• [deleted]

  • Post #62

Dear Vasiliyeva,

I read your essay with a great interest. I agree that role of geometry in physics has not been fully appreciated. However, my view differs from yours in that in place of empty space, what is there is the field (in the sense of Newton's vacuum and Leibniz' plenum). The field plays a role in every interaction without exception.

I too have taken a Geometric approach. However, unlike yours, it concerns very simple Geometric relationships leading to trignometric expressions between related phenomena. It makes relativistic phenomena quite understandable visually. I am sure you would like my essay

The gist of my essay: http://fqxi.org/community/forum/topic/1549

1. It identifies the PRIMORDIAL Foundational Problems in Newtonian Mechanics (NM) that runs through ALL BRANCHES OF PHYSICS. (Please see the short attachment "Primordial Foundational Problems").

2. It eliminates the problematic concept of POINT-MASS (common to NM, QM, SRT) to allow internal structure for a particle. This in turn enables to resolve the other interconnected primordial problems.

3. The result: By taking these two steps, ALL THE EQUATIONS OF SRT are DYNAMICALLY derived by identifying the trignometric relations within the energy-momentum equation, and by restoring Galileo's principle of relativity. (I request you to have a glance at the attachment - "Geometrodynamics of Energy" to verify this claim). - See also comment by L.B Crowell below.

4. This achievement will establish that I have not just treated these problems at the level a speculative discussion as in other essays, but that the problems discussed are real problems, by virtue of their solution leading to the unification of NM and SRT (by finding an equation of motion which is equally valid for slow and very fast motions).

Here is the impartial comment made by Ben Dribus (essayist in no 2 position): "One thing I will say is that it appears as if you made an honest effort to answer the question posed by the essay contest rather than just writing down your favorite ideas about physics. You will notice that I made a similar effort..... I am not sure why it was rated so low, but my impression is that many authors automatically rate other essays low to boost their own standing".

Here's the comment made by LB Crowell (essayist at no. 20 position): "The calculations I just looked at and they seem alright. ...... Your procedure appears to be some euclideanization of relativity. At the end you arrive at equations which are the same as special relativity".

In order to enable follow up of your comments easier for me, I request you to reply to this in my thread (under my essay) : http://fqxi.org/community/forum/topic/1549

Best regards,

VirajAttachment #1: 3_Primordial_Foundational_Problems.docAttachment #2: 3_GEOMETRODYNAMICS_OF_ENERGY.doc

    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!

      Mr. Fernando,

      That sounds very interesting. I will read your essay as soon as I get a free moment and will comment in your thread.

      Take care!

      Mr. Hoang Cao Hai,

      Thank you for your interest in my essay. Unlike your very advanced and far reaching work, I do not have ready answers about the concept as fundamental as space. How about you? What is space according to you? And what is your opinion about the reality of a 4th spatial dimension?

      • [deleted]

      • Post #67

      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.

        Dear J.R.,

        Thank you for your interest in my essay. You say "...plus time as a possible 4th dimension", but my model stands on the reality of the 4th spatial dimension at low energies of own own experience. -?

        Regarding your question of compressibility, the answer is yes and no. I conceive of a basic unit of spacetime as a 3D volume, which is incompressible as such. However, you can pack these "bricks" by arranging them in higher dimensions and it is in this topological sense that space is compressed.

        If you read my post addressed to Dr. Perez just above yours, I give a simple example of how a 3D volume can be packed into 4D, resulting in the decrease in the length of the dimensions. The same process can be repeated for 5D, 6D, etc, all the way to infinity. As the number of dimensions grows, their size (or length) decreases, approaching 0. The same process going in the opposite direction explains how space expands (i.e. as the number of dimensions decreases, the length of the remaining dimensions grows).

        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 Vasilyeva (this is part 1)

        Thanks for your reply. I will try to express myself so we understand each other as well as possible.

        Before 1905 people believe that space was synonymous of utter emptiness, nothingness. This was known as the Newtonian space which was mathematically represented by a 3D Euclidean space. As we all know, Euclidean space is structureless, it is nothing but the mental abstraction of physical objects (shapes, lengths, points, planes, etc.). It is thought of as a background composed of no physical entities and no internal structure; simply because nothingness cannot have structure, no energy or no substance. In the XIX (also in the XVII century) this emptiness was assumed to be filled with the aether. Some sort of material fluid having well defined mechanical properties. Then EM fields were thought of to be states of the aether (but physicists never conceived that the aether could play the role of space itself). At that time, there were several models for the aether, some people proposed that the aether was a gas like air, but they soon realized that in order to support light waves (shear or traversal waves) the aether should be a liquid or solid. In 1887-1890 Heinrich Hertz modified Maxwell equations to account for this feature. In this way he succeeded in creating a consistent model of the aether. Unfortunately, his formulation was ignored by the mainstream of the time.

        After 1905, most physicists started to abandon the idea of the aether. By doing this they not also rejected the material character of the medium but also erased from their minds the idea that the material aether could be space itself. Instead, physicists accepted Newtonian space and filled it with EM and gravitational fields. In 1908 Minkoswki proposed his space-time. This space-time was also made up of nothingness, it was only a geometrical representation (a manifold) similar to Euclidean space so that astronomical objects interacted at a distance (instantaneously) without the need of any mediator. And again this space was unaffected by matter and filled with EM fields. Einstein soon realized this deficiency (following Mach philosophy) and then developed the GR. In his theory, space is no longer a static infinite vessel but a dynamical one that changes form depending on the matter-energy content [Here the matter-energy content means any other field different than gravitational]. These fields are introduced in the gravitational equations (Einstein' equations) through the energy-momentum tensor. Solving the equations give us the form of the metric tensor (in general non-Euclidean geometry) that defines the shape and properties of space-time. This tensor plays the role of space and paves the way for the displacement of matter and fields. Under this theoretical framework, space-time is conceived as a different physical entity if compared to fields or matter. So Einstein was categorical: If we have no matter and EM fields, we are left only with the gravitational potentials (metric tensor); and if we have no potentials we are left again with nothingness, total emptiness which for him was inconceivable as well. Then, according to the GR, the metric tensor has only a relational character but not substantial. In 1917 he introduced the cosmological constant in his equations to counter balance the force of gravity. He wanted to have a static universe for, without the constant, his universe will collapse. Thus, this constant represents a perfect fluid or the energy filling the relativistic space (that is, a space without EM fields or matter) and it is found that the energy density caused by the cosmological constant is about 10^-29 J/cm^3. In his lecture delivered at Leyden in 1920 he reintroduced the notion of aether, meaning not a material fluid in the old sense but a gravitational aether in the sense of the metric tensor. The metric tensor is then playing the role of a dynamical empty vessel for the motion of matter and fields.

        Things look different from the point of view of QM. From here, one realizes that there is a state of lowest energy called the ground state and one can show that the vacuum state has a minimum energy different from zero, actually, its density is approximately 10^91 J/cm^3, a difference of 120 orders of magnitude with respect to the density predicted under the cosmological constant. In other words, from the perspective of QM the vacuum is full of a huge amount of positive energy. The time-energy uncertainty principle allows particles (virtual particles) to be created out of the vacuum for a very short period of time. In a certain sense, physicists say that these particles are created out of nothing. As I said in my previous post there is a game of words (a linguistic problem). When physicists talk about creating matter out of nothing they really mean that virtual particles are created out of the quantum vacuum which is some sort of energy reservoir called the zero-point field (take a look at the essay of Luis de la Pena and Cetto to understand this concept). So, we have a big problem here. Relativity says that the energy of its empty space should be 10^-29 whereas QM says that the energy of the vacuum should be 10^93. To hide the problem, physicists arbitrarily argue that the energy of the universe, by an unknown mechanism, cancels out to zero. They say that at the BB the same amount of positive energy (matter and fields) and negative energy (relativity space) were created, both adding to zero. To me this is non-sense since I support the idea that the energy of the universe is not zero and that there is no negative energy (take a look at this video for illustrative ideas according to the mainstream: http://www.youtube.com/watch?v=WQhd05ZVYWg&list=PLB58F0D021A12F173&index=29&feature=plpp_video).

        Israel

        Part 2.

        Now, let's talk about cosmology and the Big Bang (BB). At the beginning of the XX century most astronomers thought that space was euclidean (or Minkowskian) and that the universe was infinite in extension. This conception however lead us the so-called Olbers' paradox. How to get out of this puzzle? Well, as time went by astronomers started to estimate the velocity (through the red shift of the corresponding spectrum of light emission) of distant galaxies. They found that the more distant the galaxies were the more red shifted they appeared. Astronomers also reported that most of the observed galaxies were showing a red shift. This trend was interpreted (based on the available theoretical framework) as if the galaxies were moving away from each other. In short, they had two big problems in need of an explanation: the red shift observed in galaxies and Olber' paradox.

        In 1915-16 Einstein developed his theory and later some solutions to Einstein's equations were discovered. Some of these solutions suggested that in an expanding universe light should lose energy that should be observed as a red shift. One of these solutions matched with the observations and they arrived at the consensus that space was expanding. Then Lemaitre proposed that if we play a cosmological clock backwards the universe should compress in a single point of infinite density, that is, the BB singularity. A singularity is a point where we have an infinity (and when we have an infinity we do not know what happens there). Some other people added that if the universe started with the BB then there should be a relic cosmic background radiation (CBR).

        Let's stop here since there are two versions about the universe. There are many people who claim that there is no BB at all and that the universe is very old. They contend that the red shift, Olber's paradox and the CBR can be explained without invoking space expansion and therefore there is no need of BB. In this version the universe is static and possibly infinite. Who shall we believe? Unfortunately, these people have been ignored by the mainstream (later we will discuss their proposal). For the time being we shall consider that the BB took place. If so, what is the real situation about the BB? It is common to hear in popular media that the universe started out of nothing. And when a physicist is asked: how something can be created out of nothing? They usually replied with the virtual particle scenario, in which something is creating out of "empty" space (i.e., quantum vacuum). Above I have explained what they mean by that. However, in the case of the BB, it is supposed that space-time was also created along with the universe, so this situation is different from the previous one, because in this case we have no reservoir from where the energy can be extracted and therefore their argument becomes ambiguous. But since they assume that the total energy of the universe is zero, the BB is not violating the energy conservation (this point is debatable) and the creation of the universe can come from zero energy or nothing.

        Beyond this intuitive picture the real situation is that, at the singularity, nobody knows what happened or what the laws of physics are. At this point simply, GR breaks down completely (also at the black hole singularity). This means that nobody knows if the universe really bang. The theory has nothing to say and therefore there are no answers to the questions: What was before the BB? 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? (see this video of the mainstream: http://www.youtube.com/watch?v=4Y3rNm3QSVU&list=PLB58F0D021A12F173&index=28&feature=plpp_video)

        You also ask: 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?

        What expands is the space itself (the space of relativity). This is one of the solutions of Einstein's equations, the so-called Friedmann-Robertson-Lemaitre-Walker metric in 3+1 dimensions. But again this "space" is represented by the metric tensor which differs from the quantum vacuum. We are talking about two different notions of "empty" space. In the former case, when we have no fields and matter we only have the energy of gravitational potentials (metric tensor), but in the case of QM we have the energy of the zero-point field. QM presupposes that there is some background whereas relativity denies it.

        As an alternative you are proposing that space has an internal structure made up of a fluid or strings. You also say that "there is a concept in topology (I would like to know what this concept is) 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." Your notion is still quite ambiguous. One can have the energy-momentum tensor equal to zero (vacuum equations, see Milne and de Sitter universes). This means that even if there were no matter-energy and fields in the universe we could still have the metric tensor (gravitational field). In this sense I say that the space of relativity is mere geometry, it is not a substantial entity as in the case of the quantum vacuum.

        Israel

        Part 3

        Thus, if I understand your view well, you are saying that space exists in itself as some kind of positive energy or massive fluid, i.e., as some sort of quantum vacuum or luminiferous aether (Lae). You say in your previous posts in reply to me: "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". Besides this you also assume that this space is the medium for the propagation of light waves, i.e., your notion of space plays more the role of the medium for the propagation of light. You also argued in your previous reply to me that "I see absolute reference frame an abstraction that cannot exist in reality". So, if you support the idea that space is the medium for light, you are implicitly saying that space is the absolute frame of reference because the speed of light is defined relative to the substantial space. This is precisely what I discuss in my essay. I support the view that space is a material continuous fluid and the medium for the propagation of EM waves. And the speed of these waves is defined by the material properties (permitivity, permeability, viscosity, etc.) of this space. This view is more in alignment with the "empty space" (quantum vacuum) of QM and it considerably differs from the notion of space of relativity. In relativity, one can introduce, on the right hand side of the equations through the energy-momentum tensor, any kind of fluid field you could think of (energetic, material, gauge, fermion, etc.) and this fluid will define the shape of the metric tensor (the properties of the geometry of space), but this notion differs from the notion that physical space is a fluid. You should understand this significant difference. And I insist, the space of relativity is nothing but an empty geometrical vessel that could be filled with fields. In contrast to this view, you are proposing a space made up of some physical substance sustaining the fields, i.e., the EM fields do not filled space they are features and manifestations of it.

        If we think of space with internal structure, that is, with viscosity, dissipation, etc. we have a mechanism to explain the red shift. It has been shown, considering the dissipative and dispersion properties of a material space (as any other medium), that the redshift can be explained without assuming the expansion of the universe, just as you argue in your essay. The notion of space as a fluid also explains Olber paradox. Because as any other medium, space is dissipative and therefore light will lose energy as it travels though space. And finally, since space is a fluid it is subject to thermodynamical laws. The CBR is only the manifestation of space in thermal equilibrium with all the stars in the universe.

        In summary, I support the view that space is a continuous material medium of 4 dimensions because this could explain very easily most physical phenomena, in agreement with your essay. However, if we support this view, we are against the prevailing paradigm. If space has an internal structure means that there is no BB, no expansion, no dark energy, no dark matter, that there is an absolute frame of reference, that the speed of light is constant relative to the homogeneous space, etc. All of these ideas have already been developed in a mathematical theory [C.I. Christov, Nonlinear Analysis 71 (2009) e2028-e2044 and C. I. Christov, Math. Comput. Simul. 80 91101 (2009)] but despite the fact that the theory is consistent, it has been ignored by the mainstream because the theory contradicts relativity. In relativity space has no internal structure, as you believe, but in QM and the Christov's theory it has. These two views are contradictory. Do you get this difference?

        Israel

        • [deleted]

        • Post #73

        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.

          J.R.,

          thank you for your encouraging words and your interest. From your initials I can't figure out which is your essay. -?

          You ask "Is the dynamic part.. energy contained within space?, the passing of energy via EMR thru space?, or space itself posessed of inertial properties?, or something else?"

          It's all a matter of scale. At the very bottom of it I visualize it as a dynamic structure made of vibrating strings (which appear golden to my inner eye -?). This structure *defines* space. I.e. there is no Euclidean and no Minkowski and no Absolute space without it. Without space there is undifferentiated nothing unable to contain anything. Most people cannot conceive an absence of space and cannot conceive its structure without imagining some structure *in* space. But if they meditate on it for some time, this becomes doable.

          You say, "My question is "how is it possible for waves to propagate through an incompressible medium?""

          The structure vibrates. Just like atoms in a slab of steel vibrate. If you strike a slab of steel, it will resound and transverse waves will propagate through it. If you strike it hard enough, it will also wobble and undulate (which explains why "gravity" is the strongest force: it takes far more energy to make a steel slab wobble than to resound). But steel is not rigid enough in comparison to space. It is a well-known fact that the harder is the material, the faster the waves propagate through it. Space behaves like a super-rigid solid. That's why no 3D model can explain how matter moves through the 3D space fully occupied by this medium. Only 4D can, assuming that the additional spatial dimension is empty and does not contain this medium. For all we know, this empty dimension may be not structured, i.e. it may be the remnant of the Great Void of the singularity in which the universe was born. Since we are "crawling" on the 3D surface, what does it matter how many dimensions that emptiness has? Actually, come think of it, if the emptiness is the remnant of the Great Void, this could be the source of the energy that is pressing the nuclei into the surface (because they stick out) giving rise to mass (it's like some hard objects lying on a bed, covered by a heavy glass pane that presses them in).

          And so the fact that the structure vibrates is crucial in this model. The vibrations is what propagates as quanta or "particles". There is no continuous waves... well, from a perspective of a certain scale, the waves may appear continuous, just as the surface of the structure appears continuous from even greater scale. But when you zoom in on it, you will see the "bricks" and the fact that waves propagate in quanta of underlying vibrations.

          I am glad you made me think about "what it's made of" again... I imagine it now, from the POV of an intermediate scale, as an oily (-? I know) pliable yet very bouncy and stiff... like an oily liquid metal. Icy mercury? I really don't know. I don't think there is a material that could match it.

          To me, space, its structure and its properties is the expression of energy. Just like mass is an expression of energy. And like everything else. Everything is made of the same stuff, starting with the structure of space.

          Israel,

          very interesting posts. And you write so well! You give an excellent historical overview, and I fully agree with the 90% of your position. There are some things that I see differently. I address them in the same order as they appeared in your posts.

          You write, "As we all know, Euclidean space is structureless, it is nothing but the mental abstraction of physical objects ... It is thought of as a background composed of no physical entities and no internal structure; simply because nothingness cannot have structure, no energy or no substance."

          In my view, Euclidean space is the epitome of a perfect structure. Perfectly even, perfectly flat, perfectly regular. If it is 3D, that too is an aspect of its structure. It can be 4 or 7D, which would make it a different structure, with different properties. It appears to me that you are one of those people who take space for granted and cannot conceive an absence of space. Just like Hawking, in the video you suggested, started off making a universe with matter, then energy and, finally, space, lol. As if matter could exist without space. You super-smart PhDs view the world through the prism of abstract mathematics. Maybe that's why you overlook its most important thing, space.

          You wrote re history, "In 1917 he introduced the cosmological constant in his equations to counter balance the force of gravity. He wanted to have a static universe for, without the constant, his universe will collapse."

          See, to me this only means that Einstein, like everyone else, viewed matter as the primary... entity -? that affects space. I rather see space as primary and matter as the extension of its structure. Thus in my view this structure will sooner become empty than collapse because of matter in it.

          You wrote re theory: "What expands is the space itself (the space of relativity)."

          Again this view shows that space is taken for granted. The idea is untenable in an established universe (after the BB), since it implies that something --or someone-- is pouring energy at a constant rate into the universe and they do it evenly everywhere, except right where we are (why Sun is not getting any farther?) In a few hundred years the current period will be known as physics dark ages. Have you ever taken an inventory of your convictions trying to guess, which ones will be ridiculed by our descendants, just as we ridicule some of the most cherished notions of the past? I know, each generation, when we are still young, believe that people were ignorant in the past and that we are the ones to set things right, once and for all, for the benefit of humanity. It takes some living and a study of history to realize that we too will be laughed at hundreds of years from now. About some of our notions they will say, wow, already then they knew it! And about others... Have you ever tried to guess, which of our current believes will get into which category?

          You say about the current theories, "We are talking about two different notions of "empty" space. In the former case, when we have no fields and matter we only have the energy of gravitational potentials (metric tensor), but in the case of QM we have the energy of the zero-point field. QM presupposes that there is some background whereas relativity denies it."

          IMHO, both theories describe the same thing, at different scales. It's like digital music. At a sampling rate we hear it, it is continuous and the quality is better than when the technology was analogue. At another sampling rate, it is a collection of disjoint sounds. But it's the same music.

          GR deals with the curvature of the surface. QM bumps into the micro-fluctuations in this surface. From the scale of GR, those fluctuations are unnoticeable, just like the digital nature of our music is unnoticeable to us, until we change the sampling rate.

          You wrote, "This means that even if there were no matter-energy and fields in the universe we could still have the metric tensor (gravitational field). In this sense I say that the space of relativity is mere geometry, it is not a substantial entity as in the case of the quantum vacuum."

          I don't understand how you could have metric tensor without matter-energy. -? Ah! I guess then the tensor would always predict flat space, ok. But the way you speak about geometry is as if nothing maintains its structure. It is the same structure as in QM, only at a different scale.

          You say, "So, if you support the idea that space is the medium for light, you are implicitly saying that space is the absolute frame of reference because the speed of light is defined relative to the substantial space."

          -?? My understanding of SR is that mathematically it is equivalent to LET. In either case, Lorentz transformation assures that c remains a constant for an observer. I thought that absolute reference frame made sense only in a stationary ether model, for then you could drive a thick nail into that station, lol, and label it O. In the model I propose, nothing is ever stationary in relation to the structure, because all movement is actually driven by it. I see the universe as the ultimate perpetuum mobile where space "wants" to be empty and so it expels all deformations introduced in it locally, and that's how everything moves.

          Absolute reference frame with a dynamic structure? I completely don't get it. It's like the water in the ocean; it is totally real and tangible and you can even measure the rate with which it passes under the keel, but what use is it for navigation?

          (continued)

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          • Post #76

          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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            • Post #77

            yes, sure, you can email me

            Continued (part 2)

            Israel,

            You wrote, " In relativity, one can introduce, on the right hand side of the equations through the energy-momentum tensor, any kind of fluid field you could think of... and this fluid will define the shape of the metric tensor., but this notion differs from the notion that physical space is a fluid. You should understand this significant difference. And I insist, the space of relativity is nothing but an empty geometrical vessel that could be filled with fields. In contrast to this view, you are proposing a space made up of some physical substance sustaining the fields, i.e., the EM fields do not filled space they are features and manifestations of it."

            Thank you for your clarification. Yes you understand the issue very well.

            You wrote, "If space has an internal structure means that there is no BB, no expansion, no dark energy, no dark matter, that there is an absolute frame of reference, that the speed of light is constant relative to the homogeneous space, etc."

            I don't see how this follows. I am comfortable with BB and can even review my stand on post BB expansion. I definitely do not accept the idea of the dark matter, seeing its invention as a symptom of our lack of understanding of space. As for the dark energy, or negative energy, I don't find it contradictory to the model I propose either.

            That space may be seen as a sort of a substance is fine with me. That's how it was traditionally modeled, no? Like many here, I believe that the next greatest advances in physics will come from material science, applying the concepts learned there to model space in 4D.

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            • Post #79

            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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              • Post #80

              Hello, Mr. Reed! And welcome :)

              Yours is a position, according to which I can classify people onto those who can conceive the absence of space and those tho can't. Clearly, you're in the second category. This is a position of someone who has never given space a thought and always has taken it for granted. Thus for you, it does not even exist as such, except maybe as wrappings for some object or energies.

              It is very clear to all, except maybe a fish, that fish cannot exist without water. It is clear to a select few who have given this a thought that without space nothing can exist at all, but space can exist with nothing in it. That would be the perfection itself. That is what empty space is: a perfectly even, symmetrical, regular structure, with absolutely nothing to mare its perfection.

              Then you say: "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."

              lol, are you trolling me? 'cause this sentence hardly makes sense. Then you say: "The other important points in respect of the concept of space are: ...."

              Ah! the paragraph above was an important point in respect of the concept of space? lol and what did you mean by this:

              "-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"

              -?? I take it you're in a playful mood. I too love to have fun.

              Regarding time you said, "-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."

              See, for me time is the change in energy state (in space), not "speed of change" as you define it. At the most basic level, I see energy, time and space as 3 aspects of one and the same.

              And since you wondered in here, I am curious, what is your take on Minkowski spacetime and would you be interested if I go ahead and prove that it is all 4 spatial dimensions in time, not 3 time?

              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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                • Post #82

                Ms Vasilyeva

                "Thus for you, it does not even exist as such, except maybe as wrappings for some object or energies"

                It is not a case of 'for me', neither is it 'wrappings', but what is experienceable (or proven to be potentially so). And physical reality comprises physically existent phenomena (probably of several different types), which have shape/size (ie a relative spatial footprint). Indeed, these can be within, &/or separate from, each other. Whether there are 'areas' of physical reality which have no physical presence whatsoever in them, ie space is existent, needs proving. Note: that is different from the circumstance where there is a physical phenomenon, but it is not directly experienceable. So the point is that it is physical phenomena which exist, the concept of space being a logical corollary, an assertion which has no existential substantiation (at least, as yet).

                "lol, are you trolling me? 'cause this sentence hardly makes sense"

                No. I just used a phrase which was intended to cover all types of physically existent phenomena. Rather than the usual form of expression which implies there are physical entities (something) which are 'in something', &/or being affected by 'something', but neither of these, mysteriously, and against the rules of physical existence, have themselves any form of physical presence (ie are something). Again, the underlying point being that there are physically existent phenomena, and whether 'not-physically existent phenomena' exist needs proving.

                "and what did you mean by this"

                What it said. The concept of dimension revolves around the possible directions, either way, that any given physically existent phenomenon can have physical presence (ie its spatial footprint). 3 spatial dimensions (or 6 directions) is just the minimum that can be represented. In reality, the number of dimensions which exist is a function of how many directions the smallest phenomenon could travel from the same point, halved. Put another way around, we tend, understandably, not to differentiate any given reality down to its existential level, which does not necessarily matter, unless we then reify some feature which is only a function of that conceptual level.

                "for me time is...not "speed of change"

                Time is a duration unit, timing is the methodology. Timing can be effected without a timing device, ie by the direct comparison of the number of changes in one sequence to another. Using a duration unit as a common denominator reference just makes measurement easier, but what is still being compared is the number of changes, irrespective of type. That is, the speed/rate at which change occurs. For example: if one is using a quartz watch, then what is really being compared is number of changes against number of crystal oscillations (ie changes). And then disparate types of change can be compared, in terms of speed at which they occur. This is all associated with change, which is about characteristics of the difference between realities. Whatever is existent, can only be so in one physical form at a time. There is no change (and hence time) in whatever constitutes a physically existent reality. Put another way around, again, if reality was differentiated to its existential level, then that which was existent (ie without any form of change involved) could be identified. In the same way that if we slow a film down enough, we can identify the stills which ultimately comprise it.

                Paul