In mathematics, four-dimensional space (“4D”) is a geometric space with four dimensions. It typically is more specifically four-dimensional Euclidean space, generalizing the rules of three-dimensional Euclidean space. It has been studied by mathematicians and philosophers for over two centuries, both for its own interest and for the insights it offered into mathematics and related fields.
Algebraically, it is generated by applying the rules of vectors and coordinate geometry to a space with four dimensions. In particular a vector with four elements (a 4-tuple) can be used to represent a position in four-dimensional space. The space is a Euclidean space, so has a metric and norm, and so all directions are treated as the same: the additional dimension is indistinguishable from the other three.
In modern physics, space and time are unified in a four-dimensional Minkowski continuum called spacetime, whose metric treats the time dimension differently from the three spatial dimensions (see below for the definition of the Minkowski metric/pairing). Spacetime is not a Euclidean space.
Any object that has a length has one dimension. A length and width, has two. A length, a width, and a height, has three. An object that actually exists from the time it came into existence until it ceases to exist has a duration, the fourth dimension. The remaining theoretical dimensions proposed by superstring theory exist but we cannot sense them, although the math that describes our theory of physics says they are too small for us to percieve.
Essentially you can visualize the 4th dimension as a line connecting a version of yourself/an object in time. So if you could “see” a 4D object, then you would be looking at two different versions of it simultaneously (The ends of the “line”) and how it got from one end to another (The “line” itself). Being 3D we only see one 3D “frame” at a time, if you were to “look” at me in 4D, then you would see all my past, present and future states. We cannot move freely in time as 3D beings, but in 4D it may be possible. It’s also wrong to think that the 4th dimension is spatial, it cannot be related to Euclidean space; we are only able to perceive three dimensions and because of this convention we are lead to believe that the 4th dimension must also be spatial.
Now if you were to branch out from the line, as suggested in the first video, then you can imagine yourself standing at one end of the fork, and you “see” two paths. Essentially then the 5th dimension allows us to see multiple versions of time itself. If you looked at a person in 5D, you would be able to see the various “permutations” they have taken/will take in time, anything from your choice of clothing in the morning to career choices etc.
String theory postulates that if we probe even deeper than the subatomic level, we will find that quarks, leptons, bosons etc., which are believed to be 0-dimensional elementary particles presently, are actually composed of 1D “strings”, which “vibrate” at the quantum level to give rise to the particle properties such as spin, charge, flavour and mass. It’s a bit abstract and basically to hold true requires that spacetime posses upto 26 dimensions.
For more details review: Edwin A. Abbott’s book Flatland,and also a book by the astrophysicist John Gribbin, The Universe: A Biography
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