I’ve watched a few YouTube videos about it and read a few old post, but I still don’t get what it is besides being another dimension? And how is time involved in all of this? Also, what is a tesseract exactly?
In: Earth Science
The fourth dimension *is* time. It is the final variable needed to describe any state in space time. A way I like to explain space time is like this: Imagine that you and I agreed to meet somewhere for lunch. If I said “Meet me on October 5th at 1130,” that’s great, but you would have no idea *where* to go. If I said “Meet at Jim’s Lunch Shop,” that’s also great but you would have no idea *when* to go. It is only when I say “Meet me at Jim’s Lunch Shop on October 5th at 1130” that all the necessary information has been conveyed.
Physics is the same way. Regardless of which coordinate system you decide to use, you always need 4 variables to describe the system. In cartesian coordinates it would be the familiar [x,y,z,t], in cylindrical it would be [r, phi, z, t] in spherical polar it would be [r, phi, rho, t].
You can also show 4 dimensions trivially from a linear algebra perspective: dim[x,y,z,t]=4.
A key to remember her is that space and time are the same thing. They are completely and inseparably linked which is why you usually hear physicists refer to “space-time”. You can see this manifest experimentally through special relativity. You can say a particle experienced time dilation or space contraction and achieve the same result.
The common definition of dimensions are usually synonymous with a grid pattern and its axes (plural, hopefully right spelling). X is one dimension, Y is another. Z is pretty much the last dimension you can have using 90 degree offsets. That’s three dimensions to help describe any object you’d care to describe in 3d space. Time is often called the 4th dimension, because it kind of acts like another axis. Two objects cannot occupy the same space at the same time, but can occupy the same space at different times. Time also provides a sense of flow or continuity to 3d objects. This can be called motion. You cannot have motion without time. That’s why time is considered the 4th dimension.
Let’s start from the top. Dimensions are a mathematical concept. Dimensions describe how many numbers you need to use to describe something. To describe a location in our space, you need three numbers. Could by X, Y, and Z. Could be r, theta, and phi. Whatever you choose, you need three. To fully describe something, you need a time *and a place*, which adds a fourth number. So, our universe has three spacial dimensions and one time dimension.
Since dimensions are mathematical, we can imagine a universe with extra (or fewer) spacial dimensions, but keep in mind that this is purely imaginary. A tesseract is a simple cube, but extrapolated to have a fourth dimension. It’s not particularly interesting, and not unique from a 4D sphere, and if a real one existed it would just look like a cube or rectangular box.
We have to distinguish between temporal dimensions and spacial ones. Based on what we know of the universe there is a 4th dimension called time in addition to our 3 spacial dimensions. We can imagine what additional *spacial* dimensions would be like. They would be no different than the other three we have but simply having more dimensions than three leads to strange things.
A tesseract is just a fancy name for a mundane object in 4D, specifically a “cube”. A square is made of 4 lines (1D objects) for its “sides”. A cube is made of 6 flat squares (2D objects) and a tesseract is made of 8 cubes (3D objects) to form its “sides.”
Latest Answers