A Question

Discussion of theories involving time as a dimension, time travel, relativity, branes, and so on, usually applying to the "real" universe which we live in.

A Question

Postby TeamFarrell » Mon Jan 16, 2006 5:35 am

Okay, this is probably a very elementary question, but bare with me. Everything I know about the 4th dimension I have learned for myself out of interest. I have a better understanding of some things than I do others.

My question is whether or not we know definitively that time is the fourth direction of motion like length is the first, x, width the second, y, and depth the third, z.

I've come up with a very basic theory based on that assumption and would like to know if that's even correct or if my theory started off on the wrong foot.
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Postby houserichichi » Mon Jan 16, 2006 5:41 am

When we talk of time as being the fourth dimension it's usually in relation to relativity theory (or some derivative thereof). Relativity works on an entity called spacetime. Time is defined (no need for proof) to be "the fourth"...that is three spatial + one time = four dimensions. Whether time is dimension number 1, 2, 3, or 4 is irrelevant. I reiterate, time is defined to be one of the four, it's not up for debate. If you want to work with space alone and not spacetime then no, time is not the fourth.

Did that help?
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Re: A Question

Postby Keiji » Mon Jan 16, 2006 5:13 pm

TeamFarrell wrote:My question is whether or not we know definitively that time is the fourth direction of motion like length is the first, x, width the second, y, and depth the third, z.


Well, like houserichichi said, it doesn't matter what order the dimensions are in so long as you define it when giving coordinates. The same can be said about 3D space - from your post, you are defining "length" as x, "width" as y, and "depth" as z (even though, you don't seem to have a height in there - which one is height? I'll assume length is), so that makes x the up to down axis, y the left to right axis, and z the front to back axis. What I (and many many people) usually use is x as the left to right axis, y as up to down axis, and z the front to back axis. Some people like to use x as left to right, y as front to back, and z as up to down.

So, the exact same goes for time. Most people (those who treat time as a dimension, that is) put time as the 4th "dimension" because we already have 3 dimensions, so changing the order of them will only confuse things.
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Postby wendy » Tue Jan 17, 2006 7:53 am

It makes sense to re-order the dimensions if one is to consider higher dimensions, viz

1. length, bredth, height, time

This is the standard order

2. time, height, forward, across1, across2, ...

In 4 and higher dimensions, only time, height (gravity), and forward (motion), make any particular sense. In these dimensions, everything else is freely changable.

It probably is better to think of time as dimension 0 or something.

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Postby faranya » Wed Jan 25, 2006 12:16 am

Why exactly is time a dimention? I know this is a stupid question, but I just don't understand how it fits in with lenght, width, and hieght...anyone want to go back to the basics of dimention theories? :)
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Postby jinydu » Wed Jan 25, 2006 5:29 am

faranya wrote:Why exactly is time a dimention? I know this is a stupid question, but I just don't understand how it fits in with lenght, width, and hieght...anyone want to go back to the basics of dimention theories? :)


Because it was convenient for Einstein's Theory of Relativity to deal with four-dimenionsal vectors called "spacetime" vectors.
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Postby wendy » Wed Jan 25, 2006 8:19 am

Einstein did not actually invent the space-time thing. He did invent relativity, though. Minkowski actually found the relevant space-time geometry needed to expound Einstein's relativity.

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Postby houserichichi » Wed Jan 25, 2006 2:37 pm

faranya wrote:Why exactly is time a dimention? I know this is a stupid question, but I just don't understand how it fits in with lenght, width, and hieght...anyone want to go back to the basics of dimention theories? :)


Length, width, and height require three independent variables to make a proper description. If something is x units along the axis that you would measure length, y units along the axis you would measure width, and z units along the axis you would measure height, then to describe the position of a point in that triple axis system we would write (using P for position)

P_space = (x,y,z)

That's a three dimensional "thing" because it requires three independent numbers to describe its position. If we wish to describe the position of P at time t then we would write

P_spacetime = (x,y,z,t)

since, as time progresses, the position P_space can and would change if the object was moving. Since P_spacetime requires four numbers to properly describe it we say that time is the "fourth dimension". It's all about counting up the independent variables used to describe something.

Did that help?
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Postby faranya » Fri Jan 27, 2006 12:33 am

Thanks, it fits when I look at it like that
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Postby lobster » Wed Mar 01, 2006 7:44 am

faranya wrote:Why exactly is time a dimention? I know this is a stupid question, but I just don't understand how it fits in with lenght, width, and hieght...anyone want to go back to the basics of dimention theories? :)


It is possible it is genius dementia, now you mention it . . . ;)

It all seems about positioning. Tomorrow and 3 miles do not exist except in relation to today and the start of 3 miles . . .

Being 3D creatures we can walk 3 miles
If 4D we could veer into yesterday

I wonder if that makes sense?
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Postby moonlord » Sat Mar 04, 2006 3:45 pm

I think time is regarded as a spatial dimension only for theory and calculus reasons. As it was stated numerous times, time travel raises some problems, the worst of them all being casuality.
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Postby jinydu » Sun Mar 05, 2006 5:12 am

The reason that time is treated as a dimension in special relativity is because, when converting the position and time of an event in one frame of reference to another, it is necessary to use 4-vectors, with the speed of light multiplied by time as one of the components.

Try looking up Lorentz transformations.
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Postby moonlord » Sun Mar 05, 2006 3:41 pm

So it's only for calculus, right? Or not...
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Postby jinydu » Mon Mar 06, 2006 2:15 am

Special Relativity (like any other serious physics theory) can't really be understood without understanding the mathematics behind it.

In special relativity, the basic notion is an event: a point in spacetime. In any given reference frame, an event is represented as a four-component vector: the first component is the speed of light multiplied by the time at which the event occurs, and the second, third and fourth components are the x, y and z coordinates at which the event occurs. The values of the components will in general be different in different frames of reference. To convert from one frame of reference, you have to multiply the 4-vector by a 4x4 matrix whose entries depend on the relative motion of the two reference frames. This process is called a Lorentz transformation.
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Postby moonlord » Mon Mar 06, 2006 12:55 pm

Seems confusing. I'll talk to my physics teacher about it.
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Postby PWrong » Fri Mar 10, 2006 11:21 am

Don't worry Moonlord, Jinydu's just trying to scare you. The maths of SR isn't that difficult. Just multiply everything by gamma = 1/ sqrt(1 - v<sup>2</sup>/c<sup>2</sup>). That gives you length contraction and time dilation. In the two-week introduction that I had last year, there was very little calculus used (even though calculus was a prerequisite for the rest of the physics course). But the concepts are so non-intuitive that you won't notice how easy the maths is.
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Postby bo198214 » Fri Mar 10, 2006 1:43 pm

Wow, that was to the point! Everything agreed.
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Postby jinydu » Sat Mar 11, 2006 5:29 am

PWrong wrote:Don't worry Moonlord, Jinydu's just trying to scare you. The maths of SR isn't that difficult. Just multiply everything by gamma = 1/ sqrt(1 - v<sup>2</sup>/c<sup>2</sup>). That gives you length contraction and time dilation. In the two-week introduction that I had last year, there was very little calculus used (even though calculus was a prerequisite for the rest of the physics course). But the concepts are so non-intuitive that you won't notice how easy the maths is.


Well, ok. There are many relativistic effects you can derive without using four vectors, or even Lorentz transformations. I guess it depends on how deep you want to go into it. The impression I got from a workshop I am taking was that real special relativity (the version used by researchers, as opposed to the version taught in an introductory course) uses four-vectors and lots of matrix multiplication.

I guess it is sort of like the distinction between high school Newtonian mechanics (F = ma, plug in a number for F, plug in a number for m, solve for a) and college level Newtonian mechanics (write F = ma as a second order differential equation, solve for position, apply initial conditions). Admittedly, this analogy is a bit exagerrated; the derivations of time dilation are certainly more rigorous than the high school use of F = ma, but you get my point.
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Postby bo198214 » Sat Mar 11, 2006 11:21 am

To the original question, whether there is good reason to regard time as 4th (or better 0th) dimension:
Those 4-vectors (though Id rather would call them 4 dim vectors, to avoid confusion with k-vectors in exterior algebras/wedge product) may compactify a bit calculus, on the other hand time is still specially treated. Swapping time (or more exactly c*t) with a space coordinate leads to different results in computation.
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