First of all, the "universe" in our neigborhood is flat, or - group theoretically - locally Lorentz SO(3,1) or ISO(3,1), Poincare, respectively. Next we have to study (possible) all geometries which are locally Minkowskian and the first decision would be, is space, or time, or space time (globally) compact or noncompact.  As SEGAL noticed, redshift and cosmic background radiation may also result from compact models. So Einsteins model could include S3xR or S3xT, T = Torus. I personally prefer a suitable noncompact version of D(3) or D(4), Cartan classification.

Is this proposal not just one possible shape of the BB model for positive curvature?

https://en.wikipedia.org/wiki/Shape_of_the_universe#Universe_with_positive_curvature

On the Evolution of Curves via a Function of

Curvature. I. The Classical Case

by BENJAMIN B. KIMIA* et al. ...

nothing found about "Shape of the universe"

Dear Anton and George:

Thanks for your answers.

My question is, if we were to assume that the geometry of motion of matter or light is limited to a 3-spherical surface; then light would travel in circular geodesics which would have, depending on the curvature, a lensing effect on the wavelength of light coming from far away galaxies (redshift).  Since this property is cited as evidence for the BB, then the BB theory could lose some support.

The same can be said about the CMB as cosmological evidence for the BB. In this case, any light coming from the other side (the antipodal hyper-hemisphere) of the 3-spherical motional surface would be diffused and could appear to us as a CMB.  In this case the CMB would be just a form of “horizon” and would say nothing about cosmological expansion.  This would also account as to why the earth appears to be at the center of the universe.

The purpose of my question is to learn if this type of reasoning has been considered by BB supporters or by those opposed.

Anton: By the way, what is SEGAL?

Regards, Bernardo.

BSV: The purpose of my question is to learn if this type of reasoning has been considered by BB supporters or by those opposed.

My previous response is that what you describe is one of the three standard possible geometries considered in the BB model. It corresponds to a positive curvature which would be the case if the energy density of the universe were slightly greater than the critical value. The 'lensing effect' would occur as you suggest but the CMB would still be from the very early universe, the time taken to reach us from the anitpodal location would be much greater than the age of the universe.

AS: nothing found about "Shape of the universe"

"Shape" is perhaps a misnomer but it is a commonly used term. See the links for example.

https://en.wikipedia.org/wiki/Shape_of_the_universe

http://map.gsfc.nasa.gov/universe/uni_shape.html

Dear George and Bernardo,

"Irving Ezra Segal ... has devoted much of his life to an axiomatic theory of spacetime, called chronometric cosmology (CC), which is generally ignored by astrophysicists". This is from: http://www-groups.dcs.st-and.ac.uk/history/Biographies/Segal.html

This "steady state" model of the universe is constructed on a compact space time, opposed to the "dynamical" BB version of the universe. On the other hand, his model is rather artificial, BB is pretty straight forward AND SIMPLE! Similar Bernardo he explains redshift and CMR as an effect of radiation emitted from "very far", however, even as a brilliant mathematician, he lacked demonstrating this by - f.i. - solving the wave equation on compact manifolds like Einsteins S³.

I can't see a problem for a decent expert on differential geometry to solve the wave equation on Sn, but I found nothing useful in the literature: The Laplacian in Rn is well known, so add the condition x12 + ... + xn2 = 1. 

On the other hand Sn is a metric space (spherical metric, VERY well known). It should be possible to show, that a fixed length - the phase: (kx - µt) - becomes extended by moving towards an observer. 

This spherical Einstein model is locally Euclidean (flat). My model - elliptic space - is locally spherical or Einsteinian. Space time is as a consequence double elliptic, the symmetry group is SO(4,4), the automorphism group of the pseudo-octonians. Causality is given by further (like Segal) assuming, that "time" is presented by the universal cover of the torus, which is R.

George and Anton:

If we define the Universe as that which is composed of all matter/energy and its motion, then we can discuss the motional geometry of matter/energy and therefore also discuss the motional geometry of the Universe.  In this sense, the Universe has geometry and therefore a “shape”.

I take issue at assigning some kind of “fabric” to the void and then giving it properties such as, inflation, curvature, etc., as in Einstein/Minkowsky spacetime with a BB.

If we stick to matter/energy and its motion we can then discuss the geometry of its trajectories.  That’s what I mean by the motional geometry of matter.

Having said that, my task is to determine if it’s possible that the cosmological evidence that appears to support the BB, can be explained by 3-sphere motional geometry only, without a BB.

So far, I have been able to explain de Broglie waves, the isotropy of the speed of light, Special Relativity, kinetic energy as rotational energy and other physical concepts in terms of Information Theory and Digital Signal Processing techniques that imply a 3-sphere motional geometry of matter.  Obviously, the BB does not fit in.

I’m not a mathematician and thus not well versed in spherical geometry.  As you can see, it would be of great help if you could lead me in the right direction, if possible, in my attempt to explain BB cosmological evidence in terms of 3-sphere geometry alone.

Regards, Bernardo.

BSV: I take issue at assigning some kind of “fabric” to the void and then giving it properties such as, inflation, curvature, etc., as in Einstein/Minkowsky spacetime with a BB.

Many scientists would agree that seeing spacetime as a "fabric" is to misunderstand GR.

BSV: If we stick to matter/energy and its motion we can then discuss the geometry of its trajectories.

Start with a simple example. Three small test particles, A, B and C, of negligible mass are sitting in deep space, not moving. We measure the distances A-B and B-C finding them to be 3km and 4km. We measure the angle ABC and find it is 90 degrees. I think the Pythagorean Theorem will apply and I predict that the distance A-C is 5km.

Is that a legitimate prediction given the specific circumstances?

If so, does it imply that the vacuum has the property of obeying Euclidean geometry or if not, how can I justify making any prediction of the distance A-C?

If we accept that the vacuum should obey some rules of geometry, is it not the correct scientific approach to determine which rules apply by experiment and observation?

Just to be clear, I have assumed Euclidean geometry above only to illustrate the philosophical argument that some geometry should be applicable, not which geometry.

To all:

George: In your three point scenario (A,B,C) in the vacuum,  if matter did not exist at each point, there could be no measurement, therefore the Pythagorean relation is a property of matter’s position, not of the vacuum.

Two of the fundamental properties of matter are position and displacement (motion) and these two properties alone can combine to form geometry, but that geometry is a property of the configuration of matter not of the void.  That particular geometry is what I refer to when I discuss the motional geometry of matter.

What I have found is that de Broglie waves, the isotropy of the speed of light, relativistic motion and the kinetic energy of particles are possible experimental evidence that the motion of matter, in general, is restricted to a 3-spherical geometry, as follows:

• De Broglie wave.  As the equivalent wave (wavicle) formed by the trajectory of a point particle constrained to a geodesic of S3.
• Isotropy of the speed of light.  Evidence of the positive circular curvature of the motional geometry of matter.
• Relativistic motion. As a circle based constraint of motion.
• Kinetic energy.  As rotational energy.

That is why I am eager to find more evidence for a universal 3-spherical geometry, such as the cosmological evidence leading science to what I consider a very ugly BB.  I agree with Anton that the BB is a relatively straight forward and simple concept, but it has very ugly implications, such as singularities and infinities that in my opinion are very unphysical.

I am very sure that it is possible to explain the redshift of distant light by means of spherical geometry, I just can’t prove that it would be the redshift that is observed, this is where I would love some guidance.

If you are interested in my ideas on the motional geometry of matter, I have attached RG links to my latest monographs on the subject.

Regards, Bernardo.

Research Matter-waves and Discrete-transitional Motion

Research The Isotropy of the Speed of Light and its Implications

Research The Motional Geometry of Matter

Hi Bernardo, write down the Laplacian in R4 and separate in spherical coordinates, Then the hyperspherical harmoics are the solutions on S3. Now you may solve the homogeneous wave equation and then introduce certain sources, like delta or exp(it). Then you may see redshift and cbr. Looking forward seeing soon your results!

George: In your three point scenario (A,B,C) in the vacuum, if matter did not exist at each point, there could be no measurement, therefore the Pythagorean relation is a property of matter’s position, not of the vacuum.

Bernardo, I agree that we can see geometry as possibly being emergent, but the matter can exist with different values of "distance" between "positions" in different geometries. Which of the possible geometries applies to our universe is something that can only be determined by observation.

George:

“Bernardo, I agree, we can see geometry as possibly being emergent, but the matter can exist with different values of "distance" between "positions" in different geometries. Which of the possible geometries applies to our universe is something that can only be determined by observation.”

I agree. That’s exactly my point.  What I have found is that:

• The numerous de Broglie-wave interferometer experiments with particles (molecules) even as large as 10,000 amu, are observations that imply that natural motion in the absence of forces is circular, because the wave properties of those particles can be derived, as I have done, from exactly that motion.
• The many measurements that have confirmed the isotropy of the speed of light imply that the natural motion of light is rotational; whose maximum tangential speed is c0.  Because isotropy requires constancy in all three dimensions, a Euclidean geometry is not supportive.  Nevertheless a 3-spherical hypersurface can naturally accommodate constant tangential speed trajectories in all directions, everywhere and emanating from a single point.
• The orthogonal nature of the Lorentz factor in SR also implies circular motion, where β=v/c0 is the angular speed (in radians per cycle) of a particle moving with tangential speed v.  The constant c0 being the radius of curvature.  I have also shown how SR can be easily derived under such premise.
• Relativistic kinetic energy and momentum relationships can also be shown to be rotational in nature using the de Broglie wave properties.  This was very surprising to me.

All of the above are very strong evidence for the motional geometry of matter to be S3, because, I believe, only S3 geodesics can all be (great) circles in three dimensions.  There may be other geometries that may fit the above evidence, but once more, as I have explained before my mathematical knowledge is not good enough to assert to that last statement.

So George, I am not assuming a particular geometry, I’m just following the evidence trail that I have found so far and such evidence is becoming very overwhelming.

Obviously, all of the above is only valid for isolated particles in the absence of forces, but I think it is a good start for the understanding of the motional geometry of matter in general.

Regards, Bernardo.

Anton:

I’m going to do my best to follow your suggestion using the Laplacian in R4, but remember, my mathematics have been rusty for a long time, so it is possible I will hit a dead-end very quickly.

If you have any ideas on a possible approach using spherical optics (perhaps in S2), I may be able to do better with that.

I appreciate your help very much.

Regards, Bernardo.

Bernardo, my maths is also rusty, probably more so than yours, however there are three questions I would leave you with.

First, when you take the signature of the metric into account (-+++), would that not mean your solution is equivalent to the usual cosmology finite-and-nearly-flat 3-sphere surface for positive curvature?

Second, going on from that result, would it not also hold with perhaps a slight alteration to the definition of the curvature for negative curvature?

Third, if it holds for positive and negative, would it not also hold for zero curvature? I'm unsure of that since obviously the result could be singular.

Bernardo, solve the inh. wave equation on S1, next: S2, finally S3. This would show how waves propagate on compact manifolds. More or less an exercise, eventually may be found in literature. Finally: the Maxwell equations on S3. Good luck!

Amrit, your statement above: "Something that is infinite cannot expand" is nonsense, and I wrote you this earlier. Look into a textbook on real analysis! 

Dear Amrit:

My question contains a conditional statement that asks that if the shape of the Universe is…, or if it were…, or assuming that…, then.  The question is not about whether the shape of the Universe is or it is not…

I appreciate your comments, but I'm sorry to say that they are not relevant to my question.  Having clarified that, I would appreciate if you want to comment on it in accordance with its intent.

Regards, Bernardo.

Dear Bernardo, for me the 3-spherical geometry looks like the most natural geometry for closing a 3-dimensional entity. 3-spherical geometry requires a fourth dimension of metric nature, the 4-radius of the structure. Such a system may only exist as a dynamic system – as a “spherical pendulum”, which releases its energy of gravitation into the energy of motion in a contraction phase towards singularity (like the BigBang point) – and returns the energy of motion back to the gravitational energy in an expansion phase. The search for a static system was the problem Einstein met in his 1917 article (and made him add the cosmological constant to the theory).

Obviously, we are now in such an expansion phase. The 4D motion is observed as the rest energy of mass, E=c*|p|=c*mc. Velocity c can be calculated from the energy balance applying the Hubble radius and the mass density of space, which give the velocity of light as c = SQRT[GM(tot)/R4] = 300 000 km/s. Adding a velocity in a space direction (Re-axis) gives the total energy of motion as a complex function,

E=c*|p|=c*[i mc +p ]=c*SQRT[(mc)2 +p2], where the fourth dimension is denoted as the Im-direction. Relativity in dynamic 3-spherical space is expressed in terms of locally available energy instead of in terms of distorted time and distance like in SR and GR. 3-spherical space with motion and gravitation in balance leads to precise cosmological predictions without dark energy of any other adjustable parameters.

Bernardo, I think your questions will be answered in the thorough analysis of space as dynamic 3-spherical structure given in the book “The Dynamic Universe, Toward a unified picture of physical reality” and in several papers loadable at www.physicsfoundations.org.

Regards, Tuomo

http://www.physicsfoundations.org/

Article The Dynamic Universe – Space as a Spherically Closed Energy System

Deleted research item The research item mentioned here has been deleted

Dear Tuomo:

Thanks for your answer.  I can’t promise I will read your book at this time, but I will browse it to see where I can find some answers for my research.

The idea that Reality has 3-sphere motional geometry comes naturally as you say.  Obviously, we were not the first to speculate on that.  In my case, the idea of a 3-sphere geometry came from implications by some of the theoretical results that I have obtained by extrapolating the Gaussian wavefunction of QM from the quantum (atomic) scope to the stellar (us and the stars) scope.  The intent was to be able to model a motional geometry of matter at all levels (scopes) of reality by parametrizing the wave function via different scopal scale-constants.

First I got rid of the concept of mass and replaced it with the spatial frequency property of matter-waves (I call it spatial density to attach some sense of substance to waves) and then I was able to model the stellar scope’s motional space via the Spatial Density Spectrum (SDS) of the stellar wavefunction.  This then led me to establish that the Compton and de Broglie wave properties are identical properties of the motional geometry of matter at the atomic and stellar scopes respectively, by just changing the value of the scopal scale-constant (4-radius, as you refer to it).

By the same method, I also modeled Special Relativity kinematics by applying a simple cosine apodization function to the stellar wavefunction’s SDS.

The whole idea is to model Reality as a discrete-event system that is more like an informational process than a physical reality; thus getting rid of forces and force fields and replacing them with spatial density transactions that change the state of the overall stellar wavefunction.

With the above context in mind, let me discuss the Big Bang.

You seem to refer to the Big Bang as composed of a Big Crunch then Big Break (as in billiards) that solves the Universal stability problem, but that can also occur in 3-spherical geometry without a change in the hypersphere radius.  All matter could collapse to a constrained minimum volume (not a singularity, but some form of “ground” states) and remain in one of those states until some external density transaction occurs (Big Break or set of Big Breaks), from outside the stellar scope, to start matter moving again, until it collapses again (no infinity).

My conclusion is that the Big Bang is possible but there is no need for an expansion of the geometry itself, which seems to be the generally accepted idea (I would say almost cast in stone).

Getting back to my question, I suspect that the cosmological evidence that apparently supports the Big Bang can be explained by motion constrained to 3-spherical geometry.  For instance:

• The redshift of the light from distant galaxies.  Could be an optical illusion caused by us expecting the light coming from the galaxies to travel in straight lines instead of circular geodesics.  Because the stellar scale-constant (4-radius) is so enormous, we would not be aware of that effect.  This I call, the flat-earth syndrome, because it appears we may not have learned our lesson in 1492.
• The Common Microwave Background (CMB).  Again an optical illusion caused by diffused light coming from the earth-antipodal hyper-hemisphere.

Presently of course, these are possibilities that I can’t prove mathematically nor geometrically that would result in the exact cosmological observable evidence, which is the reason I posed the question.

Your thoughts?

Regards, Bernardo.

Amrit, I know that you believe and are thoroughly convinced that space is Euclidean and I am not disputing that, but I would like to know the reason(s) why you believe that it is not possible for Universal motion to be constrained to a 3-sphere; what makes that impossible?

Also, as you can tell, I am not a big fan of the Big Bang, but don’t you think that calling it “fantasy” is a bit harsh?  I’m a firm believer that when a lot of highly intelligent and educated people appear to be thinking what appears to me as nonsense, perhaps it is time for me to consider the possibility that I am missing some information that is legitimately leading them to think that way.  That’s exactly the reason for my posting.  I want to pick everyone’s brains, because if I ‘am wrong, I want to understand why, as soon as possible.

By the way, don’t tell me that space is Euclidean because NASA has confirmed it.  Do you believe the Higgs boson exists solely on the premise that CERN confirms it?  But Amrit, that’s a rhetorical question, please let’s not get into it :).

Best Regards, Bernardo.

Dear Amrit / Bernardo, it is important to distinguish between what the physical reality really is, how it is observed, and how it is described. Any model is just a description, which is evaluated both in a comparison with observations/predictions and on the other hand for its internal coherence and logic, and its ability to make nature understandable. Present models have succeeded well in matching the descriptions with observations – in some cases at the cost of additional parameters. At the same time most physicists agree, that the present theories do not make nature understandable and that they are partly in conflict with each other.

Examples of observations/reality:

Euclidean space: An early conclusion (De Sitter 1931) in the FLRW cosmology was that galaxies do not expand with the expanding space. This conclusion, based on the local nature of the GR, together with the reciprocity theorem (based on the relativity principle of SR, Etherington 1933) and the GR-based metrics resulted in the prediction of non-Euclidean appearance of galaxy space. For example, in a holistic approach relying on zero-energy driven expansion in 3-sphere space, galaxies and any other gravitationally bound systems expand in direct proportion to expansion of the 4-radius. Such an approach does not rely on relativity principle – altogether, the resulting prediction is that, in spherically closed space, galaxy space is observed (the optical appearance) in Euclidean geometry.

The velocity of light: The constancy of the velocity of light is regarded as “an empirical fact” – and the theory of relativity was built on that fact. At the time the choice was made, there were very limited means to measure the velocity of light other that the phase velocity. The quantum mechanical solution for the characteristic frequency of atomic clocks shows that the clock frequency is proportional to the rest energy of oscillating electrons / the Planck constant (f ~ mc2/h). From Maxwell’s equations, by solving the energy emitted into one cycle of radiation / unit charge transition, we find that the Planck constant is proportional to the velocity of light. This means that the frequency of atomic clocks is directly proportional to the velocity of light (f ~ mc), which guarantees that the velocity of light, c, is observed as constant when measured with atomic clocks. The constancy of c observed in interference measurements (like the classical M-M experiment) can also be returned to the properties of the test setup.

“Cleaning” of the “hidden c” from the Planck constant has major importance in understanding the wave nature of mass: The Planck equation obtains the form E = hf = h0*c*f = h0/lamda*c2, where h0 =1.1049*2*pi3*e2*my0 = h/c, and the quantity h0/lambda has the dimension of mass [kg]. Other way round, a mass object can be described as a resonator with the internal wavelength lambda(Compton) = h0/m. Bernardo, I think this linkage may be worth studying in your particle/wavicle considerations.

A unified theory structure requires that same postulates apply in all branches of the theory. Such a situation may be difficult to obtain in theories based on immediate observations or “empirical facts”. Also, in any theory, it is very difficult to apply conclusions drawn from another theory based on different postulates.

Kind regards, Tuomo

Tuomo:

Here is a small excerpt from The Motional Geometry of Matter that I hope will help us understand each other:

An object’s behavior is defined by its properties.  If the object’s properties are categorized under some common set of characteristics, the categorization does not necessarily change the structure of the object.   Consequently, in order to resolve confusion in this monograph, we will use the term particle to refer to an object’s material properties and the term wavicle when referring to its wave-packet properties.  This distinction will allow us to ignore the question whether a particle is structurally matter or wave, rendering it irrelevant.

If we ignore the structural details of matter and focus on it its wavicle motional behavior (motional properties only), a de Broglie wave can be simply interpreted and demystified as the equivalent wave traced by a point wavicle (or particle) traced by a circular trajectory.  This I have modeled in: Matter-waves and Discrete-transitional Motion by means of the Fourier transform and the Spatial Density Spectrum (SDS) of the stellar wavefunction.

I believe that models, although they are not the physical reality, should be rationally acceptable.  By this I mean that we should be able to interpret their correspondence to the physical reality, hopefully on a one to one basis.  Special Relativity (SR) for example, is easily understandable if we interpret it in terms of wavicles but very difficult to accept if interpreted in terms of particles.  Concepts such as “time dilation” as a result of motion, throw a wrench in the thinking process because the concept of time is too intertwined with our consciousness and apparently any attempts to separate them blur together.  Nevertheless, discussing an increase in wavicle frequency with motion can be easily visualized, leaving the concept of time untouched and SR’s length energy and momentum formulations easily interpretable.

In the case of the Big Bang, the concept of the expanding 4-radius of spacetime as if space and time had some kind of substance (fabric) is a much bigger wrench.  I could much more easily accept an expanding constraint on the motional trajectories of matter, but why resort to that, if the Big Bang’s cosmological evidence can be possibly explained by means of 3-sphere motional geometry within a constant 4-radius.

In regards to the speed of light, I believe that the isotropy of the speed of light is an “empirical fact” that testifies (as the scale-constant) to the curvature of natural motion and also, as you have mentioned, to the validity of SR.

Also, in my opinion, we should not hide c0 within h0, because the Planck constant, I believe, is more of a unit conversion factor, than a fundamental constant, while c0 in contrast, can be interpreted as a motional constraint expressed by the fundamental spatiotemporal relation lambda*f=c0.  I have attached a section of The Motional Geometry of Matter that includes a table with a list of a few of the particle/wavicle/energy/angular momentum relationships that I have derived from the rotational motional properties of matter and the SDS of the stellar wavefunction.

Best regards, Bernardo.

Einstein matrices are based on 4 matrix x 4 matrix  components suggesting as you infer a three sphere but not an ordinary three sphere in so far as only 10 of the 16 components are filled suggesting a 3 x 3 spatial metric and one component of time.

Having said this time has a different component. This implies that space time has a fabric which includes a temporal component and as we know space-time has inherent energy.

The fabric of space time then has a temporal component for obvious reasons, c provides the fundamental back drop of space time the universal metric, the energy density then provides (curvature) and as a result the  presumed force of gravity which objects "feel" and provides the motional geometry of orbital matter.

As for subatomic matter, theory of everything states that space time, E-M radiation and matter itself all derive form the same components.

UNIFICATION of GRAVITATION and ELECTROMAGNETISM 

I unified at Quantum level, Electromagnetism and Gravitation with Ferent equation for the energy of a photon:

E = h × f + a × f

Ferent equation for photon – graviton interaction:

E = h × f + a × f - a × ν

where - a × ν is the negative energy of the graviton

ν is the frequency of the graviton

“I am the first who understood and explained Gravitation with high speed gravitons   v = 1.001762 × 10^17 m/s, with Negative Momentum, Negative Mass and Negative Energy” Adrian Ferent

https://www.researchgate.net/publication/299135595_Ferent_Gravitation_theory

Article Ferent Gravitation theory

 Andrew:

Please explain to me what you mean by “…not an ordinary three sphere in so far as only 10 of the 16 components…”. In other words, what 10 components out of what 16 components and why they make the sphere not ordinary? Also, why does that imply that the fourth dimension is a time component and not another spatial metric?

Maybe I misunderstood you. I think that if Reality lies within a 3-sphere we can infer a 4th dimension, but we shouldn’t be able to observe it, thus we can’t know if its time or space, let alone have a fabric.

The isotropic relationship λf=c0, relates time to space through motion without the need for a fabric in the fourth dimension. As a matter of fact, it also expresses the curvature of motion together with the relation β=v/c0, where β can be interpreted as the angular speed (in radians/cycle) of a point wavicle (de Broglie) on a rotational uniform geodesic trajectory of S3. I know very little about spherical geometry, but I strongly suspect that by assuming c=c0 to be a constant, the Lorentz Transformation (LT) indirectly also assumes a circular motional curvature.

Regards, Bernardo.

Experiments to test Ferent Gravitation theory!

In the double slit experiment the interacting observer is an instrument, detector…

My experiment is: if you replace the detector with a piece of metal the wave will collapse into a particle because of my theory photon – graviton interaction:

Ferent equation for photon – graviton interaction:

E = h × f + a × f - a × ν

where - a × ν is the negative energy of the graviton

ν is the frequency of the graviton

Here we know the frequency of the photon f and the frequency of the graviton f. With different metals we have different frequencies of the graviton ν.

A lot of experiments can be done, and will result a lot of data!

Ferent gravitation theory explains the double slit experiment!

https://www.researchgate.net/publication/299135595_Ferent_Gravitation_theory

You can read on my theory:

Decoherence explained by my theory

The electromagnetic wave is the superposition of 3 sinusoids; this means the electromagnetic wave will be collapsed by the presence of an electric field, of a magnetic field, of a gravitational field, by another electromagnetic wave… 

In my electromagnetic theory, gravity does collapse quantum superpositions, gravity bends light because light has 3 sinusoids, has a gravitational sinusoid!

In Maxwell electromagnetic theory, gravity does not collapse quantum superpositions, gravity does not bend light, because light has only 2 sinusoids!

So decoherence is due to the gravitational field, for example to the gravitational waves generated by the observer in the double-slit experiment.

Article Ferent Gravitation theory

Don't spam other people's questions Adrian, go away and work out the proofs for the questions you've been asked first.

@Bernado

The principle is that a 3 sphere is a 4 dimensional object. Conventionally it has a volume of  pi^2/2 x r^4 implying that the 4th dimension is space as the volume has increased.

If it were described by a 4 x 4 matrix, it would have 16 elements.

(and by the way to calculate a 4 x 4 matrix would take 16  3 x 3 matrices to solve it)

Einstein's matrix is  is a 4 x 4 matrix but only has 10 elements, because the tacit assumption is that the 4 element is the time element, in 4 dimensional space-time.

Most FRW models of the Universe are based on this assumption - i am not saying I absolutely agree with this, but that is the common perception

Hope this helps

The surface of the 3-sphere is 2.pi2.r3 which would presumably be the volume of our universe.

AW: Most FRW models of the Universe are based on this assumption

I think generally most texts I've seen make the point that FRW has this form only if the energy density exceeds the critical value. The "balloon model" is an easy explanation of expansion without boundaries but is misleading in that it inherently implies a finite universe when the question is really open.

Dear Bernardo ~

This may interest you (-:

Article Geometry of the De-Sitter Universe

Dear Bernardo, does this help?

Working Paper Hypersphere Cosmology

Regards, Pete.

Some very simplistic thinking suggests to me the universe is a 3-sphere. This then leads to some very simple estimates of a number of physical parameters, such as the Hubble constant (and why the reciprocal of the Hubble constant equals the age of the universe). A reasonable estimate of red-shift vs distance. Why everything in the universe is moving at exactly the speed of light (as proposed by Prof Brian Cox when discussing special relativity). It even produces a mass for the universe which agrees very well with estimates by others. I think it also explains inflation, which is a virtual phenomenon, nothing ever travels faster than light.

For more detail, see https://modeloftheuniverse.wordpress.com/

Sorry, I forgot to add, there is no missing dimension. A 2-sphere, such as the surface of the earth, can only exist in three dimensions. Similarly a 3-sphere can only exist in four dimensions. A 3-sphere is in fact the surface of a 4-dimensional ball or globe. A 3-sphere requires four dimensions, presumably spacetime, to exist.

I think Einstein / Minkowski had it right early on, they insisted, that 4D really is time, the curvature is not "intrinsic", and there doesn't help to add a 5D and another "cosmic time" as mentioned by the deSitter, perhaps to mollify critics of the notion that implies that our fates were inescapable, that time is an illusion, that the universe maybe ballooned out and then collapsed, then repeated, if observers from the insides observe the clues, they will always think its expanding because expansion is required to record all that data! This is weak anthropic reasoning, but the question is mute if time is something we are able to observe only by its shadow, just as Plato knew.

Despite its usefulness, wealth-generating, simplicity, beauty, and parallels, the theory is unsatisfying to those that don't like to think that they are already dead somewhere in the universe, further out along the time axis near his habitat. If you were a 4D, god looking at the universe that he 4D printed (When time is included its covering up the insides of objects he normall can see inside, and not easy to figure out out which way is time without dissection, even for him, and the same appplies to the 3D creator of 2D universes, which i will go into later, its the very best way to think about this stuff, he could see the critic grow and then shrink to skeleton if you cut out just the right chunk. ( Einstein said this again when his best friend Michelle Besson died a week or so before he recorded his last days in his brain, which went into a jar and stopped recording or being decoded, and he added that this notion of a shared "now" or the flow of time, is an especially stubborn illusion, and stubborn as in 100 years later we are still talking about the universe "expanding" or collapsing when its 4D and thus only the hyperplane or skin thata maybe -was- expanding, and then stopped and reversed, or just stopped. The Model was 4D geometry and static, meaning ALL of time being already in place , generated, simulated, or whatever, and a coordinate of an event, discernable from the spacelike directions only by some attributes, density, symmetry, and most importantly, its cutting perpendicular to the time axis where one would see the 3D forms of observers who worry about the end of the world and try to model the whole thing so they can not be in the wrong place at the wrong time. The equations are thus functionals, if it were dynamic, then there would need to be another T variable, thats lame. Let's remember, the 4D relativity gave us GPS, bombs, space probes corrections, its useful stuff, we don't need to muck it up unless its works better. It was Steven Hawkings a brief history of Time, first edition, 1987, that made me first feel like I was already dead somewhere.. He showed how to ask the question which way is the past, relate it to entropy or the formation of memory, step down to 2D so we can have simpler observers and think in 3D instead of 4D which is impossible. Using the 1D way works but its not as relatable.

I want to add that because of symmetry, conservation of momentum that T=0 was in the center, and that it is a radial axis, along which you would find the thinking beings if you were examining one of this universe balls, say a 3D one with 2D creatures embedded in it, because it is much easier to grasp a 3d ball if it was happened to be static and stable you could just get a knife and a microscope and look for the 2D creatures. In fast Min Epistemology is an essential consideration of this matter and might explain why it got so complex and remains unsatisfying to so many, even though it was proven dramatically with the eclipse.

so the model belongs to Plato Kant Lucretius, Lewis Carrol, whos Red Queen could remember the future, was actually disturbed by the 4D quaterion math needed to describe 3d rotations observed, recorded and transmitted by other 3d minds, which i believe are embedded in the 3-sphere trying to remember the future to avoid pain or actually dying before passing on his own form in this DNA.; the father of tragedy, Aeschylus, killed by a vulture because he was outside trying to avoid his fate. Both said time really is an illusion, it is not flowing. Minkowski used 1D of space and 1D of time. With this you can make a signal ( voltage with time), which can contain a description of a Form (as in Plato), of any complexity, even one that describes our universe big bang recipe, in simple terms. we like to use 1D. we use time to take the measurements because we are Besides math and physics, A. K. Dewdey described a 2d creature that could be imagined on a 2-sphere. He explains eternity, or space-time continuum, with a drawing of extruded beings, that can observe and record. To use 3d beings, its a sphere with the creatures identifiable if one has the A priori guess, that you need to cut perpendicular to the time axis, or to be exact, peel it like an onion, and put a thing piece ( about 1 year of space-time, to see the little creature, and it doesn't look like a square or triangle as appear in the more famous but less rigorously thought out books sphereland and Flatland.

And it would seem logical that time extends in the radial direction, and so the direction of time, is explained by thermodynamic arrow of time, the weak anthropic principle, and the question "is why do we not remember the future (like the red Queen in Alice in Wonderland, which was a little quaternion joke pointed out by its author who was a mathematician at Oxford)

We must remember a time with less entropy, because as Steven Hawking explains, remembering is like encoding with an abacus, and thus, it takes more room to move the atoms around to encode all that observed information. So, of course, the part which is already observed is toward the center ( big bang, T= 0) and the future is toward the outer bounds. We always think the universe is expanding when it is doing neither, since its past to future is already formed inside. I like to think of an onion, that when peeled one layer of say radial thickness of a few days ( speed of light x days to get kilometers) , we can see that image of the 2D sentient creature embedded inside the Christmas tree ornaments like a sphere that is a curiosity to the 4D beings that created it. When Einstein said that time is an illusion, but a very stubborn one, I wonder if the continued debate about "dark matter", expanding universe, and questions such as these which require 5D or even more useless constructs just to give us some illusion of free will, then the greeks, continuous forms but one person Now is not the same as anther persons Now.

Here is why wikipedia said the static 4D hyperspere uninverse fell out of fashion:

Because the Einstein universe soon was recognized to be inherently unstable, it was presently abandoned as a viable model for the universe. It is unstable in the sense that any slight change in either the value of the cosmological constant, the matter density, or the spatial curvature will result in a universe that either expands and accelerates forever or re-collapses to a singularity. This is I think the heart of your answer. As long as its reversible, oscillatory, momentum and mass-conserving, then it might appear only to "inside observers" to be doing all this exploding and imploding, but only to the poor shadows embedded in it, that are taking measurements and making models and warning each other and stuff. There may be only a few sections where the illusion of consciousness can be discovered by dissection. I might cut out the rest of this answer, it just makes me go on, Im curious if there's something i just dont get, or if this answer makes you like your hyperspere theory.; Its my cosmology theory, I call it , "Death in the Flatland"

Subsequent to my last draft of the Hypersphere Cosmology idea, Gommel and Zimmerman have published some work on galaxy rotation curves which to me indicates that the Godel type rotation needed to prevent the collapse of a cosmic scale hypersphere also rather precisely solves the problem of galactic rotations, the new model nears completion, see here https://www.specularium.org/hypersphere-cosmology

maybe you can reduce it further.. the rank mabye 1 to high. go full d'Hooft holographic.. but all curved. less invariances apply but energy is convered only on consmic cycle . For transport exploits this would be a gift in a box.

Preprint Gravitation in Theory of Space-Time Film and Galactic Soliton

Einstein himself suggested a sphere.. i believe Neother as well for energy conservation requires time invariance and that can be done with a sphere in a box. Careful to keep Generators (2d dyanmics) and Observables (3d and persistent) separate.. covariances between ranks make 3d+1 theory covariant well untill they crash 1/0 NaN because its was E said, overdetermined. a stuck knot and thats not a breather.. expand contract repeat is a nice sysmmetry that gives Unitary and it gives an FFt of 1 and it gives a deterministic hardcopy from a function. its The Book.. we dont write it. we are in it as characters.

https://www.jstor.org/stable/1969197

https://www.jstor.org/stable/2659884

Yes, 3-space is the natural geometry of space. In the theory of relativity, the fourth dimension is called the “time dimension”, but it is measured in meters (ds4=c∙dt [m/s∙s=m]). Instead of being 13.8 Gy time from the Big Bang, any location in space is at 13.8 Gly distance from the starting point in common which means the 3-sphere with radius 13.8 Gly expanding at velocity c. Such geometry allows us to solve the dynamics of space and opens a holistic perspective of space as a whole. In such a perspective, time is absolute, and relativity appears as a direct consequence of the conservation of total energy. http://physicsfoundations.org/data/documents/Physics_Essays_34_4_2021_Suntola.pdf, more detailed at https://www.physicsfoundations.org/dynamic-universe.

i actual mean 3D space as f( x, y ,T).

what im more curious about is below , the bult here is my own interpretation and im a engineer and thankfully not a particle physicist. just a software engineer with a physic background, ahd an awareness of histroy of science and its practical application. Well ive run of of theory and the Ais have step up the game by coding fluild dynamics solvers for me. As predicted by d'Hooft the chatty bot is a word predictor that writes code that predicts and solved PDEs. completey unexpected .

https://webspace.science.uu.nl/~hooft101/lectures/intelligence.pdf

Gravitation in Theory of Space-Time Film and Galactic Soliton link is below if you arent able to understand my writing and rahter read it from the giants who thought it up. yet i can put the ideas of the giants togethre since they are so specialized that maybe they miss how to fit the pieces together, so im working with some phds just to sort of be their reality check.. give me numbers, something i can buld that goes really fast and tunnels and using very little energy. Sort of like a Besso to and Einstein and im no einstein. but he didnt have a pde solver and new surfed a solitary wave or drove a motorcycle in mud in the country that hthis scientist worked in.

yes the metric along the radial direction would be ct. to the box would need be ct x 2x13.8 Gly wide. the Bounds would determine the bulk. The is from the ADS/CFt and holographic principle. you could put the BB at the 0,0,0. its not a point if you are using soliton field theory and accounting for ontics and the black hole studies ( the mass is related to the area not the volume)

gosh i wish he was still alive i visit his country often.

"One more thing, the dimensions of the 3-sphere are assumed to be spatial and do not include time as a dimension.  The fourth dimension of the hypersphere is unobservable therefore unknown.

If that’s the case, the need for a Big Bang becomes questionable."

so here he says its unobserable.. iill change that to "remembered 2d dynamics, over time" and the future can be determined, but not by us, it can be remembed if its been observed, and the memories are alwasy of a part that had less degrees of freedom, toward the early universe ( which is like a hot dense highly energetic mass, that may reach a critical mass and explode in part.. like a supernova. to be cyclic. harmonic, and thus redundant and not require a 4d dimension to describe.

so that leaves us wiht a thin 2d shpere of "something" that expandes, has lots of clumps and dents and features, dee wells but itss toplocially simply connected. that gives 3d. and why doest the 3d have separate sets? why its it apparantly 4D. ? welll i guss i will say that we require a certain amout of time to burn memory of a group, and our brains and perception coevolved with this phase or persion and its related to the complexity.. Or that there is periodicity in the ontics that give rise to this. its basic like a movie, a set of 2d images.. we take snap shots at a certain rate.

Now this i just barely grasp.. I dont fully understand holography either. but i can understand that a 2d TV image can be a very fast 1d line and its at 60z. the awareness of a navy pilot can go to 120 hz. but his Vsync will still train to see any old CRTs in his radar.

so here "unobservable" means sort of what i mean , but ill put it another way. 4 d events are like a film strip.. They are constucted from the dynamics of 3d objects which are described as 2d functions of time, as interference patterns which are interpretated as we see holograms, as 3d. so 1D can encode a 2d hologram. ( along with stereo vsion) . a successtion of those is a 3d hologram, and a periodic successtion of those are events in 4d and appear to have dyanmic described by 3D +1 formulals, all of which are not fully determined, while the 2d analogues are.

but the 3d constrcut the are not dynamic generators. meanign if i were to have some laws of physics formula.. and if being a god, and a lazy clever creature following his own lazy action princiiple , I would want the most interesting uinverse with the least effort, like a cellulatar automaton or simply running a fluid solver. I would not want to kept the bulk in Ram or 3d print it but would liike to either burn a compressed mp3 or a CD or 1s, and 0s to show the movie to some other god. We are the actors not the screenwrites.

Coming from a DSP and physics and worldbuilding and 2d logicallly consistent physics based world building/ alife background, i naturally got pullied into this approach to thoeretical physics and its applications nad profound potential for further application such as in space transport. We are using rockets. and not going very fast Its only at high speeds that the 2d Nature of hte dyanmics becaomes apparent. Things like black holes, Scattering events like e=mc2 ( not cubed) that are truly unobservable at least in a direct sense. So Valdivias way of wording it is unque and interesting

In Einsteins 1945 paper I think he started the universe at it max potential and ran it backwards, having gravity instead of a pushing apart on the shell action, , the reverse.. Solitions are capable of transposition, replusion and attaction, as well as superpostion. thers are all little currents. maybe "Noehter currents"

I cant pretend to understand al this below but in Navier Stokes solvers and weather models on a 2d +1 shere that is not expanding ( earth), its basically voriticity. in Compressible fluids there is pressure due to to coorating and packed locally rotating parts. Evidence is the hexagon on saturn.. there we see the packing maximal shape on the north pole.

https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/noether-currents-for-eulerian-variational-principles-in-nonbarotropic-magnetohydrodynamics-and-topological-conservations-laws/F4E8ACFFA1BD0DDB993FCDFCFF972C4C

its quite an Alice in Wonderland pill to swallow but the more problems i see that remain unsolved... the more i learn about developable topology and non commutativity of operations of curves.. energy conservation, unitarity, models in general, univifactions like Netwtons laws, 3. and National Selection and Evolution ( holomolgy) and phenomology , thermodyanmics, and simulation ( out of box view) , solition as particle, the simpler all this mess of physics gets. so here i shwo a theory which has no forces and only waves.. it is a filed theory. something like it used every day.. or some variant. dimensinoal reduction. But i propose that it be treated as reality. and given more attention. Eintein has said that his GR was overdetermined.

the basic idea is it take time to observe light and create memories. Its tikes more DOF for the 30 Watts to burn those memories.

this is if quantum gravity is found to be fully deterministic and reversible. we will never know, excepting possibly by reversible simulations. 3d+1 as dynamics, leads to singularities, when used in dynamics. As observables and derivative of those generators, its 4D events. What this does is give a model which does not require the bulk to be retained.. just the first derivative.

3d+1 dyanmcis and 2d + 1 , they scale the same.

its considered a cohomology or a correspondence.

Article Dimensional Reduction in Quantum Gravity

https://arxiv.org/abs/hep-th/9409089