The Nature of Space by M. V. Vasilyeva

Dear Israel,

Thank you for your feedback on my essay. It is regrettable that you approached it with some preconceived notions and also lacking certain understanding of the 4D geometry, which is clear from your following comment:

"You are supporting the view that the 3D space we experience everyday is some sort of solid embedded in another physical space of 4D, likewise as a sheet of metal could be embedded in a solid sphere. "

It appears that you do not know that the surface of a 4D object, such as a hypersphere, is 3-dimensional in the same way as a surface of a sphere is a 2D plane. The 2D surface of a sphere is not "some sort of solid embedded in another physical space of" a sphere, but is an integral part of it. Similarly, the 3D surface is an integral part of a hypersphere. It seems all your confusion about my essay stems from this lack of basic geometric awareness. In line with other multidimensional models, I called this 3D surface a membrane, instead of always referring to it as a (hyper)surface.

In addition, I am not sure what you mean by "solid dimensions" which you differentiate from "geometrical dimensions". This seems your original definitions and usage, on which I cannot comment.

Regarding the KK model predictions that you refer to, they were based on the wrong assumption that the extra dimension was equally accessible to both matter and radiation as the observed 3. The same wrong assumption was the reason why Klein invented compactification: to ensure that the extra dimension was well hidden and thus in line with the question of why we do not see it. In my essay I show that this was both wrong and unnecessary.

Regarding your question of why ether was a wrong model, first, the concept itself stems from air, which cannot support transverse waves, and second, the theory never considered the 4D nature of space, assuming that it had only 3 observed dimensions.

You also say: "... that this paradox is only valid considering that space is some sort of fluid. Today physics does not assume space as such and therefore there is no paradox for contemporary physics. My question in this respect is: don't you think that by reviving the old problem you are also contradicting current views, in particular, the general and the special relativity?"

That physics decreed 100 years ago that space was empty is in fact the topic of my essay, in which I argue that it was the wrong turn.

In no way does my model contradicts current views. You seem to have missed the part where I say that the model is the same overall as other models with large extra dimension (which are in line with relativity).

You also say: "Something that was not clear for me is whether you think that the universe was created in the Big Bang (BB) or not. ... What reasons can you provide to explain the lost of dimensions? "

In the essay I say, "in line with big bang theory, we could assume that initially the structure had infinite number of dimensions, but once it cooled off, it settled into 4D." I presume you are aware of the high energies at first instances after the BB. These high energies correspond to higher-dimensionality of space. When space cools off, its structure precipitates from higher-dimensions into lower, i.e. it looses dimensions, as if energies hidden in higher dimensions trickle down all the way to 4D, increasing the bulk and hyperssurface area, which corresponds to expansion.

Similarly, going in the direction of increasing energy, when the structure is put under too much pressure locally, because it is non-compressible, it will bulge out into an additional dimension (and by the way, in this context, the appearance of singularities is what marks the door into a higher dimension). When the local pressures let go, the energies hidden in extra-dimension trickle back into the 4D bulk, causing it to expand, which, in turn, increases its 3D surface area, causing perceived expansion of space.

Regarding the process of "precipitation into a lower D", being only an analyst, I can't adequately speak for topology. My hunch is that the method based on Hamilton-Ricci flow, quite possibly the one perfected by Grigory Perelman in his latest work, may shed some light on the specifics.

Again, thank you for your feedback.

I have read your essay today and found it interesting, even though I cannot conceive of an absolute reference frame, for which you advocate. I see absolute reference frame an abstraction that cannot exist in reality. But it is the plurality of our views is that is valued in this contest. Best regards to you!

Hi Vic Kley,

Thank you for your question, even though I'm not sure what else to say in addition to what I already said in the essay. I offered several explanations, from simple ones, such as, why a nucleus appears so small (because it exists in 4D, outside the 3D that we perceive and is only touching it) to why voids are empty, why light gets tired, or why there is no need to invent dark matter and dark energy, because both 'attractive' and 'repulsive' gravity emerges from the same property of the hypersurface of the hypersphere, which is our world, to minimize its hypersurface area. (after e-talking to Israel above I am not sure what terms to use, since a membrane or brane confused him).

How about the solution to the paradox of space? From the exchanges with other contributors here I see now that the problem is worse than it appeared to me initially. After 100 years people have become so used to the incongruous idea of waves propagating through emptiness, without any medium, that they do not see a paradox. But this is fundamentally wrong. Waves do require a medium. The medium in question cannot be "ether", simply because the phenomenal speed of transverse waves imply a super-rigid solid. Or a surface of incompressible fluid.

It's late here. I will think over your question and post tomorrow. In the mean time, would you please tell me why what I already listed in my essay does not seem for you enough. Thank you.

Thank you Inger! You can't imagine how much I appreciate your comment.

Please see the post bellow (coming up) in response to Mr. Kley's question above in which, within the framework of my model, I attempt to dispel the mystery of the wave-particle duality.

Mr Kley,

Thank you for your interest in my essay. It was very late for me when I saw your question. In my reply I used wrong terms in the sentence which should have read: both 'attractive' and 'repulsive' gravity emerge from the same property of the hypersurface of the 4D structure of space that seeks to minimize its hyperarea.

You asked, "Can you offer up any specific experiment or present unexplained phenomena that may be illuminated by your vision of 4D Space/Time?"

Having thought your question over, I decided to address the wave-particle duality, with which physics replaced the paradox of space. This duality is best revealed in the double slit experiments. I would like to use this opportunity to demonstrate that, from the 4D perspective, there is no mystery why both matter and light appear to move in waves. In my essay I only briefly mention this in the Flatland analogy.

Before we begin, it is important to appreciate that a hypersphere has 3-dimensional surface, each point of which is equidistant from its center, in the same way as each point of the 2D surface of a sphere is equidistant from the center of the sphere. This topological fact is what makes the 3D space we perceive invariant in all 3 directions and precludes the possibility of selecting a preferred reference frame. The dynamic nature of the 4D structure also makes it unsuitable for the role of the absolute reference frame (just like sea captains can't use ocean as a reference frame and must rely on the external clues such as stars or GPS).

The other aspect of the 4D geometry worth remembering is that form a 4D perspective, each point of the volume of a cube is visible in one sweep just like we grasp each point of the 2D plane in one glance. In a sense, from a 4D perspective, a 3D volume of a cube appears flat, similar to a 2D plane seen from 3D.

With this in mind, let us see how a double slit experiments works out in 4D, on the simplified analogy of the Flatland Plane (the Flatland analogy is indispensable, because 4D is virtually impossible for most people to visualize).

First, I would like you to please take a look at the following image from google images, since I can't post images here:

http://ej.iop.org/images/0295-5075/94/2/20004/Full/epl13428fig1.jpg

The top image, (a) is a side-view snapshot of a hexagonal lattice aggregate of bouncing droplets on a vibrated liquid bath that interact via the surface waves they emit and form various types of stable crystalline clusters [1]. Suggested by Andrew Norton, it is indeed an excellent model of the Flatland nanoscale with droplets representing nuclei confined to the outer, empty side of the Plane (in the "headroom"). Please take a good look at the image again and imagine 3 such aggregations, at some distance apart from each other. These 3 aggregations of droplets/atoms represent the solid structure of the plate with 2 slits in between.

Now please appreciate the fact that light waves, an electron, an atom or a molecule, all move along the surface of the Plane (or hyperplane in 4D) that contains the EM field. The difference between a light wave and, say, an atom, is that the light wave is the transverse disturbance in the surface itself (just like a transverse wave in the surface of water) and as such is entirely confined to the EM field it contains, while "matter" (stuff with intrinsic mass) glides just above this surface in the 3rd dimension (3rd dimension in the Flatland analogy and in the 4th dimension in our world). Nuclei are integrated into the surface by their electron clouds interacting with the EM field in it. The electron cloud makes the indentation a nucleus makes in the surface locally even with the rest of the surface and at the same time acts as a sort of a roller or better yet, a surf-board on which the nucleus surfs the light waves themselves. (In this context, the increase in the inertial mass at high speeds is mostly due to the electrons interacting with the EM field contained in the surface.)

Thus there is no difference in the path a particle of light or a material object takes. A light particle is a convenient abstraction that stands for the momentum of a light wave in space (or, a hyperplane). A material object, such as an atom, can also be represented by a point that too follows the same path. It is the structure of space itself that dictates all movement by expelling the deformation introduced into it locally into the direction that gives (even though, of course, there is a difference in the transverse disturbance that we perceive as light and a longitudinal disturbance we perceive as mass).

In this model it is essential to realize that everything we perceive directly or with the help of our technology are the projections onto the 3D surface of the hyperplane. Matter moves along the same surface as light waves themselves. Thus the interference pattern seen in the double slit experiments is the reflection of the fluid nature of the structure of space itself.

I also would like to emphasize that the strict separation between matter and space of the model I propose is applicable only at low energies of our own experience. At very high energies, the number of space dimensions grows in proportion to the energy density. At high energies, in higher number of dimensions, the geometries of space and matter intermix and are best described by the multidimensional models of string theories.

Again, I thank you for your interest in my essay and for giving me opportunity to address this important question, which I could not do within the constrains of the requirements.

References

[1] A. Eddi, A. Boudaoud and Y. Couder, (2011, doi:10.1209/0295-5075/94/20004), Oscillating instability in bouncing droplet crystals. http://iopscience.iop.org/0295-5075/94/2/20004

Hello James!

Thank you for your interest in my essay. I like the vividness with which you describe how you perceive the world. I will certainly read your essay and will comment in your thread.

Mr Kley, I replied to your question in a comment below.

Thank you for your interest to my essay.

Thank you Ke Xiao for your feedback. Even though it was somewhat difficult for me to read your highly technical essay, I did grasp its main point, namely that the wave-particle duality paradox lies in the structure of spacetime itself. Here we are in agreement; and while you amply speak to the professionals, I offer a geometrical representation of the same on the simplified analogy, making it accessible to the lay public.

Xie xie!

Dear Amazigh Mabrouk Hannou,

I tired reading your essay but had a very hard time understanding your "accent in print". This is because, even though I know several languages, I have not studied yours. I think it is important to have our papers checked by a native English speaker before submission. This becomes especially important when introducing new ideas.

Regarding your question of gravity, my approach is purely geometrical and is inline with Einstein's general relativity, which treats gravity as a curvature in 4D spacetime. My take on it is that this curvature is due to surface tension of a 4D ocean of perfect fluid that seeks to minimize its hyperarea (similar to water tension in 3D).

In a topological sense, in 4D, there may be another reason for 3/4 - 1/4 distribution of energies. It may be due to the fact that a convex 4-space can be broken down into 4 contiguous, adjacent 3-spaces. This means that a convex 4D object, such as a hypersphere discussed in my essay, can be broken down into 1/4 for its 3D surface and 3/4 for its bulk. (The same does not work for a sphere, but works, with different numbers, for all n-spaces where n>3.) The same overall distribution of hypersurface to hypervolume, 1/3 to 3/4 respectively, applies to other convex 4D objects, even though actual proportions may vary a bit when they deviate from a hypersphere, which has the minimal surface area.

Take care!

Mr Hoover,

I am not certain what is meant by dark energy currently (it keeps on changing). Trying to see from where you are coming to it, I read your essay and saw this picture, which I also found on google images:

http://www.theepochtimes.com/n2/images/stories/large/2011/05/23/549761main_pia14094-43_946-710.jpg

This is an artist rendition of a 4D model of space, with one dimension removed, the green grid representing gravity (= curvature of the 3D surface on which "matter floats") and purple grid representing dark energy that pushes on matter, pressing it into the surface, displacing a volume and causing it to curve. That's how I understand it. The articles that came with the same image says, "This contradicts an alternate theory, where gravity, not dark energy, is the force pushing space apart. According to this alternate theory... gravity becomes repulsive instead of attractive when acting at great distances." I agree that gravity becomes repulsive at great distances (where voids form in my 4D model of space). This is stems from pure 4D geometry.

I personally do not agree that the universe is expanding, especially at ever-increasing rate. First, why don't we see it right where we are? The whole idea is based on the redshift and in my essay I offer another explanation to it.

But I understand what you're interested in and that is the enigma of UFOs and how they move as if inertia is none of their concern. I happened to see 2 small saucers at a very close range. I saw them about 25-30 meters away and then I ran towards them and got even closer. I was an adolescent then, and my impressions were vivid and observations sharp. Because of this I do not disregard other people's accounts.

I absolutely agree with you that there is a way to manipulate the curvature of the 3D surface (on which we live, according to my 4D model of space) which we call gravity. For this we need to have a better understanding of space, which we don't. In fact, the situation is just deplorable, as this contest demonstrates. The establishment is so entrenched in a particular way of looking at things that they are incapable of even considering anything else. And now with this idea of ever-expanding universe, which is happening everywhere except just where we are... People got Nobel prizes, defended their PhDs and built their academic careers on it, which means that they will defend it tooth and claw, all the way till the end. It will be another generation, after this one goes away, before an alternative view on things could even have a chance.