# What is Fourth Dimension?

Before people get pissed at me for asking a question that has likely been asked more than a few times, I just want to know a simple answer, if first dimension is that an object exists, (collision) Second dimension is flat, (that there is color and reflection to it) and 3rd dimension is depth, would fourth dimension be perception of time, or simply perspective (seeing at a specific angle) or can it be both?

• This is as much a question of philosophy as physics. From a simplistic point of view, time is the 4th dimension, as it fits a lot of fairly simple equations in physics. But there are both mystical and eerie quantum-mechanical hypotheses of additional dimensions. – Hot Licks Jan 25 '18 at 20:29
• So in other words, we can guess, but we don't know for sure? If that's the case then I've already broken the rules! x3 – Konix25 Jan 25 '18 at 20:34
• The "fourth dimension" in relativity is "time", but it is a measure of relative simultaneity - it is not the same thing as "change", which appears to be a much more complex derived concept involving at least a 3-way relation. – Steve Jan 25 '18 at 23:27

Dimensions in physics generally means degrees of freedom. That is how many different directions can you move something.

For example on a straight line you can move back and forth in one direction, so we say the line has just one dimension. The same is true for a curve.

On a table-top we can move in two independent directions so we say that this is 2d. The same is true for the surface of a sphere.

In space, we can move in three different directions, so we say that it is 3d.

Sometimes time is said to be the 4th dimension, but note we can only move along it in just one direction and the way we move is fixed; so in this sense, it's not really a dimension.

Mathematically, all of the above is modelled by the notion of a manifold, which we say is of dimension n when locally we can always move in n different dimensions.

Despite what I said about time, usually spacetime, after Einstein and especially after Minkowski, we model spacetime as a 4d manifold.

• "Different directions" is not quite the right way to say it. I can slide an object on a table top in an infinite number of different directions. But if you ask me where the object is on the table top, there is no way I can assign a single unique number to each distinct location. I have to report two numbers to tell you where the object is. And in free space, I have to report three numbers. – Solomon Slow Jan 25 '18 at 21:31
• @jameslarge: sure, thats why I said 'independent directions'. I didn't emphasise it. There's more to dimension that just 'three numbers' - if I had a bag with apples, oranges and pears I could assign a triple of numbers to the bag that tells me how many of each they are; and if I put two bags together then I get an addition law. But this example is far from what we mean by dimension, at least geometrically. – Mozibur Ullah Jan 25 '18 at 21:32
• "there is no way I can assign a single unique number to each distinct location" - Technically you can, since $\mathbb{R}$ is equipollent to $\mathbb{R}^n$ for any positive integer $n$. However, there's no point-to-real-number assignment that satisfies some nice properties familiar to differential geometers. – J.G. Jan 25 '18 at 21:36

Let's say someone invites you to a party in their apartment. You need to know how far to go North to get there, and how far East, and how many floors up, which covers the three dimensions of space. But you also need to know when the party is.

• Wouldn't this also include when "now" is? So this would add perspective in. Which that would mean both perspective and time are variables in the fourth dimension. Thanks for the explanation, makes things a lot easier on my tiny brain! :) – Konix25 Jan 25 '18 at 20:44
• @Konix25 If the invitation says that the party starts at 7:30pm, then it starts at 7:30pm. The start time won't change depending on whether I read the invitation at noon or at 6:42. What does matter though, is that to correctly understand what "7:30pm" means, I have to know in what time zone the "7:30" is based. Mathematically speaking, I have to know the origin of the coordinate system. – Solomon Slow Jan 25 '18 at 21:36

Yours isn't a physics question. Since this is a physics forum however I'll answer in physics terms.

In physics, one dimension means a straight line. You only need one coordinate to specify it - for example with the horizontal axis, you only need to know how many units a point is before or after the origin to know where it is. Two dimensions is a plane. In the x-y plane, you need to know both the x-coordinate and the y-coordinate to know unambiguously where a point is. Three dimensions is the world we're familiar with. You not only need to know the x-coordinate and the y-coordinate, you also need to know how high a point is above the plane.

Time is the 4th dimension in Relativity, and it's related to the other three dimensions but has a minus sign. In Minkowski space (Special Relativity), the metric is:

$ds^2 = -dt^2 + dx^2 + dy^2 + dz^2$

Here $t$ is time, and $x, y, z$ are spatial coordinates. If you don't recognize this formula don't worry about it, but the point is that these things are being added. This isn't always possible - adding time to energy for example makes no sense. The fact that we can add these means that we can treat time and space on an equal footing. However they're also not equivalent - there's a minus sign between the two that no sleight-of-hand could ever conjure away.

There're ongoing searches for more spatial dimensions, and some theories such as string theory predict there are 10 spatial dimensions, but nothing has been found yet.

• Your physics terms are much appreciated, I don't mind what kind of response it is as long as it betters my understanding of the idea behind a fourth dimension. Thank you <3 – Konix25 Jan 29 '18 at 22:50