Special and General Relativity Special and General Relativity Physics Help Forum

 Sep 7th 2019, 07:18 AM #12 Senior Member   Join Date: Mar 2019 Location: cosmos Posts: 551 More sufficient concept of space “What does X = X4x mean? i runs from 1 to 3, but your symbol X4 has not been defined?” What does X = X4x mean? It can be found in the 4D space definition in my first post in this thread. But now, I try to analyze from another angle to explore why this equation can appear. Put aside y and z, just use x to represent 3D space, for the most simplicity. The question here is what does the symbol “ – x ” mean? A.The negative part of the axis; B.Just “parity”; But what does “parity” mean exactly? C.Inversion of 3D space. We do be able to draw two opposite 3D frames. (see the second row in the attached picture, z axis omitted for convenience of watching.) 1.It is just a math game. 2.Inversion of 3D space. If the answers are C and 2, why not use +1x to represent the 3D which is in consistent with the 3D space in the first row while use –x to represent the 3D space which is opposite? Then we use the symbol X4 to accommodate the specific values of +1 and -1. We got an equation X = X4x. Ⅰ. It’s a more clear and explicit method of representation in form. Actually, it’s a representation of 4D space because there is an additional element X4 attached to the 3D space x. Of course, if X4 also represents proportion of space, it seems to be more perfect. Actually, we can zoom those two frames in the second row. Ⅱ. In meaning, X = X4x is a more sufficient/integral concept of space. It contains two parts. The part of x is length element which will vary following movement/frames while the part X4 is contrary or proportion element which will not vary following movement/frames. In the past, people emphasize on variation of space following movement. Now, in X4 theory, we emphasize on the part which will not vary following movement. ………. How to fully define the symbol X4 is the key step in X4 Theory. Next post. Attached Thumbnails
 Sep 7th 2019, 07:23 AM #13 Senior Member   Join Date: Mar 2019 Location: cosmos Posts: 551 From geometry/math to physics Fully defining X4 is the key step of X4 Theory. Again set out from the angle of space. In projection geometry, X4 is merely the proportion of space; in the derivation of the more sufficient concept of space, X4 is also the contrary or proportion of space. It’s geometry/math concept. But we are researching physics/real matter cosmos. The space we talking are physical space. I have to make an analogy here and refer to SR temporarily. What render 3D space contracted? It’s movement or in my own way, the increase of mass. So on, what render 3D space inverted/proportionate? We imagine “anti matter world” / “similar matter worlds”. If a guy considers that the physical space in “anti matter world” / “similar matter worlds” are the same, then his concept of space is a new type concept of absolute space. This direction of thought ultimately lead to the fully definition of X4 is the (matter) state dimension of cosmos. Attached Thumbnails
 Sep 7th 2019, 08:11 AM #14 Senior Member   Join Date: Mar 2019 Location: cosmos Posts: 551 time "...which then we can talk about a space-time" When I got the X4 concept in projection geometry one and a half years ago, I wondered quite a while that what should X4 exactly be in physics/cosmos? Actually, the dramatic step in development of X4 Theory was the calculation of differential quotient againt the element of X4. It's shown in rabbit htam9876's first thread. I just move it here, still in old style. What funny in history of X4 is the breakthrough point actually is from the angle of time. The Fourth Dimension of Cosmos I suppose that a straight line in the real cosmos is a so-called extension line and we use homogeneous coordinate(X1, X2) to represent a point on it in the article The Appropriate Mathematics to Explain Cosmos (Physics). Next, let’s calculate the differential quotient against X2. Pay attention please, not against time t. Here X2 is a variant. X=X1/X2 So, dX/dX2=(X2dX1/dX2-X1dX2 /dX2)/X2²= -X1/X2² = -X/X2 So, X = - X2dX/dX2 Also, X = ∫Vdt We arrive at ∫Vdt = -X2Vdt/dX2 suppose V a constant for simplicity So t +c = -X2dt/dX2 Here c is an integration constant, So (1/(t+c)) dt = - (1/X2)dX2 ∫(1/(t + c))d(t+c) = -∫(1/ X2)d X2 ln(t+c) = -lnX2 t = exp (-lnX2) For convenience, here we take c = 0 and only talk about the positive value of X2. When representing a point in the three dimension space, the homogenous coordinate is (X1,X2,X3,X4) , the symbol of the real fourth dimension change from X2 to X4. And the equation above change to be t = exp (-lnX4) We can see X4 is a real fourth dimension of cosmos, and time t is not imagined by people. It has real number corresponding relationship with X4. So X4 and time t are both real fourth dimension of cosmos. (The sufficient solution of the differential equation is t = (1/ X4) expC1 + C2, this is the "time-state equation". Details will be in the X4 Theory of Time. It will be a successive theory to X4 Theory.) Last edited by neila9876; Sep 7th 2019 at 08:34 AM. Reason: correct word
 Sep 7th 2019, 04:58 PM #15 Senior Member   Join Date: Mar 2019 Location: cosmos Posts: 551 time vs state "As to the GR comment you made GR talks about the metric of space-time, not just the metric for 3D space..." Yes, ...space-time is integral.it seems that I even can't put aside time for simplicity, but I occationally try to do that. In X4 Theory, space - state is integral. And it 's more explicit and and convenient to use state (X4). Time and state are the common fourth dimension of cosmos. So,"space-time integral" and "space-state integral" are actually talking the same kind of **** The differential equation: (1/t) dt = - (1/X4) dX4 might be called the differential form of time state equation. It seems to show that the experience of a period of time is equivalent to the experience of a series of state changes. Last edited by neila9876; Sep 7th 2019 at 05:15 PM. Reason: detailed
 Sep 9th 2019, 05:34 PM #16 Senior Member   Join Date: Mar 2019 Location: cosmos Posts: 551 The (matter) state dimension of cosmos Watch the characteristic of X4 value area below: X4 ∈ (∞,…,-n,…, -3.222xxx,… -2, -1, 0, +1, + 2,… +3.222xxx, … +n, …∞) In philosophy, the value area of (∞,…, -n,…, -3.222xxx,… -2, -1, 0, +1, + 2,… +3.222xxx, … +n, …∞) reflects zero point, contrary, similar, certain and uncertain, infinite, with border. In ancient times, people stood on the ground and asked a question: how big is the ground? They never got an explicit concept until they climbed high enough in the third dimension. Now, people wander in cosmos and ask a similar question: how big is cosmos? The question of the beginning of cosmos, antimatter, dark matter, Relativity, QM, background microwave, etc, are established things or things under exploration. How can they relate together? Cosmos is just that one thing. It demonstrates a state dimension might exist in cosmos. (Why not expect / imagine or even assume that there is such a state dimension and then try to verify it?) ……. Next, turn to SR. Here we use the symbol γ4 to represent the 4D space γ element while the symbol γ to represent the traditional 3D space γ element. Here, we use the capitalized letter M to represent 4D space mass while the small letter m to represent 3D space mass. Here we use the symbol EK to represent the 4D space kinematic energy while the symbol Ek to represent the traditional 3D space kinematic energy. Here, we use the capitalized letter P to represent 4D space momentum while the small letter p to represent 3D space momentum. When X4 ≠ ∞ , V = X4v or v = V / X4. Put it into the 4D space γ element shown in the attached picture of my first post in this thread. We got γ4 = γ. The 4D space mass – speed equation is: M = γ4m0 = γm0 = m That means 4D space mass equals to 3D space mass. The 4D space kinematic energy equation is: EK = Mc²﹣ m0c² = mc²﹣ m0c² = Ek That means 4D space kinematic energy equals to 3D space kinematic energy. The 4D space momentum equation is: P = MV = m* X4v = X4* m v = X4 p That means 4D space momentum equals to 3D space momentum multiply X4. Next, compare them to QM. We can see that, one X4 value one 4D space momentum P value. This is somewhat the same as the state of a free particle in Quantum theory, which is represented by wave function Ψnp（r, t） The value of X4 represents a state. So, X4, could really represent the state dimension. It also hints that the issue of QM might be the issue of 4D space. Li Qiang Chen September 10th, 2019 Attached Thumbnails