Thank you Inger! You can't imagine how much I appreciate your comment.
Please see the post bellow (coming up) in response to Mr. Kley's question above in which, within the framework of my model, I attempt to dispel the mystery of the wave-particle duality.
Dear Vasilyeva
Thank you for reply, I appreciate it. Some times the discussions between people is only a matter of semantics. Unfortunately, I did not express my ideas properly and so you replied with something like this: "It appears that you do not know... ...is a 2D plane." My apologies for this.
Clearly I understand geometrical dimensions, and according to your reply you propose that space has a structure. You also say this in your essay:
As to what this structure is made of, we could go with Poincaré idea of a FICTICIOUS FLUID or take the Faraday vision of vibrating lines of force, which happened to nicely resonate with the leading theories of the day. Or we could combine the two in an image of incompressible, PERFECT FLUID, consisting of vibrating strings. Details don't matter. The important thing is that we get a dynamic, vibrating structure that defines space.
So, a space with structure seen as a fluid is not only geometry but topology or theory of fluid mechanics. In this sense your proposal is not merely geometrical but substantial this is why I referred to solid dimensions.
You say "details don't matter". May be for the sake of illustration details are not important but in the construction of the theory they do matter. Today physics knows that the 3D space is filled with fields. According to you what is space filled with? what is 3D space made of? fields? matter? energy? or what?
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. That space has this kind of internal structure means that space is not geometry as GR states. This is why I ask you to define how you conceive space.
You: "I presume you are aware of the high energies at first instances after the BB. These high energies 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.
You say: Regarding your question of why ether was a wrong model, first, the concept itself stems from air, which cannot support transverse waves, and second, the theory never considered the 4D nature of space, assuming that it had only 3 observed dimensions.
There is a model assuming space as a material fluid and it works. Moreover, besides supporting transverse waves it supports longitudinal waves. But again, these are material dimensions that have clear mechanical interpretation. The fact that the model assumes space as a massive fluid (i.e., it has some internal structure) contradicts current views, GR.
Another example of this can be found in my reference 23 in my essay. There the authors argue that the sapce has an internal structure and assume it as a medium for EM fields with a degraded refractive index, but this view, again, goes against the geometrical character of the GR. Since you are not defining what space is made of, your idea of space appears to be quite ambiguous. If you define it as a massive fluid and as the medium for EM fields, implicitly you are contradicting the GR. Otherwise, I do not see the relevance of your idea. If you have a paper in which you mathematically state your ideas I would appreciate it.
Best regards
Israel
Mr Kley,
Thank you for your interest in my essay. It was very late for me when I saw your question. In my reply I used wrong terms in the sentence which should have read: both 'attractive' and 'repulsive' gravity emerge from the same property of the hypersurface of the 4D structure of space that seeks to minimize its hyperarea.
You asked, "Can you offer up any specific experiment or present unexplained phenomena that may be illuminated by your vision of 4D Space/Time?"
Having thought your question over, I decided to address the wave-particle duality, with which physics replaced the paradox of space. This duality is best revealed in the double slit experiments. I would like to use this opportunity to demonstrate that, from the 4D perspective, there is no mystery why both matter and light appear to move in waves. In my essay I only briefly mention this in the Flatland analogy.
Before we begin, it is important to appreciate that a hypersphere has 3-dimensional surface, each point of which is equidistant from its center, in the same way as each point of the 2D surface of a sphere is equidistant from the center of the sphere. This topological fact is what makes the 3D space we perceive invariant in all 3 directions and precludes the possibility of selecting a preferred reference frame. The dynamic nature of the 4D structure also makes it unsuitable for the role of the absolute reference frame (just like sea captains can't use ocean as a reference frame and must rely on the external clues such as stars or GPS).
The other aspect of the 4D geometry worth remembering is that form a 4D perspective, each point of the volume of a cube is visible in one sweep just like we grasp each point of the 2D plane in one glance. In a sense, from a 4D perspective, a 3D volume of a cube appears flat, similar to a 2D plane seen from 3D.
With this in mind, let us see how a double slit experiments works out in 4D, on the simplified analogy of the Flatland Plane (the Flatland analogy is indispensable, because 4D is virtually impossible for most people to visualize).
First, I would like you to please take a look at the following image from google images, since I can't post images here:
http://ej.iop.org/images/0295-5075/94/2/20004/Full/epl13428fig1.jpg
The top image, (a) is a side-view snapshot of a hexagonal lattice aggregate of bouncing droplets on a vibrated liquid bath that interact via the surface waves they emit and form various types of stable crystalline clusters [1]. Suggested by Andrew Norton, it is indeed an excellent model of the Flatland nanoscale with droplets representing nuclei confined to the outer, empty side of the Plane (in the "headroom"). Please take a good look at the image again and imagine 3 such aggregations, at some distance apart from each other. These 3 aggregations of droplets/atoms represent the solid structure of the plate with 2 slits in between.
Now please appreciate the fact that light waves, an electron, an atom or a molecule, all move along the surface of the Plane (or hyperplane in 4D) that contains the EM field. The difference between a light wave and, say, an atom, is that the light wave is the transverse disturbance in the surface itself (just like a transverse wave in the surface of water) and as such is entirely confined to the EM field it contains, while "matter" (stuff with intrinsic mass) glides just above this surface in the 3rd dimension (3rd dimension in the Flatland analogy and in the 4th dimension in our world). Nuclei are integrated into the surface by their electron clouds interacting with the EM field in it. The electron cloud makes the indentation a nucleus makes in the surface locally even with the rest of the surface and at the same time acts as a sort of a roller or better yet, a surf-board on which the nucleus surfs the light waves themselves. (In this context, the increase in the inertial mass at high speeds is mostly due to the electrons interacting with the EM field contained in the surface.)
Thus there is no difference in the path a particle of light or a material object takes. A light particle is a convenient abstraction that stands for the momentum of a light wave in space (or, a hyperplane). A material object, such as an atom, can also be represented by a point that too follows the same path. It is the structure of space itself that dictates all movement by expelling the deformation introduced into it locally into the direction that gives (even though, of course, there is a difference in the transverse disturbance that we perceive as light and a longitudinal disturbance we perceive as mass).
In this model it is essential to realize that everything we perceive directly or with the help of our technology are the projections onto the 3D surface of the hyperplane. Matter moves along the same surface as light waves themselves. Thus the interference pattern seen in the double slit experiments is the reflection of the fluid nature of the structure of space itself.
I also would like to emphasize that the strict separation between matter and space of the model I propose is applicable only at low energies of our own experience. At very high energies, the number of space dimensions grows in proportion to the energy density. At high energies, in higher number of dimensions, the geometries of space and matter intermix and are best described by the multidimensional models of string theories.
Again, I thank you for your interest in my essay and for giving me opportunity to address this important question, which I could not do within the constrains of the requirements.
References
[1] A. Eddi, A. Boudaoud and Y. Couder, (2011, doi:10.1209/0295-5075/94/20004), Oscillating instability in bouncing droplet crystals. http://iopscience.iop.org/0295-5075/94/2/20004
Hello James!
Thank you for your interest in my essay. I like the vividness with which you describe how you perceive the world. I will certainly read your essay and will comment in your thread.
Mr Kley, I replied to your question in a comment below.
Thank you for your interest to my essay.
Dear M. V. Vasilyeva,
It is basically alright. The de Broglie wavefunction is described in the four dimensional spacetime. The slit takes one dimension and the light-beam takes another dimension, therefore, the equations of the double slit interference can be described in 4-2=2 dimensional space-time. Of cause you can still argue about the width of slit and the 3D surface electron cloud, and so on. My essay "Rethink the double slit experiment" have the detailed calculations compared with many experiments. There are real math-physical calculations, not a graphic illustration. The most important part is the connection between the two slit by the cross-linked angle, which is derived from the particle scattering to the wave function. In that way, the particle-wave duality paradox is linked to the space-time. I have my email in the essay, please send an email if you like to talk more.
Yours
KX
Thank you Ke Xiao for your feedback. Even though it was somewhat difficult for me to read your highly technical essay, I did grasp its main point, namely that the wave-particle duality paradox lies in the structure of spacetime itself. Here we are in agreement; and while you amply speak to the professionals, I offer a geometrical representation of the same on the simplified analogy, making it accessible to the lay public.
Xie xie!
Dear 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
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.
Dear Amazigh Mabrouk Hannou,
I tired reading your essay but had a very hard time understanding your "accent in print". This is because, even though I know several languages, I have not studied yours. I think it is important to have our papers checked by a native English speaker before submission. This becomes especially important when introducing new ideas.
Regarding your question of gravity, my approach is purely geometrical and is inline with Einstein's general relativity, which treats gravity as a curvature in 4D spacetime. My take on it is that this curvature is due to surface tension of a 4D ocean of perfect fluid that seeks to minimize its hyperarea (similar to water tension in 3D).
In a topological sense, in 4D, there may be another reason for 3/4 - 1/4 distribution of energies. It may be due to the fact that a convex 4-space can be broken down into 4 contiguous, adjacent 3-spaces. This means that a convex 4D object, such as a hypersphere discussed in my essay, can be broken down into 1/4 for its 3D surface and 3/4 for its bulk. (The same does not work for a sphere, but works, with different numbers, for all n-spaces where n>3.) The same overall distribution of hypersurface to hypervolume, 1/3 to 3/4 respectively, applies to other convex 4D objects, even though actual proportions may vary a bit when they deviate from a hypersphere, which has the minimal surface area.
Take care!
Dear Ms Vasilyeva,
I write in French and I translate into English.
To be honest, I must admit that it is advisable for me what you have just made as remark.
The reason is that I discovered this contest only later.
Then, I had only two choices, to quickly write the article in my language and then translate it in a record time, or not participate at all, and wait until next year.
I chose the second option. I said to myself that if someone is interested in my ideas, we are human and I can always catch me up later.
What is important, is the idea and not the way that it is formulated.
And I sincerely believe that the idea which I have formulated will mark the history by its relevance and will make smile also by its shape, these are the vagaries of life.
If you are interested by any side of this model please let me know it, I would answer, with pleasure, your expectations.
I hope my translation is enough good for more understanding.
I wish you all the best.
P.S. your 1/4 and 3/4 interest me.
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
Mr Hoover,
I am not certain what is meant by dark energy currently (it keeps on changing). Trying to see from where you are coming to it, I read your essay and saw this picture, which I also found on google images:
http://www.theepochtimes.com/n2/images/stories/large/2011/05/23/549761main_pia14094-43_946-710.jpg
This is an artist rendition of a 4D model of space, with one dimension removed, the green grid representing gravity (= curvature of the 3D surface on which "matter floats") and purple grid representing dark energy that pushes on matter, pressing it into the surface, displacing a volume and causing it to curve. That's how I understand it. The articles that came with the same image says, "This contradicts an alternate theory, where gravity, not dark energy, is the force pushing space apart. According to this alternate theory... gravity becomes repulsive instead of attractive when acting at great distances." I agree that gravity becomes repulsive at great distances (where voids form in my 4D model of space). This is stems from pure 4D geometry.
I personally do not agree that the universe is expanding, especially at ever-increasing rate. First, why don't we see it right where we are? The whole idea is based on the redshift and in my essay I offer another explanation to it.
But I understand what you're interested in and that is the enigma of UFOs and how they move as if inertia is none of their concern. I happened to see 2 small saucers at a very close range. I saw them about 25-30 meters away and then I ran towards them and got even closer. I was an adolescent then, and my impressions were vivid and observations sharp. Because of this I do not disregard other people's accounts.
I absolutely agree with you that there is a way to manipulate the curvature of the 3D surface (on which we live, according to my 4D model of space) which we call gravity. For this we need to have a better understanding of space, which we don't. In fact, the situation is just deplorable, as this contest demonstrates. The establishment is so entrenched in a particular way of looking at things that they are incapable of even considering anything else. And now with this idea of ever-expanding universe, which is happening everywhere except just where we are... People got Nobel prizes, defended their PhDs and built their academic careers on it, which means that they will defend it tooth and claw, all the way till the end. It will be another generation, after this one goes away, before an alternative view on things could even have a chance.
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
Yes, Mr. Perez, my apologies! I did overlook your post. I am reading it now and will certainly reply.
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?
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.