Portals of Perception: Odyssey through the Enigmatic Fourth Dimension

 

           BEYOND SPACE AND TIME 

                                 4D 

HELLO, my dear  'YOUNG SCIENTICIANS'  ,we hope that you are well. And now, we are going to present our research on '4th DIMENSION' , So enjoy this roller coaster of research. let's GO:-

               INTRODUCTION TO 4D

4TH Dimension is a mathematical extension of concept of 3 dimension. While 3rd dimension is following euclidean geometry where axes are(x,y,z) but it have a extra axes ‘w’.  

The idea of adding a fourth dimension appears in Jean le Rond d'Alembert's ‘Dimensions’, published in 1754, but the mathematics of more than three dimensions only emerged in the 19th century.The general concept of Euclidean space with any number of dimensions was fully developed by the Swiss mathematician Ludwig Schläfli before 1853. Schläfli's work received little attention during his lifetime and was published only posthumously, in 1901, but meanwhile the fourth Euclidean dimension was rediscovered by others. In 1880 Charles Howard Hinton popularized it in an essay,’What is the Fourth Dimension?’, in which he explained the concept of a four-dimensional cube with a step-by-step generalization of the properties of lines, squares, and cubes.  The simplest form of Hinton's method is to draw two ordinary 3D cubes in 2D space, one encompassing the other, separated by an unseen distance, and then draw lines between their equivalent vertices. This can be seen in the accompanying animation whenever it shows a smaller inner cube inside a larger outer cube. 

                                     HISTORY OF 4d

 

Lagrange was a researcher and mathematician in 18th century and he wrote in his Mécanique analytique (published 1788, based on work done around 1755) that mechanics can be viewed as operating in a four-dimensional space— three dimensions of space, and one of time. As early as 1827, Möbius realized that a fourth spatial dimension would allow a three-dimensional form to be rotated onto its mirror-image. The general concept of Euclidean space with any number of dimensions was fully developed by the Swiss mathematician Ludwig Schläfli in the mid-19th century, at a time when Cayley, Grassman and Möbius were the only other people who had ever conceived the possibility of geometry in more than three dimensions. By 1853 Schläfli had discovered all the regular polytopes that exist in higher dimensions, including the four-dimensional analogs of the Platonic solids.

An arithmetic of four spatial dimensions, called quaternions, was defined by William Rowan Hamilton in 1843. This associative algebra was the source of the science of vector analysis in three dimensions as recounted by Michael J. Crowe in A History of Vector Analysis. Soon after, tessarines and coquaternions were introduced as other four-dimensional algebras over R. 

Higher dimensional non-Euclidean spaces were put on a firm footing by Bernhard Riemann's 1854 thesis, Über die Hypothesen welche der Geometrie zu Grunde liegen, in which he considered a "point" to be any sequence of coordinates (x1, ..., xn). In 1908, Hermann Minkowski presented a paper consolidating the role of time as the fourth dimension of spacetime, the basis for Einstein's theories of special and general relativity. But the geometry of spacetime, being non-Euclidean, is profoundly different from that explored by Schläfli and popularised by Hinton. The study of Minkowski space required Riemann's mathematics which is quite different from that of four-dimensional Euclidean space, and so developed along quite different lines. This separation was less clear in the popular imagination, with works of fiction and philosophy blurring the distinction, so in 1973 H. S. M. Coxeter felt compelled to write.

                                   VECTORS

             

Mathematically, a four-dimensional space is a space that needs four parameters to specify a point in it. For example, a general point might have position vector a, equal to

            

so the general vector a is

Vectors add, subtract and scale as in three dimensions.

The dot product of Euclidean three-dimensional space generalizes to four dimensions as

Minkowski spacetime is four-dimensional space with geometry defined by a non-degenerate pairing different from the dot product:


As an example, the distance squared between the points (0,0,0,0) and (1,1,1,0) is 3 in both the Euclidean and Minkowskian 4-spaces, while the distance squared between (0,0,0,0) and (1,1,1,1) is 4 in Euclidean space and 2 in Minkowski space; increasing b4 decreases the metric distance. This leads to many of the well-known apparent "paradoxes" of relativity.

This is bivector valued, with bivectors in four dimensions forming a six-dimensional linear space with basis (e12, e13, e14, e23, e24, e34). They can be used to generate rotations in four dimensions.

                                                                                                                           

         ORTHOGONALITY   AND   VOCABULARY

In the  three-dimensional space of daily life, there are three coordinate axes—usually labeled x, y, and z—with each axis orthogonal (i.e. perpendicular) to the other two. The six cardinal directions in this space can be called up, down, east, west, north, and south. Positions along these axes can be called altitude, longitude, and latitude. Lengths measured along these axes can be called height, width, and depth.

Comparatively, four-dimensional space has an extra coordinate axis, orthogonal to the other three, which is usually labeled w. To describe the two additional cardinal directions, Charles Howard Hinton coined the terms ana and kata, from the Greek words meaning "up toward" and "down from", respectively.

As mentioned above, Hermann Minkowski exploited the idea of four dimensions to discuss cosmology including the finite velocity of light. In appending a time dimension to three-dimensional space, he specified an alternative perpendicularity, hyperbolic orthogonality. This notion provides his four-dimensional space with a modified simultaneity appropriate to electromagnetic relations in his cosmos. Minkowski's world overcame problems associated with the traditional absolute space and time cosmology previously used in a universe of three space dimensions and one time dimension.

                                          GEOMETRY

The geometry of four-dimensional space is much more complex than that of three-dimensional space, due to the extra degree of freedom.

Just as in three dimensions there are polyhedra made of two dimensional polygons, in four dimensions there are polychora made of polyhedra. In three dimensions, there are 5 regular polyhedra known as the Platonic solids. In four dimensions, there are 6 convex regular 4-polytopes, the analogs of the Platonic solids. Relaxing the conditions for regularity generates a further 58 convex uniform 4-polytopes, analogous to the 13 semi-regular Archimedean solids in three dimensions. Relaxing the conditions for convexity generates a further 10 nonconvex regular 4-polytopes.

                    

                Regular polytopes in four dimensions

HYPOTHESIS

1.     Many of us told that time is fourth dimension, but , there is a hypothesis that time is not 4th dimension because hypothesians told that time is not real it’s only an imaginary thing which is created in our memory for distinguish past and present, this is also the part of a thinking relatism.
2.    This hypothesis is just opposite to hypothesis (1), in this there said that our brain can’t interpret 4th dimension in this they also give example that  a 2d object brain and other organ is on 2d graph so he can’t move in 3rd dimensional part, so he think that only 2d present as similarly as human is 3d organism  so he can’t move in 4th dimensional part so we think that 4d is not present and it give another hypothesis (3),it will become also part of absolutism.
3.    Last-one hypothesis  give birth to this hypothesis, which is about ghost,  as we discussed that n-dimensional organism can’t  identify n+m dimension so as example a 2d organism on xy plane can see only in x and y axes so if we the 3d organism add a square box to a point in plane then that organism open that box there is nothing but after a ‘t’  seconds if I put a 3d sphere in it and start moving then that organism will re-open that box where a ball exist and never forget that our shadow is 2d so he can’t interpret our stucture or dimension and by this all process he will  scared about it, so it can possible that ghosts are organism of  higher dimensional so we can see only their 3d part which can be there shadow. 

IS TIME AND SPACE ABSOLUTISM AND RELATISM

WE TOLD YOU ABOUT ABSOLUTISM AND RELATISM THAT’S ARE TWO TYPE OF THINKING ABOUT  SPACE AND TIME:- 

Actually from starting philosphers and mathematicians divided in 2 thinkings absolutism and relatism  
Firstly there given a theory that space and time are same for all in which a french mathematician - Rene Descartes was a supporter of absolutism he said that by mathematics we can solve this world by mathematics he plot all thing of universe on his 2d and 3d graph and it  do not break rule of universe so he conclude that space is fixed, by the experiment absolutism come in light, it become more powerful when newton proved his equation of kinematics mechanics by descartes graph and also proof that  time is also fixed. Newton think that - all object move in  this universe according to their energy but time is independent so all object move with same speed. It can more define by a proverb in INDIA from ancient time that “TIME WILL NEVER WAIT FOR ANYONE”. But there Newton got honour that he discovered calculus but it was discovered by lebiniz, because newton was great mathematician so he got this honour about it, then for counter newton lebniz come in support of relatism and give the great theories after which 
SIR EINSTEIN  told him lebnizian. Actually Newton said particles are in apace by reference and graph we can define their position but Lebniz said in his theory that particle exist with some propertiesby this space exist.

Lebniz theory get a short term position for relatism because after discovery electromagnetic waves they found that they need a medium and space to travel so the theory get losing but in ‘early 20th century’ einstein changed game by giving theory of relativity which considered that if did displacement ‘s’ in space it will decrease time’t’ and also create a worm. But, in his theory he used gravitational field which need space so this theory was in mid of the thinkings. As similarly theory come and fail but anyone can’t conclude it, but approxly 100 yrs ago to relativity 2 theory come :-

1. EMERGENCE THEORY

This theory proved that past and future exist simutaneously because of research in los angeles on a crystal that they conclude as crystal made by repeat of cell, they conclude that space and time are only imaginary.

example= this is crystal latiscum it is  dimensionally-symmetric so by this theory 

we say that our world is only 3d part of it and its 2d shadow called QUASIcrystal

is a-symmetric.

this theory also say that our universe is made up of unit particle called tetrahedron 

whose length unit is planck which is (10)’-16 times of micron.

2.  simulation theory

This theory told that we are part of a simulation world where nothing is fixed




BY THESE 2 THEORY WE CAN SAY TIME AND SPACE ARE RELATIONISM BUT THERE WE CAN’NT  CONCLUDED BECAUSE THERE IS A POSSIBILITY OF COUNTER THEORY
AGAINST THIS BOTH THEORY.

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