# Thread: A New Way to Look at Dimensions

1. People say time is the 4th dimension. This is just plain wrong. Length, width, and depth are three dimensions of space. To say time is the fourth implies that time is a way to measure space. Instead, time is a SET of dimensions.

Time is not a dimension just like space is not a dimension. Dimensions of space measure space. Dimensions of time measure time.  2.

3. if time is the 4th dimension then arent we in the 4th dimension? lets use an example shall we?

there is a cup and a table, and a hammer next to the cup. if the cup is smashed by the hammer, there was time involved for some other object to move the hammer and hit it against the cup. so with out time then the hammer could not have been moved to hit the cup in the first place.

we are in the forth dimension.  4. I don't get how that is relevant in the slightest. I am saying that time should not be classified as a higher order dimension then depth.  5. The 'number' of the dimension isn't relevant, the idea of time being a dimension was just developed after it was decided that there are three spatial dimensions, so it got labelled as the 'fourth.' There's no 'hierarchy' of dimensions though.  6. Actually, our current notion of dimensions is kinda weird imo.

Dimension 0: (non-existent dot)

Dimension 1: (non-existent line)

Dimension 2: (non-existent plane)

Dimension 3: (existent cube, human, goat, what have you)

If you have a dot(0) that doesn't exist, that makes a line(1) that doesn't exist, that makes a plane(2) that doesn't exist, that makes a cube(3), you don't get existence; you get non-existence to the fourth dimension and so on. It's basically just an abstract concept and it has nothing to do with existence. One can't get existence from non-existence. From an empirical and intuitive standpoint, there is only one dimension, call it whatever you will, but it's the one we exist in.  7. We're not in the "third dimension." We exist in 3 dimensions, 4 if you want to count time. In terms of Cartesian coordinates we're in the x, y, and z dimensions: length, width, and height.  8. math can get pretty cool when you include more dimensions though.

some really neat math shows that light doesn't travel in straight lines but actually curves.  9. Originally Posted by organic god
math can get pretty cool when you include more dimensions though.

some really neat math shows that light doesn't travel in straight lines but actually curves.
A couple of points.

The notion of "dimension" is tied to "degrees of freedom" in specifying something. This is made quite precise in the notion of a vector space, which is used in geometry first with respect to Euclidean spaces (topologically Euclidean spaces of different dimension can be shown to be non-homeomorphic) and then to the notion of dimension of manifolds. There is no necessity for the dimensions to be phrased in terms of time or space or any particular quantity.

To specifiy a meeting or a date you must specify a place (3 dimensions) and a time (1 dimension) so inherently to specify that event you need a description in 54 dimensions. In a dynamical system, to describe the state you need position and momentum for each mass, so for a system of N masses the dimension of the state space is 2N. There is nothing magic about spaces of arbitrary dimension, and one also works with spaces of infinite dimensions -- which is what you are doing without being told so when you work with Fourier series.

The description of light as following a curves requires the theory of differential manifolds and curvature of such manifolds. Space-time is modeled as a 4-dimensional semi-Riemannian manifold and light follows a geodesic path in that manifold, which is curved.  10. The notion of "dimension" is tied to "degrees of freedom" in specifying something. This is made quite precise in the notion of a vector space, which is used in geometry first with respect to Euclidean spaces (topologically Euclidean spaces of different dimension can be shown to be non-homeomorphic) and then to the notion of dimension of manifolds. There is no necessity for the dimensions to be phrased in terms of time or space or any particular quantity.

To specifiy a meeting or a date you must specify a place (3 dimensions) and a time (1 dimension) so inherently to specify that event you need a description in 54 dimensions. In a dynamical system, to describe the state you need position and momentum for each mass, so for a system of N masses the dimension of the state space is 2N. There is nothing magic about spaces of arbitrary dimension, and one also works with spaces of infinite dimensions -- which is what you are doing without being told so when you work with Fourier series.

The description of light as following a curves requires the theory of differential manifolds and curvature of such manifolds. Space-time is modeled as a 4-dimensional semi-Riemannian manifold and light follows a geodesic path in that manifold, which is curved.
ok i was just saying the maths was cool.
when you define the 3 cartesian dimensions x,y,z intuitively the quickest way to travel between 2 points is a straight line.
but if you add more dimensions then this is not the case  11. Originally Posted by organic god
The notion of "dimension" is tied to "degrees of freedom" in specifying something. This is made quite precise in the notion of a vector space, which is used in geometry first with respect to Euclidean spaces (topologically Euclidean spaces of different dimension can be shown to be non-homeomorphic) and then to the notion of dimension of manifolds. There is no necessity for the dimensions to be phrased in terms of time or space or any particular quantity.

To specifiy a meeting or a date you must specify a place (3 dimensions) and a time (1 dimension) so inherently to specify that event you need a description in 54 dimensions. In a dynamical system, to describe the state you need position and momentum for each mass, so for a system of N masses the dimension of the state space is 2N. There is nothing magic about spaces of arbitrary dimension, and one also works with spaces of infinite dimensions -- which is what you are doing without being told so when you work with Fourier series.

The description of light as following a curves requires the theory of differential manifolds and curvature of such manifolds. Space-time is modeled as a 4-dimensional semi-Riemannian manifold and light follows a geodesic path in that manifold, which is curved.
ok i was just saying the maths was cool.
when you define the 3 cartesian dimensions x,y,z intuitively the quickest way to travel between 2 points is a straight line.
but if you add more dimensions then this is not the case
Not at all. The shortest distance between two points in any Euclidean space of any dimension is a straight line. When you introduce curvature into a manifold you wind up working with the more general idea of a geodesic. A geodesic in a Euclidean space is an ordinary straight line. In the more general dase you don't have straight lines, but you may have geodesics connecting two points and the geodesic takes the place of a straight line. For instance, on the surface of a sphere the geodesics are great circles and they are the "straight lines", but they do not follow the usual postulates of Euclid -- there are no parallel great circles for instance and any two great circles intersect.  12. hmm sounds interesting, i just heard that light doesn't travel in straight lines from my math lecturer, but you know because we are engineers they don't go into deep mathematical proofs which is kind of dissapointing.

It sounds interesting though and i will do some research in my own time  13. Originally Posted by organic god
hmm sounds interesting, i just heard that light doesn't travel in straight lines from my math lecturer, but you know because we are engineers they don't go into deep mathematical proofs which is kind of dissapointing.

It sounds interesting though and i will do some research in my own time
If you want to look into this more the subject that covers this sort of thing is differential geometry and within differential geometry the subject of Riemannian geometry. Actually for general relativity you need the generalization to what are is called semi-Riemannian or pseudo-Riemannian manifolds.

Be prepared, it usually takes a bit more background in abstract mathematics than what is usually seen by engineers.  14. yeh it's a shame that as engineers we don't do lots of pure maths but you know applied maths is more important for us.
some of the quantum physics we do is cool but it isn't particularly deep.

i realise that pure maths is a study i will have to do on my own time.
I'm not sure exactly where to go from here though if i'm to strike out on my own  15. i don't think "time" is a value or a dimension. even there is no dimension at all. we have two coordinate points in a space. and the closest distance between them seems to have a strait but when you bend the space you will have two points in one coordinate. so tell me where is the dimension. even time or a distance travelling between them.

just think boys...! imagine. there should be somebody who understands me. i don't study physics or math so i can't solve by my self.  16. Originally Posted by organic god
yeh it's a shame that as engineers we don't do lots of pure maths but you know applied maths is more important for us.
some of the quantum physics we do is cool but it isn't particularly deep.

i realise that pure maths is a study i will have to do on my own time.
I'm not sure exactly where to go from here though if i'm to strike out on my own
You have a lot of choices. It depends on what you personally want to do. What is a bit of a shame is that some of the mathematics that is taught to engineers is not quite right -- one can do things like Fourier analysis, and distribution theory (like the Dirac delta) properly, but you don't get to see that.

It is not true that applied math is more important for engineers. Mathematics is really just mathematics no matter what the motivation. What tends to happen is that some professors who don't understand mathematics very well make such statements as a means to avoid addressing mathematical questions properly or head-on. That is what caused me to choose engineering professors carefully and to eventually seek better education in mathematics. It was worth it.

What I did was to finally change from engineering to mathematics after a couple of years in graduate school. That is a fairly drastic step, and not for everyone.  17. Google Imagining the 10th dimension for a great presentation on how dimensions could build on each other. I find it interesting that many people accept that from a 6 dimensional point of view, that the first three dimensions might seem like a point. Yet they don't admit there might be "smaller" dimensions then what we call the first, that WE see as a point.

It has been observed there are time-like dimensions..... What if they are actually dimensions of time? From my point of view, time is like space. It is not a dimension, but rather something measured by a dimension.  18. time is just a duration of an event we cannot use it when it happens instant or needs no time to happen at all and we are maybe just wasting time to move the objects in space together when they are definitely in the same coordinate but seems separate.  19. Originally Posted by DrRocket Originally Posted by organic god
yeh it's a shame that as engineers we don't do lots of pure maths but you know applied maths is more important for us.
some of the quantum physics we do is cool but it isn't particularly deep.

i realise that pure maths is a study i will have to do on my own time.
I'm not sure exactly where to go from here though if i'm to strike out on my own
You have a lot of choices. It depends on what you personally want to do. What is a bit of a shame is that some of the mathematics that is taught to engineers is not quite right -- one can do things like Fourier analysis, and distribution theory (like the Dirac delta) properly, but you don't get to see that.

It is not true that applied math is more important for engineers. Mathematics is really just mathematics no matter what the motivation. What tends to happen is that some professors who don't understand mathematics very well make such statements as a means to avoid addressing mathematical questions properly or head-on. That is what caused me to choose engineering professors carefully and to eventually seek better education in mathematics. It was worth it.

What I did was to finally change from engineering to mathematics after a couple of years in graduate school. That is a fairly drastic step, and not for everyone.
hmm it sounds an interesting idea, i am currently doing a masters degree in chemical engineering as it keeps my options open after i graduate  20. On the discussion of engineering I think all depends on which engineering field your entering and the depth of the program at your University. Electrical Engineering usually goes a bit deeper into mathematics then other engineering degrees. I'm an electrical engineering undergraduate and I feel like I have a firm theoretical basis in mathematics. It seems that Physics is where the suffering really goes on.

We really only get to do applicable physics, we don't dive to deeply into the theoretical physics or set a firm foundation down. That seems to be where the underlying problem with Engineering degree's are.

I am only in my second year so I haven't really made it to far in mathematics. I just finished up Calculus Three, where we went over curl and divergence and the different representations of the Fund. Theorem of Calculus. I'm going to begin Differential Equations and Linear Algebra in the spring.

As for spatial dimensions, I would say there are 3 observable dimensions and 1 time dimension for time. So I think there are 4 space-time dimensions. Nothing could move from one point to another without the 4th time dimension. So it's at least a abstract dimension.  21. Originally Posted by GenerationE
On the discussion of engineering I think all depends on which engineering field your entering and the depth of the program at your University. Electrical Engineering usually goes a bit deeper into mathematics then other engineering degrees. I'm an electrical engineering undergraduate and I feel like I have a firm theoretical basis in mathematics. It seems that Physics is where the suffering really goes on.

We really only get to do applicable physics, we don't dive to deeply into the theoretical physics or set a firm foundation down. That seems to be where the underlying problem with Engineering degree's are.

I am only in my second year so I haven't really made it to far in mathematics. I just finished up Calculus Three, where we went over curl and divergence and the different representations of the Fund. Theorem of Calculus. I'm going to begin Differential Equations and Linear Algebra in the spring.

As for spatial dimensions, I would say there are 3 observable dimensions and 1 time dimension for time. So I think there are 4 space-time dimensions. Nothing could move from one point to another without the 4th time dimension. So it's at least a abstract dimension.
Don't kid yourself. Electrical engineers see perhaps a bit more mathematics than do some other engineers, but you do not really get to see much modern mathematics and you do not see much of the fundamental theory that underlies the mathematics that you do see. EEs in control theory and communication theory get to see more mathematics than other EEs but I can assure you that while they see some pretty neat stuff, they do not see the deep theory that supports it. There is a LOT more to Fourier transforms and distributions than what you are told about.

It was in fact the huge amount of hand waving that I saw in EE courses that caused me to switch to mathematics, after an MS in EE.

If you have gotten to curl and divergence, you have seen some, but not all, of the state of the art in mathematics circa 1880. There has been a notable improvement in our understanding of mathematics since then.

General relativity would tell you that there is not a time dimension and 3 spatial dimensions, but rather a 4-dimensional manifold that includes both space and time but in which they are not clearly and globally separable. It is not space AND time but rather a single thing, space-time.

I'm a bit surprised that you find the physics basis weak. While we did not take a lot of classes from the Physics Dept, per se, we did take basic and modern physics there. But also there were classes in electromagnetics, statics, dynamics and thermodynamics taught by varioius engineering departments. Depending on your concentration there were other physics classes as well -- people in device electronics used a lot of quantum mechanics for instance, and antenna people did advanced electrodynamics. State space analysis of control systems owes a lot to Langrangian mechanics, and the linear systems analysis involved in controls and communications applies to all sorts of dynamical systems.  22. Hello,
I started an elaborate defense of the forth dimension of time. But after a couple of paragraphs I realized your point. In Einsteins Theory of relativity, an object that approaches the speed of light dilates and can move forward IN time. The object itself does not contain the dimension.
So when you look at efforts to travel through time-the efforts are all made to transport something THROUGH THE MEDIUM OF TIME. So it is logical to assume that time is NOT a dimension, but it is what you describe.
I would ask you though to look at the OTHER dimensions I have hypothesized. These dimensions ARE part of the objects in our existence. So I say that change and force of motion are dimensions.
Thanks to your post I would now say that there are but five, not six dimensions.  23. If things have dimensions then everything that is real in existence has dimension. However, space/time is a "medium" that other things travel through. Space/time is a separate, but real, thing having but two dimensions-space and time. The other things in our existence seem to travel through these, even though they do not have the same dimensions as space/time.
Space/time seems a dimension by itself. It has dimension because both space and time really EXIST. Or exist in reality.
To say that lines and non existent lines and points show dimensions is true. But do these things have any existence? I would say that points, and all sorts of lines are things only in the abstraction of the mind. These "things" gain dimension if and when they are drawn in reality. In such circumstance, they become real "five dimensional" things-graphite lines on paper have length, width and depth along with change and force of motion.
One cannot say that since love "exists" it is therefore is a "dimension". Abstractions have an abstract existence. This simply means they are not "real things", just potentially real things. Since there is only an abstract existence there is no "real" existence. Things that have substance(with the five dimensions I argue for) and space/time have "real existence. One can use any discipline to manipulate the concept of space/time in abstraction. But so can an architect when a house is "designed". The abstraction becomes real when the plans are drawn and the home is built. But until these are done, the abstract lines and points have no real existence.

Do all thoughts that exist in the abstract of the mind have dimension? There is no dimension to abstractions.
So abstraction have existence-but not "real" existence.  24. Originally Posted by Raggedjoe People say time is the 4th dimension. This is just plain wrong. Length, width, and depth are three dimensions of space. To say time is the fourth implies that time is a way to measure space. Instead, time is a SET of dimensions.

Time is not a dimension just like space is not a dimension. Dimensions of space measure space. Dimensions of time measure time.
You want to arrange a meeting with someone. In order to make sure the meeting happens, you first need to agree on a place ( this requires, in general, three coordinates in space : x,y,z ), then you need to specify a time when the meeting happens : the time coordinate t. So, in order to uniquely identify an event such as a meeting, you need four coordinates to describe it : x,y,z,t. Because four independent coordinates are needed, we live in a (3+1)-dimensional universe ( macroscopically ).
That's all there is to it.

To say time is the fourth implies that time is a way to measure space.
No. There are two different types of dimensions - there are spatial dimensions, and there are temporal dimensions. They are mathematically distinguished within an object called the metric. We live in a (3+1) dimensional universe, meaning we measure three spatial directions, and one temporal one.
If the number of spatial or temporal ( macroscopic ) dimensions were any different then (3+1), then the laws of physics as we can observe them ( e.g. gravity ) would be quite different, and we probably wouldn't be here to have this discussion.  25. So can the coordinate t be reduced to an expression involving only the three space-like dimensions?  26. Originally Posted by KALSTER So can the coordinate t be reduced to an expression involving only the three space-like dimensions?
No it can't. The coordinates x,y,z,t are independent coordinates. This is intuitive if you think of the example of the meeting that I gave in post 23 - there is no way to specify when the meeting takes place purely in terms of the spacial coordinates. You can be very exact about the location of the meeting, but the person you are trying to meet still wouldn't know if the meeting takes place today at 11am, or tomorrow at sunset, or on the 1st of June 2051. The time when the meeting takes place is completely independent of the location. You need to specify both in order to exactly pinpoint the event.  27. Thanks. That makes sense and renders my question meaningless.

I was just thinking that time can be reduced to or is defined by a measure of the rate of relative movement, i.e. the movement of point A between 2 coordinates vs the movement of point B between 2 different coordinates. But it doesn't make sense to even talk about movement without involving time. Is it then because of length contraction that time changes from different perspectives during relative movement or the other way around?

Sorry if I am talking gibberish.  28. Originally Posted by KALSTER Thanks. That makes sense and renders my question meaningless.

I was just thinking that time can be reduced to or is defined by a measure of the rate of relative movement, i.e. the movement of point A between 2 coordinates vs the movement of point B between 2 different coordinates. But it doesn't make sense to even talk about movement without involving time. Is it then because of length contraction that time changes from different perspectives during relative movement or the other way around?

Sorry if I am talking gibberish.
No, it's not gibberish, but a very valid question !
In our universe space and time are aspects of the same manifold, the spacetime. Within such spacetime you can define the term distance along each of the four coordinates; perhaps the consequences of this are best visualized by once again referring to the example of the meeting :

1. Say you have two meetings - one takes place at 11am in New York, the other one at 11am in Bangor, Maine. These two events are separated in space, but take place at the same time. You cannot go from one to the other because, as they take place at the same point in time, this would require you to move at infinite speed !
2. Now consider two meetings taking place in the same conference room somewhere in NY, one at 11am, the other one at 3pm. These events are now separated in time, but are located at the same place. Their distance is along the time coordinate only, so the distance between the two is four hours.
3. Finally, we have a meeting in NY at 11am and a meeting in Bangor at 3pm. These meetings are separated in both time and space. Whether we can go from one to the other depends on the speed we would need to travel at - it is possible so long as the required speed is equal to or less than speed of light.

In special relativity you have two related phenomena - length contraction and time dilation. Which one - if any - is noticed by two observers depends on the relative movement between the two, both in terms of speed and direction. The exact relationships are too complex to summarize in just one short post; in short, where one observer sees length contraction, another observer might measure time dilation. The idea behind it all is that all observers experience the same physical laws, regardless of their frame of reference. Length contraction and time dilation balance in just such a way as to ensure this.
Hope this makes sense ?  29. So time dilation and length contraction are basically two sides of the same coin? Also then, does length contraction and time dilation occur specifically because time is written as a 4th coordinate, is it because of the constancy of the speed of light, or is it all of the above?  30. Originally Posted by KALSTER So time dilation and length contraction are basically two sides of the same coin? Also then, does length contraction and time dilation occur specifically because time is written as a 4th coordinate, is it because of the constancy of the speed of light, or is it all of the above?
You "like"ed this post: Originally Posted by SpeedFreek Our rulers and our clocks are not absolute, they are relative. One man's space is another man's time.

If you are at rest in relation to me, then your time is passing the same as mine is and our rulers are the same length. If you are moving in relation to me, your time will be passing slower than mine, and your ruler is now shorter than mine, as you have converted some of your motion through time into motion through space, relative to me. This means you will still measure the speed of light to be the same as I measure it.
The point is that as you increase your speed you swap space for time.

If you are stationary in space, then you are "travelling" through time at 1 sec per sec; as you increase your speed (relative to me, say) then your "speed" through time decreases. Your "speed" through spacetime is constant.  31. Originally Posted by KALSTER So time dilation and length contraction are basically two sides of the same coin? Also then, does length contraction and time dilation occur specifically because time is written as a 4th coordinate, is it because of the constancy of the speed of light, or is it all of the above?
It's a bit of both, I suppose. Treating t as a fourth coordinate is a fundamental part of the mathematical formalism of special relativity; to go from one reference frame to another (moving one), one performs a coordinate transformation, which affects both spatial and temporal coordinates. This transformation explicitely contains the speed of light as a parameter. Thus length contraction and time dilation are introduced.
Refer also to post 29, Strange has another excellent way to look at it !  32. Question from a Neanderthal 8^). Is there really a "place" in space? You may be in a "place" when you are somewhere in relation to somewhere/something else (next to a dumpster on main street). But, where in "space" are you when you are next to that dumpster on main street? Meaning, where in the universe are you at that point? Where do we measure that point from? If I'm not correct, everything is moving, so there is no "here", because it is fleeting, same as in time there is no "here" in time for the same reason. Hence the reason for time dilation. It is relative to where you are in "space", and what speed in relation to your surroundings. I think I may have created more jibberish than reasonable discussion, but I see time as being dependent completely on movement in "space", although I'm not sure what we are comparing the movement against? Sorry if that does not make any sense.  33. There a rezen why one dimension multiply its self by 3 . Its good for time travel to travel at lest 3 roond . Secend roond to see what hapend and the therd roond to fix . Its because the prartical afected by intelegent . Any way when you pull aprtical in 1/r^2 its sape the small part in 3 dimension, any dirrection for the degree of r and from the ather side because you go back and forwed in time 3 times you act in force of 1/r^2 to push and pull the partical . Have a nice day  34. Originally Posted by Schrodingersothercat Question from a Neanderthal 8^). Is there really a "place" in space? You may be in a "place" when you are somewhere in relation to somewhere/something else (next to a dumpster on main street). But, where in "space" are you when you are next to that dumpster on main street? Meaning, where in the universe are you at that point? Where do we measure that point from? If I'm not correct, everything is moving, so there is no "here", because it is fleeting, same as in time there is no "here" in time for the same reason. Hence the reason for time dilation. It is relative to where you are in "space", and what speed in relation to your surroundings. I think I may have created more jibberish than reasonable discussion, but I see time as being dependent completely on movement in "space", although I'm not sure what we are comparing the movement against? Sorry if that does not make any sense.
In essence this is quite correct. There is no absolute frame of reference, so in order to localize an event in space/time you need to first decide on a coordinate system - so for example, you can say I am 5 ft to the left of the dumpster. It is a relative position.  35. Originally Posted by Vector Equilibrium Actually, our current notion of dimensions is kinda weird Imo.

Dimension 0: (non-existent dot)

Dimension 1: (non-existent line)

Dimension 2: (non-existent plane)

Dimension 3: (existent cube, human, goat, what have you)

If you have a dot(0) that doesn't exist, that makes a line(1) that doesn't exist, that makes a plane(2) that doesn't exist, that makes a cube(3), you don't get existence; you get non-existence to the fourth dimension and so on. It's basically just an abstract concept and it has nothing to do with existence. One can't get existence from non-existence. From an empirical and intuitive standpoint, there is only one dimension, call it whatever you will, but it's the one we exist in.
Its actually not so strange. If you think about a point, how many numbers would we require to specify any given point...on our point. Well the answer is obviously 0, we need no number to specify the point since its the only point there is.

Now consider a straight line with some arbitrary point named O. How many numbers do we need to specify any given point here? Well, marking off even units positive in one direction and negative in the other direction from O, we could specify any given point with a number based on how many units away from O that point is. Allowing of course a continuum of values between each unit. So in this sense 1 number can describe any particular point on the line. This we call one dimensional.

The same is of course true for a shape such as a filled in square or circle or even for a flat plane extending out in all directions, this requires at least two numbers to specify any particular point on the square(length,width), circle(Angle, radius), or plane(x,y) for example together with some point O=(0,0). It can be shown that it is impossible to describe these objects and ones similar to them in less than two numbers so naturally we call them 2 dimensional. The same goes for objects like cubes, balls and what we generally refer to as space being called 3 dimensional, all require at least 3 numbers (x,y,z) to describe a unique point on their surface or their interior.

Now an event in space happens at a particular time, get as philosophical about this as you want, but to specify an actually event happening in 3-space, we will require an extra number to describe it, a time parameter if you want. There is no way around this. So an event is described by something along the lines of (x,y,z,t). It is in this sense that space-time is described as being 4-dimensional, and is not incredibly far off the way that dimension is defined. But as mentioned above, that requires starting off with some linear algebra and getting familiar with the notion of a vector space.  36. actually, you can measure in time. for example, it would take 9 light minutes to reach here from the sun   37. incorrect, that's incorrect. It's closer to 8 minutes. (Today, 8 minutes 22.2 seconds)   Bookmarks
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