Loop Quantum Gravity

Study matter and its motion through spacetime...

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Re: Loop Quantum Gravity

#101  Postby twistor59 » Jun 28, 2011 12:32 pm

Looking forward to reading this introductory book on LQG.....
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Re: Loop Quantum Gravity

#102  Postby cavarka9 » Jul 20, 2011 10:56 am

wonderful, thanks for informing.
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Re: Loop Quantum Gravity

#103  Postby twistor59 » Jul 26, 2011 7:29 am

It's probably appropriate to point out that the discussion of LQG I gave in the posts above was cribbed from a lot of the original papers, which are getting quite old now, and the subject has moved on. For a more recent exposition with a more modern point of view see here.
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Re: Loop Quantum Gravity

#104  Postby tnjrp » Jul 26, 2011 7:38 am

:cheers:

It's good to know the basic tho even if there's been advancement.
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Re: Loop Quantum Gravity

#105  Postby Joe09 » Aug 25, 2011 1:23 pm

well i passed my 1st year of physics with an average of 58% (dam mathematical physics 1.1 lowered the average as i failed this partiucular module) and the 2nd year modules i advanced i averaged 64%

so im one year closer to understand this fantastic thread :)
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Re: Loop Quantum Gravity

#106  Postby Joe09 » Aug 25, 2011 1:38 pm

this year my core subjects will be condensed matter, electromagnetic fields, many variables, vector calculus

and i will be advancing the 3rd year modules fourier transforms and advance vector calculus :)

plus ill have all my astrophysics special modules
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Re: Loop Quantum Gravity

#107  Postby twistor59 » Aug 25, 2011 3:58 pm

Well done Joe, keep up the good work !
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Re: Loop Quantum Gravity

#108  Postby hackenslash » Aug 27, 2011 7:11 pm

:cheers:
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Re: Loop Quantum Gravity

#109  Postby twistor59 » Aug 31, 2011 6:50 am

Loops vs strings - the debate:

http://zomobo.com/play.php?id=NhNyhqyvj6Q
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Re: Loop Quantum Gravity

#110  Postby cavarka9 » Aug 31, 2011 9:27 am

saw that couple of days back, i think I got therefrom the chatbox video.
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Re: Loop Quantum Gravity

#111  Postby Joe09 » Sep 03, 2011 11:55 am

im actually leaning towards LQG myself

but the last part of the video makes me laugh, because in terms of gaining knowledge and understanding im very altruistic, so i find it silly that LQG/String theoriests dont want to work together
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Re: Loop Quantum Gravity

#112  Postby cavarka9 » Sep 03, 2011 6:41 pm

:mrgreen: :cheers:
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Re: Loop Quantum Gravity

#113  Postby Schneibster » Sep 17, 2011 6:46 am

twistor59 wrote:my understanding (maybe wrong ?) of the string landscape is that it's a landscape of possible theories, which is something not quite as nice like.
No, you're right, but not directly. The dimensions of the manifold (because it's actually N-dimensional, not a 2D "relief map") represent various parameters of the Calabi-Yau manifold, their values resulting in varying physics and determining "position" on the "landscape," IIUC in terms of relative force strengths as well as particle types and masses. It's a metaphor, not a piece of physics.

I got that from Susskind The Cosmic Landscape, 2006.

ETA: I skimmed the first three pages. Bookmarked. This will be a fun thread. Thanks for this.
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Re: Loop Quantum Gravity

#114  Postby twistor59 » Nov 08, 2011 7:12 pm

So I finally got my copy of Gambini and Pullin's book "A First Course in Loop Quantum Gravity".

It's quite an expensive book (only available in hardback at the moment). It's quite a small book. But it's a very very good book if you want to learn LQG and haven't done anything like it before.

I'd say it's suitable for a 3rd year undergrad physics (or maths if you've done some physics courses) student. It has chapters giving whirlwind introductions to general relativity and quantum field theory in case you happen not to have done them. I would say that you really need to have done at least some quantum mechanics, and be familiar with the Lagrangian/Hamiltonian approach to mechanics, and at least a small exposure to GR/tensors would be highly desirable.

It doesn't go into any of the topics in great depth, that was not the author's intention - they do a good job of keeping it brief enough to keep you interested. Probably the final third or so of the book deals with the loop theory itself, but even if you don't rate LQG, the first part of the book is a highly enjoyable read. I think it's exceptionally well written.

If it's a bit on the expensive side, try to borrow it from a library and see what you think.

Well done Gambini and Pullin :thumbup:
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Re: Loop Quantum Gravity

#115  Postby newolder » Nov 09, 2011 6:30 pm

isbn, plz?
4got teh linkee... :oops:
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Re: Loop Quantum Gravity

#116  Postby Macroinvertebrate » Dec 04, 2011 9:07 am

twistor59 wrote:Loops vs strings - the debate:

http://zomobo.com/play.php?id=NhNyhqyvj6Q


No, that's not it. Must be a typo....Try this one:

www.zombo.com

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Re: Loop Quantum Gravity

#117  Postby cavarka9 » Dec 04, 2011 9:49 am

Macroinvertebrate wrote:
twistor59 wrote:Loops vs strings - the debate:

http://zomobo.com/play.php?id=NhNyhqyvj6Q


No, that's not it. Must be a typo....Try this one:

http://www.zombo.com

:cheers:

Macroinvertebrate wrote:
twistor59 wrote:Loops vs strings - the debate:

http://zomobo.com/play.php?id=NhNyhqyvj6Q


No, that's not it. Must be a typo....Try this one:

http://www.zombo.com

:cheers:

:lol: :grin:
nice, very nice.

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Re: Loop Quantum Gravity

#118  Postby OnCue » Dec 16, 2011 4:23 am

twistor59 wrote:Anybody know how it works ?

Well I didn't until I posted this http://www.rationalskepticism.org/mathematics/physical-discontinuity-and-calculating-the-smallest-volume-t27829.html on the math Forum. Teuton gave a great reference.

"According to loop quantum gravity, space is made of discrete atoms each of which carries a very tiny unit of volume. … One consequence of this is that there is a smallest possible volume. This minimum volume is miniscule – about 1099 of them would fit into a thimble. If you tried to halve a region of this volume, the result would not be two regions each with half that volume. Instead, the process would create two new regions which together would have more volume than you started with. We describe this by saying that the attempt to measure a unit of volume smaller than the minimal size alters the geometry of the space in a way that allows more volume to be created."

(Smolin, Lee. Three Roads to Quantum Gravity. New York: Basic Books, 2001. p. 106)"
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Re: Loop Quantum Gravity

#119  Postby DavidMcC » 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.
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Re: Loop Quantum Gravity

#120  Postby twistor59 » Feb 20, 2012 8:12 pm

DavidMcC wrote: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)


AFAIK most of the people who would describe their work as LQG these days are working with spin networks/spin foams. Transport around the closed paths formed by the nodes is the equivalent of the old loops. These objects are fundamental entities in the theory, and pieces of them represent "grains of space". The connectivity of the network tells you which grains of space are near to each other. The quantum states are given by wavefunctions on the possible spin networks and describe superpositions of possible spacetimes. For some superpositions which have particular properties (they're coherent states), the spacetime you get from sewing the grains of space together starts to look like a classical spacetime we can see.

I'm not sure exactly what you mean by "hyperspace continuum" it sounds a bit like the kinetic Hilbert space I was talking about here

DavidMcC wrote:
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.


Why should our big bang cosmos need anywhere to expand into ?

DavidMcC wrote:
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.


I don't know the program you're referring to, but I'm sure Hawking knows the difference between proper time and coordinate time. The only "no god required" argument I've heard from him is related to his idea that the universe has no past boundary and hence no need for a moment of creation.

DavidMcC wrote:
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.


I'm not familiar with gravastars so unfortunately that's over my head. :scratch:
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