Why is time considered the 4th dimension?

[RichardG]

Hello all,

 

To start let me say that I have no formal training in theoretical physics, I am simply fascinated by the subject and it has become somewhat of an obsession of thought. I have a general understanding of what string theory is and I do grasp the concept of 10 (or more) dimensions.

Now for my question:

 

In my understanding of string theory, the 4th dimension is postulated to be time (correct me if I am wrong).

 

However consider this:

 

A "creature" living in 1 dimensional space would only be able to move "left" and "right" if you will. However in the course of his travels, he could consider that he is now further left or further right than he once was. This 1D creature would therefore have the concept of time, making it (from his viewpoint) the 2nd dimension. The same could be said of a creature living in 2 dimensional space, him considering that the 3rd dimension was not depth, but actually time. And so it seems to me that time (although observable) is a bit of an arbitrary as to its dimensional placement. There could be another dimension of space itself that would indeed be the 4th dimension (and it could be postulated to continue on in an infinite number of spacial dimensions).

 

Any clarification of this would be appreciated.

 

Thanks in advance,

 

Richard.

[michel123456]

Hello all,

 

To start let me say that I have no formal training in theoretical physics, I am simply fascinated by the subject and it has become somewhat of an obsession of thought. I have a general understanding of what string theory is and I do grasp the concept of 10 (or more) dimensions.

Now for my question:

 

In my understanding of string theory, the 4th dimension is postulated to be time (correct me if I am wrong).

 

However consider this:

 

A "creature" living in 1 dimensional space would only be able to move "left" and "right" if you will. However in the course of his travels, he could consider that he is now further left or further right than he once was. This 1D creature would therefore have the concept of time, making it (from his viewpoint) the 2nd dimension. The same could be said of a creature living in 2 dimensional space, him considering that the 3rd dimension was not depth, but actually time. And so it seems to me that time (although observable) is a bit of an arbitrary as to its dimensional placement. There could be another dimension of space itself that would indeed be the 4th dimension (and it could be postulated to continue on in an infinite number of spacial dimensions).

 

Any clarification of this would be appreciated.

 

Thanks in advance,

 

Richard.

I doubt you will get clarification on this subject. But you can get confusion :I am excellent in that exercise.

 

You said

 

A "creature" living in 1 dimensional space would only be able to move "left" and "right" if you will. However in the course of his travels, he could consider that he is now further left or further right than he once was. This 1D creature would therefore have the concept of time, making it (from his viewpoint) the 2nd dimension.

That is a way to to think: since you can move, the changement in position "creates" time. In this scenario, time emerges naturally from change.

 

The other way to think is that without time, it would be impossible for the creature to move in the first place. In this scenario, time comes first and change is the natural consequence of time. In this scenario also, if time comes first, the one-dimensional substract in which the creature lives is the time line, it is not space. the creature has zero dimension (a point) and simply "exist" in time. and if it is the correct interpretation, the creature, for some unexplained reason, cannot go left and right, but only right (or only left).

 

I hope that has confused you completely.

[swansont]

That is a way to to think: since you can move, the changement in position "creates" time. In this scenario, time emerges naturally from change.

 

The other way to think is that without time, it would be impossible for the creature to move in the first place. In this scenario, time comes first and change is the natural consequence of time. In this scenario also, if time comes first, the one-dimensional substract in which the creature lives is the time line, it is not space. the creature has zero dimension (a point) and simply "exist" in time. and if it is the correct interpretation, the creature, for some unexplained reason, cannot go left and right, but only right (or only left).

 

This doesn't seem to be the topic raised in the OP, and is more suited for philosophy or speculations. The idea that motion creates time is, AFAICT, untestable, so it's not science.

 

As to the OP, time is the fourth dimension because we perceive three spatial dimensions. This idea is not a prediction of string theory — it's been around far longer than that.

[RichardG]

@ michel123456

I understand what you are saying, and am actually not too confused about your idea at all. It is simply a different way of viewing the subject of time as the "underlying dimension" in which all other dimensions exist.

 

 

@ swansont

I get it, perhaps I am not strictly referring to string theory, and I do apologize for the mis-labeling of this topic. My main point of thought is that time seems to be unplaceable in terms of spacial dimensions as it is (although related) not the same idea as spacial dimensions.

 

The point which I am sort of getting at is this:

 

Why would the strings need to vibrate in 10 dimensional hyperspace? We have seen in our 3 dimensional universe that the wavelength of energy determines its properties, and if energy and matter are interchangeable, why could the vibration of subatomic particles not determine the properties of that piece of matter? (certain wavelength makes a proton, another wavelength makes an electron etc [crude example, I know, but it communicates the point]). As you said, physically speaking, all we can observe and experience are the 3 basic spacial dimensions, so couldn't the solution exist simply within those dimensions?

 

 

I originally brought up my question of time as I wanted to further understand that before delving further into this matter.

 

I realize that with all these things being theoretical, a clear, definitive answer is not likely/possible. I just wanted to get others' perspectives on the subject.

 

Thanks again,

 

Richard

 

 

[Schrödinger's hat]

Time is labelled as the fourth dimension in relativity because it is in many ways interchangable with the three spatial dimensions.

In SR, the spatial dimensions in one frame are a mixture of spatial+time dimensions in another.

We call it the fourth, simply because we added it to the three space dimensions. You can just as easily make it 0 or 2, (0 is often used, but 2 makes little sense as you split your space dimensions) and it would be the second dimension in your 1 spatial dimension universe.

 

The 10/11/26 dimensions from string theory come from a requirement in the mathematics to have that many degrees of freedom for any sane solutions to come out of the basic premises. The details are somewhat beyond my ability to explain, and I'm not aware of any succinct layman's explanation.

 

Edit: Fixed typo michel pointed out.

Edited March 7, 2012 by Schrödinger's hat

[michel123456]

(...)We call it the fourth, simply because we added it to the three time dimensions. (...)

It's a typo for sure.

[elfmotat]

It's just a label. You could call it the "zero'th" dimension (indeed, as some do), or the first, second, third (though it doesn't really make sense to not group the spacial dimensions together) or fourth.

[DrRocket]

@ michel123456

I understand what you are saying, and am actually not too confused about your idea at all. It is simply a different way of viewing the subject of time as the "underlying dimension" in which all other dimensions exist.

 

Bold added.

 

Herein lies a major problem inhibiting your understanding.

 

The phrase "time as the "underlying dimension" in which all other dimensions exist" demonstrates a fundamental lack of understanding of the term "dimension". Dimensions do not exist within one another, and in fact the idea makes no sense whatever.

 

To begin to understand dimension you should start with a course on linear algebra in which you will find the notion of dimension of a vector space discussed. Ordinary Euclidean space is a vector space (once you choose an origin) with a bit of additional structure.

 

Following that you should study a bit of topology in which you will find that Euclidean spaces of different dimension are topologically different, and that the algebraic notion of dimension carries over to the topological setting.

 

Basically, a dimension is a "degree of freedom" required to describe something. So, if you wish to schedule a meeting you need to specify where the meeting will be held (3 spatial coordinates) and when it will be held (1 time coordinate). Thus a complete description of your meeting is a point in 4-dimensional space. In special relativity this becomes a bit more sophisticated in terms of how the coordinates fit together and the metric imposed on 4-dimensional spacetime. In general relativity one takes another step up in sophistication and deals with a manifold rather than a vector space.

 

The bottom line is the the comic book concept of dimension has nothing to do with the meaning of the term in mathematics and physics.

[RichardG]

@ DrRocket

 

I understand your point. While I did not see dimensions as something out of superman's "bizzarro" world, your explanation on "degree of freedom" does make a lot of sense. I thought that if a 2d space could exist within a 3d space, then dimensions could exist "inside" one another. Your explanation well clarifies that point. A 2d space could never be fully defined as existing in a 3d space without actually using a 3rd coordinate to define where in the 3d space the "plane" would exist.

 

 

@ Schrödinger & elfmotat

 

Got it. The number assignment to time as a dimension is simply arbitrary.

 

 

Thanks for the many replies. I know I have more to study to gain a deeper understanding. Does anyone have any recommendations for a good book to study as an introduction to theoretical physics? I realize that a few prerequisites may be in order (be kind, as I hold 2 jobs and have little free time to study, but I want to better understand this subject).

 

Thanks,

 

Richard

[DrRocket]

@ DrRocket

 

I understand your point. While I did not see dimensions as something out of superman's "bizzarro" world, your explanation on "degree of freedom" does make a lot of sense. I thought that if a 2d space could exist within a 3d space, then dimensions could exist "inside" one another. Your explanation well clarifies that point. A 2d space could never be fully defined as existing in a 3d space without actually using a 3rd coordinate to define where in the 3d space the "plane" would exist.

 

 

@ Schrödinger & elfmotat

 

Got it. The number assignment to time as a dimension is simply arbitrary.

 

 

Thanks for the many replies. I know I have more to study to gain a deeper understanding. Does anyone have any recommendations for a good book to study as an introduction to theoretical physics? I realize that a few prerequisites may be in order (be kind, as I hold 2 jobs and have little free time to study, but I want to better understand this subject).

 

Thanks,

 

Richard

 

Far and away the best physics text at an introductory level is The Feynman Lectures on Physics.

 

But to understand physics you also need to understand some mathematics, particularly calculus and linear algebra.

 

At an advanced leval Course of Theoretical Physics by Landau and Lifshitz (several volumes) is very good, but it is only for those with a good deal of background.

 

Calculus by Mike Spivak is as good as any calculus text. Finite Dimensional Vector Spaces by Paul Halmos is a very good linear algebra book.

[RichardG]

Sounds good. Thanks.

[Aguirre]

Hello all,

 

To start let me say that I have no formal training in theoretical physics, I am simply fascinated by the subject and it has become somewhat of an obsession of thought. I have a general understanding of what string theory is and I do grasp the concept of 10 (or more) dimensions.

Now for my question:

 

In my understanding of string theory, the 4th dimension is postulated to be time (correct me if I am wrong).

 

 

 

"the 4th dimension" is a pseudodimension given by ct=speed of light times time.

 

Time alone does not have a dimension.

 

The Minkowski space has not simple 4 dimensiones but 3+1.

 

 

 

496=496

 

In der Ruhe liegt die Kraft

 

Sig

 

However consider this:

 

A "creature" living in 1 dimensional space would only be able to move "left" and "right" if you will. However in the course of his travels, he could consider that he is now further left or further right than he once was. This 1D creature would therefore have the concept of time, making it (from his viewpoint) the 2nd dimension. The same could be said of a creature living in 2 dimensional space, him considering that the 3rd dimension was not depth, but actually time. And so it seems to me that time (although observable) is a bit of an arbitrary as to its dimensional placement. There could be another dimension of space itself that would indeed be the 4th dimension (and it could be postulated to continue on in an infinite number of spacial dimensions).

 

Any clarification of this would be appreciated.

 

Thanks in advance,

 

Richard.

[RichIsnang]

dr rocket, you say that dimensions are a degree of freedom, in the spatial dimensions, we can theoretically travel anywhere, up down, left, right, forwards, backwards

but we can only go forwards in time and we cant do that at will.

so how much freedom do we have in the time dimension?

[michel123456]

dr rocket, you say that dimensions are a degree of freedom, in the spatial dimensions, we can theoretically travel anywhere, up down, left, right, forwards, backwards

but we can only go forwards in time and we cant do that at will.

so how much freedom do we have in the time dimension?

 

I disagree.

You must compare the single dimension of time to a single dimension of space: the line of time compared to the line of distance.

Now, you may notice that a distance is always positive. Even if you turn back to where you came from, the distance that you will travel will always have a positive value. The same goes for time.

There is no negative distance, there is no negative time. That's just the same.

[RichIsnang]

Yes but you can turn around in the line of distance and go the other way, you cannot do that with time.

[michel123456]

Yes but you can turn around in the line of distance and go the other way, you cannot do that with time.

 

If you walk 10 meters East at 1m/s, then 10 meters West at 1m/s, you will have come back to your starting point.

You will have traveled 20m in 20 seconds. Meters have added exactly the same way time has added: 20 meters, 20 seconds. At no moment you will have traveled minus meters. Change in direction does not imply that you go into negative distance.

 

Change in direction is possible in space because there are 3 dimensions of space, it allows the rotation of distance in space.

Time is alone, it cannot rotate in space.

.

.

.

Or can he?

[Spyman]

Clearly it is fully possible to return to the exact same previously visited location in all three space dimensions but not in the time dimension.

[IM Egdall]

I believe the use of time as the "fourth" dimension started with the spacetime physics of Poincare and Minkowki in 1907 or so. And it is rooted in the concept of the spacetime interval.

 

Einstein showed in 1905 that time and space are relative -- the time interval and space interval between two events is different depending on the (uniform) motion of the observer.

 

Poincare and Minkowski showed that a combination of time and space called the spacetime interval is absolute. It is the same for all observers, no matter what their (uniform) motion. From this a new set of mathematics was developed in four dimensions -- three space and one time. See link:

 

http://en.wikipedia.org/wiki/Spacetime

[questionposter]

I think time is a dimension simply because it's a coordinate, it's a coordinate you need to describe an object in reality. If you look on a graph, there's length and width and height, but more often than all of those is time.

So you can think of the 3 spacial coordinates, 1cm thick, 1 cm tall, 1cm wide, and occupies the relative time coordinate of say...13.5 billion years after the big bang, and counting, i.e. the time coordinate is changing all the time.

Edited March 31, 2012 by questionposter

[IM Egdall]

I think time is a dimension simply because it's a coordinate, it's a coordinate you need to describe an object in reality. If you look on a graph, there's length and width and height, but more often than all of those is time.

So you can think of the 3 spacial coordinates, 1cm thick, 1 cm tall, 1cm wide, and occupies the relative time coordinate of say...13.5 billion years after the big bang, and counting, i.e. the time coordinate is changing all the time.

 

Yes. You are describing the four co-ordinates of an event in spacetime.

[RichIsnang]

Time most probably is a dimension, but why is it different and what makes it different to the rest?

maybe we need to redefine our notion of dimension, if we are calling two different things the same thing

Edited April 1, 2012 by RichIsnang

[Aguirre]

Clearly it is fully possible to return to the exact same previously visited location in all three space dimensions but not in the time dimension.

 

 

 

Are you sure?

What an statement.

 

I would say not in a past spacetime location.

[questionposter]

Technically you can go backwards in time with math, but that doesn't happen in reality, time always just keeps moving forward, except maybe at the event horizon of a black hole to an outside observer.

[RichIsnang]

You can also work in 101 dimensions in maths, but that's irrelevant

Looking only at one dimension, you can return to the same point in spatial dimensions but not the time one,

When looking at them all combined or space-time, you cannot return to the same point in spacetime, but only because time disallows this

[Spyman]

Clearly it is fully possible to return to the exact same previously visited location in all three space dimensions but not in the time dimension.

 

 

 

Are you sure?

What an statement.

 

I would say not in a past spacetime location.

Yes, I am sure. What is troubling you with my statement?