Posted:

**Feb 20, 2012 1:50 pm**Even though I am not a mathematician, I've posted quite a lot on this subject in the past, mainly on the richarddawkins.net site. Basically, I still support the "loop quantum gravity" approach of defining a particle as an excitation of space (which is therefore not "nothing"), rather than as something separate, apparently existing in a sea of "nothing" (space). My reasons for this are intuitive, rather than mathematical, and inspired by various articles on the subject published over a period, before the internet There are several different approaches that I know of to the significance of the "loops" of LQG. As I understand it, they originated in attempts to solve the quantum theory version of the equations of general relativity, by the method of so-called "loop integration". Some (including one of the originators, Lee Smolin), took this to be just a mathematical method, with no physical meaning in itself.

Again, although not a mathematician, I do know that the Ashtekar approach differs significantly from this, in that it does not allow for more than one "real space", because, AFAIK, it drops the hyperspace continuum, leaving only the "spin foam" itself (his equivalent of loops).

If, on the other hand, the loops are considered to have some physical significance , this can be used to narrow down the possible variations on the maths. One of the major issues is, "How many dimensions does the 'hyperspace continuum' have?". (The hyperspace continuum being the space-like set of continuous dimensions in which quantized spaces (of which our universe would be one) exist. Hyperspace itself would not support particles, only the spaces that support particles. An important consequence for cosmology of these loops is that they create the possibility of being linked to each other, but only within the one BH - there would be no linkage betwen BHs. This means that particles and photons are trapped within their own BH, never being able to have collisions with particles within "sister" BHs, or even "mother" or "daughter" ones. (BHs are daughters of the BH/universe in which they were formed, etc)

I argue that there must be at least 4 space-like and one time-like dimension for a "big bang" universe to expand into hyperspace, and so as to allow a finite, yet unbounded "real space", containg particles, to be generated and to expand. (Thus, the loop integration isn't going to be integration over the usual 3 space-like dimensions.) All five dimensions are boundless and infinite in extent - thus hyperspace has to be of zero energy density of its own, with no edges, no beginning and no end. The "bounds" of the real spaces it contains exist only in the hyperspace, not the spaces themselves, just as a balloon's surface has no edges in it's own, 2D space even though it does have edges in the 3-space it exists in. (A balloon being a 2-shell in a 3-space, whereas real space is a 3-shell in a 4-space). In this version of space-time, a universe does have a beginning (the "big bang"), even though it is embedded in a hyperspace that does not.

It is important to realise that this cosmology makes a black hole (BH) synonymous with a universe (even though it might not make a very interesting one, if it does not have enough energy to make BHs of its own). I therefore reject Hawking's argument that clocks stop as they approach the event horizon of a black hole. As I thought was well known, they only appear to do so to an observer watching them from outside the BH's event horizon, relying on photons from the clock. If you were travelling with the clock, time would not seem to stop, and the clock would get to cross the event horizon. If it did not, a black hole could not grow, and everything it "feeds" on would be forever orbiting it, never falling in. Thus, the "stopping" is observer frame-dependent Unfortunately, Hawking appears, in one of his TV programs, to tie his atheism to this clock-stopping idea. This is not even necessary, as the alternative is still non-intelligent - BHs (at least those formed within pre-existing spaces) do not require a creator god - they only require quantum gravity, the hyperspace continuum and the gravitational collapse of a massive body. But this, as it stands, still requires the pre-existing real space, so there must also be a form of energy that does not require such a space, otherwise no universes could get started. This is the difficult bit! I can only suggest that there is the equivalent of spontaneous generation of particle/antiparticle pairs, which can exist temporarily, before popping back out of existence. If two of these spontaneous events occur close enough together in hyperspace, they might interact, and lead to a "snowballing" effect, provided new such pairs are triggered by the interaction. (Like I said, this is the difficult bit!)

The irony of all this is that Smolin proposed both the "fecund universes" cosmology and the loop quantum gravity hypothesis, yet did not see a connection between them, presumably because of the "it's just a mathematical technique" view he had of the latter. (He also withdrew the former, on what I regard as spurious grounds, concerning how he saw "natural selection" working to optimise the yield of black holes. This presupposes a huge number of generations of black holes, and this does not even make sense, given that there would come a point where a BH simply could not generate any new ones, because there is a minimum energy for a long-lived BH to form from collapsing matter, without rapidly evaporating, due to being hotter than the surrounding space.

Dark matter and dark energy might be understandable in the context of this cosmology, by extension of the physics of this universe. Consider that BHs have gravitational interactions with each other, and may collide. Such a collision would release a huge amount of gravitational potential energy as the BHs fall into each other's potential wells. I propose that this energy somehow gets converted into "zero-point" energy (ie, space) in both BH/universes, causing both to expand and exhibit "dark energy".

Another effect of the collision would be that some of the matter within both universes is very near in 4D hyperspace to matter in the other universe. I therefore also propose that gravity acts at very short range across hyperspace, so that it is still essentially inverse square within "real space", yet also produces the gravitational anomalies known as "dark matter". In this model, there are no "dark matter" particles to be found in this universe. The issue of dark matter not behaving like ordinary matter could be linked to the laws of the other universe producing a different set of fundamental particles, with different properties.

It follows in this model that "first generation" universes exhibit no symmetry violation in their laws, and therefore do not give rise to a large net amount of matter that cannot annihilate with corresponding antimatter. They would mainly give rise to BHs and radiation. The only matter would be the result of random contamination of the matter forming the BHs. However, these contaminated BHs would have the kind of symmetry violation that results in a net amount of matter, and therefore stars, planets and (maybe) life. Thus, we live in one of a large number of "dirty sisters", which are mainly assymmetric, yet add up to a symmetric whole.

A BH has been proposed, in the so-called "gravastar" model of Mazur & Mottola, to be a mass quantum effect - a superfluid of linked oscillators, by analogy to a Bose-Einstein condensate (Eg, Mazur & Mottola, http://arxiv.org/abs/gr-qc/0109035, ref. arXiv:gr-qc/0109035v5). This kind of BH also has the properties of a vacuum, supporting particles, as oscillator excitations (particles), which can collide with each other, because they are free to transfer from one oscillator (loop) to another without energy loss (in much the same way as linked pendula transfer energy from one to the next). Both Newton's first law and the non appearance of an aether follow from this model. (NB, I do not now accept the gravastar picture of a BH that they describe, because, as mentioned above, I regard the interface between universes as being in hyperspace, not "real space", as proposed by "M&M", above.

I am hoping that someone with more mathematical knowhow than I might be inspired to do some new maths on the basis of the above (or at least some of it!).

PS, sorry it's rather long, but I've spent several years thinking along these lines, and it just seemed to grow, as one thing after another seemed to fit with the general idea.

Again, although not a mathematician, I do know that the Ashtekar approach differs significantly from this, in that it does not allow for more than one "real space", because, AFAIK, it drops the hyperspace continuum, leaving only the "spin foam" itself (his equivalent of loops).

If, on the other hand, the loops are considered to have some physical significance , this can be used to narrow down the possible variations on the maths. One of the major issues is, "How many dimensions does the 'hyperspace continuum' have?". (The hyperspace continuum being the space-like set of continuous dimensions in which quantized spaces (of which our universe would be one) exist. Hyperspace itself would not support particles, only the spaces that support particles. An important consequence for cosmology of these loops is that they create the possibility of being linked to each other, but only within the one BH - there would be no linkage betwen BHs. This means that particles and photons are trapped within their own BH, never being able to have collisions with particles within "sister" BHs, or even "mother" or "daughter" ones. (BHs are daughters of the BH/universe in which they were formed, etc)

I argue that there must be at least 4 space-like and one time-like dimension for a "big bang" universe to expand into hyperspace, and so as to allow a finite, yet unbounded "real space", containg particles, to be generated and to expand. (Thus, the loop integration isn't going to be integration over the usual 3 space-like dimensions.) All five dimensions are boundless and infinite in extent - thus hyperspace has to be of zero energy density of its own, with no edges, no beginning and no end. The "bounds" of the real spaces it contains exist only in the hyperspace, not the spaces themselves, just as a balloon's surface has no edges in it's own, 2D space even though it does have edges in the 3-space it exists in. (A balloon being a 2-shell in a 3-space, whereas real space is a 3-shell in a 4-space). In this version of space-time, a universe does have a beginning (the "big bang"), even though it is embedded in a hyperspace that does not.

It is important to realise that this cosmology makes a black hole (BH) synonymous with a universe (even though it might not make a very interesting one, if it does not have enough energy to make BHs of its own). I therefore reject Hawking's argument that clocks stop as they approach the event horizon of a black hole. As I thought was well known, they only appear to do so to an observer watching them from outside the BH's event horizon, relying on photons from the clock. If you were travelling with the clock, time would not seem to stop, and the clock would get to cross the event horizon. If it did not, a black hole could not grow, and everything it "feeds" on would be forever orbiting it, never falling in. Thus, the "stopping" is observer frame-dependent Unfortunately, Hawking appears, in one of his TV programs, to tie his atheism to this clock-stopping idea. This is not even necessary, as the alternative is still non-intelligent - BHs (at least those formed within pre-existing spaces) do not require a creator god - they only require quantum gravity, the hyperspace continuum and the gravitational collapse of a massive body. But this, as it stands, still requires the pre-existing real space, so there must also be a form of energy that does not require such a space, otherwise no universes could get started. This is the difficult bit! I can only suggest that there is the equivalent of spontaneous generation of particle/antiparticle pairs, which can exist temporarily, before popping back out of existence. If two of these spontaneous events occur close enough together in hyperspace, they might interact, and lead to a "snowballing" effect, provided new such pairs are triggered by the interaction. (Like I said, this is the difficult bit!)

The irony of all this is that Smolin proposed both the "fecund universes" cosmology and the loop quantum gravity hypothesis, yet did not see a connection between them, presumably because of the "it's just a mathematical technique" view he had of the latter. (He also withdrew the former, on what I regard as spurious grounds, concerning how he saw "natural selection" working to optimise the yield of black holes. This presupposes a huge number of generations of black holes, and this does not even make sense, given that there would come a point where a BH simply could not generate any new ones, because there is a minimum energy for a long-lived BH to form from collapsing matter, without rapidly evaporating, due to being hotter than the surrounding space.

Dark matter and dark energy might be understandable in the context of this cosmology, by extension of the physics of this universe. Consider that BHs have gravitational interactions with each other, and may collide. Such a collision would release a huge amount of gravitational potential energy as the BHs fall into each other's potential wells. I propose that this energy somehow gets converted into "zero-point" energy (ie, space) in both BH/universes, causing both to expand and exhibit "dark energy".

Another effect of the collision would be that some of the matter within both universes is very near in 4D hyperspace to matter in the other universe. I therefore also propose that gravity acts at very short range across hyperspace, so that it is still essentially inverse square within "real space", yet also produces the gravitational anomalies known as "dark matter". In this model, there are no "dark matter" particles to be found in this universe. The issue of dark matter not behaving like ordinary matter could be linked to the laws of the other universe producing a different set of fundamental particles, with different properties.

It follows in this model that "first generation" universes exhibit no symmetry violation in their laws, and therefore do not give rise to a large net amount of matter that cannot annihilate with corresponding antimatter. They would mainly give rise to BHs and radiation. The only matter would be the result of random contamination of the matter forming the BHs. However, these contaminated BHs would have the kind of symmetry violation that results in a net amount of matter, and therefore stars, planets and (maybe) life. Thus, we live in one of a large number of "dirty sisters", which are mainly assymmetric, yet add up to a symmetric whole.

A BH has been proposed, in the so-called "gravastar" model of Mazur & Mottola, to be a mass quantum effect - a superfluid of linked oscillators, by analogy to a Bose-Einstein condensate (Eg, Mazur & Mottola, http://arxiv.org/abs/gr-qc/0109035, ref. arXiv:gr-qc/0109035v5). This kind of BH also has the properties of a vacuum, supporting particles, as oscillator excitations (particles), which can collide with each other, because they are free to transfer from one oscillator (loop) to another without energy loss (in much the same way as linked pendula transfer energy from one to the next). Both Newton's first law and the non appearance of an aether follow from this model. (NB, I do not now accept the gravastar picture of a BH that they describe, because, as mentioned above, I regard the interface between universes as being in hyperspace, not "real space", as proposed by "M&M", above.

I am hoping that someone with more mathematical knowhow than I might be inspired to do some new maths on the basis of the above (or at least some of it!).

PS, sorry it's rather long, but I've spent several years thinking along these lines, and it just seemed to grow, as one thing after another seemed to fit with the general idea.