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Quantum foam.

  1. Mar 26, 2005 #1

    wolram

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    From Wikipidia
    John Wheeler derived the concept of the quantum foam in 1955. It is also referred to as spacetime foam and bears a superficial resemblance to the old concept of the ether (or Aether).
    How does the time component of this" foam" progress? is it governed
    by the expansion rate of the U? or some more basic evolution.
     
  2. jcsd
  3. Mar 26, 2005 #2
    Check out the LQG introduction in this sub-forum.

    The concept is that one can construct a volume-operator and it's spectrum is discrete. This means that the manifold we work with is a mere superposition of very small grains of volume, each denoted by a quantum-number. think of space time as being made out of little grains...This granular structure of space time really is the very base of LQG. The time is not quantized ofcourse, only space is...

    But don't compare this to the aether since this way of working is background independent...

    Here is an extract :

    In LQG space has a “granular” structure that represents the fact that space is divided into elementary space-quanta of which the dimensions can be measured in LQG. The main problem of QFT is the fact that it relies on the existence of some physical background. As stated one of the main postulates of LQG is the fact that we need background independence. The diffeomorfisms give us the possibility to go from one metric to another and the physical laws must remain the same. Basically some physical state in LQG is a superposition over all possible backgrounds or in other words a physical state is a wavefunction over all geometries

    marlon
     
  4. Mar 26, 2005 #3
    Hi Wolram, and Marlon

    I am just curious about what you think of the idea that space and time are equivalent. You say, Marlon, that space is quantized but time is not...I wonder how one can be quantized and the other isn't. I believe the ST equivalence argument has to do with the speed of light, and the fact that a very small volume of space is filled with a radient event in a very short time. Doesn't quantized space then imply a time quanta?

    Thanks,

    Richard
     
  5. Mar 26, 2005 #4

    Chronos

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    I agree with nightcleaner. I see no way to quantize space and not time without introducing background dependence.
     
  6. Mar 26, 2005 #5
    are all units of quantum foam the same size ?

    Am I right in imagining a bubble bath of bubbles all connected to each other except all the bubbles are the same shape and size or as in a real bath they are not ?

    ...with each bubble haviing a universe inside it that evolved from the bubble beside it reaching a critical mass then forcing another bubble to be blown out from it..ad infinitum
     
  7. Mar 27, 2005 #6
    Maybe i should have expressed myself more clearly...sorry for that...

    First about time : indeed time is discrete but when i meant it is not quantized i wanted to say that in LQG space is divided into these little quanta of space. I should not have brought up this time-aspect because it was not my main point, sorry for that.


    Secondly, i quote my own LQG-introduction :

    The main consequence of Loop Quantum Gravity is the fact that our space-time-continuum is no longer infinitely divisible. In LQG space has a “granular” structure that represents the fact that space is divided into elementary space-quanta of which the dimensions can be measured in LQG. The main problem of QFT is the fact that it relies on the existence of some physical background. As stated one of the main postulates of LQG is the fact that we need background independence. The diffeomorfisms give us the possibility to go from one metric to another and the physical laws must remain the same. Basically some physical state in LQG is a superposition over all possible backgrounds or in other words a physical state is a wavefunction over all geometries...


    Quantization is indeed NOT the same as 'being discrete'

    By quantizing a physical theory, operators that calculate physical quantities will acquire a certain set of possible outcomes or values. It can be proven that in our case the area of the surface between two nodes is quantized and the corresponding quantumnumbers can be denoted along a link. These surfaces I am referring are drawn as purple triangles. In this way a three-dimensional space can be constructed.


    One can also assign a quantumnumber which each node, that corresponds to the volume of the grain. Finally, a physical state is now represented as a superposition of such spin-networks.

    marlon
     
  8. Mar 27, 2005 #7

    marcus

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    I am curious, in your understanding of LQG, how is the set of all geometries represented mathematically?

    Then, as you say, a physical state is a wavefunction defined on the set of all geometries. Can you give me an example of such a function? I suppose it is complex valued. If I pick a "geometry" from your set of all geometries then your wavefunction will be able to compute a complex number from it.

    I suppose then that the wavefunction, because it is defined on the set of all geometries, can be thought of as a state of geometry.

    I have deleted my objections since I dont want to argue. I think it is possible for you to have one LQG in mind and for me to have another. As long as we understand that we are talking about two different things we dont have to come to agreement. Your viewpoint may be perfectly valid and it would just be a waste of energy for one to try to convince the other.

    BTW let me point out exactly where we part company:

    in the LQG that I know space is not made out of little grains.
    and a manifold (a differential manifold, a continuum) can only be one thing. It is nothing else than a manifold as one works with it in differential geometry. In the LQG of my experience space is represented by a differential manifold, and therefore space is a continuum. It is the geometry imposed on this continuum which (along with matter) is quantized. Perhaps I am wrong to make this distinction. But I do make it, so I cannot think of space as being made up of little grains.

    I think the most comfortable thing would be for us simply to agree that we are talking about two different LQGs.
     
    Last edited: Mar 27, 2005
  9. Mar 27, 2005 #8
    Again i quote the introduction :

    Well, we want background independence, so we must be able to chose any metric or connection we want in order to describe our manifold we are working on. In the early stages of LQG all possible metrics were used in order to implement this concept of back-ground-independence. A certain physical state was then represented as a probability-density containing all these metrics. This way of working was not very practical and in the mid-eighties it was even replaced by a description based upon the set of connections instead of all possible metrics.

    So basically, when we speak about 'all geometries' then you just integrate out all the indices of the connections. This is just like the 'sum over all possible connections (and they describe the manifolds and thus the geometries)'

    ANSWER : SPIN NETWORKS

    I don't think i get your objection here, but to state my point i refer to the Rovelli-article at the end of the LQG-intro. You will need to look in my journal at the very last page...Point is that in LQG (at least alla Rovelli and friends) you connect for example three spheres by lines that are called the links. The spheres are the quanta of space...and these are the granulae i keep on refering to.

    This is a very short version of my point but please, i refer to the above mentioned article

    regards
    marlon
     
    Last edited: Mar 27, 2005
  10. Mar 27, 2005 #9
  11. Mar 27, 2005 #10
    Besides it is important to realize that in LQG, space is replaced by the spin networks and spacetime is replaced by spinfoams which are a 'history' of spin networks or the superposition of all spin networks at some time interval delta t...

    Just like a line is the description of the history of a point (eg Feynman diagrams), is the spinfoam a description of the history of a node or even a spin network. These spinfoams are DISCRETE quantumgeometries (one spinnetwork per second ...) and over a period of time, the superposition of these spin-networks evolves into a smooth continuous space if you don't look at distancescales that are 'too' small.

    Thus : spacetime is smooth but space and time apart are indeed discrete in nature. That is my point

    marlon
     
    Last edited: Mar 27, 2005
  12. Mar 27, 2005 #11
    Hi wolram

    I don't really understand much so please don't take anything I put forward as an authority. But I have found some satisfaction in looking for better questions rather than in looking for answers. Perhaps I can apply a logic to your first question here.

    "How does the time component of this "foam" progress?"

    Well surely this question can be made more compact, anyway. The idea of progress and the idea of a time component are closely connected. The problem is highlighted by asking more simply, how does time progress? I would ask then, how can it not?

    But this is not to gut the meaning from your question, but to find a way to make a better question. Perhaps the bowels of your question can be brought back in by asking, "How does this foam progress (in time?)"

    Well progress is a relitive term and may not be what you really want here? Could we substitute another word and not lose the meaning? Could we sub another word, and make the meaning more clear? Progress. Advance. Evolve. Develop.

    Well all these words seem to me to be emotionally weighted, not that that is in itself a bad thing, but is it needed here? What if we try a neutral emotive word, such as change? "How does quantum foam change in time?"

    Probably you have seen the same pictures I have seen, of quantum foam looking something like suds in a washing machine. It leaps up and down and curls back on itself and does all sorts of cute tricks. I am not sure what up and down and cute or even curl mean in quantum foam terms, but perhaps the use of these words show how wrong the picture is. It does give us an idea, but, for example, it usually is shown as a surface. Surface of what? Foam in a washing machine has a surface. But what quantum scale surface is being referred to in the washing machine image?

    Foam in a washing machine is a bright analogy and easy to remember. But like most analogy it must not be pushed to absurdity, however tempting that may be to a reductionist. Instead, let me try to find the meaningful parts of the analogy.

    Foam has bubbles. What are the bubbles meant to represent in quantum terms? A bubble is a gas under pressure in a liquid. Foam is a special case bubble, which has a closed cell structure in a liguid reduced to a collection of membrane-like surfaces under tension. Is quantum foam the bubbles, or the membranes, or a combination of the two?

    Well we know about branes in quantum theory, sort of, except these liquid membranes in soap foam are not exactly the branes of brane theory. A bubble membrane is locally a two dimensional surface which at a larger scale curves back on itself and is closed in three dimensions.

    Quantum theory seems to me to be much concerned with the idea of geometry in higher dimensions. Foam in a washing machine is a three dimensional model with time thrown in as agitation. A single instant of foam looks rather like a closed cell sponge, which has the same form without all the agitation. Throw in time as a fourth dimension and you can start and stop the action at will, something like taking a closed cell sponge and slicing it into thin layers, then looking at the layers in sequence. In a series of thin slices, you might see a bubble or cell open up, expand, and close again, more or less as a bubble in an agitated soap foam might grow, merge with other bubbles, and eventually reach the outer surface of the foam where it might pop, releasing its pressure and the tension on the membrane locally and so collapsing back to whence it came.

    Consider the sponge slices again. You can look at the sponge slices in sequence and watch a bubble emerge, grow, and collapse. But what is it really? The sponge was chosen as an image of a single instant in foam. How can we now take a single instant, slice it fine, lay it out in sequence, and see a progression in time?

    We can do this because in this case it is easy to see how space and time are the same thing. We slice space without time, and see development.

    Now to progress to a higher dimensional model, we have to do the same thing, only we are slicing a four dimensional structure into a sequence of three dimensional images. So we see the whole sponge, perhaps as a living animal or perhaps as a chemical process, and we see it first as a baby sponge, then as a slightly older sponge, then again slightly older, and so on as it grows. So a sequence of three dimensional sponges demonstrates the life cycle of a sponge in four dimensions.

    Only in a living sponge, the animal, in its growth sequence, experiences all kinds of events, some favorable to growth, others catastrophic. So each sponge that grows experiences a different history and so no two sponges are really identical. You can't really watch a single bubble develop in live sponges by slicing them into bits. But maybe you get the idea.

    A fourth dimensional view, to be comprehensive, has to include all the possible sponges. How does a sponge grow? How does a quantum foam change in time? We have to generalize. How many different ways can it change? We have to include all of the ways it can change, or our answer is incomplete.

    In this sense, looking at the washing machine model, we have to look at all the possible forms of bubbles. Some leap up and down, some merge with others, still others are divided. There is no contradiction because one leaps up while the other is falling down. There is no contradiction because one grows while another shrinks, no contradiction because one merges with another, or another divides into many smaller copies of itself. Foam bubbles do all these things.

    Compare and contrast. In what way is foam like quantum process? Where does the analogy fail to describe reality? I cannot give you an answer, but maybe I have helped you find a better question. What I have concluded from all this is that fourth dimensional reality includes every possible outcome of any situation. You will, of course, draw your own conclusions.

    Be well,

    Richard
     
  13. Mar 27, 2005 #12
    if space is foamlike what causes more foam to be made causing objects to recede from each other at sometimes faster than light speeds ???

    Is inflation happening at a boundary of an expanding spherical universe or injected into every point in the universe ???

    see white hole thread for an even more nonsensical attempted expanded form of the question.

    Sorry, if it is a dumb question or irrelevent
     
  14. Mar 27, 2005 #13

    Chronos

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    I resist the graininess analogy. I'm more inclined to think of it as blurriness. In my mind space and time are coordinate systems describing topological relationships between particles in the universe. I'm also inclined to think gravity is a form of quantum entanglement between particles that originated in the big bang singularity.
     
    Last edited: Mar 28, 2005
  15. Mar 27, 2005 #14
    This is what i think I'm talking about...

    The idea of space being made of discrete quanta might introduce further
    conceptual problems. In an expanding model new cells have to be produced
    to fill in the gaps. But if we make analogy with cell division in living or-
    ganisms, how are cells produced without error? Because presumably there
    is no analogy with DNA, there seems the need of providing “scaffolding” to
    force cells to have their correct form. One might try and claim the classical
    equations impose this by stricture, but if only a few cells are present the
    classical structure is still unformed. Constant quantum fluctuations at short
    distance have continually now to be kept in check.


    continue here...

    Contrasting Quantum Cosmologies
    D.H. Coule

    Institute of Cosmology and Gravitation,
    University of Portsmouth, Mercantile House, Hampshire Terrace,
    Portsmouth PO1 2EG.

    Abstract
    We compare the recent loop quantum cosmology approach of Bo-
    jowald and co-workers with earlier quantum cosmological schemes.
    Because the weak-energy condition can now be violated at short dis-
    tances, and not necessarily with a high energy density, a bounce from
    an earlier collapsing phase might easier be implemented. However,
    this approach could render flat space unstable to rapid expansion or
    baby universe production; unless a Machian style principle can be in-
    voked. It also seems to require a flipping in the arrow of time, and vi-
    olates notions of unitarity, on passing through the bounce. Preventing
    rapid oscillations in the wavefunction seems incompatible with more
    general scalar-tensor gravity theories or other classically accelerating
    solutions.
    Other approaches such as “creation from nothing” or from some
    quiescent state, static or time machine, are also assessed on grounds
    of naturalness and fine tuning.

    http://xxx.lanl.gov/PS_cache/gr-qc/pdf/0312/0312045.pdf

    ...can someone please interpret for me and others not mathematically inclined ?

    cheers
     
  16. Mar 28, 2005 #15

    marcus

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    hi spicerack, when you give links to arxiv it would be extra helpful if you could give the link to the ABSTRACT page like this

    http://xxx.lanl.gov/gr-qc/0312045

    that saves us the trouble of copying and pasting and then editing your link to make it not link to the PDF, before we can use it to get the abstract

    it is advisable to always look over the abstract page, with its links, first.

    if you go directly to the abstract, it is helpful because there are further links there to important things like WHO HAS CITED the paper, and
    there is often information about HAS IT MADE IT THRU PEER REVIEW into a scholarly publication
    and HOW MANY TIMES HAS THE GUY REVISED IT
    and also, very important, WHAT OTHER PAPERS HAS THE GUY WRITTEN AND PUBLISHED

    for instance this paper is a 2003 paper, so it has had a couple of years to make it thru the peer review process. I will look now and see.

    ==============

    hmmm, sorry to disappoint you
    the paper has been revised 3 times, it has not made publication
    it has not been cited to any significant extent: just once by the author himself in another of his own (somewhat marginal) papers, and once
    apparently as a courtesy in a Bojowald paper that came out within a month or so of this one.

    Bojowald refers non-committally to Coule's analysis of some other kinds of quantum gravity. He does not mention Coule's discussion of LQG

    "... generically, curvatures and energy densities still diverge and the classical singularity presents a boundary to the evolution (in some special models one can argue for a more regular behavior in a different sense, see e.g. [31])..."

    In the past, Coule, the author, has struck me as someone who is out of touch. has no reliable understanding of LQG, and who writes papers that would interest few if any working cosmologists. But I always want to re-check my impressions, because I want to be accurate in judging what papers I need to read (with limited time).

    So in this case I was glad to go to the abstract,
    check for possible publication, and use the links there to see what other papers Coule has written and where they have been published etc.
    I might have discovered signs that Coule had suddenly become creative and excellent and risen to the forefront!
    But in fact did not.
     
    Last edited: Mar 28, 2005
  17. Mar 28, 2005 #16
    thanks Marcus for the link tip

    I'm not disappointed but i would still like to know how and where units of space come from and are inputted into the universe to allow for expansion

    can you help ???

    cheers
     
  18. Mar 28, 2005 #17
    Perhaps Spicerack, you will be happy with a model of "explosive" expansion, such as would be found, for example, in a pressure cooker where the pressure and temperature were raised above the boiling point, and then the pressure is suddenly reduced, say by removing the lid. Don't try this at home.

    In this model, bubbles form very quickly throughout the liquid. A bubble forming creates a temporary balance in the pressure, but when it reaches maximum size it quits growing, and at that point the water in the walls of the bubble may be free to start new bubbles.

    If the universe we know is made of some condensed form of matter suddenly released into a vacuum, the bubbles would form and expand from the bulk of the membrane. Maybe this idea is falsifiable.

    We still havn't addressed the question of what the membrane is made of in quantum foam, nor how a super condensed matter came to be released into a vacuum. We don't really have a clear idea of what vacuum is.

    My point is that your line of speculation is possible, but we need something that can be tested experimentally, or at least by observation in the cosmic laboratory. I am also struggling with this in my own visualizations.

    Be well,

    nc
     
  19. Mar 28, 2005 #18
    I think this difference is worth exploring. But I am still not clear on the implications of the difference. My first thought is that it has to do with countability. If the discrete quanta are blurry, we may not be able to count them. But perhaps the blurr is correctable somehow, as is near-sightedness, or dirty lenses. Or maybe the blurr is fundamental to the uncertainty principle.

    I would like to know more about the difference between quantizable and discrete, if anyone has any thoughts.

    I am not sure about the purple trianges.....is this a reference to dynamical triangulations? Could we have a link here?

    Thanks,

    nc
     
  20. Mar 28, 2005 #19

    marcus

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    I will try to help.
    first the answer to any question depends on the model.
    (all human models eventually get proven wrong, you just keep testing them until they fail and get replaced by something that is better)
    right now the prevailing theory of spacetime is Gen Rel (1915)

    LQG is a possible eventual replacement but is still incomplete and untested.

    In Gen Rel there are no units of space. Space can expand simply by distances between places getting longer, without any gaps forming.
    Space is entirely unlike a material. what expands is something rather abstract---the distance-function or "metric" does the expanding. just by its distance readings getting longer. there is no material expansion.

    LQG is like Gen Rel.in this.However there is a popular misconception that it has "GRAINS" of space. On the contrary, that is not how real LQG is built. It is built on a smooth continuum just like Gen Rel.
    So space can expand, in LQG treatment e.g. in LQC cosmology papers by Bojowald, without any grains being needed!

    So i would say your question is disconnected from reality, so dont worry about it. the granularity mistake comes when well-intentioned people try to give a popular explanation and then they use simplifications, images, metaphors, loose comparisons etc. and people get the idea that they understand and that LQG space is granular and to be thought of as made of little grains. Regrettable. :frown: But it can happen

    So do not worry about it is all i can say. THERE ARE NO UNITS OF SPACE in any physics theory I know of. Certainly not in LQG, but i will keep an eye out for it in other theories just in case.
    indeed there are units of MEASUREMENT, like square inch and planck length. But SPACE IS NOT A MATERIAL SUBSTANCE so one does not need to have units or chunks or tiles or cells or grains of it.

    It worries me a little that you are asking this:
    " i would still like to know how and where units of space come from and are inputted into the universe to allow for expansion"
    Where did you get the idea that there are units of space that have to be inputted into the universe? Did someone here at PF give you this idea?
     
    Last edited: Mar 28, 2005
  21. Mar 28, 2005 #20
    Hi again.

    Space units can come from time units, via velocity. I think you really need to clear up the spacetime confusion. Have you read Flatland?

    nc
     
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