What would be the fifth dimensional property of a Tesseract?

[avemt1]

I understand the Tesseract, but What would be the fifth dimensional property? Does it have to do with tunneling properties of particles? And how would time act in the fourth dimension?

I do understand a little about physics, but in consideration that I know very little, please IN LAMENS TERMS!

 

[Mentat]

I don't quite understand the question. Are you asking about the properties of the 4th spatial dimension? Or are you talking about the T dimension (which is commonly believed to be the "fourth" dimension).

 

[avemt1]

I mean to ask what the physical properties of the 5th spatial dimension.
Like I said I understand the tesseract. Which is the 4th dimensonal base shape.

The other question I am asking is if time would act differently in the 4th spatial dimmension or would it have the same one directional properties?

 

[Mentat]

1) I'm not really sure what the properties of the 5^th spatial dimension would be like. I know that the existence of such higher dimensions helps physicists to return to Einstein's idea - that there are no "forces", but rather all that we percieve to be "forces", are just the results of curvatures in spacetime.

2) I am of the opinion that anyone point on the T dimension ("time") corresponds to all points on the spatial dimensions. This is obviously true of the 3 spatial dimensions that we're used to, and I believe that it is true of all of them.

 

[selfAdjoint]

The Kalusa-Klein theory put a compacted fifth dimension onto the four dimensional spacetime of general relativity, and with a simple Lagrangean on the five dimensional manifold thus created, was able to build a unified theory of gravity and electromagnetism (Maxwell's equations).

This would be an answer to everybody's prayers if it weren't for the quantum. The KK theory is completely classical, and the quantum, whatever groundlings want to believe, is very real.

Plus there are the other two forces, the strong and the weak, which are not accommodated in this theory.

The idea of compact dimensions was borrowed from KK theory by the string theorists.

 

[Mentat]

Originally posted by selfAdjoint
The Kalusa-Klein theory put a compacted fifth dimension onto the four dimensional spacetime of general relativity, and with a simple Lagrangean on the five dimensional manifold thus created, was able to build a unified theory of gravity and electromagnetism (Maxwell's equations).

This would be an answer to everybody's prayers if it weren't for the quantum. The KK theory is completely classical, and the quantum, whatever groundlings want to believe, is very real.

Plus there are the other two forces, the strong and the weak, which are not accommodated in this theory.

The idea of compact dimensions was borrowed from KK theory by the string theorists.

String Theory (and other ten-dimensional theories) incorporate all of the forces. Kaluza-Klein theory - quite simply - didn't have enough dimensions.

 

[Mentat]

The quantum problem?

selfAdjoint, you mentioned that if it weren't for the quantum, Kaluz-Klein theories would be more acceptable. I don't understand this. Could you please explain why the quantum theory contradicts the higher-dimensional theories?

 

[chosenone]

I thought that if you wanted to understand higher dimensional objects you had to interprete the math,not visualize it,be cause the math shows you what it is because you can't precieve it with the minds eye

 

[quantumdude]

Originally posted by Mentat
selfAdjoint, you mentioned that if it weren't for the quantum, Kaluz-Klein theories would be more acceptable. I don't understand this. Could you please explain why the quantum theory contradicts the higher-dimensional theories?

The problem is not the higher-dimensions, the problem is that Kaluza-Klein is not quantum mechanical.

It is basically a single classical field theory from which both GR and EM drop out. There are two reasons why this is not The Answer, and both reasons have to do with the quantum world:

1. The fields are not quantized.

We know for certain that the EM field is really a granular entity whose quanta are called photons. Kaluza-Klein does not share this feature. The EM that emerges from it is Maxwell's EM.

2. The weak and strong interactions are not included.

Moreover, they cannot be included, because there is no classical potential for gluons and W/Z bosons. Only quantum gauge field theories will do.

 

[steppenwolf]

to answer the question of the properties of the 5th dimension:
i read it was another spatial dimension but of the same form as our normal 3, ie very long, which is SO not the proper way to describe it but i forget the terminology; like the rest of the 15 or so theorized dimensions would have to be curled up so small they wouldn't affect us. the 5th dimension would be big enough, however the only forve to interact with this dimension would be gravity.

this is a great way to explain the fact gravity loses so much 'strength' after such short distances; it leaks away into this 5t dimension!

 

[arivero]

regular poligons and other small dimensional effects.

As you mention the Tesseract, here is an insteresting property of dimension four and higher: the only regular poli"hedra" is the generalized cube. IE the Tesseract in four dimensions, and so on.

It is interesting because we have infinite regular poligons in dimension two, five regular poli"gons" in dimension three, and only one in dimension four, five, six, etc... I have been told, at least.

Other funny property of low dimensions relates to the permutation group. Fof n>4, the Symmetric Group S_n of permutations of n elements is not a solvable group (roughly, this property says that it can not be decomposed in interesting ways). This implies, for instance, that there are no algebraic formulae for a generic polinomial of degree 5, as it has five roots to play with and the solution depends on playing with permutations of the products.

Other source of low dimensional effects comes from renormalization group. Via power-counting in the Gell-Mann RG, or scaling in the Kadanoff & Wilson approach, the dimensions D<= 4 are usually singled out as having particular properties, fixed points, etc. In some cases this can be an effect of the theories we are looking, but even so it is a remarkable thing.

 

[avemt1]

I am amazed at where my question has gone.
Now may I add (or to point out) one of my questions.

"Does the 5TH spatial dimension have anything to do with the tunneling properties of high-energy particles?"

Now if I may add a thought?
Mayby by taking a tesseract and visualizing the movement, then taking it one step further into the 5TH spatial dimension I began to visualized the consepts of multiple planes of existence in one spacetime continum.

As I tried to describe the properties I thought of 'in font of' and 'behind'.
THis was the only wy I could think of for describing what consepts I visualized. The concept might help somebody somewhere. I hope.

 

[damgo]

"Does the 5TH spatial dimension have anything to do with the tunneling properties of high-energy particles?"
No... not if you mean *observed* tunneling properties.

Touching on S_n, S_6 is also a very weird case: it is the only S_n that has an outer automorphism, and also the only S_n not isomorphic to its automorphism group. :)

 

[avemt1]

Could somebody please explain to me what he just said?
As in: 'S_n, S_6'; and 'automorphism and isomorphism'

 

[bogdan]

Highly unpredictable algebra...(and complex)...
It's something you'll learn in school probably next year...
These Ss...are groups of "transformations" represented by matrices...S means that the sum of the color "charges" is 0...
Damn complicated...

 

[Mentat]

Originally posted by Tom
The problem is not the higher-dimensions, the problem is that Kaluza-Klein is not quantum mechanical.

It is basically a single classical field theory from which both GR and EM drop out. There are two reasons why this is not The Answer, and both reasons have to do with the quantum world:

1. The fields are not quantized.

We know for certain that the EM field is really a granular entity whose quanta are called photons. Kaluza-Klein does not share this feature. The EM that emerges from it is Maxwell's EM.

2. The weak and strong interactions are not included.

Moreover, they cannot be included, because there is no classical potential for gluons and W/Z bosons. Only quantum gauge field theories will do.

So Einstein was wrong? Forces are not just curvature?

It appears that String Theory unites the Quantum view of "forces" with Einstein's view. String theory states that a certain vibration of the string alters spacetime in a certain way, so that - while the force is still caused by a particle/wave - the perceived force is still the result of a curvature (on one of the dimensions).

 

[arivero]

Originally posted by avemt1
Could somebody please explain to me what he just said?
As in: 'S_n, S_6'; and 'automorphism and isomorphism'

Avempt, S_n is standard for the group of permutations of n elements. So for instance S3 is the group of six posible exchange operations (123)-----> (123) (213) (132) (321) (231) (312). It
must no be confused with the label "S" in a Lie Group, which indicates "Special" in the sense of being a matrix group with determinant always equal to 1.

The S_n groups are also seen as coming from the A_n groups, the groups of even permutations of n elements.

In any case, they could be relevant in the thread because permutations are important when defining a volume form or any other differential form. For instance, the external product is sensible to permutations: dx ^ dy = - dy ^ dx.

As for the weirdness of S6, I was not aware of it. Damgo is claiming that it is possible to map S6 onto itself with a transformation which is not an element of S6, and that it is the only permutation group having this property. I had never heard of this.

 

[Einstiensqd]

Offering some help

I have a theory that revolves around there being four dimensions, and having time as a state of being as opposed to a dimension, and I thoroughly believe that time is NOT a dimension. If you want to check out my theory, it is in the theory development area of this site.

 

[damgo]

Damgo is claiming that it is possible to map S6 onto itself with a transformation which is not an element of S6, and that it is the only permutation group having this property.

Yup, basically. The proof for n>6 is IIRC not particularly short and pretty, but you can find it in the first couple chapters of Dummitt&Foote. The counterexample for n=6 maps something is an outer isomorphism that takes the two-cycles (a b) to triads (c d) (e f) (g h)... you can find it spelled out online I think.

 

[elas]

This is a grossly overly complicated subject, get down to the simplicity of reality.
Every measurement of distance we make is made using the EM spectrum. We cannot measure inside a SF body and any attempt to do so results in pushing the SF body to one side. We can of course measure from side to side using the EM spectrum but we cannot measure inside. Exactly the same argument applies to gravitons. SF particles are to strong and gravitons are to weak both are pushed aside by our EM instruments. The same arguements would apply if we were made of SF or gravitons.
Each force has its own Length, Breadth and Height dimensions that do not overlap, giving a total of nine dimensions so far. To this must be added Time, the dimension of history; and infinity, the dimension of the vacuum frame.Time and the vacuum frame are common to all force fields. This gives a total of eleven dimensions all of which fit into Quantum theory and Relativity as they stand without any need for strings, white or black holes, or other magical terms.

 

[Mentat]

Originally posted by Einstiensqd
I have a theory that revolves around there being four dimensions, and having time as a state of being as opposed to a dimension, and I thoroughly believe that time is NOT a dimension. If you want to check out my theory, it is in the theory development area of this site.

Perhaps you should start a thread about your idea, in the Theory Development Forum, Einstiensqd.

 

[mouseman]

The mathematical definition of a 1-dimentional object is an infinite series of 0-dimensional object. The definition of a 2-D object is an infinite series of 1-D objects. A 3-D object is a series of 2-D objects. If we take this pattern of succession on up, a 4-D object is an infinite series of 3-D objects, which is how one can visualize time progression. Now as far as visualizing a shape for it, what about this: Take a 1-D object. To make one you take a 0-D object and pick one direction (could be any) and make a line by placing them one after another in that direction. Now if we apply this to a 3-D object, let's say a cube, a 4-D object could be represented by a... what is the name for a hexahedron that's got four rectangles? I forgot. Whatever it is we could take that 4-D object and make a 5-D object by taking our pattern and rotating the succession 90^o on the same plane, so our new object looks kinda like a king-size mattress.

Would this work?

BTW the mathematical definition of any object in space makes no physical sense to me. If a 3-D object is just an infinite number of 2-D cross-sections, this would suggest that a 2-D object is infinitely thin, which is the case (length & width, no height). But no matter how many 2-D objects you stack on top of the first one, by definition, this "new" object would still be infinitely thin. Any number of cross-sections times zero height is still zero. Can anyone explain this? Or clarify my brain?

 

[mouseman]

Here's another question. If 4+ dimentions are physically manifest, we should be able to go backwards and say that 2 dimentions are physically manifest as well, right? So show me something that is physically and exactly 2 dimentions...

 

[mouseman]

Jesus Jones! Forget that. I appologize for that ridiculous excuse for a question I last posted.

 

[arivero]

Should a trajectory be something physical, to you?

Also, the plane where a keplerian orbit takes place, seems physical enough.

Note that if you are too strict about this question, actually all matter is a bunch of zero-dimensional particles. So I can not show you any physical three-dimensional object

 

[mouseman]

You're right. My bad.

 

[avemt1]

Here's another question. If 4+ dimentions are physically manifest, we should be able to go backwards and say that 2 dimentions are physically manifest as well, right? So show me something that is physically and exactly 2 dimentions...

There is nothing physicsally manifest that is 2-dimensional. Dimensional models are only used to explain the properties of the world around us.

 

[Mentat]

Originally posted by avemt1
There is nothing physicsally manifest that is 2-dimensional. Dimensional models are only used to explain the properties of the world around us.

Well, that may be your opinion (and you are entitled to it), but string theory heartily disagrees with you.

 

[(Q)]

Mentat

Well, that may be your opinion (and you are entitled to it), but string theory heartily disagrees with you.

Please, explain exactly how string theory disagrees. Show the math if it will help your explanation.

 

[Mentat]

Originally posted by (Q)
Mentat

Well, that may be your opinion (and you are entitled to it), but string theory heartily disagrees with you.

Please, explain exactly how string theory disagrees. Show the math if it will help your explanation.

Well, sting theory postulates the existence of one-dimensional strings, and two-dimensional membranes. These have physical existence (according to the theory).

 

[mouseman]

I'm sorry. I can see the mathematics behind it, but I just can't buy that anything in this universe could physically be only one dimension, let alone two dimensions. I mean we live in a world that depends on 3-D...


BTW, anyone have any feedback on my +3 dimensional "visualization" idea?

 

[elas]

Right now you have 3 dimension note that they are all part of the electromagnetic spectrum; are you prepared to accept that each force has its own spectrum?

 

[mouseman]

Originally posted by elas
Right now you have 3 dimension note that they are all part of the electromagnetic spectrum; are you prepared to accept that each force has its own spectrum?

I don't know!
I'll just be quiet now.
...wait. Maybe I understand this. By that do you mean that we perceive 3-dimensions because of light?

 

[avemt1]

I'm sorry. I can see the mathematics behind it, but I just can't buy that anything in this universe could physically be only one dimension, let alone two dimensions. I mean we live in a world that depends on 3-D...

The only reason we see 3-d is that we have two eyes, but if we had one wew would only see 2-d. Better yet, if we had three eyes we would probably see 4-d.

 

[mouseman]

But even if we had one eye, we could deduce through observation that a "2-d" object that we perceive to be as such, has length, width, and depth.