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Caesar_Rahil

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- Thread starter Caesar_Rahil
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Caesar_Rahil

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εllipse

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With the special theory of relativity, Einstein showed that space and time are relative concepts. If you watch somebody approach the speed of light, they will shrink in the direction of their motion and their clocks will slow down relative to you. In effect, their idea of "space" becomes a combination of your space and your time, and their time also becomes a combination of your space and your time. Things that are seperated by distance but happen simultaneously to you may be seperated by a shorter spacial distance to someone moving very fast but will be seperated by a larger distance in time (and not happen simultaneously)...

In Euclidean goemetry, the space axes are relative. I may describe something as moving along my x-axis, and you may describe it as moving along a combination of your x- and y-axes. It is said that Euclidean geometry is invariant under a rotation of x-y-z space. (This can be shown by the equation [tex]x'^2+y'^2+z'^2=x^2+y^2+z^2[/tex].) Hermann Minkowski proved that if you treat time as a fourth dimension, then different relativistic viewpoints can be thought of as "rotations" in four dimensional spacetime. (This can be shown by the equation [tex]x'^2+y'^2+z'^2-c^2t'^2=x^2+y^2+z^2-c^2t^2[/tex], which is "Lorentz invariant".) It is similar to you claiming a point has the coordinates [tex]x=\sqrt{8}, y=0[/tex] and me claiming it has the coordinates [tex]x=2, y=2[/tex]. We can both be describing the same point if our coordinate systems are rotated among each other. In Minkowskain geometry, both space and time can be rotated, so time functions similar to a space dimension (with a conversion factor of [tex]T=\sqrt{-1}ct[/tex]).

As Minkowski said:

The fact that space and time can be united into four dimensional spacetime is essential to the general theory of relativity, Einstein's theory of gravity. For further reading on relativity: http://math.ucr.edu/home/baez/physics/Administrivia/rel_booklist.html

In Euclidean goemetry, the space axes are relative. I may describe something as moving along my x-axis, and you may describe it as moving along a combination of your x- and y-axes. It is said that Euclidean geometry is invariant under a rotation of x-y-z space. (This can be shown by the equation [tex]x'^2+y'^2+z'^2=x^2+y^2+z^2[/tex].) Hermann Minkowski proved that if you treat time as a fourth dimension, then different relativistic viewpoints can be thought of as "rotations" in four dimensional spacetime. (This can be shown by the equation [tex]x'^2+y'^2+z'^2-c^2t'^2=x^2+y^2+z^2-c^2t^2[/tex], which is "Lorentz invariant".) It is similar to you claiming a point has the coordinates [tex]x=\sqrt{8}, y=0[/tex] and me claiming it has the coordinates [tex]x=2, y=2[/tex]. We can both be describing the same point if our coordinate systems are rotated among each other. In Minkowskain geometry, both space and time can be rotated, so time functions similar to a space dimension (with a conversion factor of [tex]T=\sqrt{-1}ct[/tex]).

As Minkowski said:

The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.

The fact that space and time can be united into four dimensional spacetime is essential to the general theory of relativity, Einstein's theory of gravity. For further reading on relativity: http://math.ucr.edu/home/baez/physics/Administrivia/rel_booklist.html

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Thus a plane is two dimensional - it takes only two numbers to specify the location of a point, x and y.

A volume is three-dimensional, you have to specify x,y, and z.

Space-time is four dimensional, you need to specify three dimensions (x,y,z) PLUS the time at which an event occurs (t), for a total of four.

An advanced sidenote: the coordinates used to specify position are required to be continuous. This means that if two points have numbers x,y,z, and t that are all close to each other, the points themselves are also close to each other.

The reason why we talk about space-time in relativity and not space and time is that the two can intermix. In relativity, one person may view two different events as being separated only in space, while another person may view the same two events as being separated in both space AND time. This is known as "the relativity of simultaneity", and is an important way in which relativity differs from newtonian mechanics.

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Phobos

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"Dimensions" indicate the extent of the universe...like if you were trying to set up a coordinate system to describe the universe. Our main model of how the universe works is that the universe is comprised of space and time. Matter and energy are things that reside in the universe...reside in the fabric of space and time.Caesar_Rahil said:

In order to describe your motion through the universe, you would need to measure it with respect to space and time (for example, 10 kilometers per hour in some direction).

There are 3 dimensions of space (3 directional lines)....forward/back, left/right, and up/down....in which we are free to move.

There is 1 dimension of time (1 time line....forward/back or "future/past")...but we are limited to forward movement in that. If there was a second dimension time, we'd somehow be able to move left/right in time without going in the future or past. That would be weird, eh?

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Caesar_Rahil

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Thank you very much.

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