These vague ideas help point in certain directions but my focus is on ways in which purely algebraic structures can lead to geometric ones. It would be nice to have an answer in my lifetime so I will happily accept the hypothesis that multiple quantisation solves the path integral over the grand ensemble of theories and see where I can go with that.

I like the group field theory approach to forming spin metworks because it gives a manifold from an group by a process of quantisation. It has to be extended to higher dimensions and to manifolds with matter content too. That is not going to be a simple generalisation.

The information angle seems to have some baring on this. The relation between redundancy of information and redundancy in gauge theories seems useful and perhaps your ideas about information transfer also relate to something algebraic such as invariants as you mentioned.

I am not looking for something 3D or 4D specifically. I prefer to explore theories in any number of dimensions. I will look at the framework of field theories and worry about real physics later. The geometric process of dimensional reduction by compactification (Kaluza-Klein) would be related to taking an algebraic structure modulo some relations so it is a very natural process from an algebraic point of view and it enriches the physics on the geometric side.

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  • Post #22

Jochen

"I'm somewhat puzzled, since in your previous reply you said: "The actual spatial location of the rainbow does not alter.", which appears to presuppose there is such a thing...

Yes, because the next sentence was: "Its relative spatial location does, obviously, because its actual spatial location is being expressed with respect to a different spatial location." And then another sentence is (in the next post, but something similar I said after that sentence without the caveat): "We cannot know the absolute position of anything. Only its relative spatial position with respect to anything within our existentially closed system".

Absolute refers to where (and indeed what, etc) it might 'really' be. Which we cannot know, or to be more precise, we can never know that what we do know is the 'absolute' truth, because there is always the possibility of an alternative. So this is irrelevant. The corollary being that we can know a definite something, ie the form of existence potentially knowable to us. And within that closed system the rainbow, or indeed anything else, exists independently of us in a specific spatial location. But we can only calibrate that, because we cannot externalise ourselves from the closed system, by comparison and the identification of difference, ie its relative special position with respect to something else.

It's all about context. And science is not in the context of every possibility we can conceive and believe in, it is supposed to be considering what is potentially knowable, which is underpinned by a physical process.

"Regarding the position of the rainbow with respect to both observers, I again don't think there is such a thing: each observer observes the rainbow in a different position"

Of course there is. The rainbow and observers are all independently physically existent entities. They therefore have, by existing, a definitive spatial location. We just do not know where 'exactly' it is. Only where it is with respect to something else. Is is the observers who are in different spatial relationships vis a vis the rainbow, not the rainbow which is 'altering' position.

Re your last paragraph. Observation and existence are different. Observation involves the receipt of a physically existent representation of the existential sequence (in sight this is light). Light travels, which takes time. So the timing of the receipt of that representation (ie which is not the reality anyway) is different, and after a delay, from the timing of the actual occurrence. This is where Einstein went wrong, because he had no observation, he conflated occurrence and observation (note his in the "immediate proximity" caveat 1905 Part 1), as he had no observational light (just a ray, or lightening, etc). Just a constant in order to calibrate distance and duration, which happened to be an example of light. It could have been anything. This error was counterbalanced by his failure to understand the reference for timing, because he followed Poincaré's flawed concept of simultaneity. In short: he shifted the real timing differential from the receipt of light, which fundamentally is a function of spatial relationship, to deeming it to be a characteristic of reality (ie relativity). Which is what you are doing with the rainbow. The fact that physical existence can only occur as a sequence, one state at a time, is a supplementary point(!).

Paul

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  • Post #23

Guys

There can be nothing, vague, chaotic, uncertain, etc, etc about physical existence. In order to be existent (as we can know it, and this is science, not religion) there must be something in a physical state (what, why, etc, is for you lot to discover, I just do the easy bit!). And in order for it to occur in different states, there must be a physical cause which results in that different state. One state, the next different state, something caused that difference. It is all explainable, if we could 'bottom it out'.

The issue is about our ability to identify that, and not make up rules about how reality occurs in order to cover over our deficiencies.

When I was young (not that I'm that old) TV was quite new. Every now and then a message would show up saying: please do not adjust your sets we are having problems with the transmission.

Paul

But consider how a rainbow works: light from the sun is refracted and retroreflected in a rain drop; if it is incident on, say, an observer's retina, this creates a virtual image, which we call the rainbow. But this is not anywhere in the world: there is no physical object that conforms to the rainbow at any point in space. How then there should be some absolute location to the rainbow seems wholly unclear to me. At best, you could argue that there's a set of rain drops, each of which contributes one 'pixel' to the image of the rainbow; but even this set will be different for different observers.

And I hear your point that observation and existence are different; in a sense, that's what I'm all about: everything we know and can make contact with (though precisely how is a problem in itself) is observation. Hence, I try to only consider observation, making no statement about 'what really exists'. Of course, this is also exactly what Einstein did, asking himself what the world would look like if he rode on a rainbow, etc. (and the functioning of my GPS confirms to me daily the correctness of his conclusions, at least in so far as there is any correctness in science).

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  • Post #25

Hi Jochen,

Very Interesting essay!

You wrote at the end of 4:

"In many worlds, both `the electron spin is up' and `the electron spin is down' are true; in the

relative-facts setting, only `the spin of the electron is (up/down) relative to the measurement

apparatus recording (up/down)' is true. A universe of relative facts is not a multiverse!"

I think there is one possibility that a universe of relative facts is a multiverse,

The possibility that the Big Bang produced fully symmetric and entangled anti-copy universes.

Then, there is at least one Charge Parity symmetrical anti-universe ( a mirror world) with equal time because all clocks over there are running (spinning) only in the opposite direction.

To make this a bit more redundant and symmetric, I propose that we live inside a 12 lobed dodecahedron raspberry shaped symmetric multiverse.

However then GOD PLAYS DICE with 12 entangled CP symmetric pinball machines where each pinball is instant connected to its anti-copy living in that other universe.

Perhaps we are even able to measure the number of these raspberry lobes if we are able to observe a definite number of neighbouring lobes in the CBradiation pattern, or even by repeating the well known Benjamin Libet experiments on reaction times and preplanning thoughts ( RPs) of test persons.

See attachments

Leo Vuyk.

http://vixra.org/author/leo_vuykAttachment #1: B.Libet_Preplanning_vs_Free_Will..jpg

    Philip, I generally try to keep as minimal as possible---so since three dimensions are all we can currently observe, that's what I'm trying to figure out (actually, that's not quite true---I'm fascinated by the apparent connection between the division algebras and the forces of the Standard Model, and in as much as the higher division algebras, the quaternions and octonions, are much more naturally connected to six- and ten-dimensional spacetime respectively, I've done a bit of thinking in that direction, too).

    I'm not very familiar with the group field theory approach, but I'd think that as far as getting geometry from algebra goes, noncommutative geometry has some interesting things to say (and of course, with my penchant for the division algebras, the recent foray into nonassociative geometry by Farnsworth and Boyle immediately caught my eye at least). About getting higher dimensions from GFT, with the close connection to spin networks, is that even possible? Generally, I thought that loop variables really only live in 4d space (though I've caught some papers by I think Thiemann generalizing them to higher dimensions out of the corner of my eye). But that stuff really is a bit out of my reach.

    Perhaps one comment about algebraically reducing the dimension to the observed 4: in an approach based on octonions, you'd naturally have the group SL(2,O) for spacetime symmetries, which is isomorphic to SO(9,1), i.e. the ten-d Lorentz group. Now it's always struck me as a curious (and perhaps deep) fact that if you 'fix' one of the imaginary octonions, you not only 'break' the automorphism group from G2 down to SU(3), but also SL(2,O) to SL(2,C), which is of course isomorphic to SO(3,1) (I think I probably got this from Baez). So we get the symmetries of spacetime as we know and love them, and the gauge group of the strong force. Now this maybe something like the large numbers (you mentioned them in the other thread): a cute coincidence that leads all too easily to premature conclusions. But I can't help wondering...

    -------------------

    Paul, to you, it seems to be axiomatic that there must be some underlying, fixed physical reality; however, our best theories appear to be telling us that this is not the case. Now, this as you rightly say is not sufficient grounds to abandon this assumption: however, these theories are, and continue to be, tested to greater precision than anything ever before. It is these experimental observations that are ultimately in conflict with the assumption of a fixed reality; every theory that should supersede quantum mechanics will include nonlocality and contextuality just as much, or else be experimentally not viable.

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    • Post #28

    Hi Leo, thanks for your comments and for finding my essay interesting. You make great leaps and bounds in your reply, and I'm unable to follow you at that speed (I've always been a bit of a slow one), so I'm not sure I can cogently reply to them... In general, I'm not a particular fan of multiverses: in particular, I have never seen the term 'universe' defined well enough in order to judge whether there's one or more of them around. It might sound facetious, but, you and me, are we in the same universe? There's things that definitely exist in your universe, but not in mine: your thoughts, feelings, experiences, etc. Furthermore, you have been influenced by events that I have not yet come in causal contact with, i.e. our past lightcones do not overlap---our celestial spheres differ. Then, you experience everything in the world from your unique vintage point---an experience I never could share.

    So in the end, what makes a universe? I couldn't claim to know. And much less so in the case of any supposed multiverses.

    Just posting to say that the above was me---I must've gotten logged out somehow.

    Jochen, you have a good collection of references at your fingertips. I had not seen the non-associative geometry development. There are connections between necklace Lie algebras and non-commutative geometry http://arxiv.org/abs/math/0010030 but I am not chasing that angle. The division algebras are also interesting. The relationships to dimensions are important and probably part of a bigger picture, but I am skeptical about connections to the low energy gauge groups. I think if we knew how much physics there was between 1 TeV and the Planck scale we would laugh at the idea.

    With all these interconnected threads the trick will be to find which part is the key concept after which everything else will fall into place. The combinatorial necklaces that are associated with Lyndon words are also related to irreducible polynomials over finite fields which are in turn related to cyclic linear codes and exceptional structures such as division algebras, exceptional groups and lattices. My goal is therefore to understand the Necklace Lie algebras first and then see how these exceptional structures appear within them and how that relates to special properties of different dimensions. Of course the whole program is ambitious and I have no idea if I know enough mathematics to make any progress even assuming there is really something to discover, but it is all fun to think about.

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    • Post #31

    Thank you Jochen,

    i realize that my proposals for the idea of a Big bang symmetry and that you and I are dealing with one or more other you's and I's living in an anti matter universe coupled by instant entanglement is too much to grasp.

    sorry.

    Jochen

    How the rainbow works, and that it just happens to involve light, is irrelevant. It is a physically existent entity. This argument has the structure of Einstein where there is always some form of light, but it is actually just a constant, which happens to be light (eg lightening on his train). Indeed, this always happens. Turn to Cox & Forshaw, a good explanation of the argument, and there we have a clock that is a light beam. The light entity is a constant against which to calibrate duration and distance, not observational light.

    Whatever the entity, to observe it involves an interaction between it as the existent sequence progresses, and something else, which creates a physically existent entity that is representational of it, ie observational light. This then travels, and some of it interacts with eyes.

    Put another way, the rainbow is not inside people's heads. As you then say, because it is to do with water and light.

    "everything we know and can make contact with (though precisely how is a problem in itself) is observation"

    No. Everything we could potentially know is determined by all the sensing systems of all sentient organisms. Which would include an alien if he/she landed here and explained a new sensory system to us. And that encompasses hypothesising so long as it is effected in accordance with the operational rules of the sensory system it is supplementing. Because, obviously, not everything can be sensed directly, therefore it is perfectly legitimate to establish what could have been so had some identifiable problem not prevented it. But this does not involve belief, which is the assertion of reality on the basis of no experienceability whatsoever. In other words, physical existence is whatever we can potentially know as enabled by the physical processes (which are part of physical existence) which feed the sensory systems, or hypothetical equivalents.

    "Hence, I try to only consider observation, making no statement about 'what really exists'."

    Indeed. But leaving aside the point that it is more than just observation, direct or indirect, if you do not start with the premise which corresponds to the form of existence we can know, then you are likely to be considering alternatives (ie what possibly really exists), albeit inadvertently. It is considered intellectually correct to presume physical existence as an abstract concept, ie presume nothing. But it is not abstract, generically it has a definitive form and modus operandi.

    Einstein did not do this, please find me an example of actual observation, ie where there is observational light and it is being received. You can't. In the AB example it is a ray of light, in the train there is another ray of light (which takes the place of the man walking-which it does not) and there is lightening.

    To try and settle the Einstein 'angle', I will post on my essay site the first 24 paras of another paper. This is only 4 pages and is easy to read, it gets slightly more complex after that.

    Paul

    Jochen

    "so since three dimensions are all we can currently observe"

    Although this is not really a function of the way observation works, as you are hinting here, the issue is how many dimensions are there in physical reality.

    In establishing what constitutes dimension, distance and space in our reality, we are using a reference which conceives of any given physical reality being 'divided' into a grid of spatial positions. And in order to 'locate' that conceptual grid it is associated with one physical entity. Any constituent physically existent states of that physical reality have definitive dimension/size/shape (ie spatial footprint), which can be defined as spatial positions 'occupied' on the grid at the given time of existence.

    'Mapping' other states that were existent at the same given time, would reveal not only both the spatial footprint of those states and their comparability with each other, but also, distance. Which is usually measured between the two nearest dimensions of the existent states, but could include any combination of dimensions. And depending on the spatial relationship of the states involved, distance could involve a relationship in terms of separation of the states, or one within another, that again being with respect to specified dimensions.

    Dimension is a specific aspect of spatial footprint, relating to the distance along any possible axis of that 'occupation'. So, three is the minimum number of spatial dimensions that is ontologically correct at the highest level of conceptualisation of any given physical reality (ie up/down, side/side, back/forth). But is not what is physically existent. At that existential level, the number of possible dimensions is half the number of possible directions that the smallest substance in physical existence could travel from any single spatial point.

    Paul

    Jochen

    "Paul, to you, it seems to be axiomatic that there must be some underlying, fixed physical reality..."

    Science is concerned with that form of existence which we can potentially know, not alternative we can believe in. Knowing is underpinned by a physical process. Based on input received, we can identify that the form of physical existence we can know has two fundamental characteristics:

    -what occurs, does so, independently of the processes which detect it

    -it involves difference, ie comparison of inputs reveals difference, and therefore that there is change/alteration.

    Therefore, the physical existence we can know must be existential sequence. The entirety of whatever comprises it can only exist within that sequence in one definitive physically existent state at a time, as the predecessor must cease to exist so that the successor can exist. To be physically existent, by definition, entails no form of change or indefiniteness in whatever is existent at any given time. And so physical existence is a spatial phenomenon, which occurs differently over time.

    Look at the bush in your garden. Over time it manifest different, colour, size, leaves/no leaves, etc. These different physically existent states do not co-exist. The same principle applies if we drill down to what physically constitutes 'bush'. One definitive physically existent state of whatever constitutes it at a time.

    Paul

    Regarding the rainbow, I don't think it's right to consider it as a 'physical entity'. Ultimately, the physical entities it derives from are a set of rain drops, each of which reflects light in a particular way. For each observer, this set of drops changes. There is no further independent entity that you could call the rainbow anywhere.

    In any case, you seem to have fixed your assumptions---and as you say over on Mikalai's essay thread, even if experiment disagrees with these assumptions, you would not be willing to revisit them. But this is too dogmatic for me: there's no reason for nature to be the way we'd like it to be. If it tells us via experiment that the assumption of a definite physical state for a system at all times isn't right, we have to accept that, no matter how little we might like it.

    Philip, yes, if one knows little oneself, one has to try to compensate by at least knowing where to find things. ;-) And you're right that perhaps the most reasonable assumption is not a 'great desert' from here to the Planck scale, and it's very well possible that near-future developments will completely destroy this possibility. But for the time being, there's a sort of mini-revision centered mainly around the work of Shaposhnikov and Wetterich, who in 2009 predicted the observation of a 126 GeV Higgs from the assumptions of asymptotic safety for gravity, and no new physics up to the Planck scale. Building somewhat on this, there's been the proposal of a 'nuMSM', a standard model minimally extended with massive right handed neutrinos to account for dark matter. Whether or not something comes out of this remains to be seen, but it aligns well enough with my prejudices to at least merit some attention (for me, that is). And I think I'm really going to have to look at necklace algebras (is there some canonical reference?).

    There is not really a canonical reference for Necklace Lie akgebras. If you search you may find three things, (1) references to the free lie algebra as a necklace lie algebra. This was what I described in my essay but I had to keep it short so it may not be clear (2) references to a Hopf algebra studied by Le Bruyn, Ginzburg, Bocklandt. This is a little messy and I dont read those papers much but it was seeing this that made me start calling my structures Necklace Lie Algebras because they fit the same idea. (3) comments by me referring to the algebras I defined e.g. here http://vixra.org/abs/0907.0033 The structures are quite elegant but I dont know how well I explained them. Recently I have been getting to know these things better and feel the need to write a new paper about them. The Yangian lie algebras that appear in scattering theory are also kind of similar.

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    • Post #38

    I thought a second time about your statement:

    you wrote:

    "In many worlds, both `the electron spin is up' and `the electron spin is down' are true; in the relative-facts setting, only `the spin of the electron is (up/down) relative to the measurement apparatus recording (up/down)' is true"

    However In my raspberry multiverse with until now still entangled anti-copy universes created in the Big Bang CP symmetry means that UP is UP and DOWN is DOWN in the Stern Gerlach apparatus.

    Over there the Noth is South and the electron is a positron.

    I realize that my proposal has the disadvantage of the huge distance between thse CP symmetrical universes, But untill know there NO distance boundary observed for entanglement experiments

    I would be shocked if there ever were a limiting distance discovered for entanglement---I don't want to be making any of those 'I would quit physics if'-pronouncements, since they seem to come back to haunt people, but it's close. So at least as far as I'm concerned, you're quite safe distance wise.

    Jochen

    Most things are comprised of other things.

    It is not a matter of fixed assumptions, etc. If you can explain how physical existence occurs in any other manner, please tell me. The experimentation is being interpreted on the basis of flawed presumptions.

    I have put up posts which clearly argue the points, if you can find fault with these, please do so.

    Paul