# Where is the fourth dimension

## Spacetime: the fourth dimension

We live in a three-dimensional world. The room has height, width and depth. In physics, space is mathematically described by coordinate systems. This method goes back to René Descartes (Latin Cartesius, 1596 - 1650). To honor him, the most common form of a coordinate system is called the Cartesian coordinate system.

In the Cartesian coordinate system, the location of a point is given by three coordinates. Usually these are called x, y and z. They are independent of one another, the directions of the x, y and z axes are at right angles to one another. But there are also other coordinate systems: You can specify the position of a point using a distance from any chosen center point and two angles. So you get **Spherical coordinates**. Basically, coordinates can be generated by any complex, distorted network of grid lines. Only three values have to be clearly assigned as coordinates to each point. These can even be time-dependent. So you can define rotating coordinate systems that rotate with the earth, for example.

In addition to the three dimensions of space, one needs an indication of time in physics. In Newtonian physics, which was held to be unrestrictedly valid from the Renaissance until 1905, time was imagined to be independent of all physical processes. Time should, so to speak, set the pace according to which all physical processes are directed, without affecting time itself. Even before the theory of relativity, it was not uncommon to think of time as a fourth dimension. The time traveler explains in great detail in the novel “The Time Machine” by H.G. Wells, how one can think of time as the fourth dimension. This book was published in 1895, ten years before Einstein's theory of relativity.

If one understands time as a fourth dimension, then every object is described not only by its volume in space, i.e. length, height and width, but also by its expansion in time. That is its duration. So you can see the whole development of a person from infancy to old age as one object in one **four-dimensional spacetime** imagine from space and time coordinates. A certain point in time in the life of this person is then a cut through this space-time at a certain time coordinate.

Once you have understood the concept of spacetime, the step towards understanding the special and general theory of relativity is no longer that great. Similar to how one can describe the three-dimensional space with completely different coordinates, the four-dimensional space-time can be provided with different coordinates. The time coordinate does not have to be the same in every coordinate system. I will come back to coordinate systems later. Next, I would like to report on the processes with which one converts different coordinates into one another: coordinate transformations.

Last change: 06/22/2011

© Joachim Schulz

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