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Thread: Fundamental Theory of Reality,“Reality is nothing but a mathematical structure, literally”.

  1. #1 Fundamental Theory of Reality,“Reality is nothing but a mathematical structure, literally”. 
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    Quantum Statistical Automata




    “Reality is nothing but a mathematical structure, literally”.




    In This letter I shall derive the laws of nature from a simple mathematical system that forces itself upon us because it is the only system that leads to a dynamical universe using fundamental entity. Such an idea has long been suspected to varying degrees by different scientists and philosophers from past to present. As evidence mounted stronger, advocates albeit few have argued for the cause. Max Tegmark of MIT has been the leading proponent of such hypothesis.
    Because our understanding of nature has grown tremendously in the past hundred years or so, it was the scientists in the field who got to consider that nature looks like it has more than this casual relation with mathematics. It was not just the suggestion of that casual relation but also the deeper understanding of how nature seems to be constructed. While we don’t understand a lot of things about nature, it was this comprehendible thing about it that made many scientists make that connection.

    The quote of Wigner’s “Unreasonable Effectiveness of Mathematics in the Natural Sciences” is very well known and pointed to as one of the first hints. Another hint you can see in the classic textbook by Wheeler , Misner and Thorne GRAVITATION where the first attempts were made to drive the law of physics by logic which they called pre-calculus. As our knowledge increased more people got to consider it like Wolfram in New Kind of Science, Conaway’s game of life, all kinds of automata ideas, Fractals and not the least as we got hints from how computers generate virtual realities. But the grand slam belonged to Dr. Tegmark with his MUH. So this idea did not happen in one go but in a continuous fashion. But the man who put that in words that I think is most beautiful is wheeler.

    Behind it all is surely an idea so simple, so beautiful, that when we grasp it - in a decade, a century, or a millennium - we will all say to each other, how could it have been otherwise? How could we have been so stupid?





    I will show the following in the upcoming posts

    1. How I arrived at the idea.
    2. Basic results that shows how QM arises, written in BASIC program.
    3. Description of two particles interacting and explaining the program in C++.
    4. Showing the results for Bohr atom hydrogen 1s simulation.
    5. The amazing formulas deduced from the system.
    6. How spin arises from 2D simulation.
    7. The appearance of the mass of the electron through simulation.
    8. How gravity arises.
    9. Other results and discussion.


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    How I arrived at the idea.



    Reality exists hence we say it is true. But what is really true besides that more than anything else which we can really trust, it is mathematical facts. So, to my mind I connect both since both seem to be a statement of truth. So I took a guess that reality is something akin to a circle (truth). The relations between the points give you a mathematical structure whereby you get PI which defines the structure of the circle.


    So I was thinking the relation(s) between what entity(s) could give a rise to a universe (truth). To come up with a structure with some entities, the easiest way was to see if I could draw two entities and define some kind a rule for their interaction. At that time I was familiar with fractals and vaguely heard of Conway’s idea, but I did not know about neither Dr. Tegmark nor Wolfram’s- New Kind Of Science-. I said let me see maybe I will be smarter than Conway and get some really fancy rule between some triangle or circles or lines or whatever. But as soon as I put a blank sheet in front of me, for a short while I thought to myself this sounds very enigmatic, first by what criteria I am going to choose my entity, and which characteristic of that entity I was going to interrelate them and what expression. Choosing by trial and error was not very natural.
    My intuition was telling me I needed something more natural. Being an engineer and a programmer we learn to be efficient in our designs. So I opted first for the simplest configuration and that was point and to start simple and not to draw points all over the paper, I restricted myself to a line. Now, if I iterate on an artificial formula I will just get fractals which has already been tried which gives you beautiful suggestive pictures but that's all. Also the different formulas I could use were most unnatural. So I thought the only way out is to throw random numbers on the line and see what happens. Off course, after a bit more than few seconds it was obvious I am going to get a uniformly distributed points on the line, I don't have to tell you that I was sad at that point( although I should have been happy as hell, you will see why). How I was to get out of this conundrum, other than mangling that paper, throwing it in the garbage can and go to a party.
    The only other thing to do was to throw random lines that did not exceed an original line of length L. One more choice was necessary is to choose where those lines started, the obvious choice was random position on that line L.
    After that thought analysis I went to my pc and downloaded a simple BASIC program and started coding the idea thinking I was going to get some fractal like universe or something useless. Creating the random length lines and their random positions was straightforward, but now I had to decide on what logic/constraint to use to eliminate the lines which were going outside of the original line. I tried few of them with not too complicated expressions and the output, the random positions, looked jittery but when approximated looked like some kind of a trigonometric function. So I superimposed a sine, cosine, sin^2, cos^2.

    Using the simplest expression for the constraint I was in a shock, it matched perfectly sin^2, and that was the solution for Schrödinger's equation for a particle in a 1D box, with the probability of the particle position directly (no complex wave). Just from that I knew at that time that I was onto something big. Reality was nothing but random numbers (representing lines and their positions) just like what I have suspected.

    The next natural thing to do is to generalize to 2D and 3D, I was in a shock again, it was so simple, just repeated the code for 1D and labeled appropriately, and plotted, a perfect probability wave for first energy level in 2D and 3D. The amplitude came out also perfectly once I normalized the probability positions to the number of throws, 2/L, L being the original line length. That was natural because probabilities had to add up to 1.



    The next question that presented itself was how to calculate the energy for the particle in a box and what does it take to get the higher energy levels. It turned out, just like it should, that both questions are linked. The only obvious choice for calculating the energy was to somehow add up the lengths of the random lines. It did take some testing to see the correct expressions, because, you could take several expressions like...

    but only one matched the behavior that we get from solving Schrödinger eq. to get the energy level and that is adding up all the line lengths for each point. Calculating energy that way (after normalizing) it was quadrupling when the distance of confinement was halved in a perfect match to the higher energy levels.



    For a moment at that time the situation looked hopeless, how can I get any interaction going, even simpler, how to add some potential? I was having some doubts about the model, on one hand, it was reproducing sh. eq. on the other I noticed early on that I could reproduce any function in math by randomly throwing lines and applying certain constraints more complicated than the one which reproduced sin^2. I asked myself could it be that what I have discovered was just a math trick.

    That situation did not last long because this model is amazing in more than one way. In a way creating these function was a blessing, because now I have a choice, very few actually, to create an interaction between the particle in a box and a potential like function ,say 1/r or exp(x) or a step function, for example. The reason why I said amazing, is that the only choice I had for interaction is to set a relation between the random lines for the different entities, mostly, if two lines crossed or not. Then I only keep the probability position for the lines that did not cross. Long and behold, you get probability waves similar to solving Schrödinger equation with a potential. The model was pushing me to do the only available choice which led to the right results.

    And that led me to the next step, setting up a particle in a potential well. I could use a step function or just another particle in a smaller range within the original particle space. And the result was perfect. I got the exponential decay for the parts which were overlapping and the tunneling with continuity automatically satisfied. There was no turning back at that point.


    Last edited by qsa; May 14th, 2012 at 09:07 PM.
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    Description of twoparticles interacting and explaining the program in C++.


    the thumbnail shows 1D implementation. 1,2,3,4,.... are the number of loops. in each loop I throw two numbers for each particle denoting their position and length. if the lines cross (star) I ignore I don't register the position( the round marks) or don't do anything with the lines. But if they don't cross then I have a counter that updates the number of times a hit happened in the particular position (the squared marks). then for each particle I have a counter that simply adds the lengths of this line to the previous total for each particle.

    I do that(loops) a million, sometimes a 100 trillion times. then I normalize to the number of throws. the totals of the lines(normalized) are the energy. the numbers of hits for each positions is operated on to get the expectation values. normalized position hits are the probabilities that are similar to the ones we get from the "squaring" of the wavefunction. Without interaction the expectation value is the midpoint of the particle. But when interaction happens the expectation value moves. lets say to left in the left particle and right in the right particle. That denotes a repulsion. you can also get attraction with different logic. But more on the logic part later.

    then the particles are moved to a different distance and the operation is repeated.

    Now I explain the code in more detail. see attached file.



    The code that you see is the cleaned up version of the one in the website.

    1. define variables/types

    2. set the particle widths (d0,d1) , which I interpret as the compton wavelength, I assume lamda= h/mc the model shows (I will show why) that h=c , so lamda =1/m ,then I choose m to be in au hence if m=.0005485 then lamda=1822.8885 units of length on the axis/line . more on scale later.

    3. set the interval (intr), that is used as a quantity to increas the distance between the particles after the calculation finished for certain distance.

    4. start the mk loop that will increase the distance between the particle after each iteration.


    5. based on mk value set the positions of the particles,zero out some of the variables need be. f1 is the number of hits for crossing f for not crossing. Zero out the arrays (S[],Sy[]),that hold the hits for each position on the axis/line.


    6. next is the j loop the heart of the program, it iterates on the random throws

    7. don't worry about these lines, not important


    long r= rand();
    double rndm=(double)r/((double)RAND_MAX);

    8. calculate the start of the lines from inside of the particles and the length of the lines shooting to the other particl all based on random numbers.

    9. use if ( st1+p1 + li1 > st0+ p - li) to check if lines crossed or not.

    10. if not crossed update the position hit by incrementing the counter S[] for that position. add the random line to an acummulation counter (en). I do that for one of the particles only. the other will be similar.

    While I said I don't do anything when lines crossed but in this program I do the same using Sy[], en1 just for information. I will talk more about it later.

    11.go to 6

    12. when done with j loop normalize the energy en to the numbers of throws accepted frf = (double)f/en; //energy of the particle

    13. calculate the expectation value for the position array S[] -over the width of the particles.

    edx = edx + (( n) * S[n]);

    calculate how much exectation is offset from center of the particle


    ex[mk] = (double)edx / ((double)f)- (0.5 * int(w*d1))+.5 ;

    14. update all data in file for that seperation.

    15 . go to mk loop for new seperation distance

    16. done

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    Showing the resultsfor Bohr atom hydrogen 1s simulation.



    Here is the most important first result from the three results that I will show. The results confirm that the classical Bohr Model falls out from QSA model which encompasses QM and QFT.


    Please always refer to these wiki

    Bohr radius - Wikipedia, the free encyclopedia
    Bohr model - Wikipedia, the free encyclopedia

    this is the result of simulating two particles with a width of 1823 which is close to 1822.8885 for electron compton wavelength (just simplification)interacting at a seperation of around Bohr radius which is
    1/(m*alpha)=1/(.00054858*.007297352569) = 249801.3

    the raw data is below from the program with int=50. also make this change in the program to get these results
    for (mk = 2475; mk <= 500000000; mk++)
    also
    d0 =1823; // Particle 1 size
    d1 = 1823; // Particle 2 size

    long long kj =20000000000; // # of random throws (approx 30 min for each distance)
    but next I give the important data that we will discuss
    Code:
    distance  energy (P.E.)     charge^2(e^2)     Expectation value(Ex)   
    249323 0.0000120326 3.000003457 2.219640631
    249423 0.0000120278 2.999998876 2.219325817
    249523 0.0000120229 3.000000804 2.217591031
    249623 0.0000120181 3.000000809 2.217731633
    249723 0.0000120133 2.999998829 2.215744702
    249823 0.0000120085 3.000006682 2.215434488
    249923 0.0000120037 2.999998356 2.214921159
    because I have the 1/r law I interpret the energy as e^2/r , e=charge
    so if you multiply distance *energy= e^2=3 as shown, the average of above e^2= 3.000001, but we will take 3 to simplify.
    then because we know alpha I deduce that ( from alpha=e ^2/(h*c))
    h*c=e^2/alpha= 3/ .007297352569= 411.108
    from other arguments I have h=c= sqrt(411.108)= 20.2758
    Now, the important part which Expectation value(Ex for short)
    after inspection I find it to be related to the classical bohr model variables
    Ex=v^2/(2*m*e^4) ---------- eq 1
    solving for v^2=(2*m*e^4)*Ex --------------- eq 2
    from above simulation the average of Ex= 2.2172 almost
    hence v^2= (2*.0005485*9)*2.2172= 0.0218936
    v= sqrt(0.0218936)= 0.14797
    now we compute v/c=0.14797/20.2758= 0.0072976
    v/c should be alpha we have a very good match with some error mostly because of Ex which we can simulate with higher j thows to get more accuracy and also due to the approxomation of 1823 and 1822.8885
    Great we proved that Ex is what it is and h=c
    next
    from eq 1 we can compute the kinetic energy
    K.E.= (m^2*e^4)*Ex=(1/2)*m*v^2=.5*.00054858*0.0218936
    = 0.000006005195544
    2*K.E.= 0.000012010
    That is Bohr Model P.E.= 2*K.E.
    So the energy has the interpretation of potential energy and Ex is related to K.E. , that makes perfect sense
    also if we take 1/(2*Ex)=1/(2*2.2172)=0.22551 almost m*c^2
    m*c^2=.00054858*411.108= 0.225526
    errors should be taken into account as mentioned earlier

    Q.E.D



    Code:
    2475   249323   1.2032598102434993e-005 5.9941919763095141e-006  3.0000034566933995   1.823      2.2196406306904919   -2.1562643940237649
    2476   249423   1.2027755561853412e-005 5.9917972737823617e-006  2.9999988755041636   1.823      2.2193258174578432   -2.1564566940604664
    2477   249523   1.202294299276971e-005 5.9894015680537819e-006  3.0000008043848765   1.823      2.2175910306876858   -2.1541575969249607
    2478   249623   1.2018126569310113e-005 5.9870183764102081e-006  3.0000008086108982   1.823      2.2177316327685048   -2.1541184268552342
    2479   249723   1.2013306059579073e-005 5.9846252913626688e-006  2.9999988291162647   1.823      2.2157447018220182   -2.1534291553698495
    2480   249823   1.2008528765272037e-005 5.9822392351484673e-006  3.000006681726556   1.823      2.2154344880241297   -2.1517840085696207
    2481   249923   1.2003690562073311e-005 5.9798542464554e-006  2.9999983563450483   1.823      2.2149211586316824   -2.1521569239379232
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    The amazing formulasdeduced from the system.


    check out these formulas that I deduce from my theory, these are NOT a guessed formulas.

    fine structure constant ,alpha=α = 7.297352568 × 10−3

    let

    1/m_e= 27*(1/(2*alpha) -(.5*alpha) -1) + (alpha/(2*PI))

    1/m_e=1822.888474(approx).....

    the term (alpha/(2*PI)) it is related to spin, this term is not deduced from my theory(just a guess but it is small)
    .................................................. .................................................. ..............

    Also first term 27*(1/(2*alpha) )=1849.98599...
    Two terms 27*(1/(2*alpha) -1 )= 1822.98599
    average (1849.98599+1822.98599)/2 -1/3= 1836.15266 electron-proton ratio !!!

    Actually 27=3^3, 3 is equal to e^2(charge squared!!) in my system, the long term not the running phase.


    Also reversing the relation I find

    1/alpha= (2/3)(1/m_e*e^4) +2 +(3/2)(m_e*e^4) Approx.(m_e=1/1822.8885) (e^2=3), e^4=9

    beautiful symmetry. all these equation can also be written in a form that uses the golden and silver ratios (google)

    also


    electron g-factor=(4m_e/3eh)*(2/(3*m_e*alpha) - 2*e^2 -1)

    =2.00231934...

    .. e=3(charge square),h actually h_bar=(e/alpha)^.5=20.2758.. m_e=.00054858
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    qsa,

    I don't yet know what questions to ask

    To generalize your proposal, could one say that reality can be described by a set of equations, right? You are describing this truth of reality as a circle, right? And you are using random numbers in these equations?

    So that I could understand your proposal better, could you summarize your proposal verbally in a few sentences like these with a single meaning to it?
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    Quote Originally Posted by forrest noble View Post
    qsa,

    I don't yet know what questions to ask

    To generalize your proposal, could one say that reality can be described by a set of equations, right? You are describing this truth of reality as a circle, right? And you are using random numbers in these equations?

    So that I could understand your proposal better, could you summarize your proposal verbally in a few sentences like these with a single meaning to it?
    What I am saying is the reality is similar to a circle (or triangle or a cube .....) in CONCEPT, as a simple example of structure. I use a computer program to illustrate the concept and get some results quickly since it is very natural to the idea. But I hope one day the system will be converted to the usual mathematical formalism. But it will look very complicated.

    Here is a summery

    I derive the laws of nature from the hypothesis that "Nature is made out of mathematics,literally". I present a method to design a universe using simple rules which turn out to have the properties similar to our reality. Particles are modeled as end of lines, one end is confined to a small region and the other goes to allover other particles in the universe. The Coulomb force-1/r law- (when lines cross) and gravity (when lines meet) -with the approx. order of strength-appear naturally and they are two aspects of one process involving the interaction of these lines. I am able to calculate what appears to be the Fine-structure constant. Gravity also appears with surprising results(inferred), it shows that gravity becomes repulsive when distance is great. At this time I have only done 1D full simulation with interaction and 2D and 3D and indeed nD without interaction. Iam working on 2D interaction now and already showing very surprising results (may be spin). Time and space could be looked upon as derived quantities. In my model the ultimate irony is that our reality came about because there is only one way to design a dynamic universe and that only one allowed our existence.
    Last edited by qsa; May 15th, 2012 at 04:50 PM.
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    Quote Originally Posted by qsa View Post
    Quote Originally Posted by forrest noble View Post
    qsa,

    I don't yet know what questions to ask

    To generalize your proposal, could one say that reality can be described by a set of equations, right? You are describing this truth of reality as a circle, right? And you are using random numbers in these equations?

    So that I could understand your proposal better, could you summarize your proposal verbally in a few sentences like these with a single meaning to it?
    What I am saying is that reality is similar to a circle (or triangle or a cube .....) in CONCEPT, as a simple example of structure. I use a computer program to illustrate the concept and get some results quickly since it is very natural to the idea. But I hope one day the system will be converted to the usual mathematical formalism. But it will look very complicated.

    Here is a summery

    I derive the laws of nature from the hypothesis that "Nature is made out of mathematics, literally". I present a method to design a universe using simple rules which turn out to have the properties similar to our reality. Particles are modeled as end of lines, one end is confined to a small region and the other goes to all over the universe. The Coulomb force-1/r law- (when lines cross) and gravity (when lines meet) -with the approx. order of strength-appear naturally and they are two aspects of one process involving the interaction of these lines. I am able to calculate what appears to be the Fine-structure constant. Gravity also appears with surprising results (inferred), it shows that gravity becomes repulsive when distance is great. At this time I have only done 1D full simulation with interaction and 2D and 3D and indeed nD without interaction. I am working on 2D interaction now and already showing very surprising results (may be spin). Time and space could be looked upon as derived quantities. In my model the ultimate irony is that our reality came about because there is only one way to design a dynamic universe and that only one allowed our existence.
    OK cool! What about Wolfram's proposal that reality can be better-described by programming combined with mathematics as you have done?
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    His automata were ad hoc, not derived from a fundamental concept like mine and no important results was obtained. Please read the second post and contemplate it , maybe it will clarify what the main idea is.
    Last edited by qsa; May 15th, 2012 at 04:53 PM.
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    Now I have more information in the website.

    2. Basic results that shows how QM arises, written in BASIC program.
    7. The appearance of the mass of the electron through simulation.

    and also the 1/r law and the running phase for the charge.

    QSA Theory

    I will explain spin and gravity in later posts.
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    This is a short summary of my theory for the benefits of those who don't what to read the relatively long text.


    I will just recap about what my theory is about, and then talk about the Schrödinger and Dirac equations. In my system I try to find out what design can lead to our reality(PHYSICS) sine I conjecture that it is nothing but a mathematical structure that is like a circle or a triangle but has a dynamic property. So after some trials I end up with just RANDOM LINES on an axis which turn out to lead to a model a lot of known physics with other surprising results.


    In my whole simulation I use three constraints and assumptions which I think they will be replaced by more fundamental principal eventually. These are

    A- a simple constraint to model a particle that does not interact with other far away particles


    if ((double)(d0-p-li)/(double)d0 < rndmx || (double)(p-li)/(double)d0 < rndmy)

    B- Particles have certain width (you could say the Compton wavelength) and random lines start from inside the particle width to another particle and all the points between them.


    C- to make the system invariant under rotation I am constraint to make the random lines start from one region of a particle and ONLY end up on a region of another particle.

    So when I tried to design the universe I did NOT say ,oh, what is the structure that will give me 1/r law or a particle in a box. No, I said WHAT ARE THE POSSIBLE DESIGNS. And the ONLY possible one that leads to a dynamic structure automatically lead to the 1/r law, the running phase and all the other results that you see. Later I hope to prove a very strange property of this structure and that is that the most complex structure is equivalent to the simplest ones and that is because of the statistical nature of the structure. But that is in the works.

    Because my system is inherently is based on probabilities (and lengths interpreted as potential energy) The results that I get for a particular setup( like particle in a box or in a finite potential) AGREES with Schrödinger equation Born rule interpretation which are probabilities but it does not reproduce the wavefunction ITSELF since it is imaginary most of the time and there is great controversy as to its physical meaning anyway. While it might be somewhat complicated to SETUP more elaborate problems of Schrödinger equation but there is NO problem in principle. For instance, my model does a excellent job( better than QM) with the Hydrogen 1s orbit as you can see from my Bohr atom simulation. But it is more tedious to do the higher orbit ones. But please read that Bohr atom section and see how the relation between potential and Kinetic energy is clearly spelled out, World's first as you put it.

    AS you know the Dirac equation is seen as the stepping stone to QFT and I have not delved into how it is represented in my theory. Suffice to say that I get similar things to its results like particle and antiparticle(I have not shown that yet) AND when I go to 2D simulation then I am forced to use the C- constraint to make the system invariant under rotation (i.e. relativistic) then I automatically lead to spin and when I calculate the probabilities , lo and behold I get the electron g-factor.
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    http://www.fqxi.org/community/forum/topic/1877

    This is fqxi contest entry.also please check the website for the added programs.
    Thanks.
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    qsa
    now that you have defined reality, you might try finding it?

    Reality(if I might borrow the words of someone else) is a tale told by an idiot, full of sound and fury and signifying ......................nothing.
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    Quote Originally Posted by sculptor View Post
    qsa
    now that you have defined reality, you might try finding it?

    Reality(if I might borrow the words of someone else) is a tale told by an idiot, full of sound and fury and signifying ......................nothing.
    I have defined nothing, just presented a theory in the usual sense of physics. The theory seems fundamental and point to the stated conclusion. I hope you read it and comment on the content and if you can understand it.
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