Essay Abstract

A fundamental assumption embedded in our current worldview is that there exists an as yet undiscovered `theory of everything', a final unified framework according to which all interactions in nature are but different manifestations of the same underlying thing. This paper argues that this assumption is wrong because our current distinct fundamental theories of nature already have mutually exclusive domains of validity, though under our current worldview this is far from obvious. As a concrete example, it is shown that if the concepts of mass in general relativity and quantum theory are distinct in a specific way, their domains become non-overlapping. The key to recognizing the boundaries of the domains of validity of our fundamental theories is an aspect of the frame of reference of an observer which has not yet been appreciated in mainstream physics. This aspect, called the dimensional frame of reference (DFR), depends on the number of length dimensions that constitute an observer frame. Edwin Abbott's Flatland is used as point of departure from which to provide a gentle introduction to the applications of this idea. Finally, a 'metatheory of nature' is proposed to encompass the collection of theories of nature with mutually exclusive domains of validity.

Author Bio

Armin Nikkhah Shirazi studies physics and philosophy at the University of Michigan, Ann Arbor because of a deep curiosity and passion for understanding the basic aspects of nature. He is also a composer and pianist, having composed about 100 musical works(some of his works are available on his Youtube channel). His work as a pharmacist funds the pursuit of his other passions.

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Dear Armin Nikkhah Shirazi,

Unification of fundamental particle interactions is not vindicated in a Coherently-cyclic cluster-matter universe model, in that the fundamental matters are considered as string-like structures. Thus, only gravity and electromagnetic force are expressional in this scenario of string dynamics, in that these forces have a common origin.

With best wishes,

Jayakar

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    • Post #3

    Hi Armin,

    Great essay highlighting some of the fundamental obstacles that we need to overcome in order to develop a TOE [and that is where I disagree with your conclusion]

    Space is limited here in this reply but I but in short here a number of points I would like to make in consideration of your essay:

    1. Tetryonics is a unified Theory of Everything that has developed from equilateral Energy geometries [as opposed to the spherical geometries currently supposed by physicists]

    2. It is a change in the underlying geometry of physics - not its mathematical formulation and to date I have produced over 1300 illustrations detailing its application to QM, QED, Chemistry & Relativity [SR& GR] with considerable success.

    3. One of its major priori points is the strict definition and distinction of mass vs Matter (and their geometries wrt spatial co-ordinate systems] which goes a long way to providing a suitable framework to advance the unification of numerous physical disciplines.

    4. 2D EM mass in 'Flatland' manifests as 3D tetrahedral [standing-waveform] Matter [as opposed to the cubic geometries you employed in your illustrations]

    5. Gravitation [as defined by Newton and Einstein] is based on observations of the force created by bodies of large-scale Matter [whereas in reality it is the nett attractive force created from the gravitation of Matter and the interactive forces created by its associated quantum masses [radiative magnetic & kinetic energies etc]. GR is Newtonian gravity with SR effects [8pi vs 4pi]

    6. The GR 'bending' of light is thus revealed to be, in fact, a SR effect [refraction] and the use of photons & EM waves to measure gravitational effects should be abandoned under the proper definitions of mass & Matter as afforded by Tetryonics [particularly as GR's Stress-energy tensor doesn't differentiate between either mass-energies or Matter]

    7. All Forces (& physical constants) can now be shown to be the result of super-positioned Energy geometries [save gravitative Matter which can be modelled as such hence its similarity to Coulomb's force law in Newton's formulation of it]

    8. Dimensionality [as defined by EM energy vectors] can be reconciled with Flatland, Cartesian co-ordinates, Relativity & Tetryonics (as attached).

    9. A TOE is possible as evidenced by Tetryonics - the Charged geometry of EM mass-ENERGY-Matter [I don't call it a TOE as I believe that term is over-used and its current title better reflects what it represents].

    I trust you will take a look at my work [and FQXi essay] and start a dialogue so we can discuss the finer points of my theory and how it may lead the way to a better understanding of physics and our Universe in general (perhaps it may very well change your mind on this matter).Attachment #1: 3_Figure_01.03__Spatial_geometries_800x600.jpgAttachment #2: 1_EM__massENERGYMatter_800x600.jpg

      Armin,

      Interesting essay. A few thoughts and questions come to mind.

      1. What do you mean geometrically/topologically when you say that "spacetime reduces to a 2+1 dimensional analogue?"

      2. You refer to "actualizable worldlines," but Feynman's sum over histories doesn't give a probability amplitude for worldlines, it gives a probability amplitude for terminal events. It seems that you gain a spatial dimension when you consider all maps from "areatime" to "spacetime," but you lose the time "dimension" (causal direction or extent) when you measure, since all you know is the terminal state. Are you really changing dimensions, or just converting 2+1 to 3?

      2. You reject the dichotomy of existence and nonexistence, but I am not quite sure what you mean by "existence" in the first place. Evidently more than mathematical existence, since Feynman's world lines exist in that sense. The actualizations seem to exist and are distinguished by interacting dynamically with the 3 (+1) space. Is that the point then, that things "exist" if they interact dynamically with the space in which they live? If so, is areatime dynamical too?

      3. If spacetime is not special, presumably areatime is not special either. Taking this to its logical conclusion, you could imagine maps from time to line-time, line-time to area-time, and so on. The constant feature here is a partial order which may be identified with causality. But then, we should realize that manifolds themselves are quite "anthropocentric" as well. If you take a step back and think of morphisms of partial orders, you get something like my "causal metric hypothesis" described here: On the Foundational Assumptions of Modern Physics.

      4. Finally, on a lighthearted note, string/superstring/M-theory involves "branes" of different dimensions too, but no one can agree on what the "M" stands for. Perhaps you should suggest "M" for "meta."

      Take care,

      Ben Dribus

        Jayakar,

        Thank you for your comments. I did take a look at your paper, but must admit that I got lost. Perhaps this is because my knowledge of string theory is very little, you may be better advised to consult with a string theorist on your theory.

        Thanks again and take care,

        Armin

        Kelvin,

        I looked at your essay, it has some very nice illustrations and the narrative gives a rough idea of what you are trying to convey.

        Unfortunately you make a number of very strong statements of fact without showing how they follow from the mathematics associated with your idea. For example, you write:

        "It [i.e. your theory] effortlessly merges all the tested features of Classical mechanics with the statistical probabilities of quantum mechanics and scales up to the cosmological scales of General Relativity."

        without showing any equations to substantiate this claim.

        I know that in your post thread you said that you are not a mathematician, but, for better or for worse, mathematics is the language of science and for no science is this more true than for physics. In fact, our most fundamental theories of nature tend to bear a greater resemblance to mathematics than to physics because they often involve concepts that are beyond our ability to visualize. One is left in those instances to fall back on mathematics to provide an unmatched level precision of expression, an ability to check the implications of a given relation as well as the consistency of an conceptual structure.

        I came, like you, into this area from outside mainstream physics, but I have attempted to take the lesson to be taken from this to heart. The paper in which I presented my full theory contains a mathematical derivation of the Feynman path integral for the simplest situation, a single free particle, from my ideas. My derivation might be imperfect in the sense that involves only a special case and that the expression of some of the ideas could benefit from greater precision, but given an attitude which accepts that mathematics plays a fundamental role in any theory that models nature (which is an inducement to improve one's mathematical abilities, these issues will likely be resolved over time).

        I would suggest that you either reduce the strength of your statements, in which case you might frame them more as philosophical speculations, or to present the mathematics that back up your very strong claims.

        Finally, I would strongly advise against including any statement like the concluding remark of your essay ["This is my gift to our Planet and all future generations"]

        Good luck and take care,

        Armin

        Hi Armin, good to see that you posted your essay. It is indeed a further thinking of the earlier one, this one is more detailed and with avery good ending the metatheory.

        Your perception : " The key to recognising the boundaries of the domains of validity of our fundamental theories is an aspect of the frame of reference of an observer which has not yet been appreciated in mainstream physics" is also my starting point only you let diminish the dimensions and I just draw a line at the Planck length and time.

        When I read your DFR concept, it again brought me to essentials like "a square has only one side" or is two sides ? for a flatlander it has only one side , and a moebiusring does not exist in his 2 dimensional universe. On page 5 you are creating the column of squares, just as a straight line , a fixed z coordinate, however the Z coordinate can take any value, so that any form is "actualizable".

        This part I like tha "actualizable" can become actual. 5What I name the Total Simultaneity is in fact all the actualizable histories possible and non possible (in our perception).

        Your page 6 is in fact the same as the theory of the collapse of the wave function, even the comparision to the Feynman path, I like your description of area time as "it manifests itself to spacetime observers as asuperposition of two actualizable matter distributions describable by ....". The only remark here is that you accept already the existance of the "observer" (!)

        On page 7 you mention "two or more objects described by the same non-factorizable wave function who share the same wave-function, share common wave factors", I came to a different interpretation (with almost the same result) and introduced the Objective Simultaneity Speres, together forming a foam being the origin of "decoherence".

        I fully agree that "anthropocentrism" in the way some theological theories apply it to our universe is not the whole truth, however the way we are experiencing our "reality" is the result of our perceptions and in this part of the "metaverse" it is by the decoherence of all our observations that it "seems" as if we are the center of the universe, of course we are not, but really if you want to know more please read THE CONSCIOUSNESS CONNECTION that I wrote about the subject, there you will also see why I could ask you how you could see the "observer" as already existing.

        I liked very much you schema of the "METATHEORY OF NATURE", very good , the only thing you could think about is that the dimensional frames could also go to the negative side and perhaps there all the dark energy and so on can be found.

        I hope that you take the time to comment also on my essay, this tile I took also at heart your posts wher you gave me indications how to be more clear.

        best regards and the best of luck

        Wilhelmus

          Dear Ben,

          Thank you for looking at my especially and thank you especially for your serious questions about my framework. I will attempt to answer them the best I can, and I hope that if I failed to be clear or if you disagree with something I say, you will let me know.

          You asked: "What do you mean geometrically/topologically when you say that "spacetime reduces to a 2+1 dimensional analogue?"

          A more mathematical statement would be this: consider a four-volume x^0x^1x^2x^3 in some frame (x^0 denotes time in this fourvolume). We can write very generally the following statement:

          [math]

          \lim_{x^1x^2x^3\rightarrow0}x^0x^1x^3x^4=k

          [/math]

          where k is taken to be a constant because of homogeneity and isotropy of space. Now, I believe that, although I have not seen this stated explicitly, it is generally tacitly assumed that

          [math]k=0

          [/math]

          This would seem to be implied by the fact that we model elementary particles as point (i.e. zero dimensional particles) which means that we are not considering in our current mainstream theories any spaces or objects of intermediate dimensionality between zero and three.

          I believe, however, that already special relativity gives us a hint that this conception cannot be quite correct. Consider that objects described by v=c undergo complete length contraction along the direction of motion. In other words *they are reduced by one spatial dimension* (as opposed to three).

          So, in my view, it is not true that k=0. In fact, the first axiom of my theory specifically postulates that

          [math]k=|U_{3max}|

          [/math]

          where the term on the right is defined as a constant quantity with dimensional units of areaxtime of variable shape (the variability in shape is analogous to the variability of a four-volume in different inertial frames even though its magnitude is constant as the Lotrentz factors for one direction in space and for time cancel).

          Now, I agree that this is statement is still imprecise in the sense that it does not specify exactly how this limit is approached. This is an area I am still trying to figure out, but my suspicion is that due to the close association of mass with the emergence of spacetime in my theory (recall, acutal mass--> finite spacetime proper time--> actual worldline --> spacetime) this geometric limit manifests itself to us as a dynamical limit with dimensional units of action.

          There are some additional ideas I have on this, but in order to make this response manageable, I will defer mentioning them to a future point in our discussion.

          You said:"2. You refer to "actualizable worldlines," but Feynman's sum over histories doesn't give a probability amplitude for worldlines, it gives a probability amplitude for terminal events. It seems that you gain a spatial dimension when you consider all maps from "areatime" to "spacetime," but you lose the time "dimension" (causal direction or extent) when you measure, since all you know is the terminal state. Are you really changing dimensions, or just converting 2+1 to 3?"

          Well, you are of course correct in your statement about probability amplitudes in Feynman's formulation and if you thought that this is what I claimed, then I failed to clearly express my ideas. In my defense, it was not so easy given the small amount of space available to summarize my idea.

          I was implicitly already referring to the canonical formulation in my paper where I said something about the "vanishing probability amplitude"as the situation it referred to involved a two-state system.

          In my formulation, as in standard theory, each path contributes equally to the overall path integral, so I think we completely agree.

          You said:"You reject the dichotomy of existence and nonexistence, but I am not quite sure what you mean by "existence" in the first place. Evidently more than mathematical existence, since Feynman's world lines exist in that sense. The actualizations seem to exist and are distinguished by interacting dynamically with the 3 (+1) space. Is that the point then, that things "exist" if they interact dynamically with the space in which they live? If so, is areatime dynamical too?"

          Excellent observation! Yes, with one qualification: Massless objects evidently interact with spacetime objects, too, but they always cease to exist during those events.

          As for "mathematical existence" I believe (and please forgive if this sounds pretentious) that this involves an area of mathematics where there exists a distinction that has so far been overlooked. I recently gave a talk at a conference in which I presented my ideas, and the first 7 minutes of that talk may be relevant to your question. The talk is here:

          http://youtu.be/GurBISsM308

          I am sure that you will have additional questions, so I'll let you take look before discussing this further.

          You said" If spacetime is not special, presumably areatime is not special either. Taking this to its logical conclusion, you could imagine maps from time to line-time, line-time to area-time, and so on. The constant feature here is a partial order which may be identified with causality. But then, we should realize that manifolds themselves are quite "anthropocentric" as well. If you take a step back and think of morphisms of partial orders, you get something like my "causal metric hypothesis" described here: On the Foundational Assumptions of Modern Physics."

          Yes indeed, the first part of your response makes me think that you might not have seen the appendix to my paper, for it takes this idea exactly in that direction. Did you see the appendix?

          As for the second part, yes, I will take a look at your paper and comment in your thread.

          You wrote: "Finally, on a lighthearted note, string/superstring/M-theory involves "branes" of different dimensions too, but no one can agree on what the "M" stands for. Perhaps you should suggest "M" for "meta.""

          Ha! I did not even think of that, that's funny. It reminds me of this quote by Nathan Seiberg at the 80th anniversary IAS conference:

          "Most string theorists are very arrogant," says Seiberg with a smile. "If there is something [beyond string theory], we will call it string theory."

          or, rather, M-theory :)

          Finally let me mention that I present a more mathematical version of my theory in a paper called "A Dimensional Theory of Quantum Mechanics" which, if you like, you can access here:

          http://hdl.handle.net/2027.42/83865

          Basically, in my theory I start with a set of axioms and attempt to derive the usual Feynman formulation, i.e. sum over histories, each of which is associated with a phase factor e^iS/hbar(and its complex conjugate)which then allows one to go from there to canonical quantum mechanics.

          I feel that there are several shortcomings in that paper, including some concepts that could be stated more precisely, some misconceptions that reflect my lesser understanding at the time, and some awkward wording which might potentially turn off readers, so I am working on an updated version, which, if you are interested, I can let you know about when it is completed.

          Again, thank you for your questions and I hope I was able to at least address them somewhat.

          Armin

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          • Post #9

          Hi Armin,

          Noted your comments and would like to point out that my full work is peppered with the relevant equations but I do note that they are not included in my competition essay [if that is what you are referring to].

          I was limited by space and had to condense the 1300 illustrations I have produced to a short essay for the comp [but I did include the unified equation for EM mass-ENERGY-Matter].

          The application of equilateral energy geometries to the current Math does not change the current Math formulations as they apply to physical processes, only the 'assumed' geometry underlying them - and in turn it explains many of the mysteries at the heart of physics today - mass, Matter, wave-function probabilities, wave-particle duality, constants etc.]

          These 'errors of mathematical perception' are readily corrected, as outlined in the essay, when equilateral geometry is applied as the foundation of the mathematics used to describe physics - and I stand by my statements particularly as they apply to the advancement of Science - more detail is available in my full eBooks [and a 4th eBook will detail its application to GR and gravity culminating in the true 'fusion' mechanism at the heart of Stars and how we can replicate this process on Earth for clean, limitless energy]

          However I do understand where you are coming from with regard to succinctly conveying my entire theory [especially in the context of an essay competition]

          Thanks and good luck in the comp.

          Hi Wilhelmus,

          Good to hear from you, too. Thank you for your detailed comments, I did see your essay but will take another look and post a comment on your thread.

          Thanks again,

          Armin

          Hi Kelvin,

          Thank you for the clarification, based on your statement it appears that you have done a substantial amount of work. I did look for a reference in your paper but did not find any. If you did not reference your ebooks, may I ask why you didn't?

          Hello again,

          This reply comes after the previous (below, inadvertently posted separately). I just realized that I may have partially misinterpreted your second question (1st labeled 2.)

          Upon re-reading, I'm actually not sure if I am understanding. The propagator clearly allows us to proceed from an initial state to a final or terminal state. I understand, in particular, the path integral to help us determine a state given an initial earlier state. If this is correct, then it would seem to me that one would not lose the time dimension. If you could clarify, I will try to give a better answer.

          Hi Steve,

          I am sincerely sorry to hear about your misfortune. I hope that things will work out for you, I would have expected that in France (where I assume you live) there might be help available for people in your situation. In any event, don't give up hope.

          All the best,

          Armin

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          • Post #14

          Armin:

          Great essay. The 1-D, 2-D, 3-D versions of observed and observer are key to differences of gravity and quantum approaches. Perhaps you may see better, from a mathematical point of view, my say @

          To Seek Unknown Shores

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

          I have attempted to look at the problem globally, difficult to do in 12 pages, but..it's my attempt.

          Comment(s)?

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            • Post #15

            Dear Mr. Shirazi,

            I quite enjoyed reading your very well written cogently arranged essay, although due to my lack of a formal education I did not fully understand some of the portions of it concerning fundamental physics. I do have a question for you concerning the observation of a square. I believe that one real Universe can only be occurring eternally once in one real dimension. One real dimension can only be verified from its interior by the singular use of two real observation points. That is why every animal, bird, fish, and most insects have two eyes in the front of their heads. What pragmatic proof is there that there are three dimensions?

              Hi Armin,

              I come from Belgium, the french part, not from France.

              I am thanking you. I am trying to solve but I am not good in administrative pappers. I must found a bank who helps me. But I don't know how I can do. If I could, I will take my mother with me and I will go in an other country. We are disgusted by our country. We have been stolen and anybody listens us. The politic of my wallon part is very bizare.

              I have even lost all my production of flowers. And you know what, I live at 400 meters of the greenhouses, abandoned.They do not want that I produce plants. I am disgusted.I would simply create jobs me and put into practices my inventions. I am disgusted by these years of probelms. I don't understand the human nature.

              Even, a job I don't have you know. I have just my theory and my inventions.I must be strong for my mother, she is tired by these years of bankrupcy. They want take the house. But there is a solution, but they do not want to listen it. Disgusted is a weak word. You imagine you, a productor of plants at 400 meters of greenhouses abandonated ? If there there is not a probelm??? I am there to create jobs and I cannot? You understand that you ?

              I can imrpove my region and they block me ! If it is that the earth ??? Where are we going ?In a wall I think simply.a chaotical wall.

              What a world.

              Regards

              • [deleted]

              • Post #17

              Hi Armin,

              No references were quoted as the work is a completely original work on quantum geometry by myself [equilateral vs Spherical geometries used by all scientists and text to date].

              If I was to quote references then I would have to list all textbooks, science mags etc. in print along with Wikipedia [but as I only used then to point out the current Math formulations & problems in physics I was solving for using Tetryonic geometry I thought it was completely futile to list them]

              Especially when so much of Tetryonics is devoted to changing the underlying geometric foundation to physics and correcting the 'errors' arising in physical Maths as a result of this incorrect perception.

              Even basic formulations for Energy [hv=E=hf] had to be redefined [2hv^2=E=hf] to correct for errors made from Math without models approach historically used [along with many, many more examples found throughout my full EBooks online]

              All the geometry, illustrations and changes to accepted physics formulations found in Tetryonics are my original work [done over the past 4 years] but I do acknowledge that "if I have seen further it because I was standing on the shoulders of past giants in the fields"

              • [deleted]

              • Post #18

              Dear Mr Shirazi

              I have deep passion to 2D world.

              See http://fqxi.org/community/forum/topic/1413

                Armin,

                You're right, I did miss your appendix; I didn't look below the reference page. I also watched your video, so I have a somewhat better idea of what you have in mind.

                It seems that by definition you can't work with manifolds and get the limiting properties you need. This isn't necessarily a bad thing in my view, but at some point one would need to know the precise definitions and properties of the "spaces" involved.

                One thing I would like to point out since you mentioned the limit of length contraction is that this is partly what motivated the deformed special relativity theories (DSR), which use the postulate that the Planck length is the smallest possible length. These theories involve noncommutative geometry; I mentioned them briefly in my essay. I don't know if using a fundamental scale like this would be helpful to you or not; a "layer" would be information-theoretically two-dimensional, but it would also exist at a particular place in the larger space, which you prefer to avoid, since objects in the lower-dimensional space are supposed to be actualizable in different places.

                This also reminds me of the holographic principle and the AdS/CFT correspondence. Both involve lower-dimensional information "actualized" in a higher-dimensional space.

                I agree that the scale-dependence of various types of interactions from the nuclear forces up to dark energy has some meaning that has not been fully grasped by modern physics. I also agree that dimension is probably scale-dependent in a sense, although my framework has non-integer dimensions in general.

                It's interesting that the string compactifications involve higher dimensions at small scales, while you propose lower dimensions. I lean toward higher dimensions associated with matter-energy density.

                  • [deleted]

                  • Post #20

                  Hi Armin. Direct bodily experience (seen and felt) is fundamental to physics, as it is necessarily fundamental to the unification and elucidation of the most fundamental, integrated, and important physical ideas.