Dimensionality of energy and mass

[OneSpace]

Mass is 3 dimensional and energy i would think is 1 dimensional. I think this because energy is not an object as in 3D and it does not have a spatial area as in 2D but it has a momentum due to its spin even a rest although you may correct me on this.

 

You did ask if there are any competing ideas, so if i may?

Energy and mass are the same thing (e=mc2) so if all the mass in the universe were converted to energy would we have a 1D universe?

So could it be that the origin of mass is a 1D thing?

 

I believe the dimensions are said to be arbitrary and one cannot exist without the other but i have yet to find a satisfactory reason for this beleif and this mass energy conversion just seems to reinforce the idea that dimensions are built one at a time from lesser dimensions.

 

From wiki:

In an atom, electrons in motion around the nucleus possess orbital angular momentum in addition to their spin, while the nucleus itself possesses angular momentum due to its nuclear spin.[65]

 

How many dimensions does an electron have? is it 2D due to it's own spin and would it be 1D without spin?

 

I am studing and trying to find my own answers but there is little discussion in relation to the dimensions of things and how they interact with one another. I wish i could be more specific but fear this would be seen as hijacking the thread.

[Klaynos]

Why is energy 1D, how could that possibly work?

[swansont]

I am studing and trying to find my own answers but there is little discussion in relation to the dimensions of things and how they interact with one another. I wish i could be more specific but fear this would be seen as hijacking the thread.

 

No problem — new thread started.

[ajb]

I wonder if you are mixing the ideas of a particle (0D) and it's phase-space? (or something similar like configuration space)

 

Look up phase-spaces, and in particular how to do non-autonomous mechanics in double extended phase-space. In this set up energy (Hamiltonian) becomes another coordinate "dual" to time. So we have a space with local coordinates {q,p,t,-H} (minus H for a reason, but I forget). You can then formulate geometric mechanics on this space via symplectic geometry.

 

(For those that know, contact geometry (extended phase-space) can also be used for non-autonomous mechanics, here we have the local coordinates {q,p,t} which is of odd dimensions. I rather use double extended, as we have a symplectic structure.)

 

 

This is the closest thing I can think of to what you have been trying to say.

[OneSpace]

Thanks ajb i took that on board.

Here is a phrase from wiki on phase space that helped me understand:

 

For simple systems, such as a single particle moving in one dimension for example....

 

1.

So what they're saying here is a particle, a 3D oject, is moving one dimensionaly.i.e. along a single line of momentum?

 

This would explain why everybody has been saying that 3D can move/exist in all dimensions. I didn't get it until now but i think i see how the thought process works.

 

I have another way of thinking about it for your consideration:

 

2.

Time moves along a single line of momentum in one dimension creating that one dimension. 2D is created when time under-goes a continuious change (spin, angular momentum) of direction resulting in the formation of 2D space.

 

This idea seems to be given a very poor reception and i don't understand why. I look at the two ways of thinking and see big holes in the thought process of the first.

 

To explain,

The only thing that is 1D is time, space 2D and matter 3D. I think everything (1D, 2D, 3D) moves in 1D time, second by second. I don't see anything wrong with saying a 3D object can move in one dimension, because it really does.

Every higher dimension moves in the ones below.

Everything that is 3D(matter) moves in 2D(space) and 1D(Time) for instance.

And 2D(space) moves in 1D(time) to, higher moving in the lower.

The problem with the thought process of the first is the question of whether or not dimensions are arbitrary.

Can lower dimensions move in higher ones? If they can then dimensions are arbitrary, if they can't then dimensions are not arbitrary.

Does the lower 2D(space) move in the higher 3D(matter) or is it only ever the other way around, the higher 3D(matter) moves in the lower 2D(space)?

I would say the later, they are not arbitrary.

[ajb]

A particle is by definition 0D.

 

Mechanics is really the study of paths in some configuration/phase/or other space. These paths are parametrised (usually, but not always) by [math]\tau[/math] which sometimes, but not always has the interpretation as time.

 

To me more concrete, consider standard (conservative) Hamiltonian mechanics with phase space [math]T^{*}M[/math] which has natural local coordinates [math]\{q^{a}, p_{a} \}[/math].

 

A curve/path [math]\gamma[/math] is a map from [math]\mathbb{R}[/math] to [math]T^{*}M[/math]. If we give [math]\mathbb{R}[/math] the local coordinate [math]\{ \tau \}[/math] then a path is described (locally at least) by

 

[math]\gamma : \mathbb{R} \rightarrow T^{*}M[/math]

[math] \tau \mapsto \{q^{a}(\tau), p_{a}(\tau) \}[/math]

 

This path is then interpreted as the trajectory of a particle in phase-space. The parameter [math]\tau[/math] is interpreted as time. I don't think we have the machinery need to continue yet; we need to understand vector fields, differential forms, Lie derivatives...

 

What I will say is that in relativity a similar thing happens. The difference here is that [math]\tau[/math] can be interpreted as the proper time for a massive particle only. For massless particles it is "just" some parameter.

 

To me, when doing mechanics anyway time is just a parameter that describes curves in some space. The physical interpretation (if there is a meaningful one) comes later.

[insane_alien]

Onespace, physics and mathematics have a very precise definition of a dimension. it has been used for hundreds of years. thousands actually.

 

what you are trying to do is redefine 'dimension' to mean something totally different. In science, you just can't do this as it creates confusion. if you want to describe something different you use a new or at least different word.

 

i'm not sure how you get a line of momentum. momentum is a vector. it is a 3 vector to be precise it has a magnitude in all three spatial dimensions(x,y,z). this magnitude might be zero in any particular dimension.

 

also, space cannot be 2d. to define a point in space i need at least 3 coordinates(4 if it is moving wrt to the coordinate system and i want to mark where it will be at a particular time.) this means there are 4 dimensions. now, 4 does not equal two. so space cannot be 2d

 

i don't know how matter could possibly be a dimension unto itself. it makes no sense at all with the definition of dimension in a scientific context.

[Royston]

i'm not sure how you get a line of momentum. momentum is a vector. it is a 3 vector to be precise it has a magnitude in all three spatial dimensions(x,y,z). this magnitude might be zero in any particular dimension.

 

Not meaning to be pedantic, but it depends on the situation i.e momentum isn't confined to solely 3 dimensions, there are plenty of problems that can be solved in two dimensions, it's purely based on the information that's required for a given problem.

 

I think what Onespace is overlooking, is exactly that though, that extra dimensions are redundant depending on the application, this doesn't mean they don't exist, but reading through the other thread there's a mix of Newtonian mechanics, relativity and QM, where if you start comparing the use of dimensions without understanding the application and what can be discarded, you'll run into pitfalls.

 

For example, I'm not going to use a (x,y,z) co-ordinate system for a linear collision if I can express it in two dimensions. So the dimensions I'll be using will be the parameters that I need to solve the problem, that could be having time as heading in the x direction and acceleration in the y direction, that doesn't mean time is 1d and distance is 2d, it's just pointless having a 4 vector space for predicting some basic motion problem. So I can discard extra dimensions, and label the ones I do have to express the motion of the particle.

 

So you can't state there's a discrepancy with the use of dimensions, if the application of those dimensions are completely different. Hope that makes sense.

[OneSpace]

If a particle is defined as 0D and not as a 3D object then i am not only on the wrong page but in the wrong book.

 

A 1 dimensional thing to me is something that can only move in a straight line along a single axis as represented on a 3D graph. If it stops it is 0D and is represented by a point.

A 2 dimensional thing to me is something that can be shown on a flat sheet of LxB, without any depth. It can be shown on a graph using two axes.

A 3 dimensional thing to me is something that can be shown using three axes on a graph giving the thing LxBxW.

 

I thought this was a pretty standard way to think of dimensions.

I am a 3D object for instance, space is 2D and time 1D.

You can not graph 4D without using imagination.

 

I don't think i can discuss dimensions any other way, sorry.

 

Edit add>

I looked but could not find the post but i have read somewhere here that a point in space is described using the x and y axes only, the z axis (depth)being time.

I am not presenting this as a scientific principle it is just what i read.

[ajb]

1d is a path on a space. It is not necessarily "straight". See my other post. This is the correct way to describe a a "particle moves". (see also world-line)

 

Two dimensional "objects" can be locally represented in a "graph" as you put it. Not always can you describe the whole object in one go in one graph.

 

Same holds for 3d, or any d.

 

(manifolds can always be seen as subspaces of some large dimensional flat Euclidean space. However, we usually like to discuss them in their own right and think about intrinsic properties of them)

 

Space, our space is 3d right? You can walk right/left, forwards/backwards and then you can go up/down (use stairs or a lift for that one!).

 

Space-time is then considered as 4d. But you should not really confuse the extra dimension with the time an actual observer measures. It is a little more involved than that.

[thedarkshade]

We ,as matter, belong to a 4d universe (ignoring ST for a second), and as energy is a very fundamental characteristic of matter, than I see no reason why would that be 4d too! I mean, if energy is considered as 1d then I get a picture like only a very very tiny fragment of the universe might be considered as energy.

[OneSpace]

ajb

I would agree the path need not be straight,

Dark

I would like to ignor string theory altogether but that is just me.

 

The whole hypothisis is that of a linear universe of only 1 dimension.

The other dimensions are built from this 1 dimensional thing.

 

I don't doubt we live in the classical three spatial dimensions, the ones i defined anyway, but speculate they are all built from the same 1D QM wave.

 

What I see is being called the fourth dimension here is time but again the speculation is that this 1D QM wave is time. It appears as a 2nd dimension>TIME in 1D, it appears as a 3rd dimension>TIME taken to travel along the z axis i.e.depth in 2D space, and appears as a 4th dimension> TIME to 3D objects, what we experience.

 

One wave appearing as everything in the universe, a new(afaik) and different view of the classic world but it now being the same as the quantum world. It does not change any of the evidence gathered about these worlds and in my opinion is a lot better explaination.

 

It might be just me but i beleive that the universe, like evolution started from the simplest of simple things and got more complicated and complex with time.