# Deriving Spacetime in Four-Dimensional Euclidean Space Without Time and Dynamics

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Is it possible to build spacetime based on system without time and dynamic?

It looks as it is not possible.

However, seems as there is way to derive spacetime based on system without time and dynamic.

I wrote article how it can be done.

Or, direct link to pdf document: https://vixra.org/pdf/1812.0157v5.pdf

In the article, I propose following model:
1. Time and dynamic is absent on fundamental level. No any motion, no energy, nothing related to time and dynamic on fundamental level
2. On fundamental level there is Euclidean space, with al least 4 dimensions. (And yes, I know about impossibility to derive hypersurface with Lorentz metric in Euclidean space. There is solution for the theory)
3. All dimensions are equal, there is no preferred direction.
4. Reiterating that was written before – time and dynamic on fundamental level is absent. Completely. No anything like time dimensions etc.
5. There is some field or field on fundamental level. The field(s) are defined at each point of fundamental space and have values belonging to set of real numbers (scalar field). (Scalar fields, described in textbooks for QFT, have different properties than these fields, so statement about insufficient degrees of freedom is not applicable here. But lets put it aside of the discussion) There is no time or dynamics. Thereby, the fields also have no dynamics. It also means full determinism. I will call these fields fundamental ones. I suppose that the fundamental fields are smooth and are described by certain partial differential equations. Each of the fundamental fields is independent of other fundamental fields. This means that there are no other fields in the equations describing any fundamental field.
6. Quite obviously, it is not possible to add observer to the model in traditional way. Observer always requires time for its existence. Absence of time means it is necessary to add something else to add observers. Instead of time dimension, I use space dimension. Details are in article. All space dimensions, as I already write, are equal, no preferred direction. Observer is able to observe changes because I postulate that changes on consecutive 3-d hyperplanes in fundamental space can lead to appearance of observer. [These is hardest of understanding point of the model].
7. Because observer appear as result of changes of field(s) on consecutive 3-d hyperplanes in fundamental space (I reiterate, there is no changes in fundamental space, But state of projections of fundamental field(s) on consecutive hyperplanes can change), observer is not exists objectively. And even more, Universe is not exists objectively. It exists only when there is some observer which observe it. Without observer, spacetime in the model is just mathematical abstraction.
So, I propose subjective idealism in foundation of my theory. Fundamental space with defined on the space field(s) exists objectively. But, because observer cannot exists without time and dynamic, the space and fields exists in quite nontraditional way, without any ability for direct observation. Their presence can be verified only indirectly, based on how well the theory fit to observations.

As one can notice, there is no relativism at the model. There is no aether at the model. There is no motion at the model. There is no gravity at the model.
What I claim as done in the article in scope of the theory:
1. Derived anthropic principle. Yes, derived, not postulated
2. Derived principle of causality
3. Derived equations of special relativity
4. Derived principle of locality
5. Found what is gravity
6. Derived equations of general relativity. And I derived in in such way, that there is clear explanation why gravity part is absent in tensor of energy-mass.

And all above done on model without time, without dynamic, without principle of locality, without gravity.
So, I remove lots of phenomena from list of fundamental ones.

The claims, as it can be seen, are quite big. I am interesting in testing the theory, test are the results correctly derived, are any obvious weaknesses.

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Your time and space have infinitely many singularities. And there's no inverse mapping from the alphas. It doesn't look like your v's map to the world we know and love.

And no offence, but the rest of it looks like you're just copy-pasting common physics and puffing it up with lots of words, TBH. Example: Because there are hypersurfaces, there must be curvature, and thereby, there must be a geodesic equation. So you write down the geodesic equation. Nice.

Why? What particles are moving along them? Where are these particles?

You also copy-paste the Lagrangian of GR as if it were derived from your idea. It's not. You've just attached it to your idea.

You also talk about conscience giving rise to the world. Whose conscience? Mine? Donald Trump's? How many are there? How do they give rise to the world?

You also talk about energy long before you talk about Lagrangian formalism or anything that logically amounts to it. And energy is a consequence of it. Energy is not a primitive concept.

I have also serious doubts that you can construct pseudo-vectors like angular momentum, helicity, etc.

Need I say more? Maybe I do.

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5 minutes ago, joigus said:

Your time and space have infinitely many singularities.

Many singularities? May you show even one?

6 minutes ago, joigus said:

And there's no inverse mapping from the alphas

Sorry, what is alphas?

7 minutes ago, joigus said:

And no offence, but the rest of it looks like you're just copy-pasting common physics and puffing it up with lots of words, TBH. Example: Because there are hypersurfaces, there must be curvature, and thereby, there must be a geodesic equation. So you write down the geodesic equation. Nice.

First I derived hypersurfaces with certain properties, next started to use them. So, their usage come from ideas of my theory, not simply copy pasted from somewhere.

9 minutes ago, joigus said:

Why? What particles are moving along them? Where are these particles?

It is question, not considered in the article. I have answer to it, but I prefer to not discuss it. Reason - it will lead to necessity to talk about how quantum physics arise in the model. And the article is about how spacetime arise in the model, more narrow topic.

11 minutes ago, joigus said:

You also copy-paste the Lagrangian of GR as if it were derived from your idea. It's not. You've just attached it to your idea.

It is simply wrong statement.

Do you disagree with derivation of action variation in my article? If the derivation of action variation is correct, it means I derived equations of GR too.

13 minutes ago, joigus said:

You also talk about conscience giving rise to the world. Whose conscience? Mine? Donald Trump's? How many are there? How do they give rise to the world?

Looks as you read the article too fast, because there is answer to the question in the article. Conscience of any intelligent observer.

15 minutes ago, joigus said:

You also talk about energy long before you talk about Lagrangian formalism or anything that logically amounts to it. And energy is a consequence of it. Energy is not a primitive concept.

Energy is primitive concept. It is  enough to have symmetry to time translations, and you would have energy conservation law. I wrote how symmetry to time translations arise in my model.

18 minutes ago, joigus said:

I have also serious doubts that you can construct pseudo-vectors like angular momentum, helicity, etc.

Such questions are not covered in the article, in order to make it more simple. What can be tested - is SR and GR are really derived in such model without fundamental time and dynamic.

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18 minutes ago, joigus said:

You also talk about energy long before you talk about Lagrangian formalism or anything that logically amounts to it. And energy is a consequence of it. Energy is not a primitive concept.

Sorry, you do introduce it later. But I don't see how this emerges from any new assumptions of your own.

Just now, andsm said:

Sorry, what is alphas?

𝑣=𝑣𝑡tg(𝛼)To find the components 𝑣, one can divide the rotation into relative to the axes rotations: 𝑣𝑥=𝑣𝑡tg(𝛼𝑥) 𝑣𝑦=𝑣𝑡tg(𝛼𝑦) 𝑣𝑧=𝑣𝑡tg(𝛼𝑧)

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3 minutes ago, joigus said:

Sorry, you do introduce it later. But I don't see how this emerges from any new assumptions of your own.

How energy emerge from assumptions of my theory?

I derived space and time. Build it in such way, that time  will have symmetry to translations. Next, I can use existing math and Noether theorem to show I have energy and energy conservation. So, I can use energy in my equations.

About inverse mapping - you mean what there is no bijection for the mapping or what?

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3 minutes ago, andsm said:

23 minutes ago, joigus said:

You also copy-paste the Lagrangian of GR as if it were derived from your idea. It's not. You've just attached it to your idea.

It is simply wrong statement.

Do you disagree with derivation of action variation in my article? If the derivation of action variation is correct, it means I derived equations of GR too.

You do. And I quote:

Quote

The action for a physical system in some field usually looks like: 𝑆=𝑆𝑚+𝑆𝑓+𝑆𝑚𝑓 Here, 𝑆𝑚 is that part of the action that depends only on the particles properties, i.e.

Then you narrow it down to a simpler form. And then you pull the rabbit out of the hat about here:

Quote

Now we can proceed to the derivation of the gravitational field equations. These equations are obtained from the principle of least action 𝛿𝑆=0, 𝛿𝑆=𝛿(𝑆𝑚+𝑆𝑔)=𝛿𝑆𝑚+𝛿𝑆𝑔

Variation 𝛿𝑆𝑔 is equal to [5,p. 355]:

𝛿𝑆𝑔=𝑐316𝜋𝑘(𝑅𝑖𝑘12𝑔𝑖𝑘𝑅)𝛿𝑔𝑖𝑘𝑔𝑑Ω

And what is [5, p. 355]? Nothing other than:

Quote

[5] L.D. Landau, E.M. Lifshitz, Field theory, vol II, izd. 7, MoscowNauka” 1988

You're copy-pasting, as I said, from excellent physics books. How could I disagree with Landau and Lifshitz, Field Theory, Vol. II? What I'm saying is that none of this appears to follow from your ideas. Not as far as I can see.

Here's a try to guess at what you've done:

1) Define an arbitrary map (not even well defined mathematically) from t, x, y, z and claim that you've shown space and time as "emergent" from your singular variables.

2) Copy and paste standard equations from physics books.

3) Puff it all up with lots of words. Throw in "conscience" and "observer" and "hypersurface". Big words.

Only thing I can say is I'm sorry I can see right through it. We must be connected through a hypersurface.

32 minutes ago, andsm said:

About inverse mapping - you mean what there is no bijection for the mapping or what?

Exactly. Not invertible at infinitely many points. What's that multi-branching? Conscious projections? Observers?

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10 minutes ago, joigus said:

Then you narrow it down to a simpler form. And then you pull the rabbit out of the hat about here:

Quote

Now we can proceed to the derivation of the gravitational field equations. These equations are obtained from the principle of least action 𝛿𝑆=0, 𝛿𝑆=𝛿(𝑆𝑚+𝑆𝑔)=𝛿𝑆𝑚+𝛿𝑆𝑔

Variation 𝛿𝑆𝑔 is equal to [5,p. 355]:

𝛿𝑆𝑔=𝑐316𝜋𝑘(𝑅𝑖𝑘12𝑔𝑖𝑘𝑅)𝛿𝑔𝑖𝑘𝑔𝑑Ω

And what was written right above the equation? Derivation of how action should look in my model:

Quote

The gravitational field in the model under consideration is the hypersurface curvature, necessary for the fulfillment of the principle of causality and the sameness of the laws of physics. This means that the gravitational field is determined by particles completely. It follows from this that there is no interaction between the gravitational field and particles, the particles configuration determines the gravitational field. Then, for the gravity and particles interaction

Smf=0

Consequently,

S=Sm+Sg

where Sg – gravity action.

So, I not take Smf=0 for gravity out of nowhere, it it result of my model.

And next yes, I took Sg from excellent textbook. I can do it, because in the textbook the action is calculated based on curvature only - exactly what I need.

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2 minutes ago, andsm said:

And next yes, I took Sg from excellent textbook.

Thank you. Some gibberish you invented must be zero. Only non-trivial stuff comes from a book.

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19 minutes ago, joigus said:

Here's a try to guess at what you've done:

1) Define an arbitrary map (not even well defined mathematically) from t, x, y, z and claim that you've shown space and time as "emergent" from your singular variables.

2) Copy and paste standard equations from physics books.

3) Puff it all up with lots of words. Throw in "conscience" and "observer" and "hypersurface". Big words.

It is wrong right at start. I define function of fundamental field not on (t, x, y, z), but on 4d Euclideam space without time. Time dimension is absent in my model. Next, I derive from the space with field, defined on the space,  spacetime. And here, during the derivation, I have to use observer and conscience, because there is no other way to derive spacetime  from space without time and dynamic.

As for standard equations. Yes, I use them, but only after I shown how and why  they can be used in my model.

2 minutes ago, joigus said:

Thank you. Some gibberish you invented must be zero. Only non-trivial stuff comes from a book.

Hmm, if you think it is gibberish and invented by me...

Really, no questions.

Just some hints. You may look on it in textbooks, for your self education.

1. Action for any force, except gravitation, is S=Sm+Smf+Sf

2. Smf=0, for gravity, is one of greatest mysteries in GR.

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4 hours ago, andsm said:

Many singularities? May you show even one?

All of them, AAMOF:

$f\left(\alpha\right)=\tan\alpha$

$\alpha=\frac{\pi}{2}\left(2k+1\right),\:k=0,\pm1,\pm2,\cdots$

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8 hours ago, joigus said:

All of them, AAMOF:

f(α)=tanα

α=π2(2k+1),k=0,±1,±2,

Thanks, you confirmed what my theory have same "singularities" as special relativity when approaching speed of light. Quite expected "singularity", I would say.

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17 hours ago, andsm said:

Energy is primitive concept. It is  enough to have symmetry to time translations, and you would have energy conservation law. I wrote how symmetry to time translations arise in my model.

Energy is not a primitive concept. You can actually re-formulate classical mechanics pretty much without it with the Jacobi variational principle. Take a look at Barbour-Bertotti mechanics, e.g., who re-discovered the Jacobi action principle. The action would be,

$S_{BB}=\int dt\sqrt{T}\sqrt{-V}$

The theory would be diffeomorphism invariant with one constraint equivalent to E=0. You can solve classical mechanics one energy at a time. But energy as we know it looses its "primitive" meaning. No version of mechanics, GR or other dynamical theory of physics is built from the concept of energy.

As always happens with physics, the more general your framework is, the more abstract the primitive quantities become. The primitive entity is the Lagrangian, but the meaning is much much less clear.

Oh, and in GR energy is not conserved in general. Some metrics have a time-like Killing vector and then you can derive a particular "version" of energy. Energy in GR is not a very useful in general, very fundamental concept.

I could say more, but this is starting to be a pain in the neck.

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You never derive spacetime in your article? Also, your article made me think about how little we know about gravity. What is gravity after all? I think there would be something to gain if you wrote about it. There is a series of things you consider that I don't like. First, you consider that the world is mathematical abstraction. How could we even create mathematical abstraction without mass? It makes no sense. We would simply be not able to perceive certain concepts, as it happen with objects with over 3 dimensions, that doesn't make them mathematical abstraction. Then, you disconsider the existence of energy, motion, time and dynamics. Things that have technological implications even. I understand that you believe in a world where the observers make up the existing things, but this is never put in a clarifying light. Why you believe this that is. You simply say the observer is fundamental.

Oh, and thanks for introducing me a site where I can upload articles. I was looking for one.

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On 7/26/2020 at 2:03 PM, joigus said:

Energy is not a primitive concept.

It depends on point of view.

Also, classical mechanics can be formulated in multiple ways. For example, it can be formulated with symmetries.

On 7/26/2020 at 2:03 PM, joigus said:

Oh, and in GR energy is not conserved in general. Some metrics have a time-like Killing vector and then you can derive a particular "version" of energy. Energy in GR is not a very useful in general, very fundamental concept.

I know about problems with energy conservaton in GR, I studied GR in university.

How it is rrelated to the topic?

On 7/27/2020 at 6:54 AM, lagrangian said:

First, you consider that the world is mathematical abstraction.

No, I not say what the world is mathematical abstraction.

Mathematical abstaction, in my theory, is spacetime without intelligent observer. Reasons are explained in the article.

On 7/27/2020 at 6:54 AM, lagrangian said:

How could we even create mathematical abstraction without mass?

In the article was not shown how mass arise in such model, because the article cover more narrow topic. However, it is easy to show how mass arise in the model. So,m absense of mass (and energy) at fundamantal level is not a problem for the theory.

On 7/27/2020 at 6:54 AM, lagrangian said:

You simply say the observer is fundamental.

Here I conpletely disagree.

I not just say that observer is fundamental. I show, what if fundamental structure of Nature have no time and no dynamics, it leads to physical models where observer is more fundamental than observable spacetime.

Basically, say that time and dynamic ansent at fundamental level - and one only possible physical model would require observers whichs are more fundamental than observable spacetime and it means subjective idealism.

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1 hour ago, andsm said:

Also, classical mechanics can be formulated in multiple ways. For example, it can be formulated with symmetries.

OK. Give me the dynamics of the Solar System with only integrals of motion derived from continuous symmetries.

You can't. And the reason is that the system is not integrable (the number of integrals of motion is insufficient, far less than the number of degrees of freedom.)

1 hour ago, andsm said:

I know about problems with energy conservaton in GR, I studied GR in university.

How it is rrelated to the topic?

This is how: You wrote down Einstein's equations in the vacuum from the Einstein-Hilbert action. I just assumed you were talking about GR. Were you not?

I know (and I've told you so) that there are problems that you can solve with an energy-like integral of motion. Example: Using the Schwarzschild solution to derive the anomalous motion of Mercury. But this is not generally valid. If you think it is, give me the integral of the energy for the FRWL metric.

You can't. And the reason is that the metric does not have time-translation symmetry.

Need I say more? Something tells me I do.

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Posted (edited)

Just looking at your premises I find the following conclusion.

Premise 2 simply proposes the existence of a fundamental Euclidian space.

Premises 1,3 and 4 are redundant since they are already implied by premise 2.

Premise 5 add new material but does not properly define the Field variables, which are necessary for the existence of any scalar field, since they are not one of the Euclidian axes.

Premises 6 and 7 are a complete mish mash and need to be rewritten.

They appear to introduce an 'observer, deny the existence of the observer and yet allocate 'properties' to this non existent observer.

Edited by studiot

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7 hours ago, joigus said:

the number of integrals of motion is insufficient, far less than the number of degrees of freedom.

Far fewer. I hate to make grammatical mistakes!

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3 minutes ago, joigus said:

Far fewer. I hate to make grammatical mistakes!

Disgusting. You’re dead to me now /throwing up in my own mouth

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4 minutes ago, iNow said:

Disgusting. You’re dead to me now /throwing up in my own mouth

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23 hours ago, joigus said:

OK. Give me the dynamics of the Solar System with only integrals of motion derived from continuous symmetries.

You can't. And the reason is that the system is not integrable (the number of integrals of motion is insufficient, far less than the number of degrees of freedom.)

I not remember, is it possible to define Newtonian gravity in symmetries. If it is possible, it would result in exactly same equations.

But it is not related to the topic.

23 hours ago, joigus said:

This is how: You wrote down Einstein's equations in the vacuum from the Einstein-Hilbert action.

No. Einsteain postulated his action. I derived the action, not postulated.

And, as we found earlier, your knowledge of GR is far from perfect.

GR  in the article was derived near end of article.  There is  derivation of spacetime earlier. There is derivation of SR, also earlier than GR. Lots if the theory can be checked for logical correctness without good knowledge of GR.

21 hours ago, studiot said:

Premise 2 simply proposes the existence of a fundamental Euclidian space.

Premises 1,3 and 4 are redundant since they are already implied by premise 2.

Hard to say anything about any of numbered premises, because I not know what each number means.

21 hours ago, studiot said:

Premise 5 add new material but does not properly define the Field variables, which are necessary for the existence of any scalar field, since they are not one of the Euclidian axes.

I guess it is about adding scalar field? I have no equation for the scalar field. And, for purpose of the article, I not need it. All what I need: the field shoukld satisfy certain restictions, described in the article.

21 hours ago, studiot said:

Premises 6 and 7 are a complete mish mash and need to be rewritten.

May you name them? I would like to improve article, if there are some weak spots in it, but I not see them.

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Posted (edited)
51 minutes ago, andsm said:

Hard to say anything about any of numbered premises, because I not know what each number means.

They are your premises, not mine and you numbered them not I.

51 minutes ago, andsm said:

I guess it is about adding scalar field? I have no equation for the scalar field. And, for purpose of the article, I not need it. All what I need: the field shoukld satisfy certain restictions, described in the article.

I don't know, your premise 5 was quite unclear as I have already said.

However it is where you first introduce a fundamental field so it must be necessary.

So what are the field variables ?
It is up to you, as the author, to define them.

Please don't tell me you know what General Relativity is, but don't know what a Field is?

51 minutes ago, andsm said:

May you name them? I would like to improve article, if there are some weak spots in it, but I not see them.

Both 6 and 7 have mixed unsupported statements with premises.

Premise 6, for instance introduces an 'observer'. Any statements of the properties of this observer must fllow by rational deduction from 6 plus the previous 5 premises alone. No other material is allowable.

Edited by studiot

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3 hours ago, andsm said:

GR  in the article was derived near end of article.  There is  derivation of spacetime earlier. There is derivation of SR, also earlier than GR. Lots if the theory can be checked for logical correctness without good knowledge of GR.

Ok, I'm not too good with physics and mathematics, but first you said that velocity is zero then you use the maximum interactions velocity for a lot of things. I think maybe you think this velocity in special has a lot of unique attributes we haven't found about yet? Because you use the maximum velocity to say that time does not fundamentally exist. And isn't velocity the rate of change of space/position in time?

The other thing I notice it's you just put the equations for general relativity out there, with no special meaning. So, supposedly, there is a fundamental action that depends only on the existence of particles, and the variation of those actions is supposedly the space-time? Isn't general relativity supposed to create space-time? Everything would be always in maximum interactions velocity? What do you mean by those things? I think that what you try to prove is to extensive to be presented only with these few pages.

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20 hours ago, andsm said:

I not remember, is it possible to define Newtonian gravity in symmetries. If it is possible, it would result in exactly same equations.

But it is not related to the topic.

I do remember: It's not possible.

It is completely on-topic, as we're talking about symmetries and conservation laws in dynamics, which is relevant here. You haven't answered any of my questions/objections, or anybody else's really, which can only mean one thing: You have no answers but just insist on foisting your idea on everybody by means of a war-of-attrition tactics. Repeating your initial point over and over and not paying heed to anything anybody tells you won't get your idea very far.

And I honestly think I'm being very generous by saying "your idea".

If you're so sure about it, why don't you send it to a peer-reviewed journal?

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22 hours ago, studiot said:

They are your premises, not mine and you numbered them not I.

Checked. I not found any numbering in entire article except one part, but it have numbers only  from 1 to 6. So, I not understand it.

22 hours ago, studiot said:

However it is where you first introduce a fundamental field so it must be necessary.

So what are the field variables ?
It is up to you, as the author, to define them.

As I said, knowledge of exact equation of the field is not required for purpose of the article. Properties, which are required from the field, are described.

22 hours ago, studiot said:

Please don't tell me you know what General Relativity is, but don't know what a Field is?

Field, which I use, is not some well known type of field.

Reason - it is defined not on spacetime, but on space without time and without  dynamic.

So, while it is scalar field (all values belongs to set of real numbers) , it have different propertiesthan scalalr field from textbooks for quantum field theory.

It means, it is not possible to try to use typical properties of fields for field in the article, properties are different.

22 hours ago, studiot said:

Both 6 and 7 have mixed unsupported statements with premises.

Premise 6, for instance introduces an 'observer'. Any statements of the properties of this observer must fllow by rational deduction from 6 plus the previous 5 premises alone. No other material is allowable.

As I already  wrote, I not see numbered premises in the article.

19 hours ago, lagrangian said:

Ok, I'm not too good with physics and mathematics, but first you said that velocity is zero then you use the maximum interactions velocity for a lot of things.

19 hours ago, lagrangian said:

Because you use the maximum velocity to say that time does not fundamentally exist.

No. First I said time does not fundamentally exist,  next derived from it special relativity with its max velocity which is same in all IFRs.

19 hours ago, lagrangian said:

The other thing I notice it's you just put the equations for general relativity out there, with no special meaning.

I not just put them.  First< I derived action for curved spacetime. Unlike Einstein, who postulated the action, I derived it. Resulting equations are same, but path to the equations is different.

19 hours ago, lagrangian said:

Isn't general relativity supposed to create space-time?

No, it was never purpose of GR. GR just describe gravity, but it  nor describe creation of spacetime.

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16 minutes ago, andsm said:

Checked. I not found any numbering in entire article except one part, but it have numbers only  from 1 to 6. So, I not understand it.

I can't imagine why not.

You wrote it.

On 7/25/2020 at 4:38 PM, andsm said:

In the article, I propose following model:
1. Time and dynamic is absent on fundamental level. No any motion, no energy, nothing related to time and dynamic on fundamental level
2. On fundamental level there is Euclidean space, with al least 4 dimensions. (And yes, I know about impossibility to derive hypersurface with Lorentz metric in Euclidean space. There is solution for the theory)
3. All dimensions are equal, there is no preferred direction.
4. Reiterating that was written before – time and dynamic on fundamental level is absent. Completely. No anything like time dimensions etc.
5. There is some field or field on fundamental level. The field(s) are defined at each point of fundamental space and have values belonging to set of real numbers (scalar field). (Scalar fields, described in textbooks for QFT, have different properties than these fields, so statement about insufficient degrees of freedom is not applicable here. But lets put it aside of the discussion) There is no time or dynamics. Thereby, the fields also have no dynamics. It also means full determinism. I will call these fields fundamental ones. I suppose that the fundamental fields are smooth and are described by certain partial differential equations. Each of the fundamental fields is independent of other fundamental fields. This means that there are no other fields in the equations describing any fundamental field.
6. Quite obviously, it is not possible to add observer to the model in traditional way. Observer always requires time for its existence. Absence of time means it is necessary to add something else to add observers. Instead of time dimension, I use space dimension. Details are in article. All space dimensions, as I already write, are equal, no preferred direction. Observer is able to observe changes because I postulate that changes on consecutive 3-d hyperplanes in fundamental space can lead to appearance of observer. [These is hardest of understanding point of the model].
7. Because observer appear as result of changes of field(s) on consecutive 3-d hyperplanes in fundamental space (I reiterate, there is no changes in fundamental space, But state of projections of fundamental field(s) on consecutive hyperplanes can change), observer is not exists objectively. And even more, Universe is not exists objectively. It exists only when there is some observer which observe it. Without observer, spacetime in the model is just mathematical abstraction.
So, I propose subjective idealism in foundation of my theory. Fundamental space with defined on the space field(s) exists objectively. But, because observer cannot exists without time and dynamic, the space and fields exists in quite nontraditional way, without any ability for direct observation. Their presence can be verified only indirectly, based on how well the theory fit to observations.

Seems very clearly numbered 1 through 7 to me.

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