Essay Abstract

Space, whose structure and properties dictate all characteristics of matter and forces in it, has been underappreciated by physics. That empty space has a property of a rigid solid constitutes the central paradox of science. For 150 years it has remained unresolved. The work has been neglected due to physics’ century-old decree that declared space empty, which was an act of frustration with ether models that could not resolve the paradox. Pressing ahead without solving the problem led to the current situation where paradoxes have become physics’ distinctive feature and matter and space are fused into an inseparable totality of fields. Mathematical models attempting to describe this totality abound, and yet there is no model of space. In its place is a tradition that discourages discussion of the structure of space for fear of resurrecting old ether theories. This essay attempts to open such a discussion and offers an example of how the topic can be approached with very few assumptions in mind. It shows that, consistently applied, a simple organizing principle can lead to a straightforward solution to the old problem and reveals a dynamic, 4-dimensional, vibrating structure, in time, that conjures up an image of a 4D ocean, the 3D surface of which is the visible Universe.

Author Bio

Ms. Vasilyeva grew up in the former Soviet Union. She graduated from NYU with a degree in computer science. Having worked in the industry in NY and LA, she now lives with her family in the woods of Pennsylvania, pursuing her interests in history of ideas, physiology and physics. A gifted analyst, she loves a good puzzle.

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Ms. Vasilyeva,

The arguments you present in your essay are a danger to the establishment, which has convinced various funding sources to give them $billions to prove what I consider to be a fallacy.

I note that your references follow the Chicago Style, and I wonder if you were requested to provide that format? Many of the essays do not follow that style.

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Dear M.V. Vasilyeva,

I really enjoyed your essay. You make a couple points which I think are crucially important:

1. You note at the very beginning that "space," whatever we take it to be, dictates the characteristics of matter and forces in it. I do not think that this fact is adequately appreciated. It's not that no one knows this; anyone who reads Weinberg's quantum field theory books, for instance, learns how important the Poincare symmetry group of Minkowski space is in determining the properties of particle states. However, people often don't realize just how great an assumption they are making when they ascribe certain properties to space. A lot of otherwise very good ideas in physics just won't work if you try to apply them to the wrong spacetime model.

2. You point out the necessity of understanding the actual physical structure of space. Many people, even physicists, are content to imagine spacetime as 4-dimensional real space, possibly curved, but fail to appreciate the difference between this mathematical abstraction and the actual physical space that interacts dynamically.

You and I have perhaps different ideas on the nature of time; I view time as a manifestation of causality, and my approach to building up spacetime is to use causal relations. I describe this in my essay here: On the Foundational Assumptions of Modern Physics.

In any case, you have written a very intriguing essay, and I wish you the best of luck in the competition. Take care,

Ben Dribus

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Dear M.V.

I hope you can read Russian

What is common between this flatland and your flatland?

http://modcos.com/articles.php?id=201

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M.V.:

Your essay touched on the core of a physics problem.. "space". In space one can observe the motion of mass and keep track of all energies involved, but rarely consider the concomitant "growth" that can occur to affect energy balances..

My model, To Seek Unknown Shores

   http://fqxi.org/community/forum/topic/1409

developed in detail in "End Notes", suggests 1-D, 2-D, and 3-D "spaces" achieve 6/16, 9/16, and 1/16 " respective probabilities for growth as motion proceeds.

Comment?

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Excellent!

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Ms. Vasilyeva, you wrote: "Your solution, i.e. that "The speed of light, as measured by the observer, varies the speed of the light source" contradicts my view, on which I cannot compromise, and that is: the speed of light is the property of space. As such, it is a constant."

Is the speed of light "the property of space" in the same way in which the speed of sound is the property of air? If yes, the speed of light, as measured by the observer, varies with the speed of the observer, and your community rating may plummet.

Best regards, Pentcho

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Hi M.V. Your essay was a fun read, and I think the picture you have of how things work is better than many. I agree that forces and particles should both be described in terms of spacetime geometry (topological solitons of some type), and also that large extra dimensions may be involved. I think you would enjoy reading about the bouncing droplet system -- it is a lot like your flatland. If you have no journal access send me an email, otherwise some references are given in my essay.



Andrew

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Dear M.V. Vasilyeva,

It is my essay:

http://fqxi.org/community/forum/topic/1516

Comment?

Mare
k

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Ms Vasilyeva,

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

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Dear Ms Vasilyeva,

I have by now read your most interesting and thought-provoking essay several times with growing intrerest and, at least I hope, also with some growing understanding.

What fascinates me most of all is that you, more or less in one blow, explain both the large-scale structure of the Cosmos, and the small-scale structure of elementary particle interactions. The fluid in the "headroom" above the 3D membrane being in both cases the medium of interaction, and the membrane the border between matter and space.

Or have I completely mis-understood? If so, since I'm netither a physicist nor a mathematician (as you already know) I don't apologize for my lack of knowledge. It is better to try to understand and miss the point, than not trying at all - and be sure to miss it

Your history of time is perhaps a bit brief in comparison, but I like your concept of time as energy - and your down-to-earth Tick-tack. "Tack", as we say in Sweden when we mean thank you! You have given me more than a lot to think about.

My very best wishes!

Inger

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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/epl1
3428fig1.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

Dear M. V. Vasilyeva,

In Coherently-cyclic cluster-matter paradigm of universe, the dimension of time emerges from 1D eigen-rotational string that demonstrates 3D tetrahedral-brane transformation from 2D membrane surfaces by the eigen-rotational phases of that string.

With best wishes,

Jayakar

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Dear M. V. Vasilyeva,

" To remove water from a cup, it is necessary to fill it instead of water by the air. Further, in my

interpretation to remove air from a cup, we should fill the cup instead of air by the ether. Thus,

the cup can not be empty, only one medium can be replaced by another. Ether, according to

Aristotle, "is more subtle substance" than the air."

I also think the gap or space is not empty but full of energy; Nothingness does not exist.

I read your essay with carefully. It is interesting approach and I would like to have your view point about a gravity question : what do you think about gravity and space or dark energy, which relationship do they maintain between them.

Do you think that the expansion of the space is a force opposite to the Gravity ?

http://www.fqxi.org/community/forum/topic/1552

Thank you and lall the best.

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Ms. Vasilyeva,

You say:

"But in this model there is no gravity per se. What we call gravity emerges entirely from the interaction of mass (which is displacement of volume) with the surface tension of the structure wanting to minimize its surface area."

What are your thoughts on dark energy as opposed to gravity?

Jim

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Dear Vasilyeva

Just to remind you that I have replied to you in my previous post above (Sep. 11, 2012 @ 17:14 GMT). I thought you may have overlooked it.

Israel

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attachments: 3_Primordial_Foundational_Problems.doc, 3_GEOMETRODYNAMICS_OF_ENERGY.doc

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Dear Vasilyeva

Sorry, if I am bothers you.

I watched very carefully your essay, but really did not find your final conclusion about the nature of space.

May also be due to my poor English skills, hope you will be directed.

Kind Regards !

Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY

August 23, 2012 - 11:51 GMT on this essay contest.

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Dear Dr. Perez,

very sorry for the delay. First I overlooked your post, and now I got lots of work... I very much value your feedback and want to continue our discussion. I will answer your questions as time permits and will post them in the end of the thread, so they won't get lost.

First, regarding the structure of space and what it is "made of", there is a concept in topology where a structure not only fully occupies a space but also defines it. That's how I mean it. And yes, like everything else, the structure of space is a particular expression of energy, just like charge is an expression of energy and so is mass, etc.

You say: "It seems that you haven't realized that by conceiving space with an internal structure as a fluid or strings you are contradicting the background independence of the general theory of relativity."

Not at all. In fact, the model I propose is just an extension of the geometry of GR. It suggests that the 3D space GR deals with is the surface of a 4D structure. It seems that our difficulty lies in accepting the reality of the 4th spatial dimension and Minkowski spacetime was a step in the right direction.

You say: "That space has this kind of internal structure means that space is not geometry as GR states."

-?? Geometry implies structure. Geometry is all about a structure. There is no geometry without a structure.

You say: "You: "The high energies at first instances after the BB correspond to higher-dimensionality of space." From where did you get that? The BB theory is based on GR and it assumes that since the beginning of time the universe is 3+1 dimensions, no matter how hot or cold the universe was."

Thank you for bringing this up. I did overlook this point, as we often do when an issue appears self-evident to us. And so I have a question to you in turn: what does BB have to say about how exactly the whole of the universe fit into a point and then a very small volume which then expanded? Or, where did that given 3D space come from in the first place, i.e. how does it appear out of nothing? And what constitutes the expansion of space, i.e. what is expanding and exactly how? And, not to forget, why 3D? Why not 4 or 5? Does BB have anything to say about all this? Not to my knowledge. The theory is completely silent on all these questions.

In contrast, my conceptual model gives answers to all these questions. Namely:

The universe fit into a point because it was compressed into an infinite number of dimensions. As it was cooling off, the number of dimensions diminished while the length of the remaining dimensions increased. This is what constitutes the expansion.

To illustrate this, I give you a simple example: you can take 8 cubes (edge length = 1 unit) and stack them in 3D so they make up a larger cube with the edge length of 2 units. You can arrange the same 8 cubes in 4D to make up a tesseract (a 4D cube) with the edge length of 1 unit. So, if the length of the edge stands for the lengh of a dimension, you just squeezed 3D space with dimension length of 2 units into a 4D space with the dimension length of 1 unit. The opposite process is when you take a tesseract and rearrange its volume in 3D. The size of the dimensions in 3D is twice as large. This explanation is as simple as it gets.

In the similar fashion, when the whole volume of the universe is compressed into an infinite number of dimensions, the length or size of those dimensions approaches a point. And as it cools off, the number of dimensions diminishes, i.e. the volume hidden in higher dimensions trickles down into the lower dimensions increasing their length. This constitutes the expansion.

I have to run now, but in the next post I will show why 3D. And I will certainly address all of your other questions. Thank you!

Dear M.V.

Well written essay

Aside from the seemingly obvious properties of space existing in three (XYZ) dimensions plus time as a possible fourth dimension, (I seek intrinsic mechanical properties) do you perceive space as being a compressible medium? J.R.

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Dr. Perez,

here I continue our discussion and will show now how the model I propose explains "why 3D?"

As I stated in the reply to J.R. above, the basic unit of spacetime I propose is 3D. From topological point of view, 3D is the minimal volume that is preserved in all n-spaces where n > 2. I have shown in the example above how 3d volumes can be packed into 4D with the result that the volumes themselves are preserved, while the length of the dimensions decreases. That's how, in principle, you can pack the whole of the universe into what can amount to nearly a point, as the number of dimensions grows to infinity.

Please keep in mind that each n-space, in topological sense, has its own characteristics and properties. Mathematicians often overlook this and thus loose the appreciation of the role of topology in physics. Laymen too, usually make a mistake when starting learning 4D visualization, which they do by heavily relying on analogies, applying the relationships in 2D->3D to 3D->4D. Most people do not realize the crucial difference between 2D->3D and 3D->4D, and that is: you can pack 3D volumes into 4D, just as I showed on the example above, where all 8 cubes are aligned face to face and edge to edge, thus filling in the whole of the 4D volume, while their own 3D volume is preserved fully intact. The same is not true about 2D->3D. You can take an infinite number of 2D planes and no matter which way you stack them, they will still amount to exactly 0 3D volume. What 2D planes can do is to enclose a 3D volume and with the size of their area give an indication of its shape.

And so 3D is the basic unit of volume, in which all other n-volumes (n>2) can be expressed. It is in this sense that 3D can be viewed as a given, always present as a subspace of any other n-space.

Now, we have a dynamic, vibrating structure that is initially packed in infinite number of dimensions (corresponding to its high energy density) and so the question becomes, as it cools off and expands, at what number of dimensions it will settle. I claim it is 4D, because of the unique properties of this space.

4D contains the largest number of regular polytopes (a.k.a. platonic solids), which is 6, compare with 5 in 3D and 3 in all other n-spaces (n>2). This is important, because it speaks of the number of symmetries n-space permits. In addition, in space of an even number of dimensions rotation takes place around a point, a plane, or some other axis-space of an even number of dimensions, while in space of an odd number of dimensions the axis of a rotation is always of an odd number of dimensions. Thus 4D, unlike any other space, offers the maximum number of symmetries, which is important for a structure that seeks to harmonize the vibrations of its components.

True, this needs to be backed by a proper theorem. Perhaps it, or something similar, already exists. If not, it should be proven. Namely: a dynamic vibrating structure of N-dimensions will find its lowest energy state in 4D.

Assuming this is so, what we get is a hypersphere, which geometers call a 4-sphere and topologists, a 3-sphere. This differences in definitions may be confusion for a layman, which is why I use 'hypersphere'. Also, calling the object a 3-sphere, topologists are mainly concerned with its 3D surface, while I insist on considering the object as a whole.

Now, the surface of a hypersphere is 3-dimensional, each point of which is equidistant from its center, making this 3-space continuous and invariant in all 3 directions.

At low energies of our own experience, matter (stuff with intrinsic mass) is confined to the surface of this hypersphere, with nuclei sort of gliding just above it in the 4th empty dimension, supported by their electron clouds. The EM field is confined _entirely_ to this 3D surface, making it in effect a 3D display that "shows" what is attached to it (other details can be found in my essay).

To summarize, the word we perceive is 3D, because it is the surface of a 4D object (a hypersphere). It is the shape in which an N-dimensional dynamic vibrating structure found its lowest energy state. If 5D were a space corresponding to the lowest energy state, then we would be crawling on a 4D surface (in the 5th dimension). But we "crawl" on the 3D surface, in the 4th spatial dimension, aware only of this surface and seeing only what is attached to it.

In the next post I will address the questions you asked above and also demonstrate the advantage of this setup in various problems in physics.

Dear M.V.

I re-read your essay and all of the posts above in an attempt to better understand your views. It is very refreshing and inspiring to see all the creative effort you have invested in this essay. It's appreciated!

In one post to Eckard you describe space as a dynamic fluid structure which coincides with my own opinion, except that I would use the term medium rather than structure, as structure seems to denote rigidity or immobility. Is the dynamic part.. energy contained within apace?, the passing of energy via EMR thru space?, or space itself posessed of inertial properties?, or something else?

In another post you say that you agree that waves do require a medium for propagation. In response to my post you say that you perceive 3-D space as incompressible. My question is "how is it possible for waves to propagate through an incompressible medium?" (not on the surface of)

About your idea of 4-D space representing the lowest stable energy state for space to exist in... very unique approach and seems to be a cosmological possibility, once the properties of space are better determined.

J.R.

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Hello M.V.

Your response is appreciated and I find it enlightening.

I do not have an essay posted here, having only discovered this site in the last week, but am very excited to have discovered it and especially your essay. We have similar interests relating to space apparently, and perhaps more similarity in an approach to comprehending and articulating it.

I do not wish to monopolize or contaminate your forum with my ideas but would very much like to communicate more with you on this subject. May I contact you via the e-mail address you posted for someone else above?

J.R.

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Ms. Vasilyeva

Within the confine of how reality is manifest (ie science, not belief), there is only physical presence. Space is non existent. It is a conceptualisation of ‘not-physical presence’, and has two aspects: 1) the size and shape of any given physical presence, 2) the differentiation between any given two. In other words, physical reality is conceived of as being overlayed by a grid which enables the identification of relative spatial position. The points on the grid being a distance apart which equates to the smallest physical presence in reality. Then, as at any point in time, any given physical presence can be conceived as occupying a certain configuration of spatial points, and that can be compared to any other. Whether there are spatial positions which, at any given point in time, are not occupied by a physical presence, is an open question.

I have deliberately used the phrase physical presence, as there is an incorrect ontological tendency to view physical reality as comprising ‘something’, and then in addition postulate other forms of ‘something’ which are deemed to have physical effects, but no physical presence. But, by definition, anything which has any form of physical influence must have some form of physical presence.

The other important points in respect of the concept of space are:

-for spatial dimension, physical reality has half the number of possible directions that the smallest physical presence could travel from any given spatial point, not 3. The latter being the minimum number possible when reality is conceived at the highest level

-time is not a dimension, as the concept is concerned with the speed of change. And change is associated with how realities differ. It is not a feature of a reality, which can only exist in one physical form at a time.

Paul

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Dr. Perez,

don't know if you saw my posts under your last ones -? They are sort of hidden.

____

Mr. Reed,

I decided not to wait for you and to go ahead and show that Minkowski spacetime is all about 4 spatial dimensions in time, not 3D + time, as it is touted. I claim that Minkowski model of space worked out so well for GR, because the underlying reality *is* 4D, just as I argue in my essay. For some reason people have difficulty with this simple notion.

That Minkowski spacetime is all about 4 spatial dimensions, in time, I will show on an analogy with a graph that plots the trajectory of a cannonball. That simple graph is also a spacetime, just as Minkowski model is, even though, of course, it lacks its sophistication.

In a cannonball graph, we have 2 spatial dimensions, X and Y. We dispense of the 3rd dimension for simplicity and on the grounds that our idealized cannonball follows a parabola on a plane. So, our graph represents the familiar 3D space: we have horizontal X and vertical Y, while the depth of Z is implied but dismissed for simplicity. Agreed?

Now, we add time to our model. For this we simply align the time axis with the X axis, remembering that X, first of all, stands for a spatial dimension. We could set time diagonally, at 45° to both X and Y, or at any other angle, or even align it with the Y axis, which would be less convenient for the application at hand. Instinctively, we align the time dimension with the X axis and also set its origin where the cannon stands. We also set its direction with the direction the cannon fires. Imagine if we set the time direction opposite from which the cannon fires? That would be very odd. Perhaps we still would be able to figure things out, but it is most natural to simply align the time axis with the X axis, in the direction where the cannonball is fired.

And so, in this simple graph what we have is a 2D representation of the underling 3D reality, and we aligned the time dimension with one of the 3 spatial dimensions. That's what makes our graph a spacetime. Just like Minkowski's.

Now we plot the trajectory of the cannonball. In line with Minkowski model, and just as people often picture it, instead of a simple parabola, we draw a fat, ugly line reminiscent of a giant ... in the sky. That's the worldline of our cannonball in spacetime.

I hope you noticed the uncanny similarity between our graph and Minkowski model. Can we call our model 2D + time? Both dimensions are actual, bona fide spatial dimensions (the 3rd is implied but dismissed for simplicity). The time dimension is not something extra. It is *not* an additional dimension. In our simple example, it is aligned with the X dimension. The fact that the time dimensions is aligned with it does not make the X dimension any less spatial.

In the same way, all 4 dimensions of Minkowski spacetime are bona fide spatial dimensions. Just like in our cannonball graph, the direction of time is selected, and it is done in the manner that makes sense and is convenient for the application at hand. Normally we align it with the direction of the movement, just as we did in the cannonball graph.

Certainly, Minkowski model is a sophisticated mathematical tool, unlike our simple graph. It has built in provisions, one of them to account for the finite speed of light, which is irrelevant for our cannonball application. Perhaps it is the complexity and sophistication of the Minkowski model that veiled the plain fact that it *is* set in 4 *spatial* dimensions. But in principle it is the same as our graph, which has 2 spatial dimensions X and Y, while the time dimension is aligned with X. In exactly the same way, Minkowski spacetime has 4 spatial dimensions, with the time dimension chosen and set at convenience.

And now the moral of this exercise: Minkowski spacetime is all about 4 spatial dimensions. That's why it worked out so well in GR. Because the underlying reality *is* 4D. GR describes the curvature of the 3D surface of a 4D object, IN FOUR SPATIAL DIMENSIONS. Minkowski camouflaged this fact by claiming that the 4th dimension is time, perhaps to make the idea of the 4D model of space more palatable for himself and others.

I present this for your consideration as yet another evidence of the reality of the 4th spatial dimension and welcome your comments.

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Dr. Perez,

I replied to your post in the same thread above.

_________________

Mr. Reed,

yes, the anon above is me, MV. Sometimes the sys looses the id. I was logged in, as I am now.

Re our discussion, we appear to have irreconcilable differences. You deny the existence of space, but then what do you measure between the 'stuff'?

To my plain and obvious 'There is no time without change' you reply, " Not so. There is no physical existence without change. Time is just the duration unit.... It does not exist. "

What's duration? See, to me it is the duration that does not exist. It is a series of changes in some system with which you measure "duration" of another. So, all that exists really, are some changes, and at the lowest level, where there is nothing to compare them with, you can't tell how long it is between each change. You can only register the fact that a change took place.

And so on and so forth. There are such vast differences in our appreciation of reality that I do not see a point in continuing our discussion. You will never convince me of your POV, because it is very different from where I stand. We are all entitled to our own views; what's forbidden is to impose them forcefully on others.

Good luck with the competition and take care!

Dear Ms. Vasilyeva,

I enjoyed your essay and thought the first half was quite brilliant. However, I am convinced there is a more simple explanation than your view of 4D space.

Your comment below is correct.

"The important thing is that we get a dynamic, vibrating structure that defines space."

The simple solution is that 3D space exists, it has complex plane waves flowing through it in all directions, thus time is really this wave motion of space.

From this foundation, and the use of complex quaternion wave equations to represent these plane waves, you find you can deduce the central equations of modern physics.

I hope you will read my essay on this and discuss this with me - you have a fine mind for this kind of work.

http://fqxi.org/community/forum/topic/1548

Also, Declan Traill's essay shows that Einstein's relativity can be deduced in this Euclidean 3D space given the velocity of light changes with the energy density of space. See;

http://fqxi.org/community/forum/topic/1363

Best wishes,

Geoff

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IS IT NOT QUITE AN IRONY THAT THE ESSAY THAT IS UNBEATABLY ESTABLISHED AS NO.1 (WITH 361 RATINGS AND AVERAGE SCORE 8.7)IN PUBLIC RATINGS IS ALSO THE VERY LAST IN THE COMMUNITY RATINGS?

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MV

Wonderful first part to your essay. See Richard Kingsley-Nixeys essay for where matter stops and space begins, (Shock section from the 'Cluster' probes Fig.2.) as Maxwells near far field term 'TZ'. These form the frame boundary 'membranes' as real physical dynamic boundary condition, implementing 'fluid dynamic coupling' of frames by scattering at local c each side.

I think your essay lost touch with underlying reality with branes and extra dimensions. However that may be a useful language to adapt to help recruit string theorists to the bus trip back down to a hard reality. There are other analogies to strings. I did not read the last parts in detail (speed reading and time have limits). A pretty good score due anyway. Your response so far?

(I always try to read the essays of hose who comment) I hope you read my essay again, and other papers.

Why no name? I'm intrigued.

Peter

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Ms. Vasileyva,

I received your kind words about my essay, and decided to try putting up a Powerpoint to help explain it. I included in towards the end the equation I derived for when gravity becomes repulsive but haven't yet posted what I think about the perfect fluid tensor.

You stated "Is there a way to ruffly estimate this radius? I have a visual approach to physics and understand GR as if it describes the curvature of a 3D hypersurface of a hypersphere, similar to a 2D surface of water in the ocean, with the troughs of the waves corresponding to attractive gravity and the crests, repulsive. To paraphrase the saying, my geometrical approach (in 4D) states that "what curves in must eventually curve out", which implies that the repulsive aspect of gravity manifests itself in intergalactic voids, thus explaining why they are empty. In this regard, I would very much appreciate your feedback on my essay ( fqxi.org/community/forum/topic/1547 )"

If I were to follow your analogy (since I think visually also) I would say that matter itself are also troughs in your ocean traveling as waves. These depressions always seek symmetry but when they are within a specific radius of another wave, their depressions interfere (superposition) causing a distortion of the height between them than what is on the other sides. Seeking symmetry, they move towards each other. If however, they are outside this specific radius then they would apparently seek the farthest distance possible from each other. Least that is the way it looks to me now :). So I would view your intergalactic voids as random regions outside this radius that does repulse matter since matter should randomly clump up.

Let me know what you think of the Powerpoint. Hoping I haven't goofed an equation.

Thanks

Jeff

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Dear M.V.

I tried contacting you via your private e-mail about a week ago and didn't receive any acknowledgement. I feel it might prove interesting and mutually beneficial if you can respond. Will try again. Thanks

J.R.

e-mail name... rojaro45

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Hello Ms Vasilyeva,

Going through past essays. I am a new participant on the FQXi forum. I came across something similar to my proposal for digital motion in your essay, "...we can propose that the main organizing principle of the structure is its propensity to keep as even and regular as possible. Applied to each contiguous segment of space, this principle becomes the source of all movement: any deformation introduced into the structure locally is immediately expelled; the same happens in the next segment, then the next, and so on, like in a game of hot potato. A deformation is expelled into the direction that gives, which in a perfectly balanced structure is opposite from where it comes". I agree. I propose the principle as conservation of displacement, a vector quantity. Like most action-reaction, a vector quantity is usually conserved.

Best regards,

Akinbo

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