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Asked by anon-251974 on 29 Apr 2020.
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David Sobral answered on 29 Apr 2020:
Usually on top of the 3 dimensions we experience, time is often thought as the 4th dimension, because space and time are deeply connected (and often called space-time). That’s comes for example from General Relativity that allowed us to realise that matter (even us!) bends space-time. It does not just bend space, causing what we see as gravity – it actually bends time itself! That’s the fascinating reason why time runs slower on Earth than in space: the Earth bends-space time and makes time run more slowly. On the extreme, really close to a black hole, space time is so bent that time basically runs incredibly slowly, almost stops!
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Paul Saffin answered on 29 Apr 2020:
The number of dimensions is just how many numbers you need to tell where you are. For example, a (very thin) washing line is one-dimensional because I just need to give you one number to tell you where a peg is, e.g. 2 metres from the post. The surface of a football pitch is two-dimensional because I need to give you two numbers to tell you where the ball is, e.g. go 12 metres forward and 3 metres right. A fish tank is three dimensional because I need to give three numbers to say where a fish is, e.g. 10cm forward, 20cm left and 6cm down.
The thing that we have missed in all the above is that things move, and so I also need to tell you when the fish is going to be somewhere. So, as well the three numbers saying where the fish is, I need to also tell you it will be there at 12 o’clock, which is now four numbers, and so four dimensions.
Mathematicians create all sorts of wonderful objects in their minds, including cubes that have four, five, six,… dimensions. We can’t draw these very easily in our world of three space dimensions, but you can still imagine them, and work out their properties. You can create a 4D hypercube by inventing a new dimension and stacking normal cubes along that dimension, in the same way that you can stack squares on top of each other to make a cube. Good luck trying to picture it though! -
Marios Kalomenopoulos answered on 29 Apr 2020: last edited 29 Apr 2020 11:27 am
As a suggestion, rather than an answer, I would recommend the following book: https://www.goodreads.com/book/show/580082.Very_Special_Relativity
The 4th dimension, is usually connected with time and Special Relativity and this small book is a very smooth introduction to it (+ the famous E=mc^2 equation), just following and understanding nice diagrams.
However, as Paul explained, the 4th dimension can just be one more spatial diamension, like the usual x, y, z coordinates that we use for our 3D word. Just imagine we add one more letter. Then the algebra can become more complicated (and less intuitive, since we can’t visualise these objects) but we can more or less generalise all our known geometrical shapes (like spheres, cubes etc) to these higher dimensions.
By the way, if you want to go one dimension down, to a 2D world, there is this famous book (https://www.goodreads.com/book/show/433567.Flatland), descibing life on a plane! 🙂
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Susan Cartwright answered on 29 Apr 2020:
As Paul said, the number of dimensions is essentially how many numbers you need to use to describe where you are. In that respect, time is indeed a fourth dimension: if you are arranging to meet a friend (post coronavirus lockdown!), you need to specify when you want to meet as well as where – for example, you might give the map grid reference of a building (that’s two numbers, locating you on the Earth’s surface), the floor of the building (that’s height, the third dimension) and a time (the fourth number, so the fourth dimension).
However, it is in possible to make mathematical constructions that have more than three space dimensions, and the maths of such multi-dimensional spaces is perfectly self-consistent. A hypercube is a four-dimensiona version of a cube: a line is one-dimensional, a square (each of whose sides is a line) is two-dimensional, a cube (each of whose sides is a square) is three-dimensional, and a hypercube would be a four-dimensional object each of whose sides is a cube. For a long time this was purely theoretical, but many theoretical cosmologists have constructed models in which our universe is one three-dimensional “side” of a four-dimensional space, and string theory (a popular candidate for unifying quantum mechanics with general relativity) only works if there are more space dimensions (a total of 10 or 11). These theorists suggest that we do not perceive the extra dimensions because they are very small, and curled up on themselves: for example, a long pieve of thin string is one-dimensional to us (you can specify a position on the string by quoting one number, the distance from one end), but its surface would be two-dimensional to a micro-organism (there are two directions, along the string and around the string).
So, in short, we reallt ought to talk about “a” fourth dimension, rather than “the” fourth dimension: time is a perfectly valid dimension, but it is possible that there are additional dimensions that we cannot perceive.
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Joel Goldstein answered on 29 Apr 2020:
It is interesting to note that while we certainly seem to live in a universe that has three spatial dimensions (in addition to one time dimension), scientists are actively doing experiments to check that this is really the case!
Some people have speculated that there are really extra spatial dimensions that we are not aware of, either because “normal” particles (photons of light, electrons, quarks etc) cannot travel through them, or because they are curled up very small (think of the washing line in Paul’s answer – it looks one-dimensional from a distance, but when you look closely you see there is the possibility of going around it in loop as well).
One sort of experiment looks at how the laws of nature change at different scales: we know that Newton’s law of gravity follows an inverse square law, but this is due to space being 3D. People are looking for signs of different behaviour at very small scales.
Other experiments, for example at the LHC, look for evidence that new types of particles have been created that then disappear off into invisible dimensions.
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Paula Koelemeijer answered on 29 Apr 2020:
For us in Earth Sciences, the 4th dimension is almost always Time, while the other 3 dimensions are the three different spatial coordinates. Time is really important for us for a several reasons: one rule of thumb is that the present is the key to the past, and that processes we see happening on the Earth now, also happened thousands and millions of years ago. Time is therefore important as we try to understand the past of our planet, how has the Earth evolved to a habitable planet and how may it change in the future to come.
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