All the dimensions out there ????

[Alyoshya (nutjob)]

Ok, now first of all I never really had a clear or *satisfiable* definition or explanation for any of 12 or (13/18/........) Dimensions Out there.

 

So I took the time to get your help

 

Now is there any dimensions called *imaginary dimensions* the one in which ( the events occur with respect it your thaughts //the events occur as you imagine them )

 

How do you explain or prove the very existence of each dimensions that are out there.

 

Discus the basic concept of dimensions ie. What is a space dimension

 

What's a temporal dimension

 

How many dimensions do we exist in ( I aynt talking about the 3 dimensions ¤ I was referring to the space dimensions)

 

Is there a relation or link between the events that occur in each dimensions. ( Are the sequence of events of one dimension dependent on the sequence of event in other )

[SamBridge]

Dimensions are a way to identify a the position of something in any extension of a coordinate system. Temporal dimension means a 4th dimension that is orthogonal to all spacial dimensions in which spacial coordinates can vary in relation too, which is impossible to see visually, but still has real effects. A 5th dimension is orthogonal to all those, and a 6th is orthogonal to the previous 5 and ect. If you have the point (7,1,0,3,6,-4), it exists in 5 dimensions, 7 units along one spacial axis, 1 along the other, 0 along the third, 3 along the temporal axis and -4 on the axis that is orthogonal to all those. Even though we can't see extra dimensions directly, we can observe how matter moves in accordance to vectors that can only make sense if you give them 5D coordinates or 6D coordinates and use 5 dimensional distance formulas which are somewhat related to the Pythagorean theorem to explain that the movement of space at one point in time is based on how the 5 dimensional object travels to a coordinate along the 5th dimensional axis. You can sort of think of it parametrically. Otherwise the only ways to visualize higher dimensions is by adding more visual effects like color or using vector space.

Imaginary space is just how it sounds, only its normally used with real numbers as well to make complex space. Complex space arises from using Fourier transformations in 3 or more dimensional coordinates and also can be used in distinguishing imaginary components of vectors that travel along a different axis with quaternions. Physically, complex space doesn't mean much, it's basically just an "in between" dimension that can modulate between a set of complex numbers to distinct values like 1, -1, i and -i or j and -j or k and -k and ect. to allow someone to use the square root of a negative number over a wide range of different real components and angles to get accurate results.

Edited April 22, 2014 by SamBridge

[ajb]

Ok, now first of all I never really had a clear or *satisfiable* definition or explanation for any of 12 or (13/18/........) Dimensions Out there.

Why 10 or 11 dimensions are considered as a possibility is because superstring theory is only quantum mechanically consistent in 10 dimensions. 11 comes from the possibility that superstring theory and a supergravity theory arise as particular limits of an 11 d theory known as M-theory.

 

Other numbers of dimensions I don't think have such clear motivation.

 

How do you explain or prove the very existence of each dimensions that are out there.

You look for evidence that these extra dimensions exist. The two tests I am aware of, and there maybe more, are

 

i)look for missing energy in high energy particle collisions as these could signify gravitons carrying energy off into these extra dimensions.

 

ii) look for the energy scale at which micro black holes are created again in high energy particle collisions. The scale of quantum gravity can be lowered if we have extra dimensions.

 

Discus the basic concept of dimensions ie. What is a space dimension

Similar to what SamBridge has said, the number of dimensions of a (vector)space or indeed a manifold, is the number of numbers needed to describe a point in any coordinate system. This is independent of the specific coordinate system employed.

 

For example on [math]\mathbb{R}^{3}[/math] we need three numbers, (x,y,z) say.

 

 

What's a temporal dimension

This requires some knowledge of special relativity. Here we have what we call the Minkowski metric, it is just a way to define "distances" is space-time. So I take standard 3-d Euclidean space, bolt on another dimension and state that we now have a metric in 4-d of the form

 

[math]\eta_{\mu \nu} = \textnormal{Diag}(-1,1,1,1)[/math].

 

It is this minus sign that signals I have a temporal dimension. In some coordinate system adapted to this metric (ie. and inertial frame) I can pick rectangular coordinates (t, x,y,x). As an aside the symmetry group of special relativity are all possible transformations that preserve the Minkowski metric.

 

So topologically I just have [math]\mathbb{R}^{4}[/math] but with this weird way of defining a "distance". In particular I can have negative and zero distance between distinct points!

 

More generally I don't need the metric to be diagonal like that, but at any point I can always write it in this diagonal form. Extending this to higher dimensions is straight forward.

 

How many dimensions do we exist in ( I aynt talking about the 3 dimensions ¤ I was referring to the space dimensions)

To the best of our knowledge we seem to be living on 1+3 dimensions, that is one time three space. But other possibilities exist, as you know.

 

Is there a relation or link between the events that occur in each dimensions. ( Are the sequence of events of one dimension dependent on the sequence of event in other )

Assuming that the metric in higher dimensions is like the one we have in our 1+3 Universe then there will still be standard causality. That is information can only move at most as fast as the speed of light.

[Fred Champion]

The commonly recognized three spatial "dimensions" are imaginary constructs convenient for a particular geometry (the geometry of three planes intersecting at equal angles). One can form consistent geometries with 4, 5, 6, and 7 spatial "dimensions" as well. The term "dimension" in some models may not refer exclusively to spatial constructs. Qualities of objects may be called dimensions. For example, the color of one's hair (especially if it is green or hot pink) may be an expression of identity.

[SamBridge]

The commonly recognized three spatial "dimensions" are imaginary constructs convenient for a particular geometry (the geometry of three planes intersecting at equal angles). One can form consistent geometries with 4, 5, 6, and 7 spatial "dimensions" as well. The term "dimension" in some models may not refer exclusively to spatial constructs. Qualities of objects may be called dimensions. For example, the color of one's hair (especially if it is green or hot pink) may be an expression of identity.

Yeah, but, I bet you can't name a single accredited model in physics that uses someone's hair as a dimension.

[MigL]

A dimension allows us to relate two different events.

As an example Alaska and Siberia can be related events in space-time, as the two events were connected by a land bridge of a certain length about 15000 yrs ago.

Not a physical model, but Fred is absolutely right.