The answer to your question should be sought in the dynamics of flows on the seven-dimensional sphere. The fact is that the vacuum flow is given by a foliation that has the topology R^3 x S^3. Thus, the unclosed part of a typical vacuum foliation layer determines the dimension of the observed space. Details in the book Research Proposal MATHEMATICAL NOTES ON THE NATURE OF THINGS

“Why is space 3-dimensional?…Is anyone doing research, investigating reasons for space being 3-dimensional.…”

- attempts to answer in the mainstream physics the, indeed one of utmost fundamental physical questions, thread question are rather rare, since most of mainstream physicists quite frankly think that this question is inessential; and so, say, besides some inessential publications, in which it is shown that, say, that the fundamental Nature forces with long range 1/r potential [Gravity and Electric Forces] can act only in 3D space; while in the mainstream there exist numerous “theories”, etc., where the Matter’s space has well more arbitrary dimensions, etc.

From this is only one exclusion – the indeed outstanding first 1950s von Weizsäcker “Ur hypothesis”, where he had shown that if Matter is based on binary logics, then it is necessary and sufficient for the space to be 3D.

The “Urs” are binary alternatives, i.e. “bits”, but to underline the Urs’ fundamentality he named them so – “Urs” in old German mythology are ultimate base of World.

However real utmost universal Matter’s space is 4D – in accordance with other indeed outstanding late 1960s Fredkin-Toffoli finding, where they have shown that energy doesn’t dissipate from binary systems, if the corresponding the systems “binary gates” are reversible; and that is answer to the other one of utmost fundamental physical questions – why in Matter the energy conservation law acts?

So, as that is so completely rigorously scientifically postulated in the Shevchenko-Tokarevsky’s Planck scale informational physical model, which is based, first of all on the findings above, 3 main papers are

https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics

https://www.researchgate.net/publication/367397025_The_Informational_Physical_Model_and_Fundamental_Problems_in_Physics

https://www.researchgate.net/publication/369357747_The_informational_model_-Nuclear_Force

- utmost universal “kinematical” Matter’s space is 4D space with metrics (cτ,X,Y,Z), where XYZ are “von Weizsäcker’s” [standard in physics space] dimensions, and cτ is “Fredkin-Toffoli’s” one.

In mainstream physics till now the cτ- dimension is the time dimension.

Really the Matter’s space has also specific dimensions that relate to fundamental, at least known now 4 Gravity, Weak, Electric, and Strong/Nuclear Forces, and the Matter’s spacetime is fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct),

- where the Matter’s ultimate base – the (at least) [4+4+1]4D dense lattice of primary elementary logical structures – (at least) [4+4+1]4D binary reversible fundamental logical elements [FLE] is placed; practically for sure, as that is rigorously scientifically rationally shown in the SS&VT model above, the FLE “size” and “FLE binary flip time” are Planck length, lP, and Planck time, tP,

- whereas everything that exists and happens in Matter is/are some specific disturbances in the lattice, which constantly and always move in the universal 4D space above with 4D velocities that are identical absolute values be equal to the standard speed of light, c, c= lP/tP.

Cheers

BTW, in a talk at the Leopoldina in Halle in the 70-ies, he said that the symbol u_r shows that, here, the child in the man has played.

Christian Baumgarten #

Dear Christian, you write,

"A single degree of freedom does not enable to describe interaction. We can not expect to derive physics based on non-interaction. Especially spacetime can only be explained based on interaction. Furthermore[,] one oscillating degree of freedom implies turning points, where the momentum (or kinetic energy) is zero. At these points there is a moment without change. An hypothetical observer could not experimentally decide, whether the direction of time has changed at these points or not. Only in case of two (or more) dimensions there is an additional constant of motion - the angular momentum - that (if it is non-zero) ensures that there is change at all times. In [the] case of two dimensions and spin, time reversal is always connected to a non-zero action. Therefore the 2 × 2 case cannot be generalized and is rejected as too simple."

What about the elastic impact in 1+1d or the pendulum? Time is not determined by those motions but by an independent clock.

IMHO, time reversal is a theoretical imagination. I'm not arguing against CPT invariance of equations. However, that does not yet imply the existence of time reversal. Newton's equation of motion is T-invariant if F is, but I'm unaware of any classical mechanical process that exhibits time reversal.

Aren't you interested in how Euclidean space is formed at the local level? The equivalence of the Lie algebra so(3,1) and sl(2,C) is well known, but it is little known that sl(2,C) can be represented by the algebra of vector fields tangent to tori lying on the 3-sphere, and therefore the current lines of the generators of the algebra sl(2,C) can be compared to the coordinates of the Minkowski space. In this case, the dynamics of vector fields on the 3-sphere forms not only our Euclidean space, but also the Minkowski space.

Dear Steve Faulkner ,

Why do you think that space is 3-dimensional? Certainly, not every physicist does: https://en.wikipedia.org/wiki/Extra_dimensions

There are many ways to answer this question.

A mathematician: what's your definition of a dimension?

A physicist: because the force is in 1/r².

An engineer: 3 is quite enough.

A philosopher: not so fast, why is there space in the first place?

A politician: what's wrong with 3 dimensions?

Claude Pierre Massé: Great! Additionally, there are left- and right-handed things in 3D that cannot be transformed into each other by rotation. Admittedly, I don't know whether that argument applies to different dimensions.

It applies to every odd dimension.

The thread question is rigorously scientifically answered in the SS post page 1, March 22, if quite briefly – that is because of the Matter is a rather simple informational system that is based on binary reversible logics [+ at least 4 known no fundamental Forces logical marks], and everything in Matter is/are some disturbances in the Matter’s – the (at least) [4+4+1]4D dense lattice of primary elementary logical structures – (at least) [4+4+1]4D binary reversible fundamental logical elements [FLE], etc., that is placed in corresponding Matter’s fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct),

- where 3 space X,Y,Zdimensions are .necessary, as that von Weizsäcker proved in early 1950s, to make binary operations.

More see the post here only a comment to

“…There are many ways to answer this question. A mathematician: what's your definition of a dimension?....”

- in the Shevchenko-Tokarevsky’s really philosophical 2007 “The Information as Absolute” conception, recent version of the basic paper see

https://www.researchgate.net/publication/363645560_The_Information_as_Absolute_-_2022_ed

- it is rigorously proven that there exist absolutely for sure nothing else than some informational patterns/systems of the patterns that are elements of the absolutely fundamental and absolutely infinite “Information” Set. The Set - exists absolutely objectively, because of it fundamentally – logically - cannot be non-existent and so exists absolutely eternally, having no Beginning and no End. At that utmost general definition of the so absolutely fundamental phenomenon/notion “Information” is

“Information is something that is constructed in accordance with the set/system of absolutely fundamental Rules, Possibilities, Quantities, etc. – the set/system “Logos” in the conception”;

- some examples of “Logos” set elements: “Space”, “Time”,“Logical Rules”, “Energy”, etc.

Including an informational system “mathematics” by no means differs from informational system “Matter” in that in both systems the Logos set elements “Space”, “Time” are absolutely fundamentally obligatorily actualized by the same way – as the space and time dimensions, the unique difference is in that while Matter is fundamentally dynamical system, and so it absolutely obligatorily changes also in the time dimension, ct,

- while mathematics is in some sense “fixed” system, and, while in all/every concrete mathematical branches mathematical structures exist absolutely obligatorily in innumerous concrete spaces, the time dimension in mathematics doesn’t exist; though mathematics well describes what exists and happens in time in Matter, by using time dimension as an variable.

“…. physicist: because the force is in 1/r²…”

- yeah, that mainstream physicists as a rule say, and frankly believe that that is scientific answer. What is evidently strange explanation – really just in Matter for really mystic reasons some “1/r² forces” exist and act, for what yeah, space must be 3D.

And, that

“….A philosopher: not so fast, why is there space in the first place?...”

- see above - really is quite natural – and so correct - question, though really in the quote is incorrect, any mainstream philosopher even doesn’t suspect about this question existence; and here it is since author is a physicist.

SS post in

https://www.researchgate.net/post/NO39Doubts_about_General_Relativity_4-Who_should_determine_the_spacetime_metrics_of_matter_itself is relevant to this thread question

Cheers

In general In summary, space appears three-dimensional because of mathematical conventions, human perception, the laws of physics, and observational evidence.

The thread question is rigorously scientifically answered in SS posts on pages 1, 2,

- so here only a note, to

“…In general In summary, space appears three-dimensional because of mathematical conventions, human perception, the laws of physics, and observational evidence.….”

- including since that is recommended. Again – see SS posts above, everything in Matter, including Matter’s space/time/spacetime, fundamentally by no means, of course, “appears because of mathematical conventions, human perception” etc.. Everything in Matter, including its spacetime, existed – and exists – fundamentally without paying any attention to anything what humans do, including what they precept.

At that, including, some humans perceptions can be, and are, simply wrong – as the “three-dimensional space” above. Real Matter’s space [more see SS post, page 1] has (at least) [4+4] metrics (cτ,X,Y,Z, g,w,e,s), utmost universal space has 4D metrics (cτ,X,Y,Z,).

That is another thing, that in mainstream philosophy and sciences, including physics, and, of course, in everyday humans practice, the really space cτ-dimension is postulated/used as the time ct-dimension.

That happens because of in Matter all fundamental Nature forces, first of all well observable Gravity and Electric Forces, act in most cases, in everyday practice always, as 3DXYZ Forces, while the ct-dimension becomes be observable only at high energies, say, when a gamma-quantum with energy more 1.022 MeV creates e± pair.

At that electron and positron really , besides 3D motion, move also in opposite directions in the cτ-dimension – only provided this the momentum conservation law is valid, however again they . are observable mostly in 3D space. But that happens not always, and so, say, to “explain” some such physical effects in QED the really transcendent/mystic “Feynman–Stueckelberg interpretation” is postulated: that for/by some mystic reasons/ways antiparticles move mystically “back in time”,

- what is fundamentally impossible. Everything that changes absolutely for sure at every change moves only in positive direction of real ct-dimension of Matter’s (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct) / utmost universal metrics [5]4D (cτ,X,Y,Z,ct)/

For the readers that really want to know the scientific answer to the thread question more see the SS posts above and links in the posts.

Cheers

according to my information,The laws of physics, as we currently understand them, seem to operate in three dimensions. For example, Isaac Newton's laws of motion and gravity, as well as Albert Einstein's theory of general relativity, all describe the behavior of objects and the structure of space-time in three dimensions.

While it's true that our perception and understanding of space-time are mediated through consciousness and conceptual frameworks, it's not accurate to say that space-time itself doesn't exist. Rather, it's a mathematical and conceptual model that has proven incredibly successful at describing the behavior of the universe on large scales, from the motion of planets to the bending of light by massive objects.

The thread question rather in detail is scientifically answered in SS posts on pages 1, 2.

Cheers

Space is not 3 dimensional. We have "invented" a measurement methode dat makes it possible to determine the position of every "point" within a volume with the help of 3 rulers (under 90 degrees to each of them) and the rulers have the same metric.

The methode is not space. Space is itself and we think about it as a volume (actually a box without walls).

With kind regards, Sydney

Dear Cosmin Visan

Consiousness is an effect and not a cause. There are really nice experiments that show that your body is aware of changes before your consiousness is aware of the changes. In other words, your consiousness "walks behind".

So if I follow your reasoning, your next step is that your body isn't real because it is just an idea in your consiousness?

With kind regards, Sydney

Dear Cosmin Visan

Your right! Because consiousness doesn't exist because consiousness is just an idea of the body. Like the experiments of Bejamin Libet show.

With kind regards, Sydney

Suppose we have a really large cube and the cube is made of a solid. A solid is made of molecules and molecules are made of atoms. Can I determine every thinkable point within the volume of the cube with 3 rulers? No, for us it is technically impossible.

Does it mean that space itself isn't "solid" at all? No, we don't know if space is a solid because we and our instruments are "build up" by mutual relations. Like the molecules and the atoms of the cube. We don't represent absolute properties.

There is the argument (philosophy) that mutual relations must have an underlying reality that is responsible for the creation of the mutual relations. If we change this concept slightly we can say that the underlying reality has variable properties too. So "our reality" is composed by the mutual relations between the variable properties of the underlying reality.

But the existence of variance is impossible without an internal structure. Because a volume without a structure is 100% homogeneous and therefore 100% static (no variance).

So if we accept our concept of space as a volume that creates mutual relations, we have to incorporate the idea that space must be some kind of a solid with a structure and properties that generate variance within at least a percentage of the whole structure.

If we speculate that there exists no underlying solid, only variable properties, we have to face the problem of the existence of the universal constants. Like the quantum of energy (h) and the constant velocity of the quantum of energy (c). Be aware that both constants represent dynamic variance although the variance itself has a constant metric.

Thus the question "Why is space 3-dimentional" is not a simple question. Although we don't bother any more about the ancient religious interpretations (the variance is "earth" and the absolute properties are "heavenly").

With kind regards, Sydney