Each dimension is perpendicular at all another

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The discussion centers on the nature of dimensions in geometry and their representation in both mathematical and physical contexts. It highlights that while dimensions can be graphically represented in three dimensions, higher dimensions do not necessarily adhere to the principle of perpendicularity, as defined by linear algebra. The conversation also touches on the difficulty of visualizing dimensions beyond three, suggesting that dimensions are abstract mathematical concepts rather than physical realities. Additionally, it proposes that the geometry of space may be dynamic, evolving from lower to higher dimensions, and emphasizes the importance of understanding these concepts through linear algebra. Ultimately, the complexity of higher dimensions remains a challenge for visualization and comprehension.
  • #31
Antonio Lao said:
You are right about frugality of nature. So knowing that nature will never allow itself to waste space, energy and matter, that is why nature prefers to work only in 1D of space and 1D of time, it conserved energy between potential and kinetic aspect, and practically all fundamental particles are points and also massless. The graviton, the photon, the gluon (although, I am doubting its existence), the neutrino (?) are all massless.

The graviton is responsible for the fundamental gravity force.
The photon is responsible for the fundamental electromagnetic force.
The gluon is responsible for the fundamental strong nulcear force.
The neutrino (a fermion), at one time were thought to be responsible for the fundamental weak nuclear force until the discovery of W's and Z's bosons which broke the massless symmetry by acquiring mass through the Higgs mechanism. Although broken symmetry works perfectly for the electroweak force, it still did not resolve the problem with dimension until the advent of string theory.

I have an impression, that you want to load me with all terms from the physical dictionary irrespective of a theme of discussion. It corresponds to the Russian expression “ to powder a brain ” (пудрить мозги).
Believe, please, this is I do not need in.
Please, think even just for a minute before a post sending.


Michael
 
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  • #32
Michael F. Dmitriyev said:
...load me with all terms from the physical dictionary irrespective of a theme of discussion

The point I am trying to make is that concept of mass can be built using 1D space and 1D time. There are too many zero mass particles in physics that which each origin can be related to the concept of dimension and only possible if we clarify the physical meaning of dimension.
 
  • #33
Antonio Lao said:
The point I am trying to make is that concept of mass can be built using 1D space and 1D time. There are too many zero mass particles in physics that which each origin can be related to the concept of dimension and only possible if we clarify the physical meaning of dimension.
Ok.
What your point is based on?
What is a mass in your opinion?
 
  • #34
Michael F. Dmitriyev said:
What is a mass in your opinion?

In a nutshell, mass is the local motion of 1D space and time. This motion formed two distinct topological geometries. Let's just say two distinct Hopf rings, H+ and H-.

When the H+ and H- interact, the result is mass. The salient point is that only if they interact, for they can co-exist without interaction. When they co-exist, this state is the vacuum state. When they interact in odd numbers, the outcomes are the fermions. When they interact in even numbers, the outcomes are the bosons. The more they interact, the more is the value of their mass.
 
  • #35
Moe said:
Now you have lost me.

We exist in all dimensions. That doesn't mean we can understand them. And in mathematics, you can have as many dimensions as you like. There is no need for a physical representation of those dimensions. For example, it might be feasible to express certain characteristics as a multi-dimensional vector. In Relativity, you use 4-D vectors, one component is time, the other three are speeds, or one is energy, the other three are linear momenta. Stop trying to visualize it - it won't work.

Now, if you want to, you can view time as the fourth dimension. In that case you could maybe visualize a 4-D cube by looking at a video of a 3-D cube that is being deformed. But what would a 5-D cube look like then? So let me rephrase my original sentence:
Our mind works in three spatial dimensions only.

"Speak for yourself John.", AKA Moe.
 
  • #36
Hi Michael!

I am not sure what exactly you are trying to do.

Do you want to theorize what n-dimensional objects would behave or look like to our senses?

I don't know what good this would do.

We are only able to perceive three spatial dimensions (plus time of course, but since we are talking objects and I find it hard to add time-character to a cube, I'll leave it with 3D-space...)

But that doesn't mean, our senses leave us with any valid information about the "real" dimensionality of our universe.

It could be 11, it could be 1 or 2 "projected" to a 4D-spacetime - I think we don't really know yet (maybe just I don't know...)

It is simple but frustrating: we can only see, what we are able to see. We don't have any possibility to imagine, what something would look like.
We are not even able to imagine, how UV looks to insect-eyes, and that's just a few bits of wavelength up our capabilites.

So how can we try to visualize additional dimensions ?

I may be a little pragmatic here, but I really like to know what your idea is - and what it's good for...
 
  • #37
Muddler said:
Hi Michael!

I am not sure what exactly you are trying to do.

Do you want to theorize what n-dimensional objects would behave or look like to our senses?

I don't know what good this would do.

We are only able to perceive three spatial dimensions (plus time of course, but since we are talking objects and I find it hard to add time-character to a cube, I'll leave it with 3D-space...)

But that doesn't mean, our senses leave us with any valid information about the "real" dimensionality of our universe.

It could be 11, it could be 1 or 2 "projected" to a 4D-spacetime - I think we don't really know yet (maybe just I don't know...)

It is simple but frustrating: we can only see, what we are able to see. We don't have any possibility to imagine, what something would look like.
We are not even able to imagine, how UV looks to insect-eyes, and that's just a few bits of wavelength up our capabilites.

So how can we try to visualize additional dimensions ?

I may be a little pragmatic here, but I really like to know what your idea is - and what it's good for...
Hi Muddler,
I hope you have read this thread from a beginning.
I hope also you are agree the geometry of spacetime is not the static.
 
  • #38
Michael F. Dmitriyev said:
Hi Muddler,
I hope you have read this thread from a beginning.
I hope also you are agree the geometry of spacetime is not the static.

Of course I agree that the geometry of spacetime is dynamic.
Still I am not understanding what you are trying to accomplish (and I really like to! Believe me! I like new ideas, especially if they are of such an imaginary power like yours!)

I have been wondering about the visualization of mulitdimensionality myself and I think I understand your image of the sphere as being the manifestation of 4+ dimensions.
Im just not sure about your idea of rotation being the adequate medium of additional dimensions.

If you have a 3D-object and you like to rotate it, you still have to describe the rotation in 3 dimensions or axis - that doesn't give it an additional dimension.

Sure, rotation is an operation, but I think it is essentially different from the process that creates a cube out of a square (by only rotating a square you don't get a cube, you have to offset and assemble it)

I agree that our "reality" is more like a movie than a picture, but you have to admit that a movie is made of single pictures. And even if our "pictures" are so infinitely small that we will never be able to catch them for sure, our understanding of physics is based on "single pictures" (an if it's just because you have to start calculating somewhere...)

I don't think a fundamental understanding of dynamic dimensionality can be reached without figuring out what distinct static states would look like.

And even these static multidimensional forms are something my mind is not able to visualize.

But please: I don't mean to offend you. I really like to understand your thoughts - but so far I just don't get it...
 
  • #39
Muddler,

I did not want to repeat becoming banal philosophical sayings about variability of our world and a constant movement in it. This is an axiom and I have just applied it to geometry.
It was necessary to find conformity of real dynamic objects to the static objects of geometry. I think it was done by me. In the dynamic geometry of spacetime each dimension is the some action (force). For example, the line is an propagating point, the plane is an propagating line, etc. It means that 1D makes active 0D, 2D makes active 1D i.e. the following dimension is the time for previous. By analogy 4D is the time for 3D in the establishment physics. The principle of mutual perpendicularity of dimensions in a static geometry is the angular momentum in the dynamics . It results in rotation of objects. This a cause of the static square be transformed to a rotating circle ,and the static cube be transformed to a rotating sphere. I think, an attentive look at the nature will find enough acknowledgment of my correctness.

Regards.
Michael
 
  • #40
As this a thread has been moved here from General Physics for a mention of the supreme spheres, then it is a good occasion to discuss this question here.
I suggest to make it from a such position:
higher dimension - more complex structure and movement.
So, what the supreme spheres (more then 4-D) are?
 
  • #41
Michael F. Dmitriyev said:
As this a thread has been moved here from General Physics for a mention of the supreme spheres, then it is a good occasion to discuss this question here.
I suggest to make it from a such position:
higher dimension - more complex structure and movement.
So, what the supreme spheres (more then 4-D) are?

Gravitational Anomalies?

I can follow your thinking:) Tell me if supreme sphere is right in corresponding link?
 
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