Unitarity, Locality and Spacetime Geometry: Foundations That Are Not Foundations by Lawrence B Crowell

Hi Lawrence,

I get the feeling I understood more of this essay than last years. So it is, I think, more accessible. (I made two separate attempts.) The history was interesting. I understood a chunk of problems you pointed and the reasons for then considering each in turn, though not the mathematical explanations themselves. My own failing I know. It is probably straightforward to those with the necessary familiarity with mathematics.

As I rarely understand much of what you write I think we have both done rather well with this essay. I wish I was able to give more positive feedback. I hope you get lots of informed readers who will be able to properly understand and talk to you about the essays content, which is probably far more fascinating than I can appreciate. Good luck in the competition.

Hi Lawrence:

I enjoyed reading your paper, especially the discussion related to the widely known "Foundations that are not Foundations."

The fundamental question is how to determine what is the most fundamental reality or physical process that governs the Foundation of the universe. I demonstrate in my posted paper -" From Absurd to Elegant Universe" that current crisis in physics and cosmology as evidenced by the well-known paradoxes and singularities are artifacts of the missing Foundation of the fundamental physics of the spontaneous decay and birth of particles. Hence, many of the so-called foundational assumptions or phenomena are shown to be artifacts rather than foundation of the universe or a universal theory. When this missing foundational physics is counted in, it not only successfully predicts the observed accelerated expansion of the universe and galactic star velocities but also resolves paradoxes and singularities of the Cosmic Conundrum today. It also provides understanding of the inner working foundations of quantum mechanics.

I would greatly appreciate it if you could please review my paper and provide your comments.

Thanking you in advance,

Best Regards

Avtar Singh

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

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.

I become completely crazy you know Lawrence. My parano is important. I cannot stop you know.

ps think about the finite groups and the serie of uniqueness.

Regards

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.

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