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Quantum Space Entanglement

  1. Dec 20, 2005 #1
    Talk about not knowing enough on the topic! But it fascinates me to no end...

    I've read that, according to Lee Smolin, there are discrete units of space and that there is mathematical support that upon dividing this space, it creates another unit of space of equal "volume".

    Furthermore, if there is discrete parts of space, then they must contain systemic properties (direct or indirect) of their own. (depending on what you are using to explain these bits of void)

    Would it be possible to entangle two (or more) units of space so that their causality networks (for lack of a better term... the "thing" that determines that void bit A is connected to void bit B so all matter passage from A will go to B) would be identical but inverted? Or is proximity alone enough to describe the causal connections between void bit A and B?

    Basically: causality between two quantum bits of space.... is it theoretically possible to reassign it via entanglement or another similar process?
     
  2. jcsd
  3. Dec 20, 2005 #2
    anyone? :(
     
  4. Dec 21, 2005 #3
    can i at least get a no so i can go back to the drawing board? :(
     
  5. Dec 21, 2005 #4
    Stated:I've read that, according to Lee Smolin, there are discrete units of space and that there is mathematical support that upon dividing this space, it creates another unit of space of equal "volume".


    This depends on what you are actually deconstructing?..what makes up the "first-space", dictates what you end up with after deconstructing/separating it, or discretizations? a unit of "space",(the paramiters needed to describe your space, are reliant upon the dimension it exists within) in 2-Dimensions, does not equal a unit of "space" in 3-D.

    Lets say for instance that you have a spherical space of certain size, volume, lets called it a 'Bubble of Nothing'?..can you sperate this BON into two discrete portions?

    Take an implement(lets say a scissors is used to part the volume, just for simplistic visulizing action) to disect this void, remember that you cannot actually locate a "real" bubble of nothing.. unless your Ed Witten!..but lest give the space a low energy signal, the lowest energy possible?

    The moment you try to disect this space, the impliment you use will be adding energy to the system!..so thus you destroy the low-energy you are trying to locate and catagorize, the mathematical speration of "Space" will forever remain singular and detached from reality, by its very nature?

    Entanglement, is the low-energy seperation of certain energies, which happen to spread out over space, rather than be contain within a specific space volume.

    So simplistically speaking, all spherical 3-D volumes can be spread, collapsed would be a better discription, over a 2-D field.

    "Basically: causality between two quantum bits of space.... is it theoretically possible to reassign it via entanglement or another similar process?" ..you cannot undo what you have allready done, in order to assign it a specific action?..can you see that you cannot put a 3-D volume in dimensional space 'less,2-D' than what you need to maintain its dimensional status.

    Let me ask you the same question put a different way.

    Lets say you have a finite limit of length, call it a Planck Length. You have two systems that you want to reduce down to the planck limit, system one is 3-Dimensional, and system two is 2-Dimensional.

    Any 3-D energy you choose to reduce, will arrive at a finite 3-Dimensional limit, above that of 2-D, you cannot just discard/remove one "bit" of the energy in order to transform the 3-D energy to 2-D?..if you chop up the 3-D energy into ever decreasing finite "bits"..you may end up at the planck length, but the energy content will be not the same as if you STARTED with a 2-D system and reduced that down to finite "bits".

    If you start with a 2-D space, you actually start and end up with MORE energy!..simply because 2-D energy is spread out to an un-constrained limit, field energy, again by its very nature is increased by fact of it extends beyond a constrained volume?

    Thus according to Smolin statement of discrete units of "space", this equates to there being discrete units of "fields"..but this would, in the 2-D domain, equate to the Vacuum Selection Background, having a very identifyable solution.

    Which then leads to the fact that if you have Quantum Discrete field "units", then there is no difference in reducing a volume of space from [3-D>>2-D>1-D] to a specific size, to that of extending a volume thus [3-D>>4-D>5-D......].

    Which goes against the whole principle of Observation and Measure!

    As a specific example , the reduction of 3-D energy is eventually stopped by fact that you cannot pinch off a single Quark and place it in isolation.
     
    Last edited: Dec 21, 2005
  6. Dec 25, 2005 #5
    I apologize for the delay in replying.

    Very well-written and explained. I understand.

    But perhaps our BON operates like a capacitor instead of a particle.. where matter/energy inside of it means that the BON state of void has collapsed. Since the matter/energy that is inside the BON can leave the BON, the "state of void" has... "reassembled".

    If the default of space is "proximity determines causality" was in anyway to be altered, (albeit I do not know the mathematics of quantum space [does anyone?]) a piece of space would not float off in it's own astral dimension. Instead, the piece would, by some law of quantum gravity, "reestablish causality" with the closest bit of space. Although I understand this sort of thing is borderline aether, by bit of space, I refer to it in the relativistic manner as opposed to background dependant. (I.E aether)

    To quote Smolin on this:

    In case it is not obvious, let me emphasize that harmonic oscillators are not relevent here, and can play no role in a background independent quantum theory, precisely because the division of a field into harmonic modes requires a fixed background metric. Thus, the physics of the problem REQUIRES an alternative quantization.
     
  7. Dec 25, 2005 #6
    I actually think that Smolin,(a paper of his/ co-authored, I have) has lead myself into a domain that I believe has a very relevant benefits.

    I am not qualified in any way to place a good enougth explanation on this subject, but I am trying my best.

    The "problem" of a new interpretation on the Pauli Exclusion Principle, and its formulation within current physics is where I believe the answer lay.

    The interchange of 3-D Particles, and 2-D Fields has some interesting workings, one being the 'Potentiallity' of exchange, in certain Electro-Magnetic-Vacuum/Mediums?
    Hopefully After everyone has enjoyed their holiday break, this can be further inquired upon.

    For now Happy Holidays everyone.
     
  8. Dec 25, 2005 #7
    This is interesting and may be parallel to a line of thought I have been pursuing. If I may interject a few reactions of my own...

    Reasoning from the principle of space-time equivalence, space-like views and time-like views are two different ways of seeing a single thing...spacetime. So if there is a smallest space it also defines a smallest time, which may be calculated as the time it takes light, as the fastest velocity, to cross the smallest amount of space.

    With this equivalence in hand, we may do well to think of spacetime in terms of action, thus uniting space and time in a single unit, and thus (partially anyway) relieving ourselves of the burden of defining what, exactly, we mean by space or by time. Then we can consider that there is no space without time, and no time without space. Instead, we have the action as the square root of the product of space and time.

    Now we are free to consider the idea of action as the fundamental unit. What is the least change?

    What do we mean when we consider the idea of an object, such as a fundamental particle? It has duration and it occupies space. If we select a convenient frame of reference, we can say that the object "does not move", which is merely to say that it is co-moving, or co-varient, with the frame we have chosen. The frame is a background. The fact that we chose it, put it in by hand, so to speak, tells us that it is not an absolute feature, but something that we, our conscious selves, have imposed.

    Einstein tells us that there is no absolute frame of reference, that is, there is no universal space which occupies a single unmoving time, nor is there a universal time which defines eternally all of space. Space and time are inextricable. From the beginning, the zero dimension, they are the same. Space and time are the same in the first dimension, in the second, the third, and so on.

    For this reason, questions such as 'What happened before the beginning" and "What lies beyond the end of the universe" are meaningless. They reduce to the absurdity of establishing by arbitrary act of will a largest or a smallest frame, and then asking what lies beyond its borders in the first sense or within its borders in the second sense. The borders are arbitrary. The question negates the definition of the border. Hence the question has no meaning.

    The problem of equations that blow up, or give infinite answers, when time or space is taken to zero, are also meaningless for the same reason. The frame of reference that we set is arbitrary, an artifact of the conscious process of measurement, and has no reality in any fundamental sense. No physical process is defined or constrained by our artificial setting of a boundary condition.

    We cannot gain anything by defining an arbitrary unit and then asking what happens physically when it is divided again. Of course the mathematics tells us that it takes infinite energy, for example, to divide the smallest unit into smaller pieces. But this is not a physical process at all. It has nothing to do with the physical reality of fundamental particles. It has only to do with the arbitrary limits we set when we choose a referential background in which to consider the length or time in which the action occurs.

    So there is no absolute frame of reference. We are left with the option of choosing one or more "natural" frames, and they exist in plenty. The width of a hand or the length of a thumb will do for most purposes, but we have more detail if we need it. We can measure length in terms of wavelengths of light or time in terms of decay rates. We even know how to use hyperbolic functions to determine what happens to these rates and lengths if the observer takes on motion.

    The position and the motion of the observer then becomes a part of fundamental reality. Two observers of a single event may have differing senses of the order and magnitude of the event. They may even have conflicting senses. It is even possible that what qualifies as an event for one observer may not exist at all for another observer in a suitably different condition of position and movement. Or that one observer in one set of motion and position determinants may see an event happen in a different sequence from that seen by another observer. One may see an electron emit a photon. The other may see the electron absorb a photon. Yet another observer in yet another frame of observational reference may see no process of action at all.

    Of course these extrema mean little to us as we throw and catch a ball, or sit in an earthly laboratory and watch for the decay of a proton. All of us on earth are in very nearly the exact same frame of reference. The differences are so small that our universes are nearly exactly the same. You throw a ball, I catch it, and it never just dissappears into hyperspace along its ballistic path. Even so at a fundamental level we have to agree that the ball you throw and the ball I catch are not really exactly the same ball. Much has changed, fundamentally, along the path of flight.

    We can both observe much more fundamental processes. An electron emits a photon. Every one of us will agree that the electron emitted the photon. Yet we can imagine and calculate the determinants of an observer who would see the same electron (or a positron in this case) absorb the photon. We cannot communicate with that observer or accelerate ourselves into that observers frame of reference, but we can hypothesize that such frames, and observers, could and probably do exist.

    So what is the action, if it can be said to exist independently of a background imposed by the conditions of the observer?

    Well first of all perhaps we can agree that we are not going to talk to people who do not see the emmission at all, or to those who see it as an absorption. We do not share sufficeint conditions with those people to allow for discussion anyway. We are only interested in communication with people in our own frame, or in one close enough to ours to allow for meaningful communication. We are, in a sense, in "the same" laboratory. Fortunately this is a rather large laboratory, since it includes everything we can observe in our common universe. There is plenty of room for us to talk comfortably.

    break
     
  9. Dec 26, 2005 #8

    So, going back to the OP, I can't speak for Smolin, but I have had similar thoughts on my own.

    If there is a smallest space (that is, a discrete unit), and you divide it, then the quotient is once again the smallest space. Since the smallest space must be equal to the smallest space, there you have it. There can be no smaller volume. No matter how many times you divide the smallest volume, it is still the smallest volume. This is the same result as dividing zero by any number in math, or the same as saying it requires infinite energy to divide the smallest space.

    Really, in physics now intead of philosophy or math, there is a more practical limit on how small a space we can divide. Dividing a small space is equivalent to inserting a wave into that space. We know that waves confined to small spaces are more energetic than waves in large spaces. This means that to divide a smaller space, we need a more energetic wave. But we only have so much energy available to us. Even if we could convert all of the energy of the observable universe into dividing one small space, that space would still have a definite size greater than zero.

    There is still one more way to see this. I don't know if it is mathematics, physics, or general philosophy. Start by imagining an entirely empty universe, no boundaries, no interior structure of any kind. Now mentally insert a single fundamental unitary object...how big is it? It has no internal structure. There is nothing outside of it to compare it to. How big is it? Do not be surprised if you cannot find a reasonable answer. Now divide this object any way you wish. Is there any way, consistant with the universe we have just created, to compare the parts of the divided object? Are they close together or far apart? Are they equal in size or different? Is there any way to uniquely name the parts as individuals?

    I suggest from the above logic that there is no way to evolve complexity from uncontained emptyness.

    How then is complexity obtained?

    It would seem that complexity requires a bounded universe (call it a background if you wish) containing two or more fundamental, comparable, inequivalent objects. It seems to me now that there is no other way to construct a basis. Without these conditions we cannot talk meaningfully about size, location, motion, or any of the other physical quantities.

    "

    I am not sure how you came to the conclusion that discrete parts of space must contain systemic properites of their own, nor how these supposed properties would differ directly or indirectly. Of course if you are imagining discrete parts as pieces of a larger structure, what you say would have to be true. In physics, we can crush salt into smaller and smaller bits, each of which has the structure of salt, until we come to a certain limit. Anything smaller than the size imposed by that limit is not salt.

    Objects smaller than the limit have new properties of their own which we can investigate. Sodium and Chlorine are atoms which make up salt. If we reduce the limit further we find sub-atomic and then sub-nuclear particals. Protons and neutrons have internal parts, called quarks and gluons. The standard model of particle physics lists the most fundamental known objects. There is some speculation that quarks may be made of preons or axions or some other more fundamental bits. However we have now passed beyond the limit of energy available to our technology. We have no current means to physically define discrete objects smaller than that.

    But these limts are still actually rather large. A proton is about 10^-9 cm. It has three quarks. Each quark then would occupy about a third of the volume of the proton. Compare this to the size of the Planck length, the smallest theoretical length in physics, at 10^-33 cm. You must realize that this is an exponential scale...the Planck length is as much smaller than the proton as you and I are smaller than the known universe. The Planck length was determined by calculating the size of the space a proton mass would have to be compressed into to turn it into a Schwartzchilde singularity, or black hole.

    If you have followed this logic of scale, you will see that matter in the forms we know it cannot be thought of as inhabiting a fundamental unit of discrete space. In fact, the smallest units of matter we know would have to occupy billions upon billions of discrete fundamental units of space.

    The questions of interest on this board have to do with the geometry such fundamental discrete units of space would have to obey in order to produce the large statistical effects we know as phenomenology. How can we account for the behaviors of matter such as mass, electomagnetics, the weak force which holds nucleons together, the strong force responsible for quark confinement into nucleons?

    Returning to the top of this liturgy, space and time are equivalent, and at the Planck scale, in fact, anywhere below the Fermi scale, it will not do to consider one without the other. This is why it is better to think in terms of action rather than of spatial continuity or temporal flux alone. An electron emits a photon. This action occupies both space and time in some measurable quantities. The photon has a length and a velocity. The electron occupies a position and has a momentum. You would think we could pin everything down quite nicely with this information. But HUP and SR throw in some wrenches. Quantum effects at measurable scales are counterintuitive. Time and space are not well-behaved. They stretch and compact and require topological logic instead of rulers and clocks.

    Actually, causality itself is under siege. I have become suspicious that causality will have to be relegated to a secondary effect....dependent on the state of the observer, and not a thing in itself. Sure, we all agree that A causes B, but that may only be because we are all in roughly the same region of space and all headed roughly in the same direction at roughly the same velocity. We are free to imagine contrarian observers, for whom B causes A, or other observers for whom B and A have no logical connection whatever.

    Fortunately we are saved from total confusion by the practical fact that we cannot discuss A, B, or C with such observers. They would be outside of our light cone.

    Now I intend to occupy what time remains to me in considering the possibility that somewhere below the Fermi scale, where quantum effects predominate, there is a measurable region in which the light cones all must interact. If so, then there is a very small, very short, but ubiquitous region in which we do communicate with our banished other selves. I suspect that in these regions there are only a few possible alternatives, maybe a handful, but not the infinity of multiverses that so disturb the economists among us. I think we shall find, not far beyond our current limits, a fundamental space-time structure in which there are perhaps two or three alternative optional universes, probably not more than eight from any juncture.

    Happy New Year.

    Richard T. Harbaugh
    0512261307 170 views
     
    Last edited: Dec 26, 2005
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