Can you make a concept of the 5th dimension?

[R A J A]

We know that the 1st dimension is length (a line), the 2nd dimension is length + width (a polygon), the 3rd dimension is length + width + hieght (a cube), and the fourth dimension is length + width + hienght + time (a moving cube). Does anyone know what is the 5th dimension? Is it heat, colour, chemical properties or something like that? This is a serious matter to discuss.

[Schrödinger's hat]

I suppose you could call any degree of freedom a dimension, but this generally one is talking about something measured in the same units as space (time and space are often both measured in metres or seconds -- or natural units -- by relativists).

 

If you're talking about the fifth (and higher) dimension as it is used by string theorists, then I only have the vaguest idea of what it means for one dimension to be smaller than the others. As I understand it, only one of the dimensions they refer to is time-like, the rest are all space-like.

Going from three spatial dimensions to four is just like going to three from two.

Take the example of making a cube.

You get one square, lay it out in your two dimensions (x and y)

Place another square on each edge

fold the net you have made at 90 degrees in a direction that is not x or y -- call it z -- at each join.

then place a square on top.

 

If you had access to four dimensions you could make a hyper-cube the same way.

Get a cube

put another cube on each face (6 more cubes)

fold the net you have made 90 degrees in a direction that is not x, y, or z at each join

place another cube in the gap

 

One other way to build intuition is to look at projections of 4d

http://www.urticator.net/maze/

http://sourceforge.net/projects/dtris/

 

If you have four spacial dimensions and time -- that makes five.

Apply the same process again to get six

etc etc

[Externet]

First why do you assume there is a fifth dimension ?

 

From your answer, what prevents then a sixth, seventh,... dimensions to exist ?

 

If someone wants to theorize, it could be as you say temperature, color, composition, location...

 

(Besides a music group from the seventies...)

[R A J A]

But I didn't answer my question, I only doubted whether the fifth dimension will be color, shape, or size. I only asked whether it can be.

[ajb]

The thread here maybe of interest.

[Realitycheck]

This may help:

 

http://www.superstringtheory.com/experm/exper5.html

 

All of the other dimensions are considered spatial in orientation.

 

Also, I found this other site which was a lot more comprehensive in that aspect.

 

http://www.pbs.org/wgbh/nova/physics/imagining-other-dimensions.html

Edited August 25, 2011 by Realitycheck

[finiter]

...Is it heat, colour, chemical properties or something like that?

Length, area, volume, mass, time, temperature, colour, charge, etc. are the physical properties exhibited by matter. Each can be regarded as a separate dimension of the object under reference. However, all of these can be expressed in terms of length, mass and time (L,M and T).

Space is L³. Space-time is L³T, what it should represent is the time varying space (volume), but whether it is used in the same sense or not is not clear. Something requiring L⁴, L⁵, etc. to represent it, does not refer to volume, it can refer to some arrangement in space. So terming the dimensions as 1st, 2nd, 3rd etc. is meaningless (in my opinion)

[khaled]

Lets say that you want to build a computational model for physics, that does not only represent objects, but also their atoms, down to the quarks and all of their properties,

 

You would need to model the universe as a (99+)-dimensional, as they're degrees of freedom to contain more realistic view

[Wilmot McCutchen]

If you were a Flatlander, the fourth dimension (height) would be ordinarily invisible, except as it leaves a footprint in Flatland. Flatlanders would know time, so the fourth dimension for them is height. Now take this a step further with existence in 3-D spacetime. The extra dimension would only be evident by its footprint in 3-D spacetime. Thanks to the recent advances in chaos theory and quarter-power scaling laws, now we can see such footprints.

[R A J A]

the fourth dimension is space-time. Height is the third dimension.

[TheLivingMartyr]

But wait, according to general relativity, one can represent gravity as a curvature of spacetime into another, inaccessible dimension. Obviously, the three spatial dimensions will need a fourth hyperspacial dimension to curve into, and the one temporal dimension will need a second hypertemporal dimension to bend into. So 4 dimensional spacetime, is situated in 6 dimensional hyperspacetime, into which it can curve and bend. Is this not one of the modern understandings of mass', energy's and velocity's affect on space and time?

[ajb]

But wait, according to general relativity, one can represent gravity as a curvature of spacetime into another, inaccessible dimension.

 

No, you do not need any extra dimensions to have the notion of curvature. It would be consistent with general relativity if 4-d space-time was embedded in a higher dimensional space, but it is certainty not required.

[Schrödinger's hat]

No, you do not need any extra dimensions to have the notion of curvature. It would be consistent with general relativity if 4-d space-time was embedded in a higher dimensional space, but it is certainty not required.

 

Is there any advantage to embedding in a higher dimension, other than slightly easing the cognitive burden?

[ajb]

Is there any advantage to embedding in a higher dimension, other than slightly easing the cognitive burden?

 

 

Probably not where general relativity is concerned, typically. There are several embedding theorems for Riemannian manifolds.

 

The Nash embedding theorem says that any Riemannian manifold can be isometrically embedded in some Euclidean space of sufficiently high dimension. If I recall the dimension of the Euclidean space is large as compared to the Riemannian manifold. I think this partially generalises and some Lorentzian manifolds can be embedded in higher dimensional Minkowski space-times. There are probably some technical conditions floating about. You will have to look that up.

 

One can weaken this. The Campbell-Magaarrd theorem says that any n-dimensional Riemannian manifold can be embedded in an (n+1) dimensional Ricci flat Riemannian manifold. This generalises to Lorentzian signature.

 

So in general relativity people embed 4-d space-times into 5-d Ricci flat space-times. Recall that Ricci flat space-times are vacuum solutions to the Einstein field equations. So non-vacuum solutions in 4-d can be analysed from the point of view of 5-d vacuum solutions. I am not sure what technical assumptions are used here, so I would not claim that all 4-d space-times can be understood this way. This too you would have to look up.

 

Now, neither of these theorems say any thing like "our Universe must be embedded in a higher dimensional space". It could be, and string theory suggests this maybe the case. From the point of view of classical general relativity their is no reason to introduce a 5-th (or higher) dimension, other than it could be a useful mathematical trick to analyse the 4-d physics.

Edited October 13, 2011 by ajb

[questionposter]

Is there any piece of data that suggests there "HAS" to be higher dimensions in order for an abject to be the way that it is? Like does a gluon really need to have 11 dimensions in order to keep atoms together? What suggests that?

[R A J A]

I got a new idea of the fifth dimension!

 

 

Lets see the fourth dimension as a line called space-timeline. Then the fifth dimension should be with branches or rays of space-timelines starting from the present pointing towards the future side of the fourth dimensional timeline. It practically means that the fourth dimension is the normal space-timeline in which the past, present and the future is already written or called in holy books as 'fate'. If anyone is living in the fourth dimension, it is sure that he will be in the definite place in the definite time in future. He can't do anything with his future, because it is fixed. The fifth dimensions which comes with branches or rays of space-timelines pointing towards the future side from the fourth dimensional space-timeline means that from the point of present time any object has infinite chances to be any where in anytime. I can explain this that if I am a robber and after a theft, when I am running to escape and a policeman shoots me with his gun, if I am in the fourth dimension, it is sure that I will be shot dead, but if I am in the fifth dimension, there are many chances that I may get shot dead, or I may dodge the bullet, or while shooting, the policeman may slip and fall down. So there are infinite chances for the future in the fifth dimension. The new space-timelines starting from the fifth dimension will always be towards the direction of future because a space-timeline representing the future is impossible to com to the direction of past!

Edited October 31, 2011 by R A J A

[superball]

We know that the 1st dimension is length (a line), the 2nd dimension is length + width (a polygon), the 3rd dimension is length + width + hieght (a cube), and the fourth dimension is length + width + hienght + time (a moving cube). Does anyone know what is the 5th dimension? Is it heat, colour, chemical properties or something like that? This is a serious matter to discuss.

 

I Had read something Maxwell described as adding another dimension, I think he called it the Z axis, in laymen terms everything can cast a shadow.

 

I don't know what the 5th dimension would look like, hypothetically gravity or some kind of spin energy, or a doughnut.. just make mine jelly.

 

Cheers.

Edited November 21, 2011 by superball

[Esis]

Raja

The 5th dimension is at bes speculation. The notion of time branches as i see it requires an infinite amount of time perception within the laws of math. Ex. Imagine a timeline perpendicular to ours. The time would pass from hologram to hologram experiencing every change possible at the hyperperceptual speed limit between two dilations of our forward time.

 

Think of an instance in 4 5 6 hyperspace. From all 6 angles time has a radial connection to the adjacent singularities or stems. We only recognize time as a line when there is even a higher measurement of length making time possible to be other curves peice wse funcs or scatter plots depending on how 4 5 6 are organized.

 

Theres where it becomes problematic. There are infinite possibilities but since hyperspace as 3 similar dimensions are infinite i must assume there is a different hierarchy. And thats only talking bout singularities or single snapshots holograms deviations whatever.

 

The fifth that you speak of time may exist on a higher level actually. Same concepts apply but it has to fit within its container plane. Which yes absolutely exist indefinitely. I beleive if we have positive dimensions we must have negative or fraction dimensions.

 

As you speak of moving positively along branches negative slopes are also existant. From any origin at any slope there is a mirror image in the opposite direction. It is this balancing of equation that allows the timeline to exist. As these lines form hyperspheres the balance there allows a singularity to exist.

 

In this model physics apply as always but using hyperdimensional algebra and calculus. A being perceiving our timeline in a negative direction would experience effect before cause as normal and balanced. Think again of a perpendicular timeline. There are infinite of them. Maybe we are moving backwards.