Some considerations:

- A true 'light cone' will only exist from a point in space that emits light.

- Each point in space can be considered the starting point of a potential light cone (is this what you mean by 'center of'?). However each point will also be included in the light cones of very many (potentially infinite) other light cones. The other cones maybe influencing (via gravity or other means) a point within their cones. This is likely a difficult item to separate out.

- A number of people have noticed that 'time' lacks certain characteristics of physical dimensions and so 'spacetime' is more likely a useful method of modeling events than an accurate model of reality. So the characteristics of time that do not conform to a physical dimension need to be accounted for.

In this set of characteristics is the directional nature of time vs the bidirectional nature of physical dimensions. Modeling events using 4 dimensional spacetime needs to address the directional nature of time. If it can provide verifiable predictions that explicitly require the bidirectional nature to exist (that cannot be understood otherwise) - then spacetime can be considered more than a useful model. To date I am not aware of such predictions and the model does not account for the directional nature of time, thus putting into question the accuracy of the model.

Personally, I believe the world needs to be understood as consisting of (at least) 4 physical dimensions, since we must identify the scale of an object as well as its 3-dimensional position. Time could then be modeled as a 5th dimension (I believe it can always be modeled as an additional dimension to how ever many physical dimensions we ascribe to.) There are a number of aspects of a scale-included space that could be explanatory.

Answering on this first response I want to mention following:

This response was seen as a discussion about the definitions used in the question and not as an attempt to answer it.

It is correct that a light cone has at its origin a source of light. This is the case when we talk about a light cone towards the future. This is the cone where we follow what influence a point P in space has on the surrounding space. We can, however, also think of a past light cone. That is the sum of all those light cone segments, lines, form all other points in space that have an influence on one point P in space at a given moment. Both cones, the forward cone to the future and the backward cone to the past have geometrical properties that are similar. They are 3-dimensional structures with concentric spheres with 2 space dimensions and one radial time dimension. For the forward cone one such sphere is the unity of points that will receive any influence from the point P after the same amount of time since it was sent out form P. For the backward cone each sphere is the union of points that did send their influence the same amount of time ago towards the point P. Because we assume all those influences to travel with the speed of light the radius for such sphere is equal to the speed of light times the travel time.

For each point P in space this past light cone is its only reality. Anything outside of this light cone does not (or not yet) exist for P. Anything inside the light cone may have causal connection but that influence, like the image of my self in a mirror, reaches me via scattering. The last point of scattering is always on the surface of the backward light cone.

For the problem setting of this question we focus on how energy density inside space changes the curvature of space under the condition of a homogeneous and isotropic distribution. The normal relation of the curvature of space as a function of its contents is described in the Friedmann equations. The deduction of these equations makes use of mathematics that treats space-time as a 4-dimensional space with 4 completely exchangeable dimensions. Whether space really curves as a result of its energy content is challenged here.

Whether we want to add more dimensions to the discussion is another issue. In mathematics we use imaginary numbers. These numbers can be obtained when we take the square root out of a negative number. In many cases we can get good mathematical results when we take these numbers as a next dimension. This does not make this imaginary axis a real kind of dimension. Here I only restrict my self to the 4 dimensions as used in the mathematics of the general relativity theory formulas. That does not mean that we can think of yet more dimensions. However in the mathematics of GR a 4-dimensional spacetime is used where the time dimension is treated as yet another space kind of dimension.

Until now I see the first response as an attempt to clarify the definitions in the initial question. However, in that response no attempt was made to come to an answer of the question.

Our living space is a continuum that vibrates, deforms and vibrates dynamically. Physical reality generates is dynamic geometric data as a combination of a real number valued time-stamp and a three-dimensional spatial vector. A quaternion can store this combination. Quaternionic differential calculus describes the dynamic behavior of these data and of the embedding continuum. The embedding continuum transfers the information from the event where the information is generated to the observer. Consequently, the observer perceives in spacetime format. The Lorentz transform describes the conversion from the Euclidean storage format to the perceived spacetime format. It is a hyperbolic coordinate transform. Since the carrier can deform, the information path can deform as well. Therefore, the perceived information must be described by tensor calculus, which combines differential calculus with coordinate transforms. https://en.wikiversity.org/wiki/Hilbert_Book_Model_Project

I see this answer as a venting of a new way of thinking without relating that thinking with the original question.

I vind het vreemd dat mensen niet kunnen ingaan op de vraag maar alleen hun eigen ideeën willen luchten.

It is strange to me that people can't engage with the questions but only want to vent their own ideas.

It might be that this new kind of calculations could give an answer on the question. The show how that is related and how my assumptions, my definitions and my deductions are transformed by that.

Maybe I'l have a look into your linked place.

Let's talk form point of view of orthodoxal general relativity.

You did not prove that any point is not influenced by others.

You proved that each point is equivalent to each other.

Gravity affect the space-time curvature. But the curvature is internal curvature. The space-time is not bended in some higher dimensional space-time. Just the internal geometry of space-time is different form flat geometry of Minkowsky space-time.

Spatial geometry of the case you consider is just geometry of constant curvature space, i.e. Euclidean geometry (excluded, it is flat), spherical geometry (geometry of sphere surface) or Lobachevsky geometry.

Thank you for your answer.

You try to use orthodox general relativity. You say that space-time is curved internally. That is a statement without any explanation. With that it is a citation of general scientific views. Of cause I know them. How do we come to conclude that space is internally curved?

I give here a deduction how we can detect if space is curved or flat.

That deduction is similar to the deduction that Professor Leonard Susskind from Stanford university uses in his lectures about cosmology.

When you want to see how this works you can observe the geodesic through a point.

My statement is that if the second derivative of the equation of the geodesic has coefficients for the dimensions x, y, z that are not equal to 0, then that geodesic is curved. If all geodesics have only maybe non zero coefficients in the time direction and zero valued coefficients for the dimensions x, y, z in their second derivative, then whole space is flat.

The General Relativity equations need to combine on the left side the space terms in the Einstein tensor G with on the right side we the energy density tensor T. To do this we have to make use of the theorem of Gauss. That theorem says that:

The gravitational flux PHI through any closed surface is proportional to the enclosed mass.

I can only set up the equations for the GR with mass that is related to each other. Mass that has no relation with my centre point has to be taken account of in other calculations. So I try to get a solution for one point of the present and see if I can expand that over the whole rest of the present.

I observe that any point of space is in the centre of its own light-cone and that only that light-cone is reality for that point. So if I want to write my GR equations for my point then the result is a centre point in the present and a sphere around that of points of the past.

To have an effect I need to find a surface that encloses mass.

For this centre point there is nothing. It is on all sides surrounded by equal amount of past mass, energy. So the geodesic of the centre point is the same as the geodesic of the whole sphere.

This sphere, however, has its outer surface at the start of space. It makes no sense to assume start of space to move somewhere. So the geodesic of our centre point has no coefficients for the space dimensions x, y, z.

If you now try to find the curvature of this one light-cone, then you would go outside of the centre point C to another point P.

That point P is on a sphere with a radius R1 and all points outside of that sphere, according to newton already, have no influence on the gravity for P. we would say that points inside that sphere will have an influence. However, that whole inside sphere consists of points that are in the future of our point P. Also the centre of gravity of this sphere is in point C. The line from P to C is in pure time direction towards the future. With that we have only matter in the future and its combined influence would only work towards the time direction. For P this whole sphere does not exist. With that our attempt to get a geodesic with non zero second derivative coefficients for x, y, z fails. If we come up for each point of the present with a straight geodesic and also for each point of the past with a straight geodesic then I have to conclude that space is flat.

It is more correct to see spacetime as a coordinate system, just as the Cartesian coordinate system and polar coordinate systems are coordinate systems that add a topology to a flat continuum that is formed by a quaternionic number system. A quaternionic function can then define a vibrating and deformed continuum to which the coordinate systems map.

Energy as well as mass are carried by excitations of this continuum.

See: Article Rediscovered dark quanta

This is an interesting answer. In this answer it is assumed that for the description of the problem is it better to describe space with Cartesian coordinate. From this answer I have deduce that my description of the light cone is not yet clear.

I use the polar coordinates in stead of the Cartesian coordinates because I make a distinction between space coordinates and the time coordinate. I hold the fact that time only can be traversed in one direction from the past through the present to the future.

With that any extension that holds this characteristic is kept separate from the rest.

The light cone has concentric spheres of points that share the characteristic that from there to the centre light travels in the same time. That means that these points all have the same world line length. The world line is the path along the time dimension of a point in space since the start of the universe.

Because in the light cone these concentric spheres are a union of points with same world line length these points all exist in the same time in space.

That is why I use a polar coordinate metric for the light cone. With that it is clear that the radial direction has the time characteristics that information can only travel inward and not outward.

I think that the conclusions of my deductions are in contradiction with currently accepted views. I try to get an answer if my deductions show that the calculations based on the General Relativity lead to wrong conclusions.

It might be that using the General Relativity theory to describe reality is completely wrong. However I don’t put that in question here.

Describing space with a quaternionic number system means we use different mathematics. There the question is whether these two mathematical descriptions, GR and quaternionic, are equivalent or mutual exclusive. That means are they both ok or can only one of them be correct. That question is very interesting but not the topic of this thread.

The light cone only becomes relevant when information is transferred from the proper-time-space location where the information is generated to the location and time of the observer. Reality offers two views. One is the creator's view, which can also be called the storage view because the creator archives ALL discrete dynamic geometric data in quaternionic storage bins in a read-only repository that is formed by separable Hilbert spaces. The other view is the observer view. Observers travel through the repository with the current static status quo and can only retrieve information that is archived with a historic time-stamp. An embedding field transfers the information from the storage bin to the observer. This affects the format of the information. Therefore the observer perceives in space time format. The Lorentz transform describes the coordinate transform from the Euclidean archival format to the perceived spacetime format.

The embedding process deforms the embedding continuum. For example, elementary particles hop around in a stochastic hopping path and each hop landing generates a spherical shock front that locally and temporarily deforms the embedding continuum and globally expands the embedding continuum with the volume of the Green's function of the embedding continuum. These tiny deformations overlap and together they cause a significant and persistent deformation of the embedding continuum. The deformation affects the information path and indirectly this affects the transferred information. Both the deformation and the expansion of the continuum have effect. This happens at small scales, but due to the expansion of the embedding continuum it must also have effect at cosmic scales.

At the beginning, when no hopping occurred, the function that describes the embedding continuum does not reduce to a single point, but instead it is identical to its parameter space. Each hop increases its volume. At the first instant an immense number of elementary particles started hopping.

Thank you for that answer. This answer is an attempt to explain how the exchange of influence between a sender point and a receiver point could happen as seen from the Hilbertbook theory. For the question that we are looking at here it is not of big importance how the gravity effect is transferred. Do we agree that the effect of gravity travels with the speed of light from the sender to the receiver point? If we agree then we are one step further.

The light cone is no real space. It is a 3-dimensional representation of the information that is present at a point of space. Space is real 3-dimensional and always in the present.

The light cone represents in its radial direction the time the effect of gravity traveled from a sender point of that effect to the centre point. In its angular coordinates it represents the direction from where the effect of gravity reached the centre point. But all gravity effects are at the centre point together and the reaction of the centre point is based on the sum of all effects. That is also the reason why this result is only valid for this centre point. Any other point of the light cone is outside reality.

It may be interpreted as residing in some Hilbert space. But that does not help in the answer of the question.

The question is if, with a homogeneous and isotropic energy density distribution throughout space, there is a curvature of this space as a function of the value of this density.

According to the calculations of the GR there is curvature.

According to what i have explained here there is no curvature.

If my view is right then many current cosmological models have a problem.

When the existence of super-tiny spherical shock fronts is accepted and is accepted that they carry a standard bit of mass, then these objects are distributed over space. Energy is carried by super-tiny one-dimensional shock fronts and result from special processes that emit these vibrations. All shock fronts proceed with light speed.

The amount of mass of a spherical shock front relates to the volume of the Green's function of the carrier. It quantifies the deformation of the carrier by the spherical shock front.

Each generation of a spherical shock front expands the carrier with the volume of the Green's function. The carrier represents the universe.

If the universe does not expand, then with each addition of a spherical shock front the volume of that shock front must reduce. Thus, the amount of mass carried by the shock front must reduce. 'This is a strange procedure.

Let us assume that we have a theory of some phenomenon. With that theory we can explain and predict most of the observations of that phenomenon. Now we get a second theory about the same phenomenon. Under that situation we have two theories. We now have to decide what to do. We have to compare these two theories and might discard one and select the other. In order to do that we have to evaluate these two theories.

This evaluation has in principle 4 outcomes.

What I try to do in this question thread is that I make an attempt to analyse if theory one, the Lambda-CDM, has a problem with respect to the Friedmann equations that state that there is a relation between the energy in space that the expansion of space.

The answer I get here is that there exists a new theory and that in that new theory some properties of a third theory, which isn't mentioned yet, give a strange effect.

We can deviate from the initial answer and comment on the notion that mass needs to reduce.

If we sit in a train and we see another train moving then we might have the situation that we move and that other train stands still or that we stand still and that other train moves.

If we describe space in a way where all matter has a constant size and space increases its size then we come from a situation where the size of space divided by the size of matter had a smaller value in earlier time and a larger value in later time.

If we describe this same space in a different way where we state that the size of space is constant and that all matter shrinks, the we also come from a situation where the size of space divided by the size of matter had a smaller value in earlier time and a larger value in later time.

Both descriptions, (1) expanding space with constant matter and (2) static space with shrinking matter, are mathematical transformations. They are equivalent. Out of this argumentation follows that the notion, that it is strange strange procedure if matter shrinks, also means that with the exact same argumentation we have to conclude that it is a strange procedure if space expands with constant matter size.

A description of space where matter is constant in size and space expands is equivalent with a description where space is constant and matter shrinks. The difference is that we have to find properties of space to explain why space would expand versus we have to find properties of matter to explain why matter would shrink.

In my question here I try to show that the explanation why space would expand is wrong. This does not touch the validity of the conclusion if space expands or not. It touches the explanation of an observation and not the observation itself.

Only after we have agreed that this theory is wrong we have the right to propose a different, second, theory as a replacement for the previous, first, theory. Then we can see if with that new theory we can include some observations that were not explained within the first theory.

"You say that space-time is curved internally. That is a statement without any explanation."

Einstein equations relate Ricci tensor with energy-momentum tensor. If energy-momentum tensor is non-zero, then the Ricci tensor is non-zero. If Ricci tensor is non-zero, then the Riemann curvature tensor is non-zero.

If Riemann tensor is non-zero, then parallel transfer of a vector along closed curve makes the vector to be "rotated".

Hello Mikhail G Ivanov.

The mathematics in your answer is correct.

My statement is that this is correct in Minkowski space. This space makes no difference between the x, y, z, and t dimension. all can be traversed in two directions. When you relate what space is related to what part of the energy momentum tensor, then you have to conclude that each time that I move out of the centre of a light cone the energy-momentum tensor becomes zero.

This makes that in the end I still have that a vector transferred along a closed curve is not rotated.

If spacetime is the result of a Lorentz transform of a Cartesian coordinate system, then the t dimension in space time represents coordinate time, while the time coordinate in the Cartesian coordinate system represents proper time. In this sense the coordinate time interval is a mixture of spatial intervals and proper time intervals. I think it is false to suggest that in general t can be exchanged with the x, y, and z coordinates. It is only possible for some special conditions.

If the relative speed is zero, then the Lorentz transform reduces to a unity transform. If the proper time interval is zero, then only a spatial translation results.

Maybe I could make the following comment.

I checked in Wikipedia:

https://en.wikipedia.org/wiki/Lagrangian_(field_theory)

There I find under Einstein Gravity following:

The last tensor is the energy momentum tensor and is defined by

Tμν=((−2)/(Sqrt(−g)))*( δ(Lmatter(Sqrt(−g))/(δgμν))

=−2*((δLmatter)/(δgμν))+gμνLmatter.

g is the determinant of the metric tensor when regarded as a matrix. Generally, in general relativity, the integration measure of the action of Lagrange density is sort(−g)d4x. This makes the integral coordinate independent, as the root of the metric determinant is equivalent to the Jacobian determinant. The minus sign is a consequence of the metric signature (the determinant by itself is negative).

I copied the above text out of that page and tried to make the equations some how readable here. What we see here is that the energy momentum tensor is defined by a differential of a function.

δ(Lmatter(Sqrt(−g))/(δgμν)

Under all conditions where the distribution of matter is not homogeneous this differential gives a value.

However when we have the case of homogeneous and isotropic energy density distribution then this differential will give a zero for any value of the energy density.

So under the condition of homogeneous and isotropic energy density distribution we have

Rμν - 1/2 R gμν + gμν Lambda = 8PiG/C4 Tμν = 0

That part of the energy density that is not homogeneous and isotropic in its distribution has an energy momentum tensor with a value that is not zero.

The parallel transfer of a vector in space where the energy density has a homogeneous and isotropic distribution makes no sense. Each movement over a distance s in the direction a, where a is a direction in space and not space-time, will move the outer edge of space over the same distance in the same direction. With that the vector remains in the centre of space. Since space is filled as stated above there is no change. The transfer has no meaning.

The attempt to make a parallel transfer of a vector in the direction of time can not result in a closed curve because we can't move back in time.

Mikhail G. Ivanov, I would very much appreciate your comment on this.

To Hans van Leunen,

In General relativity lectures, as is stated for example in Lecture notes on general relativity by Sean M. Carroll (1997, page 10) arXiv:gr- qc/9712019

"Therefore the division of Minkowski space into space and time is a choice we make for our own purposes, not something intrinsic to the situation",

there is is made emphasis that in Minkowski space there is no difference.

In real space there is difference between space and time.

Looking forward to response.

You are assuming time is indeed one-directional. But that may be just an illusion.

The explanation is too long to just type here, but here's the article on it:

https://www.researchgate.net/project/Geometric-Model-of-Time

This notion is extremely compelling. However, it does not change anything on my situation. In the case that we look here we talk about points that have a relation to a certain point and about points that don't have such relation. This is described with the light cone. In this article anything that moves in opposite time direction never can be in contact with us. In the description here those points that are on a negative time direction are outside of my light cone.

In that article it is mentioned that we might come back to a kind of absolute frame. We have gone a long distance from assuming the earth to be the reference frame over many other reference frames to the assumption that there is no reference frame. Still I can understand that the proposed absolute reference frame would have its right of existence. However, we have given up the notion of origin. We have stopped to assume that space is rotating around us. Any reference frame where part of the visible objects move faster than the speed of light around us is rejected as a general valid reference frame. Such frame is for private use in a special environment. We have in this way any frame that rotates and instead assume that we rotate. We try to do that for translations. We now use the dipole in the wavelength of the cosmic background radiation to settle on our speed through the universe. With all this effort why do we still stick to a reference frame where most of space moves with a super luminal speed away from us? When do we come to the conclusion that this is irrational and inconsistent.

If we take space as our reference for direction and movement then we also have to take this space as our reference of size. We have to dare to come to the conclusion that space is constant is size and thus that all perception of expansion comes from the fact that everything shrinks. We have to stop searching for properties of space that allow for weird expansion profiles and start looking for properties of matter that can explain the same observations.

In the discussion here I have shown that any expansion of space does not depend on the homogeneous and isotropic part of the energy density in it. This leaves the warping of space as a model for the inhomogeneous part. With that we are talking of the waves on the surface of the ocean without knowledge of the total depth of it.

If the energy density is equal to the value as expected from quantum physics then all matter in the universe is one part in 10121. So it would be an extremely homogeneous and isotropic distribution with a very small variation.

Physical reality has a rather simple foundation. That founation does not even contain notions such as numbers and continuumsd. It can only distinghuish types of certain relations and it can determine how these relations connect. Its structure is quite similar to the structure of classical logic. However, it is not a logic system.

The structure of physical reality has a rather simple foundation. That foundation does not yet contain numbers. It is a set that restricts the kind of relations that exist between its elements. Mathematicians call these structures lattices. The considered lattice is quite like the lattice that defines classical logic. However, the foundation of physical reality is not a logical system. The set of subspaces of a separable Hilbert space has the same lattice structure. This set spans the Hilbert space. Thus, it is sensible to say that the separable Hilbert space emerges from the founding lattice. Mathematicians call this lattice an orthomodular lattice. Separable Hilbert spaces are vector spaces that as an extra feature apply the members of a division ring for the specification of the values of inner product of pairs of vectors. Division rings are versions of number systems. All non-zero members of a division ring own a unique inverse. Only three number systems are division rings. They are the real numbers, the complex numbers, and the quaternions. Depending on their dimension, these number systems exist in many versions that differ in the way that Cartesian and polar coordinate systems can sequence them.

Physical reality mixes all possibilities and puts them on top of an infinite dimensional vector space. It embeds all separable Hilbert spaces into a single non-separable Hilbert space that applies a selected version of the quaternionic number system. It also applies that version together with is coordinate systems as its background parameter space. The separable Hilbert spaces apply their versions of the number system also as their private parameter space and as the eigenspace of a normal reference operator. An orthonormal base of the vector space acts as the set of corresponding eigenvectors.

Quaternionic functions that apply the eigenspace of the reference operator as their parameter space, can specify defined operators by offering their target space as the eigenspace of the new operator, which shares the corresponding eigenvectors of the reference operators.

A real number valued progression defines a subspace that is spanned by eigenvectors of the reference operator of which the real part of the corresponding eigenvalue equals the progression value. The separable Hilbert spaces are supposed to share this scanning subspace. Consequently this scanning subspace represents the current static status quo of the model. The scanning subspace splits the historic part of the model from the future part of the model.

The resulting base model represents a very powerful modelling platform that combines Hilbert space operator technology with quaternionic function theory and indirectly with quaternionic deferential and integral calculus.

It offers a well defined progression and spatial domain. The base model acts as a read-only repository that archives its dynamic geometric data in quaternionic storage bins that combine a proper time stamp and a three-dimensional location. The storage bin features an Euclidean format.

Observers travel with the scanning subspace. They can only retrieve data with an historic time stamp.

The data is transferred from the storage bin to the observer via vibrations and deformations of a continuum that is stored in an eigenspace of a dedicated defined operator that resides in the non-separable Hilbert space. A quaternionic function that describes the living space of the observers defines this operator.

The information transfer affects the format and the content of the perceived information. The observers perceive in spacetime format. The hyperbolic Lorentz transform describes the format conversion. The deformations affect the information path. This affects the content of the information.

Apart from the floating platforms that separable Hilbert spaces represent, the sketched base model does not show dynamics. At each subsequent progression step and for each of the separable Hilbert spaces a private stochastic process generates a new location for an inhabiting elementary module. The elementary module hops around on its platform. The hops form a stochastic hopping path and a dense and coherent hop landing location swarm. The location density distribution of the swarm equals the squared modulus of the wavefunction of the elementary module. Together the elementary modules form all modules and some of the modules form modular systems.

Hi Paul,

if we consider space and time, we get complex Minkowski coordinates u given as: u=t+i*(x,y,z); with i as the imaginary unit, and a factor c/R (with a large size constant R and the speed of light c ) normalized to value one.

By an exponentiation we get quaternions q from the Minkowski coordinates u: q=exp(u).

We see that with: q=exp(t)*exp(i*(x,y,z)) and exp(i*(x,y,z))=(cos(|(x,y,z)|),sin((|x,y,z|)/|(x,y,z)|*(i*x+j*y+k*z)) The inverse transformation is then u=ln(q). (i,j,k) are the quaternion units.

The crucial point is now, that we get for any displacement u3=u1+u2

u3=ln(q1*q2) and we see that this leads to a spacially closed geometry, which cannot be left by any displacement.

This simple mathematical transformation describes a homogeneous, isotropic and finite closed space. Does this answer your question about space curvature in a homogeneous and isotropic situation?

Hans van Leunen,

You elaborate more on your views of reality. You tell again that there is a mathematical way to describe reality over Hilbert spaces and quaternionic functions. With that you repeat the information that you have a certain view of how things work. But with that you make absolutely no attempt to see how you could combine this with the question that is at the beginning of this thread. I try to see how under the condition of homogeneous and isotropic energy distribution space reacts. I try to get answers, opinions if my view has some correctness. So I hope that then someone will show that he understands my way of thinking, that he is willing to extend that with other information and that the synthesis mine and his information leads to some new understanding. You description that space is based on shock fronts, greens function etc, I have seen repeated. What is the relation of that with what is discussed here? If you add your opinion show that you can integrate your view with the question. Here we don’t discuss wether the theory of the Big Bang as described in the Lambda-CDM is right or wrong, we don’t argue if Quantum physics is the right way to describe subatomic processes or if your way is the correct one. I try to base my question on verifiable observations. I make assumptions and with the observations together I make deductions and conclusions. Then those who feel the need to join this thread should have the inner quality to stay with the subject. I feel sad that it seems that you try to bring many questions into your ideas without even making the attempt to link your views with the subject of the thread.. Maybe you have a look into other questions where I did my best to add my views. There you can see how I do my best to show where in the topic of the questions my views fit in and how these views might alter the way we think about their answers.

Wolfgang Konle,

I don’t think that I am completely happy with that answer.

I have some problems with Minkowski space. This is a 4-D space where the time direction is similar to the other directions. I made another question where I asked about the Tuv definition and the Lagrangian maybe you could also look there. I see that time only can go in one direction and space is assumed to be a limited time in age. With that every light cone is a sphere on limited extension, not infinitive. That changes the math.

Maybe we have to go deeper into this to see how my view and your explanation stand to each other.

Thank you.

Regards,

Paul Gradenwitz

Hi Paul,

we have a misunderstanding. In the Minkowski coordinates, the time coordinate is not similar to the space coordintates. There is a fundamental difference like the difference between real and imaginary numbers.

The exponentiation reveals that difference and shows the "one directional" nature of time and the "periodically limited" nature of space.

The metric in the Minkowski space is ds2=dt2- dx2, which shows the imaginary nature of the space coordinates.

Paul, our living space is a continuum that can vibrate and deform. It is a field that can be described by a multidimensional function. The continuum interacts with point-like actuators that cause excitations. These excitations carry mass, or they carry energy, but the field itself does not possess energy. Thus, if energy or mass flows, then these excitations flow. The field reacts with deformations and medium or large-scale vibrations. The excitations that carry mass deform the continuum locally, and globally they extend the continuum. This view is based on equations that have general validity for any field that can be deformed by point-like artifacts. The excitations that carry mass deform by adding volume to the carrier. The excitations that carry energy do not add any volume to the carrier. Thus, these excitations do not deform the carrier.

So, answering your question requires comprehending the mechanism that deforms the carrier. The wave equation and the Poisson equation enable this explanation.

Hi Wolfgang,

I understand what you mean with the imaginary nature of the space coordinates. When you describe this you say you get a finite closed space. How does this relate to reality? What does this describe? Does it describe the light cone or does it describe real space? When I study the lecture notes on General Relativity of Sean Carrol then I see there that he stresses that we have in Minkowski space no special difference in the 4 dimensions. I understood that the minus sign helps us with the direction of time that we call positive. Our current position is at time zero and our past is counted positive.

Maybe you can show me in more detail how your explanation takes care that a point in the past has an effect to a point in the present but a point in the present has no effect on a point in the past.

Also, since the Tuv Tensor is defined as the result of a differential operation of the Lagrange of matter, when matter is everywhere constant then how can a differential operation give a value different from zero?

Thank you.

Hi Hans,

does your solution describe correct the gravity dance of our solar system? Do you have correct description end explanation for the observed cosmological redshift? Do you understand from your description why quantum physics with its stochastic nature works? You say when the medium excites on a point then why does that happen? If you put the origin of the whole construct in the action of the medium and you have no view how the medium generates these excitations then this word medium can be replaced by another word: god. God excites point like places and carries them according to mathematical principles. Your description brings me not further in understanding the correctness of incorrectness of the Friedmann equations. The answers of Wolfgang, for me, seem to have a better chance.

Regards,

Paul

Hi Paul,

I try to answer your questions about the meaning of complex Minkowski coordinates u=(t+i(x,y,z)):

"When you describe this you say you get a finite closed space. How does this relate to reality?":

Any displacement u2 relative to a position u1 in our real Minkowski space leads to a new position and time u3 with u3=u1+u2.

The time in u2 simply describes the speed of the displacement. The time in u3 describes the time, when the displacement u2 has been accomplished.

The complex representation now allows to write u3=ln(exp(u1)*exp(u2)).

"What does this describe": It describes how movements are accomplished.

"Does it describe the light cone or does it describe real space?" :

It describes the light cone if the speed is c. In any other case it describes a straight movement with a speed

Wolfgang, I understand that you can describe movement with that. How do you now describe that when you are at u1 and you go over u2 to u3 that once you are in u3 it is impossible to go back to u1?

Paul,

it is as simple as vector addition. Going back only means using the inverse signs of the components of vector (x,y,z). The only thing is, that the time needed for any displacement must be positive. (Otherwise it would mean a negative speed.)

That is exact waht I mean. I can't go back to u1 because that is backward in time. How do you describe that in the mathematics. What in the mathematic formulas shows this fact?

Paul,

The actuators that indirectly trigger the spherical shock fronts are stochastic processes. For each subsequent progression instant and for each elementary particle the private stochastic process generates a new location on the private platform of the particle. Thus, within that platform the elementary particle hops around in a stochastic hopping path. The hopping path corresponds to a dense and coherent hop landing location swarm. A location density distribution describes this swarm and equals the squared modulus of the wavefunction. (Thus, it is possible to reason back by starting from the wavefunction). The stochastic process owns a characteristic function, which equals the Fourier transform of the location density distribution. This function ensures that the swarm is coherent. The characteristic function contains a gauge factor that acts as a displacement generator. Consequently, at first approximation, the swarm moves as a single unit. The hop landings are the direct actuators of the spherical shock fronts that generate the deformation of the carrier. The gravitation potential of the particle equals the convolution of the Green's function of the carrier and the location density distribution of the swarm.

The stochastic process is a combination of a Poisson process and a binomial process. The binomial process is implemented by a point spread function that conforms with the location density distribution of the swarm

The only mystery left is what generates the stochastic process.

Mainstream physics.stops its reasoning at the wavefunction. The above description shifts the mystery of the wavefunction to the mystery of the stochastic process.

The stochastic processes not only ensure dynamic coherence of the behavior of elementary particles. In conglomerates of elementary particles they also control the binding of the components of the conglomerate.

Hans, For a hop to happen we need a space and time. There is a hop landing location and a hop travel time and distance. Give me some numbers about these parameters. How fast is the hop, how high is the hop, how far is te average distance of the hop. Why is the stochastic process such that it is impossible to reason back and yet you are sure that you know what it is.

Matter according to my understanding has to send out gravity waves. Gravity waves can add. With enough addition of waves we can have something like breaking waves. As soon as we have that the result is that space reconnects. This reconnection creates an electron positron pair. A short time later these two annihilate. Could you give a relation between your view and my view about this kind of processes of random electron positron pair creation and annihilation?

As you might have noticed I take the gravity waves superposition as a source of randomness.

Regards,

Paul Gradenwitz

Paul, the fact, that you can't go back in time with a displacement

du=(dt,i(dx,dy,dz)) is part of the definition. The definition simply says dt>0 for any non zero displacement.

The explicit answer to your question is, that the formulas don't tell us that wa can't go back in time. We have to put this fact into the formula. We express that with the condition dt>0.

Wolfgang, Thank you. Now when I have the GR equations and a uniform density distribution where in these equations do I get this principle effective. If we have u1 and u2 where the time of u2 is later than u1 than matter at u1 could have effect on the curvature of u2 but matter at u2 can't have effect on the curvature of u1. So I have a matter distribution where part of that matter somewhere in space-time does not have effect for other matter at another part of space-time. I ask this because when I use an algorithmic approach where I construct a light cone and for each point of space calculate the gravity effects, I come to a different result than we get from the Friedmann equations. Looking forward to your answer.

Paul, I don't think that you would expect an impact symmetry in time.

Any impact at a space time position u3 with an origin at space time position u1 is caused by an impact function of the displacement u2 with u3=u1+u2. The only restriction is, that the time component in u2 is positive.

@Gradenwitz:

"Deduction:

Because each point is the centre of its own light cone, it is not under the influence of gravity effects of that cone. Because this is valid for any point in space, space itself is not under the influence of the energy density in it.

With that any level of homogeneous and isotropic energy density inside space can't lead to curvature."

That deduction is wrong. On what physical law is it based? It is just a conclusion from Newtonian physics. But Newtonian physics is wrong at the scales considered here.

Einstein's equation shows that if you have a volume filled with energy inside a light cone (even homogeneously) then the Ricci tensor of that volume will be non-zero. Hence the Riemann tensor must have non-vanishing elements, too. Therefore, spacetime must be curved. The idea that there are no gravity influences inside the cone, if the mass distribution is homogeneous is valid in Newtonian physics, but no longer true in general relativity.

Wolfgang, I think that there is an impact. Other wise the two methods should have the same result. You can see my deduction in my article under chapter 3 or in the header of this thread in a shorter form. If I think this through then I only can come to the conclusion that this has to have an influence.

To make the right hand side (Tuv) equal to the left hand side (Guv) in the explanations that I can find it is started to mention the theorem of Gauss, or Poisson. That states The gravitational flux F through any closed surface is proportional to the enclosed mass. To have this effect we have to be outside that enclosed mass. When I construct a light cone than leaving the centre point of that cone to a point U and looking from there back to the centre I have a sphere of points that are closer to the centre than me. All these points are in the future of the point U. So there can't be a gravity effect of these points to U. But when I exactly ignore that fact then I get the curvature that is given in the Friedmann equations, otherwise I get flat space.

regards,

Paul

K, Kassner, Given that what you say is correct, then every gravity simulation programs that tries to simulate cosmological evolution, is wrong. They use exactly the same method. Further, I don't say that I use Newton's law for the calculation of the result for the centre of each cone. I only state that the centre of each cone has the same geodesic as the whole cone. If I only concentrate to this one centre point I will see that it will remain on this place and won't go in any space direction. So for the homogeneous and isotropic part of the energy density I come to the conclusion that space is flat. This might mean that for that Tuv is zero. For any inhomogeneity I get curvature as normal. Since Tuv is defined also as the derivative of a Lagrangian, if that Lagrangian is constant then Tuv has to be zero. But the route one the Lagrangian is not yet clear enough to me. So I am searching to get it clear.

@Gradenwitz: "I only state that the centre of each cone has the same geodesic as the whole cone."

But that is wrong. All you can conclude from isotropy and homogeneity is that the geodesics are of the same shape, that is you can shift one into the other and they will superpose. But that does not mean that the curvature is zero. There is a mathematical theorem (Schur's lemma) stating that the curvature must be constant in such a situation, not that it must be zero.

Tuv is known for the case of a homogeneous and isotropic fluid. It is non-zero. Then the law of gravity, which is Einstein's equation tells us that spacetime must be curved.

In general the geodesic of the centre of a ball is the same as that of the whole ball. You are at the centre of gravity. But now look what is the surface of that ball? That surface is the start of space. Please show me how you can construct a movement, a shape with a second derivative that has non zero coefficients for the space dimensions, for a ball who's surface is the start of space. In the general case you are right. The geodesic of the astronauts in the ISS is the same as that of the whole ISS and that geodesic is not straight. But the geodesic of the light cone can only be in the time direction, because this cone has no space where it can go.

Now you go to the next point in space. According to GR and its curvature if this point would be initial at rest to the first point then it would start moving to this first point. But when I go to the next point, let us say in the positive X direction as seen from the first point, then the light cone of the new point will shift also in that positive X direction. That means every point if the new cone with the exception of a plane is different from the initial cone. And as a result that new point is again in the centre. What information can tell it that it has to move other than in time direction?

You can even go further. Lets us go at a very early moment in time where space is 1 second old. Now we look at two particles that are 2 seconds away. The other particle even not yet exists for each other. So how would space start to curve? I know the GR equations. But each time when I try to imagine the interaction I come to the same conclusion as I give here.

I still would like to know your opinion about cosmological simulations. They take a point, construct the light cone, calculate when the world line intersects the light cone and use that intersection point in their calculations. Because I have the homogeneous and isotropic case I can direct give the solution. For the rest there is no difference.

Tuv is known, do you take the solution from literature of have you tried to construct it your self. I know the literature but fail to reconstruct the literature value.

Dear Paul,

a backward impact in time is in contradiction to our definition of time.

Our current time definition considers something, which has happened, to be non modifyable. This implies that time machines are impossible.

Did you find some evidence which would enable backward time travelling?

Hello Wolfgang,

I have the impression that you try to convince me that time travel is impossible. I think you do not need to convince me. I fully agree with that. What I try to find is whether the equations of the GR take that into account when we derive the Friedmann equations.

So what I did was to circumvent the deduction of the se equations out of the GR. In stead I used the algorithmic approach. Like all cosmological simulator programs. With that I came to a flat space while I could be sure that I only allowed action to flow in the correct direction in time.

Because in the lecture notes about general relativity it is stressed that Minkowski space interprets time as yet another spacial dimension where you can rotate your axes if you need, I still hope to find a proof that the derivation of the Friedmann equations out of the GR guarantees that this restriction of time directionality is taken care of. I have the impression it is not.

I hope you understand my position. I try to show you that I can define a path through spacetime that is physically impossible but mathematically without a problem. The mathematics of tensors is a general multidimensional mathematic. In mathematics there is no special one directional dimension. So when I use general mathematics and apply it to physics I have to add the restriction that time goes monotone in one direction. I think that changes the mathematics and I would expect to see that mentioned in the lectures. I didn't see that. I only see lecturers ponder that from the mathematics there is nothing that prevents to run something backward but space happens not to do that.

I try to find the mathematical rules, equation special conditions, places where there are several solutions and only one is chosen, like 4=2*2 or 4=-2*-2, that show clear that here we take care of the direction of time.

Thank you for your patience with me.

Hello Paul,

our discussion is stimulating and patience is no issue.

It seems for me that what you are questioning is similar to the basic problem I am considering.

What kind of Minkowski coordinates is appropriate to describe our spacetime? Is it an imaginary space coordinate or an imaginary time coordinate. According to your considerations, it must be an imaginary space coordinate, because positive definiteness does not make sense for an imaginary component.

But with an imaginary space component, we get a closed finite size universe. We see that, if we consider a complex space time displacement du=(dt,i(dx,dy,dz)) and the displacement equation:

u'=u+du=ln(exp(u)*exp(du)). The trigonometric meaning of imaginary exponents and the according quaternion algebra shows the finiteness.

My impression is that equations, which describe impact on or relations between objects in spacetime are not helpful for finding large scale properties of spacetime.

Hello Wolfgang,

I am pleased to know you enjoy the discussion. Your question what kind of Minkowski coordinates are best to describe spacetime is an interesting question. With that you didn't answer direct my problem but put it in the context of your truth finding process.

At the beginning of the discussion you already pointed to the notation where you take time as the real axis and space with imaginary coordinates. It amused me that you put yourself in an imaginary world. It is as if we state that we live in the mirror and what we see on the other side is the reality.

I do a lot of simulation in the electronic design environment. There the performance of one singe transistor is modelled with a mathematical model with so many parameters that I even never tried to count them. Several of these parameters have physical meaning like dielectric constants and resistance. Other parameters are pure mathematical form fitting parameters. I don't care so much if these parameters have physical meaning. With them my simulator is able to predict very accurate the performance of my circuit.

I look at the GR equations in a similar way.

I disagree with you that space is is finite. I even think that, although there is a beautiful mathematical description that allows to use real and imaginary numbers, space has nothing to do with imaginary numbers. It is in my understanding wrong to start with a mathematical construct that gives a nice method to describe some kind of 4D space and then to assume that because of this nice notation method you can make conclusions about space.

Think this through. The mathematic helps us to describe reality. Reality will not adapt to mathematics even if that looks close to reality.

Let me elaborate on that a little more by coming back to the light cone. In the mathematical view this is a 3D brane in 4D space with a radial time dimension and two angular space dimensions. However this is just a representation. At the present moment in time at a point, which is at the centre of our light cone, the informations of far away points arrive. Each message, photon, gravity unit, (here I don't care how you call them), has had a different time of travel and came from a different direction of space. What we do with the light cone is that we sort all these messages that are in the present in this point, according to the time they traveled and the direction from where they came. Then we construct a 3D representation of this travel time and direction. This means the light cone itself has absolute no reality. It is only a representation that tells me in a graphical way how long a certain message has traveled and from what direction it came from.

To think that we can interpret this though construct as reality is as wrong as that we think that behind the TV screen there is a real world.

It is great to model the universe with a 4th dimension that is time times the speed of light. The reality is that we have space that evolves in time driven by the forces as they arrive at a moment at a point in the present. Space doesn't care of that force traveled for a giga year or one second. As long as the magnitude and direction is the same it will react the same. It is only our quest to understand nature that makes that we need all the mathematics.

I have studied 4 dimensional space since I was 11 years old. It resulted in a capability to imagine 4D space. From this study I came to the conclusion that time never is a dimension but only the bridge that helps you represent a higher dimension in a lower dimension.

Looking forward to your response.

Paul Gradenwitz

Hello Paul,

You write: "I disagree with you that space is is finite."

The point is:" Given that space is finite", what are the consequences?

What kind of coordinates shall we use? Are we able to describe the red shift? Do we run into an unresolvable contradiction?

"Infinite flat space", an "accelerated space expansion"," universe start in a big bang", "dark matter to explain large scale gravitation and space expansion" these are all elements of the current main stream model which do not match to our experience. If we want to ged rid of all these theoretic artefacts, we should try deriving an alternate theory and look how far this could lead us.

A very plausible start is a positive definite time, which leads us to the imaginary space dimension in a four dimensional spacetime and to a positive definite spacetime metric du²=dt²-dX², which simply means that dt must be larger or equal to dX/c or v

Hello Wolfgang,

In several other threads I have mentioned my views on how to explain the problems you mention in your answer. Your attempt is to construct another mathematical model of space.

Because you have very good mathematical knowledge let me state it here very compact. The observation of the cosmological redshift in normal theories is explained with movement. Space expands and our size is constant. All properties of scale change are properties of space. This leads the postulate of a singularity in finite time distance in the past.

The same observations can be explained by the statement that matter shrinks. Then the comoving reference frame is declared as static and all relations that emerge from the scale change in the expanding universe transpose into relations of matter change. Since the change of reference from a static size of matter to a static scale of the universe is a mathematical transformation there is no initial way to distinguish who is right. But with a static universe there is no need for a singularity because with larger matter also the time of processes with that matter is larger. In the end you can construct a process that assumes an age of the universe older than any given age.

In this explanation of the observations I make no attempt to come to a new kind of mathematics like you do with a real time axis and imaginary space axis. A finite universe has somewhere a border. Even if this finite universe is closed like the surface of a ball then we still have somewhere a maximum dimension. In my view of the universe for any given dimension of space and time there is more of space outside that dimension than there is space within that dimension.

Because I think that with an algorithmic approach I have shown that space will not change its scale for a homogeneous and isotropic density there should be no problem with this kind of universe.

There are with this universe model observations that can be explained that are categorically ignored by modern science because they have no imagination that this could have happened.

Regards,

Paul

Hello Paul,

you write " A finite universe has somewhere a border. Even if .."

Within a homogenous, isotropic and periodic space, there is no border and we do not have somewhere any maximum.

The remaining question is:

"Does a gravitational potential exist, which is susceptible only for movements and is homogenous and isotropic?"

This potential would be a product of the constant and isotropic space curvature and act on moving masses and on electromagnetic energy.

Hello Wolfgang,

With a periodic space there is the finite dimension of the period.

That potential from constant and isotropic curvature is only possible with a finite universe.

So let us assume that space did start some 13.8 GYR ago or so.

Now I understand that the official opinion is that space started such that there was an extreme high energy density but at any time space was infinite in size.

So we start at one Planck second after the begin. There is no matter yet, , no pressure, only energy. For each point in space the light cone is c times Planck second in Radius. That point of space has a complete symmetric environment that is equal to any other point. So what brings the curvature?

Curvature would mean that a ball of space after some time changed its size. If the expansion would be zero after some time the size would shrink.

Shrinking would be if there is knowledge for that ball that it exists. But any reasonable ball would consist of a lot of points that are in no causal connection with each other. So why shrink? Or with expansion why decelerate? Or with negative energy why accelerate?

If I have two mass centres like the sun and the earth, then there are Lagrange points where the curvature is cancelled. Closer to the sun the curvature is in one direction and closer to the earth the curvature is in the other direction. In the case of a homogeneous and isotropic energy density the whole space is Lagrange point with curvature zero.

A description of the space dimensions as the imaginary values of the time dimension is in my eyes a nice mathematical construct but without connection to reality. From mathematical point of view you come to some nice periodic functions but reality is different.

So, Yes the GTR equations say there is curvature. I can reconstruct what is a gradient, I can reconstruct was is differentiating. All these mathematical operations are acting on values. Any of these operations can be replaced by an algorithmic procedure. It might be an NP complete problem that would take very long to do, but many of the complex GTR problems are calculate this way. So we have to accept that the algorithmic approach should come out the same. Only in that approach I can clearly follow what point interacts with what other point. So If there is a difference I assume that it is in the fact that Minkowski space allows time to go in two directions. I did the algorithmic approach. It gives me flat space.

Any answer that the GTR equations dive a different solution will be answered by me with "yes, I know".

Then I get other functions with Minkowski space coordinates as an explanation. I don't get a proof that the equations are taking care of the unidirectionality of time.

When I have the height y with a function of a gaussian curve of a variable x then I can everywhere get the derivative of y to x. I also can integrate and get the surface under that function.

When I do the same over t, then I only can go forward, I can't go backward. That means I can talk about differentiation but not about integration. Integration means that when I come to the next value of t the previous value still should exist. I can't add two values that have no relation with each other. The past is gone. In Minkowski space it exist. But no more in real space.

As long as I make sure that enough of my light cone towards the past is so empty that I can ignore it and only nearby there is something, then I can mix past light cones with current light cones and get with the GTR correct results.

Regards,

Paul Gradenwitz

Hello Paul,

let us assume that some 13.8 GYR ago or so, there was an event which triggered all black holes in the universe, to become white holes and to emit their complete mass as high energy neutrons.

The event could have been the absence of an incoming flux of neutrinos, to keep an outer layer of the black holes populated. Without that outer layer the layered structure of the black hole crashes layer by layer and finally generates a white hole. The event "missing neutron flux" happens nearly at the same time in the whole universe, after the star fire has been extinguished.

After 13.8 GYR, an event like this would lead to just the situation, we are observing now.

The presence of remaining objects from the time before the event, even would promote star and planet building and the intense neutron flux could explain the considerably large percentage of heavy atoms like uranium and tungsten on our planet.

We see, that we do not really need a big bang, to explain the current state of the universe. Coordinated bangs of galactic scope are sufficient to provide new fuel for the star fire.

A Lagrange point reflects a inhomohenous and anisotropic local situation. We cannot deduce the impact of a constant and isotropic curvature from the geometrical properties of Lagrange points.

GRT perfectly models the local impact of masses on spacetime. It does not describe the spacetime topology.

We cannot expect that equations intrinsically know something about the uni directionality of time. It is our job to implement this property in the equations.

A theory without a well defined platform is quite probably a fantasy.

See: Structure in Reality; Article Structure in Reality

Hello Wolfgang,

You give an interesting thought of how to make a bariogenesis without a big bang. That seems to be based on a view of how a black hole functions that is new for me. It has probability of being fantasy if it is not based on a well defined platform as Hans mentioned, however that also means that it has a probability of being sound and we only need to find that correct platform that belongs to it. This in comparison to a theory based on an intrinsically wrong platform where a chance of correctness is not available.

With my Lagrange points I try to show that inside space we have local curvature in different directions and in between we have zero curvature where the effects cancel out. In my example I think that the effects of gravity cancel out everywhere.

GTR perfectly models local situations. But these situations are based on clear inhomogeneous distributions where the outside can be ignored. Because I can't expect that equations intrinsically know something that is not put in there I have the task to check if the result is consistent with a case where I have taken care of the unidirectionality of time.

If I then come up with a situation where both calculations give different results then we can't ignore that with the reasoning that the GTR equations perform so well in all inhomogeneous cases that we trust that in this case it will also be correct specially when the calculation method is a well accepted method for large scale space simulations.

Regards,

Paul Gradenwitz

Hello Paul,

recent analysis results seem to reveal an inner structure of black holes (A black hole is an ECO, an exotic compound object).

(seeArticle Gravitational wave echoes through new windows

But my idea of a baryogenesis without a big bang only should show that another possibility is thinkable, even if it is only a fantasy. But isn't the big bang also a fantasy?

Hello Wolfgang,

When a black hole grows then its radius increases. With increasing radius the tidal forces decrease. That means the difference between attraction over a part dR reduces. Now we can argue if inside a black hole surface the gravity continues to increase or if, from there, the gravity decreases as is in a solid ball. We have no information of it and thus every statement about the interior is extrapolation.

If the interior has a gravity that decreases towards the centre, then only the pressure keeps that centre together. Now, if the increasing size of the black hole reduces the tidal forces enough this force could become smaller than needed to drive an atom towards the black hole surface. In other words, the atom could sit on the surface of the black hole with a decreasing force inside and a decreasing force outside. At that moment the pressure on the surface might become too low to keep matter to enter that black hole. This could make it become a white hole.

I show you that I can make it thinkable that a black hole can become a white hole. Maybe you could do the calculation that could prove that this could become true. But keep in mind that I made an assumption about the inside of a black hole while I admit that there is no information about the inside. The article states that an echo from inside the black hole seems to come from a Planck distance below the horizon. This could mean that there is something solid enough below the horizon to generate an echo. This makes also my assumption more thinkable.

Maybe you have a look into my theory as written in my paper.

https://www.researchgate.net/profile/Paul_Gradenwitz/project/Theoretical-Cosmology-analysis/attachment/5a027823b53d2f10b0ba7293/AS:558261272104960@1510111267225/download/Big_Collapse.pdf?context=projectUpdatesLog

There I have a view of the universe without a big bang. On several answers here I have shown that an expanding universe is only a stubborn misinterpretation, under the assumption that we have the privilege of constant size, that cosmic redshift means that space expands. I assume that space has the privilege of size and thus I conclude that space doesn't expand and that we shrink.

A Happy New Year.

Paul Gradenwitz

Dear Paul,

thank you for the detailed and continuative information about possible properties of black holes. May be the following aspects may contribute as well: (I don't think that these aspects are in contradiction to your theory)

- Concerning the interior of black holes, we are not necessarily completely blind, because colliding black holes generate gravitational waves, which according to collision theory, provide a certain insight.

- The horizon is a theoretical limit, which is not necessarily reachable. It is possible that dynamical dilatation effects prevent achieving the limit.

- If the horizon limit is not reached, the exotic object still has matter outside the limit. Inside the limit is not reached as well, because there the gravity becomes reduced.

- Extremely high energy radiation could leave the object, but either there is no source of such a radiation or there are interactions like pair building, which swallow the photon energy before the photon can escape.

I do not think that tidal effects have an influence, because on the length scale of elementary particle size, macroscopic gradients are negligible.

The "atoms" which exist on the surface must be much denser than neutron material on the surface of a neutron star. May be that describing the exotic state of matter at the surface as a liquid or as a solid state or as a completely new compound state is appropriate.

I hope, you had a good start into the new year.

Wolfgang Konle

Dear Wolfgang,

In that article you recommended they find that the waves seem to come from a plank distance below the horizon. For my understanding this means that the uncertainty of where these waves come from is larger than this distance. So I see no information from inside.

If BHs don't exist but only exotic objects, then we have the same issue. A lot of mass somewhere together and a large gravity gradient outside.

You know hat one of the pillars of the GRT is that we say that we can't distinguish gravity from acceleration. Acceleration can move everything in a parallel way. Gravity is always towards a centre. But under small enough conditions we come close. There is however always a gradient. That gradient is what drives the movement. You can state that as curvature that is fine.

Take a ball. If you let this ball grow, then your curvature decreases. Your radius increases. Now you can continue past infinity and you get a hollow ball. Exact in between this, when the centre of the ball is at infinity we don't know at what side is this centre. A hollow concave ball has no gravity. A convex normal ball has. But the tidal forces are so small because the gravity gradient decreases. Leonard Suskind even mentions that according to his understanding a spaceship could enter, sail through the surface of a supper massive BH without being damaged due to the low tidal forces. It only never would get out and at least at the centre wold get crushed.

Now you can calculate at what radius is the tidal force so small that the uncertainty of the tidal force is larger than a proton, or an electron or...

At that moment the black hole can't continue to attract. It is for sure when the BH is larger than half of the universe because at that moment it is a convex shape with the black hole outside and the empty space inside. That is pretty weird but if you start to shrink space, as theories propose, then you might end up with this kind of situation.

See my update of my project there I have a discussion about this.

Regards,

Paul Gradenwitz

Dear Paul,

thank you again for your detailed information.

The following article cited in the thread "good bye black holes" describes that a shrinking star will never reach the event horizon:

Dispelling Black Hole Pathologies Through Theory and Observation

We hopefully will get further detailed information about the nature of objects we currently consider as black holes.

Dear Wolfgang,

I look in the thread you pointed me at. See my comment there.

You have a view that space is curved and can be described with imaginary space components. With your view you will end up in situations as I have described above. See also the comments in my project log.

I think that any assumption of curved space and expanding space will lead to insurmountable inconsistencies. And because of that I have concluded for my self that any attempt to try to explain our observations with space rotation, translation and scale change, have to be converted to rotation, translation and scale change of the objects inside space. Especially the last item, scale change, is in the beginning hard to accept. But it will not lead to unsurmountable inconsistencies and will not result in singularities within finite domains.This means I can accept asymptotic reaching of a zero size when time goes to infinity or similar limits.

I hope my view that we shrink and that space is static gets more acceptance.

Regards,

Paul Gradenwitz

Dear Paul,

the complex properties of nature do not allow any deviation without severe side effects. Shrinking surely would touch properties of atoms and molecules.

The only possibility to explain our existence is, that exactly the properties we currently observe have been stable during the time needed for life development, which is more than a billon years.

Because we do not observe significant differences in star properties in distant galaxies, we can assume that the properties of atoms, which determine the life cycle of stars, have been constant for an even longer period of time.

Dear Wolfgang Kohle,

Have a look into this link and

http://www.science20.com/hammock_physicist/universe_expanding_or_are_we_shrinking-118673

Article A Universe without expansion

You are completely right that it would change the atoms. But surprisingly it would not change the relative configurations of the atoms. We observe that the fine structure constant is stable. We observe that the relative frequencies of hydrogen atom light absorptions are constant and we observe that the same hydrogen spectral lines are redshifted when they come from further away. We aware that the statement that space is constant and we shrink implies that we make a mathematical transformation of what we declare constant and what we declare variable. With that there is initially no way to separate these two in favour for one or the other. Both have 100% the same observable results. If life is possible in an expanding space with constant size matter then, by definition, that same life is possible in a constant universe with shrinking matter. Since you are reading this and I am writing this, I assume that we are in such universe. You make the assumption that matter would change its relative behaviour and make life impossible. With that assumption you simply have not allowed for the right parameters to become variable. When I say once, a long time ago, the scale of the universe in relation to the scale of a hydrogen atom radius was half of the current value then that is the same as when I say, at that time the size of an hydrogen atom with respect to the scale of the universe was double its size. How that is possible? It is possible in such a way that with size reduction all other relations, chemical, quantum mechanical, etc. stay 'constant'.

So you can't come with that under that condition matter would make life impossible, because then you would have the wrong description of matter.

The simpler the parameter manipulations we need the easier it is to accept that it is possible. Wetterich showed how to do that.

Regards,

Paul

Dear Paul,

even if you were right and continous parameter modifications exist, which are in a certain range not harmful for life development, we should better assume, that natural constants actually remain absolutely constant.

The theory of an expanding universe or the shrinking content of the universe is in contradiction to that assumption and therefore probably wrong.