I’ve heard it said that time is a dimension like length or width. But, a dimension is characterized by the fact that you can move up without moving forward, and vice versa, and etc., too.
But if movement along the three spatial axes has halted, hasen’t time? If so, is it really a seperate dimension?
No, it is a separate dimension… you can prove that with this:
Say you have this block of wood: #
And it is moving:
(start)>>>>>>>>>>>># (then it stops).
(wait a few seconds, and it starts again)…>>>>>>>>>#
Time exists because you can measure the non-movement of the block of wood. If time didn’t exist, the movement of the block of wood would look like this:
>>>>>>>>>>>>#>>>>>>>>>#
but with the presence of a time dimension, it looks like this:
>>>>>>>>>>>>#…>>>>>>>>>#
I am not a physicist… I just felt like making a little example. Hope it makes sense 
Your question implies that there is a single correct answer. I suggest that it has proven useful to conceptualize time as a dimension. It is particularly useful when conceptualizing processes as nouns. It is of limited use at best when considering what you want to do in the next ten years. It is of at least intermediate use when considering the question “who am I”
Time is time. “Dimension” is a concept. Well, OK, “time” is also a concept. It’s your brain. Conceptualize to your own satisfaction. ’
It makes nice graphs.
Dimension is actually a mathematical term. Because of the way physics treats time in its mathematics, we call it the “fourth” dimension. It really is very different than the other three though, so there is a minus sign in front of its place in our metric formalism (metric formalism being a way of showing how to measure these physical concepts) to really give us a good idea of the fact that it’s a different kind of dimension.
One conceptual way to think of dimension is: how many lines can be at right angles to each other? In the spatial world, the answer is three, however if you think about time marching on in a different direction than those three, you can picture a fourth line that goes right on through the other three at yet another 90 degree angle.
If your mind just exploded, pick it up and put it back in. It’s pretty hard to picture, so if you can’t do it, don’t worry. Just imagine what it would be like to try to describe a THIRD dimension to someone who has lived in two their entire lives. (In fact, so-called Flatlanders are common subjects in many theoretical physics discussions.) Not easy to do, huh?
Staff Report: How many dimensions are there and what are they?
I believe that what the previous posters are trying to say is this: “Dimension” simply means a way of measuring things. There can be different kinds of dimensions. The three which we are used to are dimensions of distance, and time is a dimension of duration, which is a different kind of dimension, but no less legitimate.
I am reminded of the opening chapter of H.G. Wells’ The Time Machine, in which the time traveler explains these concepts to his friends. It went something like this:
Friend: We all know that there are three dimensions. An object with only length, or width, cannot exist. Lines and planes do not really exist, but a cube can. An object must have length and width and height in order to exist.
Time Traveler: I disagree. An instantaneous cube does not exist.
Friends: Huh?
Time Traveler: Just as your plane cannot exist because it has zero height, so too your cube does not exist if it is there for but an infinitesimal instant. It has to be around for a while. It must have duration to exist. This is time, the fourth dimension.
I’ve heard it explaned that just after the big bang there were something like 21 dimentions. As the universe aged a few nanosecones and cooled a bit the ‘extra’ dimentiones ‘crystilized’ out (I remember the word crystalized used) down to 4. The 4th one was about to go but didn’t go all the way - kind of got damaged and stuck in a one way direction we have today.
IIRC it is 11 dimensions, and they are still around, but most of them cannot be detected because they are infinitesimally narrow. This is connected with the “string” theory, which I have never been able to fathom, so perhaps ** JS Princeton** or someone else can fill in the blanks.
Did you really mean “infinitesimally”, or did you simply mean “extremely”.
The difference is quite critical in this area. If a dimension is infinitesimally small, what’s the difference between that and truly non-existent? On the other hand, if it is merely extremely small, then perhaps some day we’ll be able to find and measure it.
Unless, I guess, extremely narrow means wider than zero but narrower than a Planck unit (whatever the hell that means in this context…)
I can’t really fathom String Theory either but I think the gist of it is what is described in the Staff Report linked to earlier in this thread. Basically, more dimensions allows physicists more ‘room’ to manipulate their equations. When they do this it becomes easier to get to a Grand Unified Theory (GUT). Gravity stubbornly doesn’t want to play nice with the other forces but in String Theory they feel (hope) they can wiggle it in. I don’t know if that means 11 dimensions MUST exist for the theory to work or if they are just using an 11 dimensional construct to play with their math in.
I think that’s it. The Planck units do not mean there can’t be things smaller than that…just that us mere mortals can’t hope to noodle out anything past that.
For a real brain cooker realize that although the other 7 dimensions are incredibly tiny they touch every point in our universe. No one will ever be flying around in space someday and ‘see’ a tiny ball of wrapped-up dimensions lying there.
What I’m still foggy on is whether time is in fact mutually perpendicular to the three spatial dimensions. If it is so obviously different, does this mean that considering time a dimension is a useful metaphor, so that we can make nice graphs? And is this also true of the other 7 dimensions proposed in string theory?
IINAM or P, so it seems to me that part of the confusion - and my slight dissatisfaction with the staff report - comes from apparently different usages of the term dimension. One is simply any measurable quantity, that on a graph will follow the same rules of geometry as are applied to spatial dimensions. The spatial dimensions are a subset, and (here could be my problem), and existed quite independently before the Cartesian mind-fuck arrived.
I think this perpendicularity is merely a convention to make the geometry simpler. They don’t have to be at any particular angle to legitimize their status as a dimension, you only have to be able to move in a direction other that those already defined.
For example: If width means “left and right”, then a new dimension does not have to be straight up and down, it can be in any direction, as long as you get off the line or plane.
Case in point: When someone says “depth”, I’m usually pretty foggy on whether they mean “up and down” or “front to back”.
Case in point: When someone says “length”, I think they usually mean “left to right” or “front to back”, whichever is longer.
So too, putting time on a graph as perpendicular to something else is merely a convention to make the graph easier to envision.
If you want to go a little deeper into the math, dimensions don’t even need to be measureable. You can have a non-metric space, or one that’s only partly metric, where distances aren’t defined. For instance, in phase space, you have six dimensions: Three for position, and three for velocity or momentum (you can actually have larger phase spaces than this, if you have more particles). Phase space does not have distances, but it does have volume.
As for perpendicularity, it’s not necessary, but if you have N dimensions, you can always choose N basis vectors (directions) such that they are all perpendicular. Usually, this makes things a little easier to work with, so most mathematicians and physicists do so.
In special relativity, it’s very useful to consider time as a dimension. Just as you can rotate axes in 3 dimensions, to look at an object differently, you can do a special type of rotation called a Lorentz transform to rotate space and time axes. In three dimensions, no matter what your coordinate system, [symbol]D[/symbol]x[sup]2[/sup] + [symbol]D[/symbol]y[sup]2[/sup] + [symbol]D[/symbol]z[sup]2[/sup] between two points is the same. In special relativity, [symbol]D[/symbol]x[sup]2[/sup] + [symbol]D[/symbol]y[sup]2[/sup] + [symbol]D[/symbol]z[sup]2[/sup] - [symbol]D[/symbol]t[sup]2[/sup] is a constant. You can see that time works a little differently, with that minus sign there, but it’s obviously similar to the other dimensions.
As far as the “wrapping” up of dimensions is concerned…
That’s all speculation for right now. There are hints that the universe is less complicated in more dimensions than four, but the obvious question is: where are these extra dimensions and how do they manifest themselves? Skeptical physicists are likely to point out that such formulations of 11 or 26 or 7 or whatever number of dimensions (or EXTRA dimensions, as the case may be) are just as likely to be wrapped up on themselves floating around in a ball somewhere in outerspace as they are to being endemic to the entire universe. In other words, the theory right now isn’t completely satisfying.
One way to look at inflation in fact is to consider that there are all these extra dimensions in the “seed” and then only a few of them ended up expanding. The nature of how this should manifest itself is under considerable debate at the moment.
The big joke among astronomers and physicists is that string theorists are either impossible to understand or completely whacko and it’s hard to tell the difference. Who knows? Someday somebody just might get the correct number of dimensions right so everything works out. Until then, you can safely say there are at least four dimensions in General Relativity and plead ignorance on the rest while being in good company.
Of course, pleading ignorance is a bit counter to the purpose of these boards, but eventually if you ask “why” enough you’re going to have to do it.