Higher dimensions than 4?

[Oracle.Of.All]

is it possible to have higher dimensions than 4 such as 5th, 6th and maybe even greater??

[houserichichi]

It most certainly is.

[Oracle.Of.All]

Do humans have any idea how this would work??

Are the possibbilities of higher dimensions infinite??

[houserichichi]

Well it's kind of like asking how does the third dimension work with respect to the second...all it is is an extension in another direction. There is no reason (as far as I know, anyway) why the universe can't be immersed in an infinite dimensional hyperspace (which means we're confined to 3D because we can't leave the universe).

In higher math we deal with infinite dimensional spaces all the time...they tend to be interesting in certain cases.

[wendy]

i work with dimensions as high as six directly (ie without any sort of aid), and to dimensions as high as 124 by calculations.

there are a number of interesting dimensions out there, though.

W

[jinydu]

My new linear algebra textbook often talks about n dimensions, where n is any positive integer. That is, it draws conclusions that are true in any (positive integer) number of dimensions.

[eagle512]

String theory calls for 10, 11, or 26 dimensions!

A multiplicity of dimensions is definetely a possibility. However most of the these dimension are tucked so discretely within the apparent one, that they go undetected and are possible undetectable with current technology. Brain Greene (leading string theorist) discusses the mathematical requisite that there must be more dimensions that those inherently apparent.

[wendy]

Higher dimensions have been played with.

Lie theory points to sphere-packings in 248 dimensions, and higher still.

In practice, i have used dimensions as high as 124.

The phase diagrams in gas-laws use 3D for each particle in the gas, that is if there are 1,728,000 particles, it uses 5,184,000 dimensions. Pretty silly, really, since most lines would be at right angles to each other.

W

[jinydu]

There needs to be a clarification here.

Are you asking whether it is possible to have spaces with an arbitrarily large number of dimensions on paper. If so, then the answer is most certainly yes.

But if you are asking the number of dimensions this physical universe has; well that is open to question. But for everyday purposes, there are three spatial dimensions.

[bo198214]

There needs to be a clarification here.

Indeed. Regardless what oracle really wanted to know, everyone gave confident answers.

But if you are asking the number of dimensions this physical universe has; well that is open to question. But for everyday purposes, there are three spatial dimensions.

Why is this unclear? For me the number of spatial dimensions is how many bars I can put together each perpendicular to each other. And that is 3 in the space I live. It does not touch the topology or metric of the space.

[quickfur]

[...]

But if you are asking the number of dimensions this physical universe has; well that is open to question. But for everyday purposes, there are three spatial dimensions.

Why is this unclear? For me the number of spatial dimensions is how many bars I can put together each perpendicular to each other. And that is 3 in the space I live. It does not touch the topology or metric of the space.

The problem lies in the fact that at our macroscopic scale, only 3 dimensions can be observed. In other words, your bars are too big to fit in the other dimensions, if there are any, so you can only ever have 3 perpendicular to each other. To reach into the other dimensions, you'd need to use sufficiently small bars. Who knows, maybe if you were as small as a proton, you might be able to put 4, 5, or more bars perpendicular to each other.

For an analogy, just think of you were using 10-foot poles to measure the dimension of a 2-feet-wide narrow alley. You'd only be able to have two such poles perpendicular to each other, but that doesn't necessarily mean the width of the alley is zero (i.e. there are only two dimensions in the alley), just that the third dimension is too small for your chosen metric to measure. If you used 1-foot rulers to make your measurement instead, you'd find that you can easily have 3 perpendicular rulers, and therefore conclude that there are 3 dimensions possible in the alley.

[bo198214]

Ok, the question is of course how one would define dimension for the microscopic level (because we have no bars there).
I always hear of physical theories using so and so much dimensions, so I ask the experts, are these spatial dimensions?
As far as I know the Schrödinger-Equation only uses 3 spatial dimensions.

The question then is, what do I mean by spatial dimension.
For example if I take ct for a time t the unit is also meter, but I dont regard time as a spatial dimension.
I cannot give a thourough definition that covers every case but at least I would expect from spatial dimensions that they all behave in the same way. For example a particle can be at the same location at different times, but it cannot be at different locations at the same time; so there is a difference between space and time coordinates. And I would suspect that the coordinates in those multidimensional theories mostly behave in different ways.

[jinydu]

The Schrodinger Equation can work in any number of (spatial) dimensions because the Laplacian exists in any number of dimensions. However, for real physical systems (such as the hydrogen atom), the 3D version gives the correct predictions.

[bo198214]

A 4d Schrödinger-equation does not give wrong predictions, but is not applicable to our world.

[houserichichi]

String theory calls for 10, 11, or 26 dimensions!

Very simple correction...string theories require 10 or 26 dimensions. M theory, which is not a (super)string theory, requires 11 (10 space, 1 time).

Carry on :wink:

[jinydu]

A 4d Schrödinger-equation does not give wrong predictions, but is not applicable to our world.

I guess you could put it that way. Since we have good reason to believe that no 4D systems actually exist in our physical universe, the 4D Schrodinger equation doesn't make any useful predictions. Nevertheless, it is still an interesting mathematical problem.

Hopefully, you understand that the Schrodinger equation can be formulated in any number of dimensions:

i h-bar partial(psi)/partial(t) = [-((h-bar)^2)/2m Laplacian(psi)] + V psi

If you use Cartesian coordinates, the Laplacian is easily generalized to n dimensions. Letting (x_1, x_2, ... x_n) be the Cartesian coordinates, the Laplacian is:

(partial^2)/(partial (x_1)^2) + (partial^2)/(partial (x_2)^2) + (partial^2)/(partial (x_3)^2) + ... + (partial^2)/(partial (x_n)^2)

I hope you also understand that the mathematical study of higher dimensions is not some vague, idle speculation, but a precise a rigorous discipline.

[bo198214]

Nevertheless, it is still an interesting mathematical problem.
Hopefully, you understand that the Schrodinger equation can be formulated in any number of dimensions:
...
I hope you also understand that the mathematical study of higher dimensions is not some vague, idle speculation, but a precise a rigorous discipline.

Jinydu, I really dont know, why you think its necessary to state those off-topic lines. I wrote a 4D game, computed 4D planetary orbits and proposed a 4D magnetism solution, so why the hell are you assuming, that I dont understand or doubt about exactness of higher dimensions???

[thigle]

that's a trait characteristic of jin's character. he's so full of his own (limited) understanding it seems there ain't left any for other people.

sorry jin, just kidding :wink: , i really do appreciate your massive expressivity on these superb forums.

and btw, you wrote (and i believe you mistyped "me" for "we"):
"we have good reason to believe that no 4D systems actually exist in our physical universe"

actually, our universe is not a 'physical universe' per se or exclusively. 'physical' is but an attribute. so it might be that in the imaginary "physical universe" (the schene that you are projecting over the actual universe thus reducing it to its physical aspects), 4d systems are non-existent. (even though even here i actually disagree). however, in the actuality of existence (of universe), 4d systems are ubiquitous. (btw, you embody some)

[jinydu]

Jinydu, I really dont know, why you think its necessary to state those off-topic lines. I wrote a 4D game, computed 4D planetary orbits and proposed a 4D magnetism solution, so why the hell are you assuming, that I dont understand or doubt about exactness of higher dimensions???

I am sorry if you found what I wrote offensive.

[Nick]

It makes sense that their would be multiple dimensions, more than four, but would it be possible to visualize them?

We have a two-dimensional retina, which means that we can see every point on a two-dimensional plane. And, with a two-dimensional retina, we are capable of understanding a three dimensional plane, even though we cannot see every point on it.

It's easy to understand four dimensions because four dimensional beings are not seeing all four dimensions of the object they look at; they can only see three dimensions because of their three dimensional retina. Since we can make 3D projections of four dimensional objects, even though we cannot see all three sides like they can, we are capable of understanding them.

I don't think we would be able to visualize any dimension greater than 4D.

[moonlord]

I believe the possibilities of the Imagination are infinite. However, it is certainly a mind-bending task to visualise 5D or higher. Some people can, though. Ask PWrong, wendy or the other senior members of this thread :p.

[pat]

The Monster Group is a group of rotations in 196883-dimensional space.

I'm reminded of an old joke:

Two physicists who have just attended a lecture on superstrings are talking about imagining high-dimension systems. The first one says, "Four dimensions doesn't give me any problem, but I'm shaky with five, and I can't really visualize six-dimensional space at all."

The second one admits that he can't go past 6 either.

They stop a passing mathematician, and ask him if he can visualize 9-dimensional space (the subject of the lecture). "Sure," he says, "no problem."

The physiscists are astonished. "How!"

"I just imagine n-dimensional space and set n=9."

[wendy]

In hyperbolic space, it's more a matter of curvature than fabric, since the thing is essentially exponential. One can make a different curvature so that one goes as fast as the next.

But really, i am pretty sure that setting n to 9 or 15 or 18 is quite adequate, once once passes 8. Newer strange things happen that far out. I shudder to think.

The phase-space of five-dimensional rotation is something like a 9-fabric sprawled over 11 dimensions. I still have not grasped the arrow-space as yet (which is an 8-fabric in 10 dimensions), so it's more to go there.

Well, don't know.

W

[Hugh]

We have a two-dimensional retina, which means that we can see every point on a two-dimensional plane. And, with a two-dimensional retina, we are capable of understanding a three dimensional plane, even though we cannot see every point on it.

It's easy to understand four dimensions because four dimensional beings are not seeing all four dimensions of the object they look at; they can only see three dimensions because of their three dimensional retina. Since we can make 3D projections of four dimensional objects, even though we cannot see all three sides like they can, we are capable of understanding them.

We have a 3d spatial awareness sense of what's all around us. Would that 3d mental image be comparable to what a 4d being "sees"?

[Nick]

Well, yea. It follows the pattern:
A two-dimensional being sees every point on a line at once.
A three-dimensional being sees every point on a plane at once.

Therefore:

A four-dimensional being sees every point of a cube at once.