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My Cosmological Musing

  1. Feb 25, 2007 #1
    lets say we have a ball with no air in it, so it is no bigger than a dot. now we attach a pump to it that pumps air into this very elastic ball at a relativistic speed.

    1) there are an infinite number of 2-dimensional universes within the ball. all of them are of course at some radial distance from the singularity. but the singularity is not actually a part of any of these 2-dimensional universes.

    2) an observer on a surface sees himself as being in the middle of his universe.

    3) his universe is expanding at unbelievable rates.

    4) he measures his universe to have no edges.

    5) he has no concept of the 3rd dimension of volume, as he is a flatlander, and only sees in 2 dimensions.

    does this not have some eerie similarities to our own situation ? now what sort of 4th dimension do an infinite number of spheres fit into ? i have no more chance of visualizing that geometry than the flatlanders have of visualizing a sphere. but it makes me wonder.

    one thing i agree with qm - i suspect that the totality of it all is stranger than we can even ponder about.
  2. jcsd
  3. Feb 26, 2007 #2
    hi chronos,

    i am assuming your post was intended for this musing thread ? i dont see how you are making any conclusions about mathematics, or lack of it.

    i simply compared a 2-dimensional viewpoint with a 3-dimensional viewpoint.

    i suspect that the flatlanders may have mathematics to explain their universe. it may or may not be anything like our mathematics. likewise, the mathematics that we use in 3 dimensions may be like or unlike the math that is used by a 4-dimensional creature. or maybe something else completely replaces mathematics in 4 dimensions ? i dont know.

    i think the mistake you are making is one that many scientists make. they assume they can learn everything. i dont assume this at all. in fact, just the opposite - i suspect that we cant learn anything at all about a 4th dimension, if there even is one. but if there is one, i dont think it would even make any sense to us, any more than the flatlander could think about volume.
  4. Feb 26, 2007 #3
    just to add some clarification on what i was thinking.

    in the way that my limited 3-dimensional brain can think, i was guessing that the flatlanders mapped their universe with x and y coordinates. and that the 4-dimensional guys mapped their universe with x, y, z, and alpha coordinates (whatever spatial dimension alpha might be).

    and because we developed math for our universe, i was guessing that the other 2 also had their math. but i realize that these guesses are merely because of my 3-dimensional experience, and with time manifested as it is. all this may or may not have relevance in other universes. there is nothing that i would want to say with any degree of certainty.

    but i found it compelling that this 2-dimensional universe travelling through a 3rd dimension would seem to have many of the same conclusions as we have about our 3-dimensional world.

    i was simply positing "could there be a connection ?" could we be travelling through a 4th dimension ? could this curvature of spacetime have anything to do with it ? these flatlanders, if sophisticated enough, would find curvature in their world as well. but depending on how big their surface area was, it would get harder and harder for them to tell, as it would look flatter and flatter, as the surface grew.

    also, they may or may not be under the same restrictions as we are, in regard to information speed. just because we cant get info faster than C in our universe, does not NECESSARILY mean that would be true in other universes. does light and EM even exist in other universes ? i just dont think we can conclude that anything is the same, just because we experience such and such in our universe.

    another thing about mathematics that my physics teacher used to tell me. math is supposed to explain what we have experienced, not the other way around. mathematicians seem to like to develop mathematics and then assume there must be some real-world connection somewhere. this is not always the case.
  5. Feb 27, 2007 #4


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    With due respect, IMO you must be speaking for yourself. You can't see into other people's minds and decide what they can or can not ponder about.

    In the modern cosmology research that I follow---the line that seems to me to be making the most progress these days---there is no singularity (at the point where the singularity used to be in the old model).

    In the new model, time keeps evolving back and a picture emerges of the universe prior to the beginning of expansion.

    I think it would be great if we could stop using the word "singularity" as if it were something real, and not just a feature some particular theory. AFAIK there is no scientific reason to suppose that a "singularity" actually occurred in nature.
  6. Feb 28, 2007 #5


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    I agree we live in a shy universe who clever conceals her many secrets. The mathematical part must, however, be consistent in a causal universe. While the 2D observers and 3D observers will have different coordinate systems, they will [assuming no errors] agree that both models are consistent when compared
  7. Feb 28, 2007 #6


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    downright provocative of her
    could be a bit of a tease
  8. Mar 1, 2007 #7
    hi marcus,

    i stick with my statement. i dont need to be able to peer into someone else's mind to suspect that we can not understand a 4th spatial dimension, or that flatlanders can not understand volume.

    i havent read the articles presented to me by hellfire, but i was thinking that he said that according to quantum cosmology, the singularity had quantum effects that were trying to be determined. at least to me, this seems to say that this theory treats the singularity as something. of course, that is not to say that the theory is correct.

    i am merely trying to make sure i am understanding what both of you are saying.
  9. Mar 1, 2007 #8
    hi chronos,

    i did some searches on the net for "causal universe", but could not find any that talked about it from a physics perspective. what that implies to me is that for every effect, there is a cause. is this what is meant by this term ? or are you referring to something else ?

    i cant agree or disagree with your statement, only to say that i dont know. i suspect that it is the only thing that makes sense to us. whether it would actually be true or not, i cant say (about math in a 2 dimensional world.)

    we cant really imagine a 2-dimensional object, any more than we can a 4-dimensional one. sure, we understand what width and length are. and we have mathematical constructs, called planes, which have no thickness.

    but if that sort of 2-dimensional world actually exists, we could not see any sort of object, touch it, or anything else about it. it has absolute no thickness. we need all 3 dimensions to actually make sense out of a physical object.

    everything we have come to know is part of our 3-dimensional universe. i just dont think it is safe to conclude with certainty that anything is the same in another universe.

    if light exists in a 2-dimensional world, how so ? is it not a particle ? or would the 2-dimensional world see only facets of light, but not the whole thing ? and better yet, could that also be our situation ? could we only be seeing a facet of light, not its whole character ? much like when we see a shadow of a building, instead of its actual volume ?

    what about time ? is that merely something that occurs because there is motion in the universe ? there is already a huge connection between speed and time. and that changes our perception of even the reality in which we live. so if there was no motion, therefore no speed, perhaps there would be no time.

    i highly suspect that there are higher dimensions in what i refer to as the super-universe (all that is). and i also suspect that each of us is trapped within the universe in which we reside (assuming of course that there are other universes).

    we probably also tend to assume that a 2-dimensional world contains x and y. what if it contains x and alpha, or beta and alpha, dimensions that we dont understand even in our 3-dimensional world ?

    you guys all have better physics knowledge than i do at this point, so i surely cant debate that with you. i am lucky that i have found a forum that i can learn about what some of the most current thought patterns about phsyics are - from you guys.

    but if i can impart only a little bit of wisdom - it would be to not be as sure as you seem to be. i can recall when i felt that way, so i certainly relate. but i see the continual evolution of what was once thought to be so, not to be so any longer.

    i think we have deluded ourselves into thinking that we can discover a lot more than we actually can. LOL. but perhaps a little bit of arrogance is needed to keep us searching. after all, there is no way for us to know what we cant know, so we just continue to figure out what we can.
  10. Mar 1, 2007 #9


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    AFAIK the standard understanding in any kind of science is that singularities do not exist in nature.
    a singularity is where a man-made THEORY breaks down and fails to compute or gives meaningless results.

    I don't know what hellfire said that gave you the impression that a singularity is a real "something". Sometimes people talk like that when trying to communicate to a lay person. In any case I'm afraid i don't have time to go back and track down what people said and get the verbal semantic stuff sorted out

    So I have to withdraw and let you sort it out yourself, or with chronos and hellfire. You can ask someone directly "is a singularity a real something that exists in nature independently of flaws in theory?" and see what they say. Maybe they'll say yes!:smile:
  11. Mar 1, 2007 #10
    hi marcus,

    that is a bit of a catch-22 question. most of us think of nature as being part of this universe. or according to the big bang theory, that from which this universe arose.

    in the past, i have read where the "singularity" is considered as part of this universe, and also as not. however, in either case, i dont believe we can ever answer the question "do singularities exist as a real thing ?" because to do so, would require us to jump out of the black box (our universe) that we are in, and somehow make observations about the super-universe. imo, an impossibility for us in this universe.

    lets assume that the singularity is not a real thing. does that conflict with the big bang theory ? all the mass of this universe was supposed to be just a dot, and then exploded, for some reason. this mass, matter, stuff, or whatever you want to call it, existed.

    did it not exist in the singularity ?

    we have matter and energy in this universe, today. from where did it come from, then ? i guess this is the question. if it came from the singularity, then you would be hard-pressed to explain that the singularity was not something.
  12. Mar 2, 2007 #11
    after reading this article, i would assert that the author would have to describe the singularity as a "real something".
  13. Mar 2, 2007 #12


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    I used the term singularity to mean a point or a state in which the classical notion of space-time breaks down. In this sense a singularity is something real that exists. You probably use the term singularity to generically mean some kind of infinite value for a truly dynamical variable.
    Last edited: Mar 2, 2007
  14. Mar 2, 2007 #13


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    most people including scientists use the word inconsistently
    which causes ambiguity

    a major theme in quantum cosmology is to remove singularities singularities

    singularities exist in the former theory

    (i.e. points where the older theory breaks down)

    when one cures the singularity one does not remove the point from spacetime,
    one does not do anything at all to Nature or physical reality

    one cures the singularity by modifying the theory


    one can, in a loose way of speaking, refer to the PLACE in some coordinate system where the difficulty with the old theory happened

    and one can call that PLACE the "singularity"

    where the place is will depend on the system of coordinates and the geometrical model they are used in and will be subject to a fair amount of ambiguity as well

    but people do talk like that, informally, which is fine (but it can confuse a lay audience)
  15. Mar 2, 2007 #14
    i just see in my last post, that i forgot to put in the url of the article that i had just read. i cant find it any more.

    well marcus, i am confused. LOL.

    to be or not to be - that is the singularity question of the day. LOL.

    i dont know how it can be nothing, if at the same time we claim in contains something.
  16. Mar 2, 2007 #15


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    nobody claims that AFAIK
    but you basically are stuck with the language that you use
    (I can't reform you :-) you just have to keep on using words the way youve learned them)

    If you want to, listen and watch the videos of a recent conference at SantaBarbara

    "The quantum nature of spacetime singularities"

    there it is said clearly at the outset by the MC Gary Horowitz what the usual understanding is

    the name of the game is how to fix the theory or replace it by an improved theory so the singularities (blow-ups, glitches) no longer occur.


    also Einstein made this point long long ago----owing to general covariance the POINTS in the spacetime continuum have no objective reality

    all that one can attribute reality to are events

    there is no THERE in spacetime, in the prevailing way (Gen Rel) we have modeled it since 1915

    so there is no objective reality to the spacetime point or points where the classical theory had a blow-up

    and the classical theory, we know, is wrong

    (it works fine in more normal situations but it gives no realistic picture of what happens to spacetime in certain extreme situations-----it has a limited applicability)

    Nice Einstein quote about general covariance
    “Dadurch verlieren Zeit & Raum. den letzter Rest von physikalischer Realität. ..."

    “Thereby time and space lose the last vestige of physical reality”.

    mere points in spacetime do not have physical existence, space is more like the relations between real events

    many possible sources of quote including Rovelli's book Quantum Gravity but for an online source see page 43 of
    www.tc.umn.edu/~janss011/pdf files/Besso-memo.pdf

    117 In the introduction of the paper on the perihelion motion presented on 18 November 1915, Einstein
    wrote about the assumption of general covariance “by which time and space are robbed of the last
    trace of objective reality” (“durch welche Zeit und Raum der letzten Spur objektiver Realität beraubt
    werden,” Einstein 1915b, 831). In a letter to Schlick, he again wrote about general covariance that
    “[t]hereby 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 [CPAE 8,
    Doc. 165]).
    Last edited: Mar 2, 2007
  17. Mar 2, 2007 #16
    well, you are telling me that it is not a real thing. hellfire is telling me that the field of quantum cosmology is about trying to understand what the actual quantum effects of the singularity were - so as to make better guesses about it.

    i am not sure what language you are referring to, but anyone using english is gonna come up with the same conclusion that i did. it is nonsense to be studying the quantum effects of nothing.

    i dont think it takes a rocket scientist to figure that one out.

    now that does not mean that your thought processes about the singularity are wrong - simply that they do not coincide with quantum cosmology.

    as i have said before, i suspect that neither thought process has any chance of being proven, any more than my thought process of thinking that god exists, is true. the only difference as far as i can tell, is that i am willing to admit it. LOL.
  18. Mar 3, 2007 #17


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    There is actually no confusion. The definition of singularity in general relativity is a very difficult one, but for our discussion you can assume that it is a infinite value for some invariant that can be computed from the curvature tensor. From this point of view, there exists a state at which general relativity breaks down. This state is scope of quantum gravity theories. It is assumed that in a more fundamental theory of quantum gravity there will be no infinites in dynamical variables that describe the gravitational field. From this point of view this "infinite" will be removed and the infinite does not exist. marcus follows quantum gravity very closely, so he will know better than me the most used definition for singularity.
    Last edited: Mar 3, 2007
  19. Mar 3, 2007 #18


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    Hi hellfire, thanks for clarifying and moderating (which as guru you do very well!)

    There is a kind of simple rough and ready way to put the issue in a way that may suit P-L needs. this is really for him:

    In science you can have two or more models that fit the data (observed so far) equally well. then you need more observations to distinguish
    and you don't have rational grounds to prefer one over the other until you get more decisive observations (of find a logical inconsistency).

    right now we have at least two consistent models in cosmology that fit all the observations equally well---both models allow you to extrapolate backwards into the past

    A. in one model, based on vintage 1915 einstein, when you run it backwards in the past, it breaks down at a time about 14 billion years ago.
    blows up and fails to work any further (you can say that in the classic einstein model "time stops" cause you cant run it any further back into the past)

    B. in several other models, in particular Ashtekar's 2006 "new dynamics" model, that problem has been cured and the model keeps on running back in time past the 14 billion year mark.

    Both models are equally good at matching all sky observations made by people so far, because the Ashtekar model REDUCES to the old einstein a few instants after the start of expansion and gives the same numbers, as close as can be measured so far.

    Martin Bojowald should be given credit because he constructed the first model of this type in 2001 and Ashtekar's is an improvement on that.

    The conclusion, I would say to P-L, is that there is at present no scientific reason to assume that time-evolution breaks off as you go back in time. Since both models fit the data, one can't rationally prefer one over the other.

    So I don't assume that "time stops" as you go back to around 14 billion years ago, or that "time began" at some moment. That would be assuming more than we know.

    But a lot of lay people have a bad mental HABIT of assuming a beginning of time AS IF it was justified on scientific grounds. I object to this, and I attribute it to the influence of obsolete cosmology popularizations written back in the 1980s and 1990s. Not too long ago, a decade or so, the scientists themselves had a mental habit of assuming a beginning of time and they would write these bestsellers popularizing a simplified version of then-current (now out-moded) cosmology. And it seems to have really sunk in. So we have our work cut out for us, to torpedo that unjustified assumption.
    Last edited: Mar 3, 2007
  20. Mar 3, 2007 #19


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    in case anyone is curious, here is a basic paper:
    Quantum Nature of the Big Bang: Improved dynamics
    Abhay Ashtekar, Tomasz Pawlowski, Parampreet Singh
    Revised version to appear in Physical Review D
    Phys.Rev. D74 (2006) 084003

    "An improved Hamiltonian constraint operator is introduced in loop quantum cosmology. Quantum dynamics of the spatially flat, isotropic model with a massless scalar field is then studied in detail using analytical and numerical methods. The scalar field continues to serve as 'emergent time', the big bang is again replaced by a quantum bounce, and quantum evolution remains deterministic across the deep Planck regime. However, while with the Hamiltonian constraint used so far in loop quantum cosmology the quantum bounce can occur even at low matter densities, with the new Hamiltonian constraint it occurs only at a Planck-scale density. Thus, the new quantum dynamics retains the attractive features of current evolutions in loop quantum cosmology but, at the same time, cures their main weakness."

    Just a reminder: You don't have to BELIEVE either Einstein 1915 Gen Rel, or Ashtekar 2006 "new dynamics" quantum cosmology. So far, both fit the data. It will take more work deriving and testing predictions, to see which is the better fit. In the mean time I'd say best reserve judgment.
  21. Mar 3, 2007 #20
    hi marcus and hellfire,

    i didnt want to read 40 pages of really technical stuff. i had never heard of anyone thinking that time didnt start at the big bang. from everything that i had read, energy, matter, time and everything else in our universe was created by the big bang and that which followed. but that is just a theory to explain our own universe. it certainly does not explain what or if something existed or occurred before the creation of our universe.

    both of you guys have implied though, that scientists are trying to go back before the big bang. hellfire, with quantum cosmology, and marcus, with his previous post.

    i say good luck. as i said before, i dont think scientists have any better chance of doing that than they do of proving that god exists. that is not to say i want it so. i would love to know if god exists, and what exists outside of this universe. but wanting to know, and being able to know - arent the same thing. LOL.

    i have no idea what time is. i dont think anyone else does, either. so from my perspective, i dont know if time, matter, energy, space, etc. are local to this universe, or whether they exist in some fashion in the super-universe.

    we cant think in 4-dimensions. we dont know what the 4th spatial dimension is. but we can at least have musings about 2 dimensions. so i will go there, again.

    if a 2-dimensional world exists, nothing in our universe can be the same as it would appear to flatlanders. because everything here has length, width, and depth. so if what we refer to as matter is present in some form in FLATLAND, then said flatlanders would only be able to see a part of its true dimension. for sake of argument here, i am calling our perspective its true dimension - although of course we dont know that.

    so again, i posit - could this also be the same for us ? what we describe as light, time, matter, energy, etc. - are we only "seeing" 3 dimensions of things that have a higher order dimension, if their true reality could be known ?

    i dont know that time is real. but i am pretty sure that energy, matter, and space are real. i think there is at least a chance that time exists only because motion exists. one can find quite a few articles on the net about it. it certainly can not be discounted. we just simply dont know enough.
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