Is the Fourth Dimension Really Time?

Factual Questions
1

It is so taken for granted, it has become cliché. “The fourth dimension is Time.” Take the musical group The Fifth Dimension. They were named The Fifth Dimension, because there are 4 “known” dimensions, including time (that was the joke, get it?).

Anyways, when I was still in school, it was still assumed to be common knowledge the fourth dimension was time. (Einstein’s theory of relativity had something to do with it, I recall.) I haven’t been in school (or at least taken a science course) for a while. But I do sometimes watch the History and the Science channel. And they don’t seem to assume the fourth dimension is time anymore.

(Also, I should add, adding time as the fourth dimension to a 3D graph, does make for a neat, flowing, animated graph.)

So is it or isn’t it? And if it isn’t anymore, why the change so suddenly?

:slight_smile:

2

Einstein published one of the most famous scientific papers of all-time in 1905 - “On the Electrodynamics of Moving Bodies”, in it he detailed a coherent theoretical framework which we now call special relativity. In 1907 Herman Minkowski, one of Einstein’s former teachers, published a paper which showed that special relativity could be formulated in terms of a 4-D mathematical space, called spacetime (note both Eisntein and Minkowski owe much to others for these particular discoveries).

Spacetime is merely a mathematical space where every point is considered an event (i.e.something having a psotion and a time), plus a what is known as a metric (a distnace function, though technically the Minkwoski metric is not mathematically speaking a metric, but we needn’t worry about that).

Spacetime is 4-D as if you like you need 4 numbers to smoothly identify each point. But it’s not really correct to say time is the 4th dimesnion of spacetime, than it would be for example to take 1kg of sand from a 4kg pile and say “this is the 4th kg of that pile”.

Later Einstein created a theory called general relatvity that also described gravity in terms of the curvature of 4-D spacetime.

So in summary, the best statement is probably “time and space can be combined in to a 4 dimensional description called spacetime”.

3

Maybe the 4D label has gone out of fashion because of the possibility of additional spatial dimensions?
It would seem odd to have time as the fourth dimension, the fifth dimension reserved for the band, and then, say, three more spatial dimensions.

Especially if we then found there was another time dimension…

4

You can number the dimensions any way you’d like. In fact, in the most commonly-used numbering convention, time is actually the zeroth dimension. Which isn’t any more or less correct than calling it the fourth dimension; it’s just the way that physicists have gotten into the habit of describing it.

5

This seems to be one of those questions that keeps coming up here every once in a while. It was addressed most recently here: Can someone explain the 4th dimension to me?

6

We’ll make a C programmer out of you yet.

7

I already am. The Fortran stuff I post about from time to time is not of my own choosing.

8

This Boggles the mind. Would the two dimensions interact with each other? It brings the question of “What time
is it?” to a new meaning…

9

A colleague of mine has created a model of physics in which there are three dimensions of space and three of time. For the afficionado, I will mention that a point in his space is represented by a 4 x 4 skew-symmetric real matrix. These constitute a space of 6 dimensions and he identifies three of them as space and three as time. Crucial to his development is that the fact the space of 4 x 4 real matrices can be identified as the tensor product of two copies of the quaternions H. Actually, H\otimes H^{op}, but H is isomorphic to its opposite.

No, I have no idea where he is going with this, but he is not alone.

10

That sounds like the sort of beautiful, elegant model a mathematician would come up with without regard to messy details like whether it corresponds to reality.

11

A man with one time dimension knows what time it is. A man with more than one is never sure.

12

I read in a popular physics book (can’t recall which) that in n dimensional space our system of physics only makes sense if exactly 1 or exactly n-1 of those dimensions are time-like. There was no further information. Does this make any sense? And if so is there any kind of simple explanation?

13

Does anybody really know what time it is?

14

The “1 or n-1” bit is really just a re-labeling: We could describe our Universe by calling length, width, and depth “timelike” and duration “spacelike”, and it’d really just be a find-and-replace job on the textbooks.

For the other part, of other quantities not making sense, I don’t remember the details offhand, but I do remember that it was a huge mess.

15

I’m always confused by this too. IIRC, Sagan claimed we lived in a world of (at least) 4 spacial dimensions. Just as the dots on the inflating balloon is a 3D representation of a 2D world, the fact that the all (OK, most) of the other galaxies appear to be moving away from us and the farther they are the faster they are moving away from us seems to indicate to me that we are living in 4D existence. Years ago another poster made the observation that it would be impossible to create a 3D model of objects where no matter your vantage point, every object would appear to be the center and every other object would appear to be moving away from it.

.

16

you can describe an object with four variables. Its position is described in three as per Cartesian coordinates. The x the y and the z. The thing is if an object is moving there is also the time.
You can write an equation in terms of these four variables to perfectly describe something.

Lets say we have a car on a straight road that goes on for miles and miles. We could drop the z variable and the y variable since we dont care about them (the car is not going to fly or offroad). And write the equation in terms of just two variables.
X - the distance from the start of the road
t - the time since we started counting

equation ( x, t)

If you drop the x variable

equation (t)

all you have now is the time since the car started. You have no idea where it is.
You could bring back the x variable and throw in the height variable z

equation (x,z,t)

here z is always equal to 0 as the car is 0 distance from the road. OR we could have z = change is height regarding sea level as the road goes up and down inclinations.

Lets drop time

equation (x,z)

Now we have the information of the distance from the start of the journey (x) and the height (z [whichever height is important to you]). However this is only in one instant. You can measure it every instant and have an equation for every instant you are interested in. That’s a lot of computation unless you are only interested in the very start and the very end (perhaps it is a race, but even then you do not know where it is during the race.)

So bring back time into the equation

equation (x,z,t)

It does not matter in what order you write the equation. Its just convention that x is followed by y which is followed by z which is followed by t. I do not know at what level you are at in mathematics but basically replace the word equation with function and shorten it to f.

Equation describing the distance from starting point (x), the height form sea level (z) and the time since leaving starting point (t) is the same as equation (x,z,t) is the same as function (x,y,t) is the same as f(x,y,t)

Basically if u pick any object that is moving and have f(x,y,z,t) you know where that object is and therefore where it will move too etc. You do not need all four. It depends on what you are doing. If a swimmer is swimming in a race down a lane you would want the distance from the start of the pool (or to the end) and the time since the swimmer started. However if you were playing waterpolo you would want to know the distance from the end of the pool, distance from the side of the pool, the depth from the surface(or the height from the floor of the pool), and at what time the swimmer was/ is there.

The four variables or dimensions give you everything about the objects position. You can use the function to figure out lots of other information too like the swimmer’s/car’s acceleration. You can write a function in terms of other variables as well like acceleration and perhaps time and distance so you can tell where and at what time the car was accelerating. But the point is the four basic ones can get you these other results anyway.

In school one comes across co-ordinate geometry and probably starts with two dimensions then progresses to a third. time is left out. but the examples are static anyway so they don’t change. Then 3 dimensions is enough information. So most people already accept those three dimensions. Then they throw in time and say its the fourth. That covers things that do change position.

I do not know where it fits in with 11 dimensional string theory. I know they are taking about tiny spatial dimensions curled up in the original three. But if those 11 dimensions start with x,y,z, AND t is beyond me.

17

That’s certianly not incorrect curiousprincegeorge, though I think one thing that’s important is the concept of spacetime structure.

We could equally apply what you said to Newtonian (i.e. non-relativistic) physics. That wouldn’t necessarily be wrong though and you’d probably end up with something along the lines of what is known mathematically as a “fibre bundle” to describe Newtonian spacetime. The sapcetime of relativity though has more structure and indeed mathematically is just represented by a 4-D manifold.

18

Hmm. I’m not sure that equation or function is the right way of putting it. Don’t you just mean vector?

I mean, what is the output of the functions you’ve listed? Car?

Also, about this:

I don’t think they are “in” the original three any more than length is “in” width.

I think what they mean by “curled up small”, and similar expressions, is that these dimensions are very small in length, and have a closed geometry.
So if you were to get into a spaceship and fly off in dimension Q, you’d end up back where you started after a journey of less than a hydrogen nucleus.

19

Four dimensional space is integral in understanding Time Cube. Go educate yourself now by reading all about it :slight_smile: Once you have understood Time Cube theory, you will understand 4 dimensional reality.
Note: Playstation 3 also takes advantage of 4D.

20

Assumedly it’s a very small spaceship.

And it’s a common misconception that the fact that our Universe is curved implies some higher-dimensional space that it’s “curved into”. There might be, of course, but it’s not at all needed: The math works out just fine with only our own three dimensions.