So I get the first 4 (height, width, depth and time) but I’ve heard lots of scientists mention that there’s up to 12 or 14 or so dimensions on top of that?
In: Mathematics
Mathematical dimensions do not need to relate to physical ones, and physical ones do not need to relate to spacetime. It’s really a mathematical way to look at things. Let’s say you have thing moving around. It has a position (x, y, z), a velocity, a mass that may change over time, and so on. Every one of those components can be considered a dimension in a vector space defining the state of the thing.
Most things you do with numbers have nothing to do with spatial relations.
Imagine you have a dataset for multiple people: Length of thumb, length of index finger, length of middle finger. Each person (point) in this dataset has 3 attributes (dimensions) and can be represented within a 3-axis coordinate system.
Want to add the attribute “Length of ring finger” to the dataset? Boom, gained another dimension. Each point representing a person suddenly got 4-dimensional.
I think you mean physical dimensions. Mathematical dimensions work just like any other dimension (there’s nothing different about how the x dimension behaves compared to the y dimension).
Extra dimensions of space can be different. It’s possible that they’re just like the three physical dimensions we know and love. So you can move “forward” and *backward” along a new dimension just like the other three, and it sorta seems to extend to infinity, and is probably “flat” (if you walk in one direction, you will never return to where you started). So really the only different in this new dimension is that our brain can’t perceive it or even attempt to imagine it. But mathematically, x, y, z, and new dimension are interchangeable. Same rules.
But it’s possible the new dimensions are different. In one version they’re “compactified.” Instead of extending into infinity and being basically flat, they may be circular and quite small. As you move along the new dimension in one direction, you eventually return to where you started. But theyre so small that only quantum sized objects really interact with them (e.g., they’re like the size of a single electron or something). So to big things like us and a baseball, these tiny dimensions may as well as not exist. But they solve some physics problems.
In math, there is no limit on the number of dimensions. You can think of a dimension as being a direction, but you can also think of it abstractly, as a degree of freedom, or an independent coordinate. Imagine something where you need “n” numbers to fully distinguish it from all other somethings. Your space of somethings has n dimensions. As a contrived example, my phone number has 10 digits. If I consider a dimension to be the values that one digit can take, then my phone number has 10 dimensions. (Obvious alternative: if I consider the set of integers as my dimension, then my phone number has only one dimension. Both descriptions are legit.)
String theory physicists are trying to describe reality with math. They need more than the four space-time measures that we experience to fully distinguish one physical configuration from another, so they need more dimensions for those degrees of freedom to live in. Are those dimensions “real”? (And if so, *where* *are* *they*!?) That’s why string theory is open research, not settled science.
Well math is math, and not reality.
So while yes, a point on a paper can only have (x,y) coordinates/dimensions, and a point in space can only have (x,y,z) (3) coordinates/dimensions, there is nothing stopping math people from adding more coordinates/dimensions.
The math part works fine, you can do all the thing with more coordinates that you could with 3.
Sure it doesn’t describe reality, but who cares, its math, not physics!
If we want to talk about physical dimension then consider that when it comes to modelling it can be useful to have non-spatial dimensions.
For exmple if you want to map a magnetic field you need to assign to every point how much the magnetic field tugs on thing that are in that point.
And since there arer 3 spatial dimensions, that means the field can tug on the thing in 3 directions, thus you gotta have 3 more dimensions.
If you do that for fundamental forces you get to large seeming numbers.
Ofc. the “theory of everything” is as far from as as it was to Lord Kelvin, so claims about the unverse having X dimensions are just claims – for now.
In general a dimension is simply put nothing but a property something can have mapped in relation to other such properties.
You stated the 3 spacial + time dimension, these are just the basic properties of space-time.
However these properties only describe a very tiny sub-set of the actual properties depending on what you’re trying to describe.
Take a glass of water for example. If we mapped some properties in relation to time we might have the 3 spacial dimensions as the position may change, time on top of that as this is our basic relation. But then the temperature could change, the transparency of the water may change (due to collected particles), the volume may change depending on the trmperature or whether someone spills something, the color may change, the state of aggregation may change…
So to put a model together to describe these things one would have to create a 9+ dimensional description of this glass of water.
This would still not describe all properties such a glass could have, but the model would describe the glass in the fashion we stated above.
Also look at your own example, you stated:
>I get the first 4 (height, width, depth and time)
Well with these 4 alone you could describe the 3 dimensional – size – of an object in relation to time.
But that model would for example not be sufficient to also map the position of the object.
So to map the position and size of an object over time you already would have (x, y, z, width, height, depth, time) here x, y and z would be the positional coordinates within some frame of reference.
With regards to the theories however these dimensions can mean different things and even can mean – actual spacial dimensions – of space-time.
The number of dimensions is how many numbers are required to uniquely describe something. It’s not limited to physical dimensions. For example, if we could assign a number to the strength of each gene in DNA, we’d have thousands of dimensions to describe a person’s genetic makeup.
What I haven’t seen mentioned here is the matter of *metric*.
What’s a metric?
Well first off, there are already no limitations to the number of dimensions. Literally, you just need an additional number for each dimensions. If you have a physical theories that require 20 numbers, voila, that’s 20 dimensions. Most physical theories have a lot of numbers.
However, something usually missing is having a *meaningful* metric. If someone tell you that you need to walk east 3km and north 4km and ask you the length between the start and the end you can deduce that means the total displacement is 5km. But if someone ask you to raise the heater by 3degree and add 4litre of water to the tank and then ask you the total length between the starting and ending state, you raise your eyebrow and ask “what does that mean”. This illustrate the different: in the first case you have a meaningful metric, the second case you don’t.
Generally, different dimensions don’t interfere with each other, like the example above. Except for space, because for some reasons, as far we know, physical laws don’t change when you rotate. The ability for vectors from several dimensions to have the concepts of “length” and “angle” give you the metric. And this ability exist because we have rotation.
For a long time, time don’t interfere with space, or so it was believed. When relativity come, it was discovered that time and space are intrinsically linked: you can “rotate” time into (part of) space by moving very fast. Because of this, the entire spacetime got a metric, which is why both space and time must be considered together.
The next dimensions are very similar. People simply consider putting in a metric into additional physical characteristic (for example, electromagnetic potential), and consider model where you can “rotate” between different physical quantities. What matter is whether it is useful and meaningful, and this is a matter of experimental fact and opinion. The mathematics work out the same no matter what.
Mathematical dimensions don’t have to relate to physical ones. Mathematical dimensions mean that you have coordinates where changing one coordinate doesn’t effect another. So if you have a point (x,y) and you change the x coordinate that does not effect the y coordinate. and you can have vectors (coordinates) of infinitely many components. (a,b,c,d,e,f,g,h,….)
Physics usually only uses 3 or 4 dimensional vectors to separate the 3 or 4 dimensions that we perceive. But if you for example want to track a population of something or many different atoms, you could also just for fun assign a dimension (or more) to each of the samples in that population and do maths with that. So that every state of a population is mapped to a coordinate.
It’s no longer feasible to understand that when you want to translate that to the physical space of 3 dimensions but it’s able to be computed and might give you useful results.
Imagine a graph with two axis, length and width. Each axis measuring one thing.
Now add another axis measuring another thing. You’re up to three dimensions on the graph.
Now, you’ll need to add a fourth to measure another thing. It’s completely possible mathematically, but it doesn’t really work with what we can intuitively understand. So it’s usually portrayed as a video of a 3d graph changing overtime.
A 5th axis is completely possible, but it’s even less intuitive than a changing the 3d graph over time. But it can be represented in numbers and processed easily by a computer.
This applies to any higher dimension as well.
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