Thanks so much Stefan!

I had already planned to finish my first read through of your essay shortly, but there was a comment here and I found it was your enthusiastic message above. I am very glad you got something out of my essay and thought I presented my ideas well. There is plenty of interesting material to read this year, but I am happy I made your stop here a pleasant one.

All the Best,

Jonathan

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  • Post #63

Dear Jonathan,

you really earned this appreciation. Your knowledge of the relevant issues in physics is that broad and you did contemplate all of it. Thanks for having lead me to your essay!

Best wishes,

Stefan

I finally got my voting code, which I did not receive with the acceptance. I will try to reread your paper in the near future.

I indicated to Giovanni Amelino-Camelia the κ-Minkowski and his boost operator should have some connection to twistor theory. The boost operator P_μ that acts on [x_i, x_0] = ilx_i such that

P_μ > [x_i, x_0] = il P_μ > x_i

The coordinates (x_j, x_0) we write in spinor form

x_j = σ_j^{aa'}ω_{aa'}

x_0 = σ_0^{aa'}ω_{aa'},

where ω_{aa'} = ξ_a ω_{a'} ξ_{a'}ω_a. This commutator has the form

[x_i, x_0] = σ_j^{aa'}σ_0^{bb'}[ω_{aa'}, ω_{bb'}]

= iC^{cc'}_{aa'bb'} σ_j^{aa'} σ_0^{bb'} ω_{aa'}

= i|C| σ_j^{aa'}ω_{aa'}

where the magnitude of the structure matrix is |C| = l. In general this may be written for

x_j = σ_j^{aa'}ω_{aa'}

x_0 = σ_0^{aa'}ω_{aa'} iq_{aa'}π^{aa'},

where the commutator [ω_{aa'}, π^{bb'}] = iδ_a^bδ_{a'}^{b'} and the general form of the commutator is then

[x_i, x_0] = i|C| σ_j^{aa'}ω_{aa'} iσ_j^{aa'}q_{bb'}[ω_{aa'}, π^{bb''}

[x_i, x_0] = ilσ_j^{aa'}ω_{aa'} - σ_j^{aa'}q_{aa'}.

The boost operation B = 1 a^l_jP^j on the commutator [x_i, x_0] is then equivalent to the commutation between spinors [ω_a, ω'_b] for ω'_b = ω_b iq_{bb'}π^{b'},

[ω_a, ω'_b] = [ω_a, ω_b] iq_{bb'}[ω_a , π^{b'}]

= C^c_{ab} ω_c iq_{ab}.

Ed Witten demonstrated a "twistor revolution" in string theory. If this connection exists and can be explored further, it might mean that loop variables and other discrete quantum gravity ideas might bridge with string theory. It could then be that the two approaches will fix the various difficulties they have.

Cheers LC

Cheers

Hello Jonathan,

I've returned from holday and reread your essay, enjoyed it very much. Thinking about how we think and progress can be very helpful, and the points about child psychology were interesting. You mention that in cosmology there are sometimes a number of different explanations for the same data, rather than just one. This is similar to a point I make in my essay about how physics is full of equivalence - often more than one conceptual picture is described by the same mathematics.

What I think is sometimes overlooked is a distinction between the conceptual side of physics and the mathematical side - I see this as very helpful in the present situation. The conceptual side has been given too little emphasis for half a century, because the two main theories were very hard to interpret. So interpretations were somewhat devalued, and the focus went to the mathematical side. But if there are missing pieces of the puzzle, and if they're conceptual pieces as I've argued, then there may be a need to find them before we can make real progress. If so, instead of resifting our view of what we know already, and how we look at what we know - which some of your essay seems to cover - there should be a definite search for missing conceptual ideas. The solution to a puzzle is sometimes comparatively simple, once new conceptual elements are found. And without them we might make little progress.

In the questions about time, which may well need a solution before we can get to quantum gravity, it's quite easy to show that there are probably missing conceptual pieces - our present ideas about time do not between them cover enough area to fill the gaps in the picture. So I'd say there's an need to focus much more specifically on the conceptual clues we have. People looking for new ideas often ignore them. Perhaps they're ignored because we tend to assume they can't be interpreted, and would have been already if they could be. But also, the existing view we have makes these clues look like they might be unreal, and part of an illusion. I'd say in analysing how we think about physics, that side of things should be remembered. Anyway, good luck with everything,

Best wishes, Jonathan

    Indeed Lawrence,

    The 'twistor revolution' in string theory is the most important breakthrough for either twistors or strings in years. It as though String Theory has seen a lot of cloud to cloud lightning, but was stuck in the clouds having no clear path to ground. But Twistor theory provides 'leaders' from ground to air - so the air to ground lightning can connect. This explains a lot of the action we've seen with Nima Arkani-Hamed and his colleagues' work exploiting S-matrix dualities.

    But the larger issues of emergent spacetime and building bridges allowing us to redefine loop variables and other causal elements that arise when considering Quantum Gravity need considerable work, at this point. It remains promising but, as I state in my essay, I think the Octonions also offer a natural approach to spacetime evolution. I thank you for the analysis of important terms in the above comments; unfortunately, I still have not read Giovanni's essay - so I have to trace these references back once I do.

    all the best,

    Jonathan

    Wow Jonathan!

    You hit the nail on the head, that conceptual models are somewhat lacking and should always inform our Math in Physics. In my research, I have encountered plenty of examples of the opposite - things which arise from pure Math that appear to have connections to, or applications in, Physics.

    But without a clear conceptual model, these mathematical explorations have no connection back to the real world. There is always room for more than one conceptual model in my perception of the universe. As you point out, several conceptual representations can express the same Physics, or be coded by the same equations.

    But modern adults tend to forget what children know intuitively. One Cognitive Science researcher I cite, Alison Gopnik, refers to this as the "Lantern vs Searchlight" phenomenon. While children shine their lamp here and there, in search of knowledge, adults say let's shine a LIGHT on it, in a narrowly focused way. Sadly, this cancels out a lot of healthy exploration.

    all the best,

    Jonathan

    Hi,

    Well as you say, an approach of general enquiry is good, rather than with too many presumptions. But I also don't mind shining a light in a particular direction, because I think there are specific clues to be examined on the conceptual side.

    I think we forget how much conceptual progress can simplify the picture. Within the mathematics, people tend to say, well we haven't found any simple answers, so let's look for more complicated ones. To me there's a bit of that in your idea that the dimensionality of the universe is evolving. It's true that at present our theories disagree on the dimensionality of the universe, but I suspect that with conceptual progress, we might find it doesn't have to be as complicated as an evolving picture. That's my opinion - the simplicity of some of the mathematics suggests it. Anyway, let me know if you have any thoughts on my essay, I'd be grateful to hear them.

    Best wishes, Jonathan

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    • Post #69

    Hello to both of you,

    I beleive that Mr Witten has very relevant ideas. The strings are a good idea for the computing.Intersting also for our extrapolations. But and there is always a but :)it is not sufficient. It lacks the quantization of this gravitation. My equations and my theory helps. I beleive that the convergences can be very relevant with a correct projective geometrization spherization. The domains when we speak about our pure realism must be taken with the biggest determinism. If we want to simulate correctly the Universe for example, the 3D is essential and the spheres also and the rotations also and the volumes also. It is so evident. I find very relevant the fact that we can quantize this mass, the SR and the GR are harmonized. It was time no? :) The strings so can be correlated with the rotations proportional with mass.

    The space time evolution is a system which needs spheres and rotations and volumes.It permits to have the correct simulations of evolution.The entropy increases due to this evolution. The quanternions and octonions are mathematical tools. That is all. My spheres, them are real. I ask me if it is possible to create a 3D holographic sphere and after we insert the spheres inside. I beleive that it is possible to simulate this space time evolution correctly in 3D. with a real holographic sphere. We could change the parameters and variables.We could insert the duration and the volumes more the spinal speed and orbital speed.We could insert all the elements and their rules. If we differenciate the fermions and the bosons with two sense of rot.So it is relevant for the understanding of the light and its linearity. The volumes of cosmological spheres more the volumes of quantum spheres become relevant. I discussed with Dr Corda about the singularities. I Beleive strongly that the space can be inserted in this 3D holographic sphere with the same line of reasoning. It is intriguing to see that the space and the light and the mass are the same in fact. The lattices between spheres so become a key for the two scales.

    Mr Witten can perhaps create this 3D holographic Universal sphere.The universal sphere can be made in 3D in fact.It is a little if I said that we can create our card of the sky really. The beauty of sciences is to discover our universal sphere and its secrets.And the 3D is essential for our contemplations of creations.

    Regards

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    • Post #70

    Johnatan

    In my essay i catch new sense of Planck mass

    See http://fqxi.org/community/forum/topic/1413

    My conjecture: There are Base Fermion and Base Boson of the Universe. Value of Planck mass is Geometric Mean of Values Mass of Proton(Neutron) and Mass of Hawking Black hole

    Base Fermion is proton(neutron) ;Mpr=10^-24 g

    Base Boson is Hawking primordial black hole ;Mhbl=10^16 g

    Mpl=sqrt(Mpr x Mhbl)=10^-4g

    Rounding values.

      Thanks Yuri,

      That sounds interesting. A new way to define the Planck mass? I'll be sure to check that out. I hope you enjoyed my essay, or will check it out too.

      all the best,

      Jonathan

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      • Post #72

      Second law of thermodinamics is major barrier for confirmation cyclic universe.

      I try get help from Dirac.

      See my essay http://fqxi.org/community/forum/topic/1413#addPost

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      • Post #73

      The second law of thermodynamics is *not* a barrier to a cyclical universe, IF (and very probably only if) the effective number of dimensions available to radiative degrees of freedom changes. This is because the *definition* of entropy is dependent upon the number of dimensions in which it is calculated. This generally does not occur for real, but there are scenarios in GR where this could occur. In section 3 of my STUFT paper this dimensional dependence of entropy is applied to a simple toy model of a black hole, and I easily derive the form of the thermodynamic temperature and Hawking entropy of a black hole without touching quantum theory.

      In a closed cycle that crosses a change in the number of dimensions there will exist an entropy anamoly because it's definition changes. This would be true for a closed cycle of mass falling into a black hole and being emitted as radiation - the apparent 'information paradox' of a black hole is very possibly an example of such an anamoly. A cyclical universe where some subset of dimensions compactified would also display a similar entropy anamoly - this is capable of giving a cyclical universe without violating the second law. Yes ... really! (it is fairly simple to check). Dimensional reduction is rather odd and has some unexpected effects - the definitions of physical quantities changing on you is one of them.

      Michael

      Perhaps not the only way,

      But dimensional reduction does open up some interesting possibilities. Researchers thought 2-d gravity was a dead end, until they figured out the scenario can still admit topology. That was a game changer.

      The big deal for me is that adding or reducing a dimension gives you a different perspective on where you are now. Being in a 3-d space lets us see the whole circle on a 2-d page, a perspective we would not have from anywhere on the paper. But the reverse is apparently also true.

      all the best,

      Jonathan

      Thank you Michael,

      Your statement is precisely correct.

      He is right Yuri,

      So long as the dimensionality of space is mutable, any number of cyclical scenarios are possible. A dimension change can be seen as a spontaneously broken physical symmetry, in this context. In one theory; I am exploring the possibility that decoupling was just such an event. In that scenario; there was a change in the dimension of space, during decoupling, which turned the fabric of space inside out - a condition I describe in my essay.

      In a paper I published with Ray Munroe; we discuss ways that entropy might 'push' the universe toward a particular dimensionality. But at that point; I had not considered how paralellization might influence that. I'm now inclined to believe that this property is a game changer, but I will wait to say what this means.

      all the best,

      Jonathan

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      • Post #77

      Jonathan,

      On your point about measuring rods and size is relative, the compactification of dimensions can give a significant example of this point. This is certainly the case in my model where there is a compactification-inflation see-saw between a spatial S3 universe and S7 particle gauge dimensions. As you say, size is relative which is why in GR the radial scale factor R of the universe is not physically defined as measurable. Extending GR to more dimensions doesn't make this go away. My S3 universe has the same radial scale factor R as normal GR, but the S7 dimensions has its own radial scale factor X. Neither R or X are definable in a measurable way, but one can be measured in terms of the other, i.e. R/X is a physically measurable quantity. This means that every physical scale is effectively measured in units of X, including the scale of the compactified dimensions, which gives X/X=1 and the artifical impression that the compactified dimensions are of a fized size! This would mean that the Kaluza-Klein condition of fixed scale compactified dimensions is highly misleading. This is what many physicists seem to object to about KK and compactified dimensions (I certainly used to) because the fixed scale seems artifical - and actually it is! The dimensional scale can be fixed in physically measurable terms and yet be varying in absolute terms ... except in GR all size is relative and so no absolute view exists.

      A simple analogy of this measuring rod effect is given by a mass bouncing up and down on a piece of elastic but using the elastic to measure the length of itself - the measured length would be constant, giving the artifical impression that nothing is happening. This would correspond to a total energy view of the bouncing mass - which is constant - and the same sort of measuring rod effect with compactified dimensions would also give a distorted energy view as well. In addition, the definition of energy in GR is not fixed for a time dependent metric, such as that of an expanding universe.

      So with the dimensional dependence of the definition of entropy as well, our set of measuring rods will be subject to highly significant changes with the compactification of dimensions. Not taking these measuring rod effects into account will give a highly misleading view of the universe.

      Michael

        Thank you Michael, for the insights and clarification;

        The see-saw effect you describe above is one of the things I like best about your theory. The shrinking of one figure becomes the growth in another, because they share the same topological boundary. In many ways, topology drives the shape and geometry of space to evolve into what it has become. But looking straight at the fabric (or topological surface) gives us a clearer picture of what the space is doing.

        We are used to having an environment full of objects with a well-defined size. The concept of size would be meaningless, in any given space, unless there were objects in that space to define a relativity of large and small. Nor can a single observation or measurement give you the full picture, as perspective makes closer objects look larger. But the same objects seen from enough different perspectives will give a more well-rounded outlook of relative scale.

        all the best,

        Jonathan

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        • Post #79

        Dimensional reduction put into question the existence of the Planck length and Planck time, but don't touch Plank mass.See my essay in 1413

        Jonathan, I posted a new paper entitled "Gravity in an expanding universe". It may help overcome reluctance to accept my essay's derivation of the gravitational constant. By the way, I am back in our Monterey, Ca house.