Time being the Fourth Dimension VS others

[rEaLiTy]

Ok, I am new to this site, and have just become very interested in this topic what is and if there is a fourth dimension.
I have looked all across the internet, and this seems to be a place where a lot of answers are given, and ideas are shared.

So, I am seeking all the information I can get on why and why not time would be the fourth dimension or even a dimension at all. Mainly I am would like to get more info on why it is not. I believe it is not, but my prof is against me, along with the rest of my class. Any and all information would be of much use.

I'm sure this ? has come up many times, but in refreshing it I hope to aquire more up to date information.

I plan to become an avid member of this site, the more information i can get, the more it will encourage me to stay.

[houserichichi]

Well,

As far as the time-dimension thing goes it all depends on the context. Time is the fourth dimension when referring to spacetime but it doesn't even fit into the equations when dealing with (mathematical or physical) space dimensions.

Now what's the difference you may ask?

Well I shan't go into the details of relativity, but therein lie the equations that dictate space and time are intertwined, that is, you can't have one without the other. If you feel so inclined you should be able to find a derivation of these equations online and see for yourself (special relativity, not general). The merging of space and time is given its own new word (and I believe it's in the dictionary...or at least it should be), called spacetime (some write it space-time). It's the way the universe works, it's actually how things are as far as we can tell. So it's what I would call a "physical interpretation" of four dimensions. In this situation, we have our regular three-dimensional world that I'm sure you know of, and we merge it with time to be our fourth dimension.

Now from another perspective, one can look for a fourth dimension in the mathematical/theoretical world. We can take our three dimensions and set up a coordinate system therein. Let's make the typical x-y-z axes...notice anything? They're all perpendicular to eachother!! Neat! Well, a fourth spatial dimension would simply be an extension of this; that is, create another line perpendicular to the three we already have. Now we have four independent lines so we have four dimensions. You can't visualize this directly because, well, there aren't four dimensions to draw these lines in, so what we typically do is picture them in a lower dimensional space (like drawing a cube on a piece of paper. It's not three dimensional, but it looks it).

It's not much, but I'll let others take over from here. Just remember, time is a fourth dimension (it doesn't matter whether you label it first, second, third, or fourth when discussing) when dealing with spacetime (or the universe in general). It's not the fourth dimension when we are talking, say, about four dimensional Euclidean geometry or extensions of the third dimension.

[rEaLiTy]

Ok, so according to you time IS a dimension? So far to me this seems to be an opinion thing of whether it is or isn't.

What factual evidence can place it in a dimension category is what I am asking, because I see no way it falls under the heading of dimension. I agree that time is a thing, but a dimension?

And one other thing, I dont fully understand string's theory i guess, because I can completely see how we get teh fourth geometrical dimension by creating a another set of parallel lines with the others as was done in the first dimensions. But, how does string think there is over 9 dimensions?

So, basically why is geometrical and a dimension such as time or movement or w/e be placed in the same category at all?


I know this has a lot of questions it is because I have instantanously become transfixed with this fascinating and contriversial subject.

[jinydu]

I think the most accurate phrase is that time can be represented using a fourth dimension. That is, in theories like relativity, we find that the three dimensions of space are intertwined with time. To put it loosely, you can't change space without affecting time.

But this concept is very different from the concept of a fourth spatial dimension, which is what this forum is about. Whereas relativity is a physical theory, whose validity depends on experimental observations; the theory of, say 4D Euclidean space is a mathematical theory. With 100% certainty, the theorems must follow from the axioms, however there is no claim that is necessarily a description of the real, physical world. Mathematicians who only study 4D space aren't concerned about what the real world really is. Instead, they write down the postulate "It is possible to draw four mutually perpendicular lines through a point." then see what things they can prove, assuming that the postulate is true. Unfortunately, some people often confuse this with things like the theory of relativity. However, they are in fact different things, one is pure mathematics while the other is theoretical physics.

As for string theory, it is a relatively recent physical theory that attempts to explain the four fundamental forces of nature. However, in order for the theory to work, 11 dimensions are required. According to string theory, we can't observe most of these dimensions because they are curled up into tiny "balls" that are far too small to observe. Although the theory is currently popular among some theorists, because of its ability to account for many of the features of both general relativity and quantum mechanics, it should be kept in mind that currently, there is little experimental evidence for string theory. Furthermore, in physics, experimental evidence is extremely important. Thus, we shouldn't be too quick to accept the premises and implications of string theory, at least not yet.

[Keiji]

rEaLiTy, please stop coloring your text. It is an annoyance.

[houserichichi]

So far to me this seems to be an opinion thing of whether it is or isn't.

It's not really an opinion, but more an issue of what you're talking about. If you're thinking spatial dimensions like left-right, up-down, back-forward then no, in that thought experiment time is not the logical fourth dimension. Some prefer to call the fourth pair of spatial directions ana and kata but that's not generally accepted.

When we start talking physics as opposed to geometry (which is what the above was supposed to relate to) then we aren't dealing with dimensions of space anymore, but dimensions of spacetime (Einstein's typical claim to fame). Einstein came up with all sorts of fun equations, one you'd know would be E = mc^2 which says energy and mass are the same thing. Along those lines (very loosely), there are other equations that say time and space are the same thing.

So, from geometry we have our normal three dimensional coordinate (x,y,z), but in spacetime we necessarily require four dimensions to describe anything (x,y,z,t) where t obviously stands for time. It just means you need four independent numbers to describe something.

Jinydu said it better than I did the first time, so read his. All I'm saying is it's a matter of what you're talking about, not what you'd prefer.

[RQ]

Well I shan't go into the details of relativity, but therein lie the equations that dictate space and time are intertwined, that is, you can't have one without the other. If you feel so inclined you should be able to find a derivation of these equations online and see for yourself (special relativity, not general).

You don't even have to go that far. You can make a simple analogy:

Velocity=space/time. 0 Space means 0 velocity which means undefined time. If time equals 0, then velocity means undefined, and thus space is undefined.

Also, an earlier version:

It takes time for energy to have velocity, thus no time, no velocity no space (0/0=0 )and with no initial time, you can never know the speed of an object. Think of a picture, it doesn't move, its speed is 0 at 0 time yet in reality it had a speed before it reached time 0 (thus 0/0=undefined physical application tho). And if you had 0 space, then 0 velocity and you have the picture again which means 0 time (0/0=0 )

Tell me if it's confusing, because I sometimes I only explain things to my own satisfaction and it doesn't make sense to others or to me when I read it later.

[RQ]

I think Hawking mentioned that the universe is enclosed in the 4th dimension. Like connecting all the sides of a paper (not a sphere in particularly since there can be no way a 3D observer can measure a 4D shape physically and there is no observational evidence of what the 4D shape of our universe might be. This could explain the finite universe with infinite boundaries. Hawking also suggested that the universe could be infinite which would be one of the reasons that what we see all around us is the same in every direction but that's absurd since we wouldn't be here. We would be the odd man out, 1/infinity, 0.

[rEaLiTy]

I understand the topic of the physical fourth dimension itself. I fully believe that it exists, and that it is just not accessible to us.

The thing I was wondering is why time is considered by anyone to be a dimension... This is easily one fo the most intelligent topic boards that has to do with anything liek this so I came to you guys for answers hoping to stay.

If I could just get an explanation, theory or anything on or proving TIME is not a dimension in anyway, or one of string's proposed 9-11.

I appreciate all the information you have been giving me on the physical aspects and existence of tetraspace, but i am still getting to that, reading forums and stuff, the basic i have grasped, the complex is still out there, so if i could get an answer to time being a dimension i would be most grateful. ty

[RQ]

Well in whether time is a dimension or just a property of the universe is a matter of personal opinion I suppose. Like houserichichi said, it just fits like a dimension in the equations of Einstein. Whether time is a dimension is a matter of definition and with the current defintion it is one. It could be a property but then again, so would the other three spatial dimensions.

[houserichichi]

Alright, I'm replying to everything after my last post in order as they came...so it's a mix of stuff to everyone :wink:

Velocity=space/time. 0 Space means 0 velocity which means undefined time. If time equals 0, then velocity means undefined, and thus space is undefined.

If time = 0 then there's no velocity since it's defined as the CHANGE in displacement divided by the CHANGE in time. To take an instantaneous velocity (as far as elementary physics is concerned) you take a limit, not plug in zero.

The thing I was wondering is why time is considered by anyone to be a dimension

Well time is NOT a dimension when we talk mathematically. If you just mean an extension of the three we already know, all you need to do is tack on another perpendicular line to all the other three and there yuo have it, dimension 4 that has nothing to do with time. That's called a spatial dimension. Time is what we lovingly call a temporal one (and when we say that spacetime has 4 dimensions, we usually write it 3+1 because time is special and not like the others when talked about on its own). Tetraspace, the word, refers to four SPATIAL dimensions, not spacetime dimensions. So when talking about tetraspace, we're NOT talking about time. When talking about spacetime, we ARE talking about time.

Look up the Lorentz transformations if you want to see how time gets mixed into space equations. All you need is high school algebra (if even).

[rEaLiTy]

I think I understand what you are all saying now, it is piecing together a little bit easier now.

So time is considered a space time dimension not a spatial dimension, I am not totally familiar with all the properties of string theory, so in his does he talk about there being aprox 10 spatial or spacetime dimensions?

And, what properties of time put it under the spacetime dimension, I am familiar with what a spatial dimension is, but do not understand what falls under the spacetime heading

you guys have been the most of help thx

[houserichichi]

When dealing with physics, most modern theories incorporate spacetime...in some string theories, for example, there are 9+1 dimensions (9 space, 1 time). In M-theory there are 10+1 dimensions (10 space, 1 time). The media says 10 and 11 dimensional for simplicity, but I much prefer the 9+1 and 10+1 so I know how many time dimensions (or if we're even talking about time at all).

The fact that we need to use a separate coordinate ("number") to describe something in spacetime is what makes it a "dimension". We need three coordinates, x, y, and z, to describe WHERE something is in space...and we say that the object in question is located at spatial coordinate (x,y,z). When dealing with spacetime we also need to consider WHEN it is, so we need another number, call it t, to describe the object in question. We say it's located at coordinate (x,y,z) at time t, and say it's located at spacetime coordinate (x,y,z,t)...four numbers, none of them depend on the other. If you wanted to graph something with four coordinates, you'd need four dimensions.

[rEaLiTy]

Ok, so time is a spacetime dimension and is it the +1 part of it? What all did string think these dimensions could be? u believe there is 10+1, so what are the ones you believe?

[houserichichi]

Yeah, it's much easier to write 4 dimensional spacetime (in my opinion) as 3+1 dimensions, where the "1" refers to one dimension of time.

The string theorists require that the 6 additional dimensions (all spatial) are curled up at every point in space into little "balls"...very little, in fact, so little we can't probe them yet. I don't know if I'll hop on the string theory bandwagon this early, but if it turns out to be accurate (validated through experiment) I'm all over it!

[rEaLiTy]

Im definitely not a band wagon jumper kind of guy anyway. I will research it more but string seems kinda weird.

I was just wondering which is the best book to get started on the dimension subject

Flatland
Planiverse
Surfing Through Hyperspace
Beyond the 3rd dimension
Elegant Universe?

[rEaLiTy]

And, one more question... if each dimension was created by intersecting with perpendicular lines, wouldnt it stand to reason that there would be a fifth dimension by more perpindicular lines to the 4d's, and coudlnt that go on forever

or what is wrong with that

[jinydu]

And, one more question... if each dimension was created by intersecting with perpendicular lines, wouldnt it stand to reason that there would be a fifth dimension by more perpindicular lines to the 4d's, and coudlnt that go on forever

or what is wrong with that

I never claimed that the fourth dimension does exist. The theory of four spatial dimensions does not attempt to prove that a fourth dimension exists; rather it attempts to derive conclusions that follow from the assumption that it exists.

And yes, you could postulate a fifth line that is perpendicular to all the others, then a 6th, etc. It could go on indefinitely. In fact, there's a mathematical theory of n-dimensional geometry.

[rEaLiTy]

I have seen the models shown of what the fourth dimension could look like, how ours is the cube and there was a few ways that the 4th dimension MIGHT look like. But, how would u turn a sphere into a 4d object, it does not have lines to intersect to.... strange

[houserichichi]

Well in physics the fourth dimension must exist, but that's in spacetime. Kaluza-Klein theory required a fifth dimension to work with (again, this is physics, so think spacetime).

As for setting up another perpendicular axis, it's mathematically sound to do so, but you won't learn much unless you have intentions to work in that space. As it turns out, for example, it's much easier to tie knots in higher dimensions as opposed to our three-dimensional world. If there was a fourth dimension (spatial...think perpendicular axes, not time) then we could tie many more kinds of knots that just can't be done in 3D. The subject of low-dimensional topology covers this kind of stuff nicely, but you'd be looking at quite a bit more math until you're educated enough to tackle those books.

As far as intro texts on "dimension" stuff, I started off with Flatland, but it's only done in words so you won't really get a rigorous introduction. Elegant Universe deals with things, but again there's no math. There's a book by Michio Kaku called Hyperspace you might like, but again there's lots of physics (like Elegant Universe).

If you're looking to really learn about four (or more) spatial dimensions you'll have to learn some real math - geometry, algebra, analysis, topology (pretty much in that order, with other things thrown in between for good measure). If you want to do it with physics you've got an even uglier path ahead of you - everything from the math side, plus a plethora of mathematical physics and more advanced math topics. You'll be able to get by on discussion boards with just words, but if you truly want to learn something you'll really need to learn the math eventually.

As for making a glome (the word people love to use for a 4-dimensional sphere) there are many places on the net that have pictures...just google the word and see what you come up with!

Oh yeah, and just for clarification - whenever I talk about four spatial dimensions, I'm talking mathematically, as Jinydu pointed out - there's no evidence to suspect four spatial dimensions in the "real world". In the math world, however, just about anything goes if you set it up properly.

[rEaLiTy]

Ok, so which path of study is more for proving the space time and which for proving spatial dimensions?
I'm sure I wont get to that high in physics for a couple of years, but still interested

[jinydu]

Spacetime - Physics
Spatial Dimensions - Mathematics

Actually, you can learn about both in high school. My Physics course in high school did have a section on relativity. And there are some basic concepts and equations with 4D geometry that require nothing more than possibly middle school math to understand (ex. 4D volume of a tesseract).

[houserichichi]

Yeah, like Jinydu said, my high school physics class touched on relativity too. Anyone with basic calculus can get by most of the math of introductory special relativity (spacetime stuff), and actually even quite a bit of it can be learned with basic high school algebra. Take a look at some popular books on the subject to get a better feeling of things though - obviously those written without equations will be more accessible than those with if you're still in high school. Don't expect to study general relativity for a long time though, there's still a lot of math to go before you're prepared to face it.

As for four-dimensional geometry, I'd recommend scouring the net, as I can't think of any decent books on the subject (it's honestly not that interesting other than for thought experiments, until you get higher up the math mountain). Look up 4D geometry, shapes, spaces, properties and things like that. Take a look around this site (not just the discussion board), as alkaline put a lot of effort into it. Don't take everything at face value though, ask questions because on the net you're bound to find mistakes and learn incorrect arguments and not know it.

[jinydu]

Actually, my high school course did touch on General Relativity, but alas, we were taught only one equation.

(Change in f)/f = g*h/(c^2)

I guess part of the reason is that the teacher was required to assume that we hadn't taken any calculus. That's probably why, at the very beginning of the course, we had to learn the equations of motion one-by-one;

v = u + at

s = ut + (1/2)at^2

v^2 = u^2 + 2as

When those equations just appear like that, they seem like disconnected facts that come out of nowhere. But after just a few weeks learning calculus, it becomes possible to derive all those equations, and many more, from a simple and elegant law:

a(t) = F(t) / m

I'm getting way off track, so I guess my point is: Study Calculus!

[houserichichi]

This is a rough road map by Max Tegmark of the University of Pennsylvania of the math needed to tackle both general relativity and quantum field theory. It's broken down into abstract concepts so don't go looking for "algebra" or "calculus" anywhere, as those are specific versions of abstract concepts.

Anyways, hope it sets people on the right track.

[jinydu]

Hmm, that seems to be the logical order, but I really don't think its the order in which people learn.

After all, preschoolers are taught natural numbers. But logic, set theory and group theory are considered advanced topics that aren't taught until well into university.

[houserichichi]

Yeah I'd agree with you that preschoolers are taught what natural numbers are, but as I'm sure you're aware, they're just a special case of abstract structures. I think it makes life much easier learning the special cases first and then abstracting our ideas which is why we're taught in that order - and I suppose for those who have no desire to learn higher math, the basic operations involving at most the reals would suffice.

Now from the diagram I would assume that most folks are up around R^n. From there it looks like general relativity is only a few steps away, but I think it should be pointed out that those are two hefty strides and should be taken with great care. The perks of sites like this is that as one studies them further they have the opportunity to ask their peers for help, even when not situation within an academic institution.

Oh the joys of the internet, eh?

[RQ]

Spacetime dimensions are the dimensions in this universe, or a designated one, which in the common sense is this one. The other 7 dimensions you are referring to are both spatial and space-time, they are just curled up and not extended spatial dimensions like the other 3 we know. The theory is the universe broke down in its early state during the Big Bang into 7 and 4 dimensions. The 4 extended infinitely (in theory, yet not in practice as the noninfinite universe scale model shows) while the other 7 curled up into strings, I think.

String theory is basically almost complete into calculating all of these 11 dimensions which would combine the 4 forces of nature, and quantum physics with general relativity. There are "infinities" which have to be mathematically eliminated in string theory and in the elegant universe they said that most have been eliminated but there are still some left and that's what they're covering.

I wish I knew the math tho

[jinydu]

Yeah I'd agree with you that preschoolers are taught what natural numbers are, but as I'm sure you're aware, they're just a special case of abstract structures. I think it makes life much easier learning the special cases first and then abstracting our ideas which is why we're taught in that order - and I suppose for those who have no desire to learn higher math, the basic operations involving at most the reals would suffice.

Now from the diagram I would assume that most folks are up around R^n. From there it looks like general relativity is only a few steps away, but I think it should be pointed out that those are two hefty strides and should be taken with great care. The perks of sites like this is that as one studies them further they have the opportunity to ask their peers for help, even when not situation within an academic institution.

Oh the joys of the internet, eh?

What exactly do you mean by R^n (as compared to just real numbers)?

[houserichichi]

Well by R^n I'm referring to n copies of the real numbers. Cartesian product...just generalizing the concept of real number operations to higher dimensions. That is, instead of, say a+b we now deal with (a_1,a_2,...,a_n) + (b_1,b_2,...,b_n). The addition for R^n is just a generalized version as that of R.

Also, in R^n and C^n we deal with vectors in n-dimensional space (hence the branch from vector spaces)...though I'm not sure how many folks took vector space theory in high school. I believe we briefly talked about it but never studied.

But at least by high school everyone should have a general idea of what at least R^3 is.