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Quantized space-time and redshift.

  1. Aug 26, 2004 #1

    turbo

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    I have been reading about Loop Quantum Gravity and about Spin Foam, and I am stuck on a (probably stupid) idea. It seems that one of the underpinnings of these concepts is that space-time is quantized in discrete units at the Planck scale. If space-time is quantized and the universe is expanding, our local units of space-time are the oldest and largest in existence. Light that came from stars very far away originated in younger domains with smaller units of space-time and their photons would be forced to traverse larger and larger units of space-time as they come to us.

    If the speed of light is truly invariant with respect to observer, this means that the photons coming from distant objects must cross larger and larger space-time unit distances in the same amount of time, and if they have to cross each unit in the same amount of time (with length L appropriate to observers in each locality) then the photons MUST arrive here redshifted or else violate conservation of energy. If they are to maintain a constant speed with growing L, they have to pay for this by becoming less energetic WRT wavelength. Is this idea off the wall? Have I missed a really basic "Pons Asinorum" type concept?
     
    Last edited: Aug 26, 2004
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  3. Aug 27, 2004 #2

    Chronos

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    Agreed.
    Good question, Turbo. While complicated, it is not at all stupid. Only two choices with regard to expansion, as you have observed. Either the original units have been stretched, or new ones are being created. The stretching idea makes more sense. I'm not sure you could directly measure this effect since space-time is coupled according to the Lorentz transform. But, the stretching of space nicely fits with the doppler effect.
     
    Last edited: Aug 27, 2004
  4. Aug 27, 2004 #3

    turbo

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    The reason that this concept appeals to me so much is that it acknowledges the special reference frame of every observer (each observer observes that his local space-time coarseness L is the largest observable) while preserving the invariance of the speed of light in a "vacuum" for all observers. Darned vacuum energy is starting to look more and more like an aether, but let's not go there right now. :smile:

    Anyway, this stretched space-time concept can explain the cosmological component of redshift without resorting to "tired light" or a purely Doppler-type effect. I still I think there is still a LOT about redshift that we do not know, especially the redshifts of AGNs, quasars, etc.
     
  5. Aug 27, 2004 #4

    turbo

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    I would prefer not to have this post moved to theory development - I would rather be a pariah amongst acquaintances, I guess - (hi, Neried! :smile:), but here is an extension that some may find uncomfortable. :eek:

    As above, if space-time is quantized, photons that come from younger domains with smaller (less cosmologically expanded) quanta of space-time MUST decrease in frequency as they traverse the older (closer to us) domains with larger space-time coarseness. They have to shift to lower frequencies, else they would violate the conservation of energy, assuming they have to maintain a universal speed of light for all observers, crossing every local-measured unit of space in the same time for observers in EVERY reference frame. For a photon to retain its emitted frequency while travelling across expanding space-time, it would have to have stolen energy all along the way.

    If we accept the concept that the expansion of the basic units of space-time can modify the energy of light transversing it, and if we accept that mass "curves" (distorts) space-time, we should accept that mass can affect the properties of light travelling near it. Even more, we should now be prepared to model "gravitational" lensing of photons without invoking gravity at all. We can model the local distortion of space-time around massive galaxies and galaxy clusters (due to the presence of dense masses) and then predict the effects of variations in space-time density on the paths of photons passing through those domains. We do not need HUGE masses to create gravitationally-lensed arcs, as long as the the masses create gradients in space-time that are fairly well-defined and/or are curved with respect to the light path of the lensed object to our line of sight. Anything off perpendicular will produce refraction.

    Gradients in optical medium density (eyeglasses and air, for an obvious example, but in this case, the quantum texture of space-time) always result in refraction if the gradient is not oriented absolutely perpendicular to the path of the light from the source to us. Also, the steeper the density gradient, the stronger the refraction, as any optician can attest. While the concept of an aether in space is abhorrent to some, we must concede that the curvature of space-time due to the presence of mass can produce frequency-shifting and refraction of photons transversing that area, without invoking any gravitational effect on those oh-so-massless photons.

    Finally, (as if I haven't made a large enough target of myself :uhh:) if mass distorts space-time (pretty widely accepted), and if space-time mediates the sensed "gravitational force" (which will be essential to any quantum theory of gravity), we should predict that gravitational mass and inertial mass will NOT be strictly equivalent, except in local reference frames. We should expect that mass A in a space-time domain dominated by a local dense, concentrated mass, will NOT have the same ratio of gravitational mass/inertial mass that we would observe if it could be removed to a domain where the mass distribution was more homogeneous. In any local reference frame, gravitaional and inertial mass will be equivalent beyond our ability to measure, but that relationship is unlikely to hold in a general model for obvious reasons. We should expect that a successful unified theory will encompass an understanding of gravitation that allows a special frame-dependent local model (basically Newtonian, in which inertial and gravitational mass are equivalent) and more general model that allows for differential (inertial vs gravitational) mass based on variations in the density of space-time. I do not expect that the difference between gravitational and inertial mass will ever be experimentally observable, except perhaps on a galactic scale or larger.
     
    Last edited: Aug 28, 2004
  6. Aug 28, 2004 #5

    marcus

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    I'm a watcher of LQG, not a researcher. I will tell you what I think
    but I dont want it to sound authoritative. Go read
    smolin's new "Invitation to LQG" and form a direct impression.
    I've never seen where space is supposed to be quantized in LQG in little bitty planck-scale steps. that sounds like a journalist's interpretation or a
    Scientific American level intuitive way of communicating the feel.

    If you read more or less any technical intro to LQG it will say that in the 4D version of the theory there are two operators with discrete spectrum
    (discrete possible outcomes of measurement) corresponding to
    the VOLUME of some region and the surface AREA.

    so area and volume operators, corresponding to measurements of area and volume, have a discrete menu of possible outcomes
    but they arent simply the integer multiples of planck area and planck volume[b/]

    and furthermore the length operator has not been shown to be like that.
    there are some papers about it, but discrete length spectrum is not one of the usually quoted results

    again read "Invitation to LQG" it summarizes results to date, open problems, and gives an FAQ. It does not say length is quantized in the same sense as area and volume.

    http://arxiv.org/hep-th/0408048

    now if you have a technical paper that says length IS please tell me!
    I would love to have a link that would tell me something new! It is a fairly rapidly developing field with surprises and I'm going on limited knowledge. So please share any links about quantizing the length operator!
     
    Last edited: Aug 28, 2004
  7. Aug 28, 2004 #6

    Chronos

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    Rethink your position. Gravity has precious little to do with red shift. It is virtually irrelevant. Light coming into and out of a gravity field is first blue shifted, then red shifted as it passes through. Think about it.
     
  8. Aug 28, 2004 #7

    marcus

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    also turbo one more thing, then I will get out of the way and let Chronos discuss your idea with you

    in General Relativity (and the LQG quantized version) the picture of expansion is that the units of measure remain the same

    (a meter, or the planck length, are both unchanged by the expansion of space)

    all that happens is that after some expansion there are more meters, or more lightyears, between two stationary galaxies.

    that is, the distances are getting longer in terms of those very units and the units themselves do not change.

    also atoms and galaxies do not get any bigger, because they are bound structures,
    it is only the spaces between widely-separated galaxies which increase

    if there is a gravitationally bound cluster of galaxies, like the Virgo cluster, even the distances between those galaxies probably do not increase because they are orbiting each other and all feel each other's mass binding the group together.

    clusters of galaxies are a grey area. space expanding might pull apart some marginally bound clusters.

    but atoms and crystals are a clear case of not being affected at all
    so your measuring stick---the family meterstick or yardstick----is not going to change.

    so to repeat---space expanding merely means that certain very long distances become longer----and the units we measure with do not change----and that includes the planck units if you be using them to measure with----in LQG the planck units do not change with time.
     
  9. Aug 28, 2004 #8

    Chronos

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    I was wondering if you would dispute that.
     
  10. Aug 28, 2004 #9

    Chronos

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    Interesting point. Sometimes I like to expose them for what they are. Anyone care to argue? My apologies, Marcus.
     
    Last edited: Aug 28, 2004
  11. Aug 28, 2004 #10

    turbo

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    I do not think that gravity of a massive galaxy can red-shift the light passing nearby. That is an erroneous concept. Among other things, I am a board-certified optician, and I tend to gravitate :smile: toward light-based phenomena like refraction and frequency shift.

    It is often said that MOND does not properly predict the gravitational lensing observed in some galactic clusters. I would argue that lensing is caused by space-time distortions due to local mass, and is not a gravitational effect in any real sense.

    My thought is that the "curved" (would you substitute dense or distorted?) space-time around a massive object refracts light (gravitational lensing, for instance). The strength of the lensing (like in any optical media) is dependent upon 3 basic things. 1) the wavelength of the light 2) the difference in density between the lensing media and its surroundings and 3) the shape of the lensing media.

    Examples:
    1) shorter wavelengths will refract more strongly (differential refraction, or diffraction)
    2) for example, if you put a prism in a bath of liquid of equal refractive index and shine a light through it, the light goes straight through, with no refraction. There must be a difference in the refractive index of the media before there can be refraction.
    3) if the refracting media is flat and aligned perpendicular to the path of the photon, the photon's speed is altered while in the denser media, but it's path does not deviate (no refraction)

    A galactic cluster may exhibit strong lensing not only because it is rich in mass (and distorts space-time strongly), but also because the spaces in back of it and in front of it are relatively mass-poor , resulting in a steeper gradient in space-time density (in the light path from the lensed galaxy to us) than one might expect if the galaxies were more uniformly distributed. Again, the geometry of the distortion in the space-time fabric is important. A sheet of galaxies would not lens as strongly as a cluster with a more spherical distrubution of mass.
     
    Last edited: Aug 28, 2004
  12. Aug 28, 2004 #11

    turbo

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    Here are links to a couple of papers by Sergei Afanas'ev.

    http://xxx.lanl.gov/find/hep-th/1/au:+Afanasev_S/0/1/0/all/0/1

    I found an abstract of a talk he gave at Stanford earlier this year, but haven't located the text.

    http://216.239.41.104/search?q=cach...ail.asp?absID=27+Afanas'ev+"space+time"&hl=en

    If I understand him, his "quantization" of L is based on the average size of the fundamental (but formless) units of space time. He avoids space-time lattice, for instance. I like this concept, but it seems that in this case, L can be "quantized" only locally with respect to an observer in that reference frame. In domains in which space-time is highly distorted due the presence of mass, L as seen by an outside observer should be "smaller", and as measured by our yardstick, a photon passing through that "denser" space-time domain should be seen to slow down then speed up again as it exits that area.
     
    Last edited: Aug 28, 2004
  13. Aug 28, 2004 #12

    turbo

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    OK, so are there now more units of space-time in the intervening space, or are there the same number of units of space-time, but stretched to accomodate the expansion? If space-time comes in discrete units, you must either posit the spontaneous creation of additional units to fill the voids in the expanding universe, or allow the existing units to be distorted by the expansion. Since we already allow the distortion of space-time by the presence of mass (without invoking the creation of additional units), I am far more comfortable with stretching existing units of space-time to accomodate cosmological expansion. This leads me to think that L can be quantized only locally and that a general solution will encompass variable L.

    Dr. Fotini Markopoulou Kalamara (a bright young physicist) says that these basic units of space-time make space "lumpy", especially on small scales. Similar to the way shorter wavelengths (violet-blue) are diffracted more strongly by a prism than longer wavelengths, very short waves (gamma rays in particular) would experience more interference when traversing these lumpy units of space-time and thus travel more slowly than longer wavelengths. Thus would the variable-speed-of-light camel get its nose under the tent. Interesting times, indeed.
     
    Last edited: Aug 28, 2004
  14. Aug 28, 2004 #13

    turbo

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    Smolin's paper (Section 4.1.3 of the link in your post above) states that the "area, volume, and length operators have discrete, finite spectra valued in terms of the Planck length", so there are minimum possible values for each. It seems that he is prepared to accept length operators that are expressed in Planck length units and nothing smaller. Maybe I misunderstand, though.
    He didn't say anything about setting maximum bounds for each....

    Edit: I'm still trying to absorb that paper. On the bottom of page 28 (Experiment 3.) he states that some observations indicate that the fine structure "constant" (my quotes) may in fact be variable over time.

    Then in the very next line he says "The combination of all these experimental possibilities signals that the long period when fundamental physics developed independently of experiment is soon coming to a close." I harp on this theme constantly, (you guys and ladies are probably sick of listening to it) but it's nice to hear an according view from such a well-respected physicist. Of course, real science is more like leapfrog, and after the new experiments force some "back to the drawing board" reexaminations of theories and models, the theoreticians will ask the observational scientist for different, more sensitive, more accurate measurements, and so on. Then will come years, perhaps decades more of theory development until critical elements can be experimentally confirmed or disproven.

    EDIT/ASIDE: Is there a way to cut+paste or quote from PDFs? This paper has too much good stuff in it!! Anyway, the first question in the FAQ is: How can there be a finite, well defined formulation of quantum general relativity when that theory is not normalizable in pertubation theory? The reason is that the standard perturbative approaches make two assumptions which are not made in the exact approaches in LQG. i) Spacetime is smooth down to arbitrarily short distances, so there are physical degrees of freedom which propagate for arbitrarily high frequency and short wavelength. ii) The standard Lorenz transformation correctly apply to these modes, no matter how high the frequency. Neither assumption could be made in a background independent approach. Indeed the results of LQC falsify the first assumption and make testable the second. Physically speaking, there simply are no weakly coupled excitation or gravitational or matter fields with wavelength shorter than L (sub) Planck.

    This sounds very much like the test of gamma-ray retardation (propagation at less than light speed) experiment cited by Dr. Fotini Kalamara. Very high frequency waves slowed due to interference with grainy (lumpy) space-time.

    Marcus, thank you very much for this paper!
     
    Last edited: Aug 28, 2004
  15. Aug 28, 2004 #14
    If the planck length were changing over time, then chemistry would be changing over time. At some point, chemistry would change enough for life population growth rates to go negative. Not long after, life would have ceased to exist. Since this did not happen.....
     
  16. Aug 29, 2004 #15

    Chronos

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    Agreed. The planck scale does not change. Turbo is suggesting large scale effects. I do not see a problem with that. I would, however, like to see the math to explain it.. no offense intended, Turbo. I like the idea, but you really need to show the math. If I had any clue, I would do it.
     
  17. Aug 29, 2004 #16

    turbo

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    You are correct in that I envision large-scale effects, if you define large-scale as anything longer than the Planck length:bugeye:, which according to Smolin appears to be the lower limit for length, area, and volume of the basic units of space-time and for the wavelength of any disturbance in any kind of field.

    No offense taken, Chronos. I do not have the skills to provide the math for you, nor do I have time to re-enroll in college and develop them. Thanks to the Internet, I can read about observational astronomy, cosmology, quantum cosmology, gravitation, etc. I get lost pretty easily in the math, but after reading enough papers and abstracts, I can usually figure out what the various researchers are after. Then I ask "why are they following this line?" Sometimes it becomes apparent that the difficulties encountered in several fields have similar or related causes. These intersections are the types of things I like to think about, since ultimately there needs to be a theory of everything that doesn't break locally or universally at the U scale all the way down to the Planck scale.

    Often, (possibly unfairly) when I read research papers, I conclude that the researcher is simply trying to mathematically patch a complex model that is broken at some level, instead of determining what is inadequate about our understanding of the system being modeled. This is the familiar old "epicycle" syndrome, and it is likely to be unproductive in the end. I still read the papers, trying to determine what the researcher is doing and why, but I don't pursue them like I do the papers of people who are trying to develop new models.

    I must say that I admire the work done by the MOND folks. Their model is simple, and it works very well under lots of circumstances - now, we only have to find out why it works. As you may have gathered, I expect the answer will come from the quantum cosmologists - LQG seems more likely to be productive than the String variants, but who knows? I think we will find the reason for differential rotation in spiral galaxies, for instance, when the quantum cosmologists model how mass distorts space-time (what does mass do to the size, orientation, and energy states of the basic units of space-time), and then model how gradients thus created in the space-time field can effect the properties of objects in those fields. Along the MOND lines, I have been thinking about whether inertial mass and gravitational mass might be non-equivalent in the presence of a steep gradient of space-time density. :rolleyes: Anyway, I expect that dark matter will go away very soon - perhaps in the next couple of years.
     
    Last edited: Aug 29, 2004
  18. Aug 29, 2004 #17

    marcus

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    I tend to agree, and any approach to quantum cosmology that can
    make it to first base has a chance of being the one to provide an
    explanation

    I want to keep an eye on several things besides loop

    Mainly just want to concur with and emphasizeyour picture of the main agenda:
    now, we only have to find out why it works.
     
  19. Aug 29, 2004 #18

    marcus

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    embarrassed, I overlooked the business about quantizing length
    thanks for pointing this out
    I dont know why I missed this----or why it isnt mentioned as often
    as the results about area and volume
    I have to go and it may take a while for me to resolve it when I get back
    right now am clueless about the alleged discrete spectrum of length operator

    yes Smolin's "Invitation" paper is timely
     
  20. Aug 29, 2004 #19

    turbo

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    Might I ask what you're watching besides LQG - where you think the likely prospects for unification might arise? The field is so diffuse and huge that I bump into interesting leads almost every day, even if I have only a few minutes or a couple of hours to search.
     
  21. Aug 29, 2004 #20

    turbo

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    Dear Marcus, please don't be embarassed! You have probably read some papers that explain how the area and volume operators can be promoted to physical observables. AFAIK, there is no such equivalent claim for basic length, other than the positions of some LQG researchers that L is bounded by the Planck length at the lower limit. It is still not clear to me that L must be quantized by the Planck length (must exist as integer multiples of that value), although it appears likely, given LQG's track record. Anyway, those papers regarding area and volume would likely have escaped me earlier, since my understanding of LQG is still pretty superficial, and the significance of those physical observables would have been lost on me.

    I have searched for quantization of length because I believe that mass might distort units of space-time so they will orient rather like the blossoms of a thistle, and create lenticular space-time density gradients that can cause refraction. Like lenses, space-time gradients should be able to magnify or reduce the angular extent of the lensed objects. They should also be able to induce distortions, like "gravitationally-lensed arcs". This is a very serious misnomer in my opinion, which is why I placed it in quotes. "Gravitational lensing" is caused by distortion of the space-time field arising from the presence of mass in that domain. The lensing is not caused by gravity. Gravity should be considered seperately, and is *just* another manifestation of the effects of mass on space-time (and vice-versa). We've not only got to model the effects of mass on the space-time field, but we've got to define the effects of space-time on embedded masses in kinematic and dynamic terms - very messy. The dynamics of gravitation is going to be a bear for LQG researchers :grumpy:. We could sure use another Einstein right now - someone with conceptual insights and the mathematical discipline to follow through. I bet there's someone out there right now (looking on the bright side!).
     
    Last edited: Aug 29, 2004
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