Lawrence,

Concerning singularity, I decided to add new arguments here.

Your objection against Ernst Fischer were already rejected by himself.

Anyway, I appreciate your insight that pre-mathematical assumptions are decisive.

Eckard

Fischer never really countered my argument. He indeed said there was no motion, geodesic or otherwise (which is not quite right). He used a static equation of state to show that a collapsing body (not static) does not produce a singularity. It is trivially true, but this is not the case of a collapsing body so there can't be a singuarity.

There is motion, even for a body at rest, for it is moving forwards in time. For a gravitating body in a static configuration matter is on a nongeodesic motion forwards in time.

When I get the time I will read your essay.

Cheers LC

I am going to catalyze you in live.

:) you know that I am not a fan of paradoxs.

The meiosis of a sphere, interesting.or a mitosis.interesting :)

immeasurable measures ??? Not really rational that.

You know Lawrence, I find your knowledges very relevant, but you know the aim is not to enumerate the concepts but to apply them with a pure rational and dterministic road. In fact , when there are too much pseudo convergences, so it implies an ocean of confusions.Implying an impossibility to have a true general theory.

In fact you know indeed your physics and maths.But is it sufficient for the generality. I am surprised to see how you interpret the boundaries ? You know Lawrence ,forget your chains ....and open your universal heart.

The mind of a mathematicians is the same than for physics. They must be always rational and dterminsitic.

ps you can make better :)

ps2 the unitarity, the singularity,it is these central spheres, Lawrence.

ps3 I have an idea for the serie,the fractal from the main cnetral sphere, in logic the serie is universal at all scales for the uniqueness. I ask me if the primes can help, I beleive that yes for the periodic oscillation.between 1 and x. The number of planets become relevant for our universal sphere.and we take the number 1 for the central sphere. The volumes are under this logic. The primes can help for the correct serie. It is essential to have finite groups and boundaries you know Lawrence for our quantization and our axiomatizations.If not the thermodynamics are not ok.like the proportions of our universal mecanic.

It is evident you know.

Regards and good luck, your essay is very well.

Hello to both of you,

Eckard, you know the singularity is not a mathematical infinity you know.

The serie is a finite group of spheres !!!

So the continuity is specific when we want to quantize the mass. The singularities and the singularity are inside the physicality !!!

The infinity , so the light without movement, is above our physicality. It is totally different. If this universal axiom is not respected for the quantization, so it is not possible to understand the correct necessary serie.

Furthermore the principle of equivalence is so important, and the finite groups are essential for this equivalence between mass and energy.

If not we have probelms in the calculations just because the tools have not limits and domains.

There is that said a paradox about the entropy and its maximum.My equation shows that we can add or multiplicate. But in fact this maximum is not possible to reach !Furthermore just a part is sufficient. When we fractalize this energy, it is incredibly important like energy.The mass polarises the light after all on this line time. There is so a limit of maximum.But it is pardoxal.But not for the infinite light ....so the maximum entropy, physical is not a probelm but a tool ! We could nourrish our planet with 1 water drop during the eternity....the singularity and the singularities possesse this maximum entropy.

Regards

Dear Lawrence B Crowell,

I think, without quantum physics we cannot describe the events of universe coherently, in that unitarily is imperative for its completeness. Thus the unitarily of the universe and the locality of its events are expected to have their outcomes as nonzero, in that the current scenario of dimensionality from point source is contradictory.

With best wishes,

Jayakar

    Hi Lawrence. Gravitational and inertial equivalency and balancing is fundamental to balanced and equivalent attraction and repulsion and to fundamentally stabilized and balanced distance in/of space as well. Importantly (and moreover), this fundamentally proves/demonstrates F=ma.

    And, this is all consistent with instantaneity and the fact that gravity cannot be shielded. (Obviously, the fact that gravity cannot be shielded is connected with instantaneity.) Balance and completeness.

    Your essay reflects your fine ability. I encourage you to broaden and embolden your thinking.

      Your essay proposes a way in which special relativity can be extended to global spacetime. Your results are departures from standard cosmology. I suppose I am not sure how the cosmological constant depends upon the velocity of a particle. The potential you compute in equation 5 PE = ∫Gmm*dr/r, where I presume there should be a dr in there, appears to be similar to the calculation of a moment of inertia. The redshift factor z diverges as v --- > c in a special relativistic type of theory, but this runs into trouble with luminosities.

      Cheers LC

      Hi Lawrence:

      Thanks for your replies and comments on my paper.

      Yes, the results of my paper and book - The Hidden Factor show departure from the paradoxical and inconsistent results of the Standard Cosmology. My paper shows that when the missing physics of spontaneous decay are taken into account, it cures many ills of the standard cosmology and successfully predicts the observed expansion of galaxies and the universe.

      You asked - "...... how the cosmological constant depends upon the velocity of a particle?" The cosmological constant represents the kinetic energy (velocity) of the particles residing and moving close to the speed of light within the so-called vacuum space. This kinetic energy is the mechanistic description of the mysterious dark energy still un-described by the standard model.

      In response to your comment -"The potential you compute in equation 5 PE = ∫Gmm*dr/r, where I presume there should be a dr in there, appears to be similar to the calculation of a moment of inertia", a complete derivation of the gravitational potential is provided in the attached pdf file.

      Also, responding to your comment- "The redshift factor z diverges as v --- > c in a special relativistic type of theory, but this runs into trouble with luminosities", in the GNMUE model describe in my paper and as shown in figure 3, V is never larger than C; hence the luminosity equation has no singularities or infinities.

      I hope I answered all your questions satisfactorily. I would be glad to answer any other questions or comments.

      Best Regards

      Avtar SinghAttachment #1: Gravitation_Potential_Derivation__Excerpts_from_my_book.pdf

      There is a question here concerning expansion of the universe, and a comparison with the Andromeda galaxy which is indeed moving towards our galaxy. So let us start with the basics. I will outline the understanding of cosmology as currently understood.

      Let the distance to some galaxy far away be x. I find that this distance x is changing, so I assign a scale factor a. So the time evolution of a distance x is given by

      x = x(t) = a(t)x(0)

      In this way this motion of any distant galaxy can be compared to this scale factor which expands (or contracts if that were to be the case) with the dynamics of the universe.

      Now consider the next ingredient. The energy E of a particle of mass m moving in a central gravity field by some mass M at a distance r is

      E = (1/2)mv^2 - GMm/r

      The total energy E is constant, and largely can be ignored. In particular if the universe expands so there is no recollapse we can set it to zero. We concentrate on the velocity

      v = dx/dt = x(0)(da/dt) = x(0)a', prime means time derivative,

      so that (1/2)mv^2 = (1/2)(a')^2(x(0))^2. Now concentrate on the gravity part. We set r = x, the distance to other galaxies, and we assign an average density so that the mass M is a sum of all these galactic masses M = ρVol. The volume out to some radial distance x is then Vol = (4π/3)x^3 = (4π/3)a^3(x(0))^3. We put all of this together and we get the equation

      (a'/a)^2 = 8πGρ/3.

      This equation is close to what one gets with general relativity, where here we have just used Newtonian mechanics and gravity. There is with general relativity an additional -k/a^2 factor related to the constant energy E, which for a spatially flat universe has k = 0.

      How the Hubble constant is H = (a'/a), which is a constant in space, but not necessarily in time. The Einstein cosmological constant is Λ = 8πGρ for some constant vacuum energy density ρ, and so the Hubble parameter is then

      H^2 = (a'/a)^2 = Λ/3

      For some other mass-energy density, such as matter or radiation, the density is dependent on the scale factor a.

      For those familiar with differential equations the solution to a' = sqrt{Λ/3}a is an exponential function. This is the expansion driven universe we do observe. For a small scale factor this exponential is approximately linear a' ~= (1 + sqrt{Λ/3})a which gives the Hubble relation found in the 1920s v = Hd. So for a galaxy as a distance d the Hubble parameter multiplied by that distance gives the velocity. The Hubble parameter is approximately H = 74km/sec/Mpc.

      The red shift factor z = v/c, which by the Hubble law is z = Hd/c. This is an approximation, where H should be thought of as the Hubble parameter that is constant on the spatial surface of the Hubble frame. The distance is d = c/H = 3x10^{5}km/sec/74km/sec/Mpc = 4054Mpc or 1.3x10^{10}ly. The apparent magnitude of an object is m = M + 5(log_{10}d - 1), for M the absolute magnitude and d the distance. For objects at z = 1 the Hubble distance matches the luminosity distance d = 10^{(m-M)5+1}. In fact this works out to the most distant galaxies observed out to z = 10.

      This does mean that objects are commoving with expanding space faster than light. It does turn out that we can still receive photons from them. Explaining that is for another day. The CMB limit is out to z = 1100, and the luminosity matches a distance of 46 billion light years. How this is larger than the distance conversion to 13.7 billion years is due to the dynamics of space.

      Cheers LC

      Hi Lawrence:

      Thanks for your reply.

      You have provided an alternative explanation to the observed accelerated expansion that combines Hubble expansion with expanding space. But this explanation does not address the fundamental physics missing from current theories leading to the well-known singularities, paradoxes, and inconsistencies in QM and GR.

      The critical question is why the space is expanding. The so called dark energy, which is the assumed cause, still remains allusive with regard to its fundamental mechanism. The Relativistic expansion model GNMUE described in my paper explains the observed galactic as well as universe expansion with a physical model of the spontaneous decay of mass providing the expansion energy for space thus solving the mystery of dark energy or cosmological constant. Another feature of my model is that V never exceeds C, hence relativity is never violated. Further, it resolves many paradoxes of the standard cosmology and provides understandings of the inner workings of QM. The other alternative explanations of expansion, such as yours, may solve just one problem but do not address the many ills paralyzing physics today because of the root cause missing physics at the core.

      Best Regards

      Avtar Singh

      The Britto, Cachazo, Feng, Witten (BCFW) recursion relationship is a way in which a complex scattering process can be decomposed into tree level diagrams. The picture attached describes the process

      A set of gluon momenta entering a region (we set those leaving as the negative of entering as done in the STU symmetries) may be written as the sum of products of two diagrams. To start one chooses two gluons, here the k and n lines bolded. The sum is over all cyclically ordered distributions of gluons on each sub-amplitude (one with k and the other with n mometa) and one sums further over the helicities of the internal gluon.

      To formulate this requires the use of bispinors, or what are in effect twistors. BCFW recursion is a development in Witten's "twistor revolution" in string theory. The momenta for a gluon, a null momenta as it is massless, is written as p_{aa'} = λ_aω_{a'}. This exterior product is a form of twistor, and the two spinors for the inner products (λ, λ') = ε_{ab}λ^aλ^b, [ω, ω'] = ε_{a'b'}ω^{a'}ω^{b'}. (I use parentheses because carrot signs cause trouble with this blog) There is a notation convention that one spinor type has ( ) as an inner product and the other a [ ] inner product. This is the convention that has emerged and is here to stay. If we have two momenta p_{aa'} = λ_aω_{a'} and q_{aa'} = λ'_aω'_{a'} then

      p•q = λ_aω_{a'}λ'_bω'_{b'}δ^a_bδ^{a'}_{b'}

      = = λ_aλ'_bω_{a'}ω'_{b'}δ^a_bδ^{a'}_{b'}

      = (1/2)ε^{ab}λ_aλ'_bε^{a'b'}ω_{a'}ω'_{b'} = ½(λ, λ')[ω, ω']

      A tree level amplitude A(1,2,...,n-1,n) of n cyclically ordered gluons. Each gluon has momenta p_i^{aa'} = λ_i^aω_i^{a'} corresponding to the two spinors. We pick out our two gluons of interest and define a momentum

      p_k(z) = λ_k(ω_k - zω_n},

      p_n(z) = (λ_n + zλ_k)ω_n

      which are forms of the twistor equations. The momenta of the other gluons remain unchanged p_j(z) = p_j, for j =/= k or n. This theory involves then the transformations on the two elements of the bispinor as

      ω_k --- > ω_k - zω_n

      λ_n --- > λ_n + zλ_k.

      Now examine the amplitude under this transformation

      A(z) = A(p_1, p_2, ..., p_{k-1}, p_k(z), ... p_{n-1}, p_n(z)),

      Now a complex function of z. This amplitude is on shell for all z and momenta are all conserved.

      Breaking up the "blob" into these two parts is then equivalent to writing this amplitude as

      A_k = sum_{ij}A_{j+1}(1/P_{ij}^2)A_{k - i+1}

      The momentum flowing through a tree diagram is equal to the sum of external momenta. This sum in the propagator is the sum of momenta in adjacent external lines, where here the index j stands for k and n P_{ij}(z) = p_i(z) + ...+ p_j(z) = sum j_j + p_k(z) + p_n(z). By the construction above it is clear this turns out to be independent of z. In the summation we let k lie within the range i,j and n in the range j+1 ... .

      The P_{ij}(z) = P_{ij} + z_kλ_n so the square is then P_{ij}^2(z) = P_{ij}^2 - z(λ_k|P_{ij}|ω_n], here evaluated on both pairs of spinors. Thus we have

      1/P_{ij}^2(z) = 1/(P_{ij}^2 - z(λ_k|P_{ij}|ω_n]) =

      (1/P_{ij}^2)(1/(1+z(λ_k|P_{ij}|ω_n])/P_{ij}^2)

      or as

      A(z) = sum_{ij}ρ_{ij}/(z - z_{ij}), for z_{ij} = z(λ_k|P_{ij}|ω_n]/P_{ij}^2

      This then has simple poles at z = z_{ij} where the residues ρ_{ij} are evaluated with ∫A(z)dz/z. The residues correspond to internal lines which are placed on shell.

      This then in general corresponds to the recursion relationship, where we set

      A_k = sum_{ij}sum_hA^h_{j+1}(1/P_{ij}^2)A^{-h}_{k - i+1},

      where now I have included the sum over helicity states. The recursion relationship is evident where the two terms in the numerator may be further decomposed. This procedure with P_{ij}(z) = P_{ij} + z_kλ_n evaluated at the pole reduces all off-shell processes in the "blob" on the left hand side of the diagram to an on-shell process in the evaluation of residues.

      Cheers LCAttachment #1: BCFW_recursion_rule_2.GIF

      5 days later

      Dear Lawrence,

      Congratulations for the essay. I like how you walked through the assumptions about space and time, showing how they changed in the history, and how you discussed the deformations of the foundations. I found the second part more difficult to me, so I had to reread it with more care. I really hope that unitarity and locality are not lost, but if they are, the implications you foresee are very interesting.

      Good luck with the contest,

      Cristi Stoica

        If locality and unitarity are not fundamental it means there is a huge reduction in the number of fundamental degrees of freedom in the universe. In fact if you read my paper referenced in my essay you see that the number of degrees of freedom on a brane are boost dependent, and are thus not fundamental. The huge number of elementary particles we observe in the universe are just the same type of particle under multiple copies of emergent spacetime configuration variables This means there is fundamentally only one electron, one down quark, one Z particle, one Higgs particle, one photon and so forth. We observe any of these single particles under a huge number of "projections," if you will, which are due to the emergence of configuration variables on a spatial manifold.

        I think that quantum gravity is not unitary, but that it probably conserves quantum information. The issue I raised on your essay blog with coordinate change with the singularity removed to infinity connects with this. The quantum wave functions are not unitary, but with the appearance of a pole they are meromorphic. These functions are then more fundamentally modular functions, or modular forms, which operate on lattices. These lattices are E_8 or the Leech lattice Λ_{24}, which are quantum error correction codes.

        I am not very happy with how this is turning out. First off I am not garnering the type of attention I would prefer to see. Secondly my essay is languishing at #46, where 10 to 15 of the essays ahead of mine are TOTLSHT. About an equal number I fail to see as better than mine. In fact the paper by Fischer that has been near the top is basically wrong; he uses a static matter solution (the TOV equation of state) for a dense star to prove that a collapsing body (not static mind you) does not form a singularity. Thirdly, since I had to re-edit my essay, due to the fact it went over a bit to page 10, it was later hosted but I was not given a voting code. My attempts to rectify this situation have failed.

        In the near future I will try to rattle some people's cages to see if I can get more attention, and maybe a few votes that buoy me upwards a bit. I have been rather busy and frankly a bit depressed about how this seems to be turning out.

        Cheers LC

          pay attention the dream team ahahahah wait wawwwww impressing your maths ahahah.

          they have the latex in their head ahahah Chriti, Florin, Georgina,Jonathan, Joy, Ray, Lawrence, Edwin,Mickael,Don,James, JCN,goodband they say hahahah wawww imrpessing the strategy in some years, wawwww ahahah make surf band of comics ! I have seen your real heart . Dark and vanitious and without consciouness.Ahahah pay attebntion, I don't see their play, pay attention, they superimpose the algorythms, waww they are so intelligent.

          And what after ahahaha band of comics.

          I will fight with honor, faith, universality, universal love !!!

          ahaha and Joe and Frank and alan and ted an,d friends who insists ahaha poor thinkers

          Occupied with startegies instead of studying from real innovators.ahaha ironical no,

          And what after? that is all you can make ???

          You can make better perhaps become there it was easy to find the players and easy to play also. But it is just a suggestion of course.ahahah ironical.

          Jonathan and lawrence,them make surf in california, Don, Florin and Jonathan,them are at New York, Edwin and Eckard them speak about consciousness wit James and Brendan and Johan them travel of course.And who pay for these things, still the people of course like always.Georgina prefers the prime quaternionic bridge and of course joy implies the connection. and what after , a course of maths.

          You are ironical !

          Vanity of vanities , all is vanity !