

    I've also previously pointed out on these forums that if you think that the curvature due to mass-energy shapes the universe, the boundary solution for GR around a central mass should not be flat but should rather be effectively a 3D cone with a missing solid angle proportional to the local mass as a proportional of the total effective mass-energy of the universe (at least as seen from that point). This gives an effect very similar to MOND, with an additional field proportional to [itex]\sqrt{m}/r[/itex].

    GR works extremely accurately within the solar system, and any simple change to it to support Machian principles tends to cause an immediate disagreement with established experimental results, because even though the solar system is small compared with a galaxy, the GR predictions have been confirmed to high accuracy. This suggests that if something is wrong with GR, there must be at least two things wrong!

    Machian ideas would indeed suggest that G should vary with time and location, and so does Dirac's Large Numbers Hypothesis (LNH).

    It is easy to show how G could vary with location in a way that is essentially undetectable at present, as the variation with distance from the local source could simply be another way of looking at the potential and the G we normally use could be the effect of the rest of the universe excluding our sun, which is effectively constant.

    It is more difficult to see how G could have varied with time, as current experiments such as lunar laser ranging and longer term considerations such as the stability of the solar system suggest that G is not even varying proportionally or inversely proportionally to the age of the universe. However, this is a complex area, as there are other factors which could be varying at the same time, including, as you suggest, the relative rate of time (contributing to cosmological red shift). Note also that different ideas about what varies may easily differ only in the conventions used rather than the physics.

    One thing which I don't believe could be varying is the local speed of light, not only because special relativity says so, but also because we can't really measure it in any other way, in that the devices we use to measure the speed of light are made of rulers and clocks so we implicitly end up comparing it with the speed of light.

    We may not be able to discuss this area much further here; Within these forums, I'm sure it's OK to debate what evidence there is for and against mainstream theory, and to some extent to discuss the evidence for and against specific alternatives, but note that to maintain the integrity of these forums as an educational resource there are currently rules against too much speculation and discussion of non-mainstream theories (even ones presented in peer-reviewed journals).
  4. Jul 25, 2010 #3
    I view my speculation as not pointing to a weakness of GR but rather as a possible extension of its strength. As a possible answer to many current questions which have prompted much truly wild and speculative theorizing.

    Here your mathematical reference and conceptualization is basically beyond me but I think I have an intuitive grasp of the principle you are presenting. If so it directly relates to another concept I have been rolling around that would propose GR as sufficient to infer the current cosmological view of a boundless universe without surface, but without recourse to completely inconceivable and incomprehensible ideas of dimensionless expansion, dark energy, etc.
    I never suggested that it would be detectable within the solar system. QUite the opposite.
    My assumption is that if you took two identical clones of the local system including the proximate stars ,and placed one in totally void intergalactic space and the other in a space
    in the galactic center that local measurements would be exactly the same.
    But that there could be a relative difference that would not neccessarily be measurable due to the lack of an appropriate frame.AS you mention next.

    I am not familiar with the laser ranging experiments but I would offer on principle that the local aging relative to the range of aging represented by our current observations of the universe which extend through billions of years is insignificant.
    To me it appears that an overall variable G does not in any way imply any local change.
    Or neccessarily have any local effects on solar or galactic stability. It would only apply to relative zones of history with the assumption that within those zones G would apply locally as usual.

    Agreed. Once again I was refering to the galaxies and times which are far from us spatially and temporally. Where it is assumed that ancient photons that have passed through that history and varied their speeds would still have the same speed as more recent photons emited more recently locally. And in all locations and times would be measured at c as you point out.

    I certainly understand and agree with the restrictions regarding speculation which is based on conceptions or ideas that aren't consistent with empirically established physics or are founded on meta-realities etc.
    But I do wonder about those ideas or questions which are completely consistent with the fundamentals of physics and SR or GR and only seek to resolve internal ambiguities or actually extend the system. I think perhaps this itself may be a valid topic of discussion within the forum.
    On the other hand I don't want conflict with the prevailing rules and will certainly accede to your wish if you don't feel comfortable discussing this further.
    On the pedagogical issue, I understand on one level but wouldn't it perhaps be more instructive if the kids could observe the rational process of the teachers and experts as applied to an actual area of the edge of science??? Just MHO
    BTW I appreciate your objective perspective as well. Thanks
  5. Jul 26, 2010 #4
    This is not correct. GR is not a theory that allows such superpositions, it is a non-linear theory.

    In GR there exists a metric for the whole universe. Leaving special cases and theorems alone one can generally only solve a GR problem in the context of a whole universe. For instance, assume a universe with only two non rotating masses. Not only the distances and the masses would have to be given (and we leave aside the additional problem on how to define distance and mass in GR) but all initial conditions, e.g. all existing waves in this universe. Once we have such a description we can, in principle but not necessarily practically, calculate or evaluate into any other possible state of this universe in time.
    Last edited: Jul 26, 2010
  6. Jul 26, 2010 #5
    Are you saying that the calculation of G was not derived from local measurements but was based on some estimation of the total mass of the universe??

    In your universe of only two masses it would seem that the only possible derivation would be local , or am I misunderstanding you??

    If you are saying there is a single metric I think I get it. I was talking about for instance; calculating local gravitation does not neccessitate consideration of the rest of the galaxy or even local stars. Or am I wrong in this also.
  7. Jul 26, 2010 #6
    No, I did not say anything related to the gravitational constant.

    A universe with two masses would not be a non-stationary universe. In such universe one would have to describe all the initial conditions not just the mass and distance of the two masses to run an evaluation or make a calculation. GR in this respect is totally different from Newtonian gravitation.
  8. Jul 26, 2010 #7
    If you weren't refering to the gravitational constant what were you talking about????

    WHat about my question regarding calculating within the solar system and if those calculations needed to include the galaxy or local stars???
  9. Jul 26, 2010 #8
    I am talking about:

    Let's see what you are writing:
    You seem to completely ignore the fact that those spacetimes are non-stationary. You just can't 'add up' masses like that.
    Last edited: Jul 26, 2010
  10. Jul 26, 2010 #9
    I dont know what masses you think I am adding up??

    I was talking about a scale. Equivalent to the gamma scale in SR but opposite. DIlation icreases with velocity to a maximum.

    In GR it starts at the maximum with black holes and reaches minimum in intergalactic space.
    True or not??
    Those were not additions but progressions. Plotted as a curve I wouldnt be surprised if they were similar but reciprocal.

    Does the g factor also follow this progression or not?
  11. Aug 12, 2010 #10
    Some good comments Jonathan. I have also pondered the issue of variable G and the inability to detect any change vis a vis radar ranging of orbital moons - as you mentioned in another post, there is always the possibility of the MG product being constant - but this entails an entirely new set of speculations. Have you considered that during an earlier era, G varied as 1/R per Dirac - but this functional dependence ceased when the universe entered the de Sitter phase since both R and H are now constant.
  12. Aug 12, 2010 #11


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    linear frame-dragging

    It might be an aesthetic weakness, but the universe might not care about our aesthetic opinions. What matters is how Machian the universe actually is, and the only way to determine that is to find two theories, one more Machian than the other, and see which agrees better with observation. This has been done with Brans-Dicke gravity versus GR, and GR won, because the Brans-Dicke [itex]\omega[/itex] parameter is nowadays constrained to be unreasonably large. IMO this means that we tested how Machian the universe is, and we simply found out that it wasn't as Machian as many people would have liked.

    A mention of linear frame-dragging in another thread sent me off googling, but I didn't find very much. I know this is a topic you're interested in. Could you tell us more about it? What I turned up is this:

    "Linear frame dragging is the similarly inevitable result of the general principle of relativity, applied to linear momentum. Although it arguably has equal theoretical legitimacy to the "rotational" effect, the difficulty of obtaining an experimental verification of the effect means that it receives much less discussion and is often omitted from articles on frame-dragging[...]" -- http://en.wikipedia.org/wiki/Frame-dragging

    WP refers to a lecture series by Einstein published as "The meaning of relativity," http://www.archive.org/stream/meaningofrelativ00eins/meaningofrelativ00eins_djvu.txt , where the idea is discussed very briefly at "There is an inductive action of accelerated masses".

    Dennis Sciama worked on it:
    --Dennis Sciama, "On the Origin of Inertia," Monthly Notices of the Royal Astronomical Society, Vol. 113, p.34, http://articles.adsabs.harvard.edu/full/1953MNRAS.113...34S
    --Sciama, Waylen, and Gilman, Phys Rev 187 (1969) 1762
    --an oral history: http://www.aip.org/history/ohilist/4871.html

    Someone just down the road from me, at Cal State Fullerton, has some material online: http://physics.fullerton.edu/~jimw/general/

    I didn't study the first Sciama paper carefully enough to understand its significance. It develops a toy model that I guess is purely Machian, but I'm not sure what that tells us.

    Is linear frame-dragging basically interesting for the same reason that rotational frame-dragging plays a crucial role in the thought experiment described in the classic Brans-Dicke paper, C. Brans and R. H. Dicke, Physical Review 124 (1961) 925, http://loyno.edu/~brans/ST-history/ ?
  13. Aug 12, 2010 #12
    Comments on the above post #11. I doubt whether the right approach to resolving the issue of whether Inertia is the result of other matter has been discovered. If I recall, Dennis Sciama's analysis attempted to contrive inertia from distant matter motion orthogonal to the object being investigated - much like em theory produces fields at right angles to the motion - also, the results if I recall were off by a factor of 1000 or so. Dicke's approach gells down to finding why GM/Rc^2 = 1
    Using the variable G theory, the effort involved tuning G to comport with the ratio - so G had to track R inversely - but as per my above post, we now live in a de Sitter phase -so R is constant - therefore we do not need to find variance in G - it is fixed since R is fixed in a de Sitter expansion
  14. Aug 12, 2010 #13
    Let me clarify the above post a bit - Dicke argued that M is the gravitational mass and R is the radius of the universe. and if the energy of a particle of mass m is mc^2 then
    m(inertial)/m(gravitational) = GM/Rc^2 = 1. It has always been a mystery of why this realtionship is one to within the limits of experimetal values - but it is. So from here the logic of my post 12 follows.
  15. Aug 13, 2010 #14

    Jonathan Scott

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    Re: linear frame-dragging

    It doesn't seem very easy to find much about it.

    Basically, in the vicinity of an accelerating mass, GR says that the field also contains an additional component in the direction of acceleration of the mass (that is, the rate of change of its momentum), in the same way (as Sciama points out) that the electric field includes an additional component for the rate of change of the vector potential, in addition to the potential gradient. This component is too small to measure in any practical case so far.

    If you have a lot of mass accelerating relative to a test mass, the result is that this inductive force tends to accelerate the test mass in the same direction, requiring a force to keep the test mass from accelerating with it. The Machian extension of this idea is that if you had the whole universe accelerating relative to a test mass, it would require exactly the same force to keep it from accelerating as would be necessary to accelerate in the opposite direction relative to a universe which was not accelerating, exactly accounting for inertia.

    For this to be exactly true, the GR expression for the total effect of the linear frame-dragging would have to be equal to the acceleration. According to Ken Nordtvedt, the frame-dragging effect in GR has a factor of 4 compared with the naive electromagnetism model Sciama uses, but the effect can otherwise be added up as for Newtonian theory, so for this Machian explanation to work this requires that the sum of 4Gm/rc^2 for the universe should be exactly 1 (or equivalently that the sum of Gm/rc^2 is 1/4).

    I've heard that Sciama basically gave up pursuing this idea when they began to realize that the missing matter problem meant that this sum was out by a couple of orders of magnitude, but if you include the dark matter I think it still works fairly well.

    There are some useful references to Nordtvedt's work in James Woodward's notes as you've already found using Google (specific URL below), but note that he has some funny ideas (the http://en.wikipedia.org/wiki/Woodward_effect" [Broken]) about using Machian action at a distance to create a reactionless drive, which isn't generally accepted for obvious reasons.

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