Are Extra Dimensions Just Mathematical Mumbo Jumbo?

[wolram]

Why is it that it is thought that separate dimensions exist, as humans we can only exist in
a volume, three so called dimensions, so why do scientists think that these three can be separated when in all probability and experimental AFAIK they can not, length, width and
depth are just words to describe the size of a volume, put some particles in motion in a
volume and you have what you see in the universe.
As for extra dimensions, well time will tell but i think it is all mathematical mumbo jumbo,
but then may be some one can come along and take the width or the length or the depth
out of a volume, that would be a neat demo.

 

[TVP45]

I think a better way is to think of the 3D dimensions as independent rather than separate.

BTW, I have an example of 2D. I own a house lot of approximately 10,000 ft^2. I paid a mortgage on it. I pay taxes on it. It is recorded in the Deeds and Tax Offices. I can do almost anything I like on it, so it is real in an everyday sense. But, I own only a 2D surface. There is no depth.

 

[wolram]

I think a better way is to think of the 3D dimensions as independent rather than separate.

BTW, I have an example of 2D. I own a house lot of approximately 10,000 ft^2. I paid a mortgage on it. I pay taxes on it. It is recorded in the Deeds and Tax Offices. I can do almost anything I like on it, so it is real in an everyday sense. But, I own only a 2D surface. There is no depth.

Do you grow 2D veg in this garden?

 

[TVP45]

Mainly flat cabbage and plane trees.

 

[wysard]

Why do you think "seperate" dimensions exist? They are a mechanism to separate out vector forces but they are far from seperate. Each one interacts with the other through the body under consideration. We develop them to answer questions to resolve questions that cannot be answered any other way but still observe all the rules of physics we know. You should note that all the dimensions obey the same laws of physics, it's not as if there is a magical separate reality for any dimension. Force is still force, entropy is still entropy, all laws apply equally. Think of it as an advanced application of Occam's Razor. Or, the less sexy side of "And he built a crooked house".

 

[wolram]

Seperate dimensions do not exist in the real world, in a volume length width and breadth are inter changable, one can give a preferred direction some value but what ever it is an artificial value in a volume

 

[sysreset]

Wolram I am right with you on this. Describing space as 3- dimensional is arbitrary and based on the mathematical convenience of cartesian or spherical coordinates. This is especially apparent when one considers the vast differences in how space behaves within graviational clusters (where it is not expanding) and outside gravitational clusters (where it is expanding). I think the fundamental flaw is that we describe space itself, and objects with mass within space with the same 3-dimensional paradigm.

Certainly 3 dimensions is an extremely elegant and convenient tool when describing the relative positions of objects within gravitational systems. Length, width, height; or if you prefer, radius, zenith, azimuth. Both are based on the fact that coordinates oriented 90 degrees apart give static positions with the fewest number of elements. But relying on 90 degrees, and relying on the fewest elements, are both artificial selections and other artificial systems can be constructed mathematically. None of these artificial constructs alters the true nature of empty space or space with mass, and all of these constructs falsely blur the distinct characteristics of empty space versus space with mass. And all of these "dimensional" constructs inadvertently leave out motion and acceleration, which have such profound affects.

 

[CaptainQuasar]

Dimension is just shorthand for a (mathematical) degree of freedom.

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[f-h]

yep. Maximum number of linearly independent vectors. It implies that the relative location of two bodies can always be described by three numbers. That's all, there is nothing separate about the directions as you might tell by the fact that our up is the sideways of somebody a quarter around the globe.

 

[dx]

dimensions are how our minds organize what are called spatial relationships between objects. it turns out that on the large scale, the spatial relationship between two objects always need 3 numbers to specify. it could quite possibly be different on differnt scales.

 

[wolram]

Thank you sysreset, you put the case much better than i could.

 

[malawi_glenn]

Seperate dimensions do not exist in the real world, in a volume length width and breadth are inter changable, one can give a preferred direction some value but what ever it is an artificial value in a volume

depends on what you mean by "real" world..

 

[wolram]

malawi, i mean a world were we exist, not a mathematical world where many things CAN
exist

 

[malawi_glenn]

and how do you KNOW that the real world only have 3spatial dimensions?

 

[Haelfix]

Some of the large extra dimension models currently in vogue in phenomenology are quite physical, in the sense that they are consistent with observation.

 

[wolram]

and how do you KNOW that the real world only have 3spatial dimensions?

I am arguing that dimension means very little (three spatial dimensions) is not meaning full
we live in a volume, we can not live in 2D or 1D, so what is the use of extra dimensions, if
they are included in the volume they are not separate entities ,they just emerge from
abstract maths.

 

[malawi_glenn]

I am arguing that dimension means very little (three spatial dimensions) is not meaning full
we live in a volume, we can not live in 2D or 1D, so what is the use of extra dimensions, if
they are included in the volume they are not separate entities ,they just emerge from
abstract maths.

But the language of physics is math, not intuitive reasoning.

Elementary particles are point like, they have no internal structure nor volume according to best theories and observations (see many threads in this forum).

The whole quantum physics is full of things that contraditcs our daily life experince, so we can not a priori rule out everything that contradicts our daily life experience as non-physical.

So we can't just say "its only absract math"..

 

[wolram]

Malawi, i agree the world of quantum physics is not intuitive (from what very little i know)
But to try for example to describe gravity as a weak force because it leaks into some other dimension seems a cop out when dimension has no real meaning.

 

[malawi_glenn]

So even tough you have very little knowledge about quantum physics, you have much to say about the very frontline in quantum physics, namley String Theory. That is strange..

 

[wolram]

So even tough you have very little knowledge about quantum physics, you have much to say about the very frontline in quantum physics, namley String Theory. That is strange..

Quite true i know very little, but i have the right to question, and i notice that no one has yet explained how a dimension can be individual.

 

[dx]

what do you mean individual?

 

[malawi_glenn]

Quite true i know very little, but i have the right to question, and i notice that no one has yet explained how a dimension can be individual.

You don't even talk the same language as the physisits. Hence maybe no one knows how to explain to a layman how these complicataed things work?

 

[Gear300]

I'm thinking that the spatial dimensions are independent of how gravity flows through different universes. And its also true that you have the right to question. But instead of thinking of spatial dimensions as left-right, up-down, forward-backward, try to think of them as views. A 3rd dimension would be the overall view of 2 dimensional planes, 2 dimensions the overall view over 1, and so forth. The universe consists of an arrangement of these views and other dimensional stresses so that it is structured as it is; so altogether, you can consider dimensions to be the factors that structurize (if that's even a word) the universe...sort of like the architectural elements of a building. There is time, space, and according to new theory, a few others (11 dimensions in total thus far). Occuring phenomenon in the universe depend on this arrangement of time, space, etc... However, with the phenomenon of gravity...it is independent of the arrangement (not bound to it), so it may escape. Where to? Supposedly across hyperdimensional space, in which it freely roams across different universes.

 

[wolram]

You don't even talk the same language as the physisits. Hence maybe no one knows how to explain to a layman how these complicataed things work?

That may be the BIG problem, but are they complicated because they are beyond reason?
I can not think of a way to describe or imagine separate dimensions in any physical way,
may be some one has and found a way to explain them to a non physicists.

 

[Haelfix]

You want the ant on a cylinder analogy? Alternatively you could just read up on any number of popular layman oriented books on the subject (see eg warped passages by Lisa Randall) or try a Wiki.

 

[wolram]

You want the ant on a cylinder analogy? Alternatively you could just read up on any number of popular layman oriented books on the subject (see eg warped passages by Lisa Randall) or try a Wiki.

I need some thing like an infinitly flat concertina (2D) that when it is expanded gives a true volume, but then that volume could be an infinite amount of 2D slices, but then it can not as 2D has no other value ,so how would adding a third dimension give volume?

 

[CaptainQuasar]

I need some thing like an infinitly flat concertina (2D) that when it is expanded gives a true volume, but then that volume could be an infinite amount of 2D slices, but then it can not as 2D has no other value ,so how would adding a third dimension give volume?

Because it's a third degree of freedom. In addition to choosing an x coordinate and a y coordinate to locate a point, you now also have the ability to specify which 2D slice it's located in.

It doesn't have anything to do with a particular orientation of the coordinate system, it has to do with the fact that you have to have a total of three values to express the relative positions of any two points. Note that you still need three values even if you're using a http://en.wikipedia.org/wiki/Spherical_coordinate_system" instead of an orthogonal one. In 2D you only need two coordinates.

Does that still seem too abstract to you?

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[wolram]

Because it's a third degree of freedom. In addition to choosing an x coordinate and a y coordinate to locate a point, you now also have the ability to specify which 2D slice it's located in.

It doesn't have anything to do with a particular orientation of the coordinate system, it has to do with the fact that you have to have a total of three values to express the relative positions of any two points. Note that you still need three values even if you're using a http://en.wikipedia.org/wiki/Spherical_coordinate_system" instead of an orthogonal one. In 2D you only need two coordinates.

Does that still seem too abstract to you?

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The part that seems abstract to me is when extra dimensions are talked about, this implies to me that people think that dimensions are building blocks or separate entities,
when to me dimension just means a measurment made in a volume dimensions do not make that volume.

 

[CaptainQuasar]

The part that seems abstract to me is when extra dimensions are talked about, this implies to me that people think that dimensions are building blocks or separate entities,
when to me dimension just means a measurment made in a volume dimensions do not make that volume.

Well, it's more precisely the ability to make a certain kind of measurement within a volume or space. If you can make an accurate and complete measurement by specifying only two coordinates for each location, you're in a 2D space, if you need three or four coordinates you're in a 3D or 4D space respectively.

I'd agree that thinking of dimensions as building blocks is erroneous. They're really properties of the environment a measurement is being made within.

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[f-h]

wolram, it's obvious that you do not have the slightest clue what a dimension is in mathematics, and thus what physicists mean when they talk about dimension. Dimensionality is a property of a space that preceds volume, it makes sense to talk about spaces of a certain dimensionality even if there is no way to talk about volume in these spaces. Indeed that's where you start when you do GR. Take a manifold M, and THEN inroduce a metric field that supplies us notions of distance, volume, etc.

Nobody thinks of dimensions as building blocks. But it is possible that our familiar 4 dimensions are a subspace of a larger space, that we are confined to 4 effective dimensions like an electron in a thin film becomes effectively 2 dimensional.

 

[wolram]

wolram, it's obvious that you do not have the slightest clue what a dimension is in mathematics, and thus what physicists mean when they talk about dimension. Dimensionality is a property of a space that preceds volume, it makes sense to talk about spaces of a certain dimensionality even if there is no way to talk about volume in these spaces. Indeed that's where you start when you do GR. Take a manifold M, and THEN inroduce a metric field that supplies us notions of distance, volume, etc.

Nobody thinks of dimensions as building blocks. But it is possible that our familiar 4 dimensions are a subspace of a larger space, that we are confined to 4 effective dimensions like an electron in a thin film becomes effectively 2 dimensional.

It is true i know i know nothing about the way physicists think of dimensions, may be when they find one of these sub spaces it will become clear to me.
Until then i will try to understand how this volume we live in came to exist before there was anyone to put in a dimension

 

[starkind]

A dimension is just a measurement. For example, I could theoretically count how many people in New Jersey have green hair. That would be a dimension. I could count the number of people with green hair again and again, every day maybe, and make a very nice two dimensional graph of the number of people with green hair in New Jersey against every day in a year. Probably the number would peak near St.Pat's day. You see I hope that spatial length is no part of such a dimension. Area is not included because area has units of the square of length, and volume is not included because volume is defined as length cubed.

It is a very common mistake to think that a dimension or some number of dimensions or some numbered dimension is a place...you might in principle sneak your body into such a dimension, or part of it anyway. This mistake comes about because we usually first learn of the idea of a dimension as a length. Usually some time in High School we learn that dimensions, like the number of people in New Jersey with green hair, do not have to involve length, width or breadth at all.

In my opinion, physicists have made a mess of this by calling various relationships "spaces," as if you could crawl inside and hide in a representation space or a vector space. No doubt this was very clever when it was first done. Physicists have been repeating the joke endlessly ever since. Dimension X is in no way a place you can dissappear into, nor a place some creature can come from. A "space", to a physicist, does not have to involve any form of length at all.

 

[CaptainQuasar]

In my opinion, physicists have made a mess of this by calling various relationships "spaces," as if you could crawl inside and hide in a representation space or a vector space.

It's not physicists who do that, it's http://mathworld.wolfram.com/Space.html" of it: c. 1300 - “an area, extent, expanse, lapse of time,” it's never been restricted to simply physical space. You're thinking too “Space: The Final Frontier”.

But yeah, wolram, a dimension does not imply a place, as starkind says.

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[f-h]

It is true i know i know nothing about the way physicists think of dimensions, may be when they find one of these sub spaces it will become clear to me.
Until then i will try to understand how this volume we live in came to exist before there was anyone to put in a dimension

Ok so you've made up your own private definitions of dimension and volume (which you are not sharing, I guess because it is based on a vague intuition more then a tangible conceptual structure) and now are annoyed that physicists use these words according to the commonly established definitions and usages, rather then your own idiosyncratic ones?

I mean fair enough, I'm not quite sure what you're doing on physics forums though, seeing how this is supposedly about physics, and physics is what physicists do, and to understand the vast multitudes of things we have found out about reality you will have to start reading physics books written in that physics language...

 

[starkind]

I think Wolram has a point, though, about how confusing and sloppy the language of physics formalism is, to those of us who are trying to learn it. Just imagine trying to build a dictionary, or even a list of definitions, of math and physics symbols!

 

[CaptainQuasar]

I think Wolram has a point, though, about how confusing and sloppy the language of physics formalism is, to those of us who are trying to learn it. Just imagine trying to build a dictionary, or even a list of definitions, of math and physics symbols!

http://mathworld.wolfram.com/" , not too infrequently in fact.

I don't think the language of physics is all that sloppy. My own field is software engineering and I wish we used language as clearly as physicist on average do.

But I certainly think that using language precisely, or at least not being too cavalier about mixing formal and casual language, is very important when physics is being taught.

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[starkind]

What does "e" mean?

 

[CaptainQuasar]

It's a letter of the alphabet. What is the context in which it was used?

If you're referring to some constant I'll bet that there's a formal physics term for it that is much longer than ‘e’ which is probably specifically used for writing out equations. If you've got a teacher or professor who only ever refers to a particular constant as ‘e’ they ought to be using the constant's name more often. It's your teacher who is being sloppy, not the science of physics.

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[starkind]

That is my point, I guess. Symbols mean whatever the person using them intends them to mean. The trouble for the student is that specific definitions are rarely supplied...one must assume the meaning from context. But the context for one person may be very clear, while for another it may be obscure.

Perhaps a carefully structured standard course with coordinated physics, mathematics, philosophy and logic would help a student at one university understand what the professors are talking about, but an independent learner has not the advantage of such a structured standard course. And a student at one university would still have the problem of trying to understand what someone from another tradition is saying.

As a self-directed student, pursuing lines of interest rather than a course or career goal, this problem is particularly challenging for me. I suppose a traditional student would just ask someone nearby. I am trying to learn from Wikipedia and discussion forums. I suspect this may be the way everyone learns, eventually. So the problem of context and definition keeps coming back to me.

Physics is not a person and so of course cannot undertake a sloppy action. It is always teachers, students, and interested parties who go slopping about. I guess I am just venting my complaint, rather than expecting change.

 

[starkind]

Most people understand "space" as a volume we live in, the final frontier. That does seem to be the original usage. And dimension no doubt started existence as a measure of that kind of space, a length, width or volume. Someone, probably a mathematician, decided there could be a "space" of a different kind, for example a space of solutions to a formula. You can't measure this kind of space with a ruler. The dimension of such a space is not a measure of length etc. Confusion has resulted, continues, and is common. I think Wolram understands this and is playing with the absurdity.

 

[dx]

Any one who is gets to the point where they need to study spaces of solutions and other such things knows exactly what theyre dealing with. Only a lay person would be confused by such terminology.

 

[starkind]

True. And we were all lay people, once. Lay people have a legitimate interest in what physics does.

 

[dx]

Yes, and for lay people who want to understand some physics, there many good popular science books. And in these books, when words like "dimension" are used in a way that would not be familiar to lay people, the authors explain what exactly they mean. There can be no confusion in this case because it is not assumed that the readers know the sense in which the word is being used.

 

[CaptainQuasar]

Most people understand "space" as a volume we live in, the final frontier. That does seem to be the original usage.

No, the original usage was broader and more abstract already. Have you ever heard a Southerner say something like “I think I'll sit down for a space”? That's using ‘space’ to express an expanse of time. See the etymological note I made above, that's the way it was being used in the 12th century. People who have decided that it's only talking about outer space or length and breadth and depth are the ones who are monkeying with the definition.

The reason you're having trouble learning from Wikipedia is that Wikipedia is sloppily written in many places. An equation or expression like

v(t) = v_0 + \frac{1}{2} a t^2​

Should always be followed by a series of qualifications like “Where v_0 is initial velocity” that define each of the symbols used.

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[Gear300]

hehehhhehheheeehehheh...I see now why this was moved to philosophy...exactly how different is physics from philosophy?

 

[TVP45]

No, the original usage was broader and more abstract already. Have you ever heard a Southerner say something like “I think I'll sit down for a space”? That's using ‘space’ to express an expanse of time. /QUOTE]

Interesting usage. Where I came from, people would "set a spell".

 

[CaptainQuasar]

hehehhhehheheeehehheh...I see now why this was moved to philosophy...exactly how different is physics from philosophy?

A philosopher would probably say that science in general is a form of philosophy called http://en.wikipedia.org/wiki/Empiricism" .

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[CaptainQuasar]

Interesting usage. Where I came from, people would "set a spell".

I've heard both. Maybe I'm wrong and it's Midwesterners who say “for a space” in reference to time. In any case, if you look at my etymological reference above it supports that “space” has always been used to refer to things other than length, width, and depth.

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[Noone]

There could be infinit dimensions if we were in side a black hole, and that would mean that space would be infinit kinda like Ablert.E. spoke of. a black hole within a black whole, we see it happen in space, but what's inside a black hole and what happens to the madder it eats? is there a vacuum in a black hole that suck's madder in? Well what even contains are own vacuum of space that we live in? :D *we could be in a black hole and never be able to prove it with any form of science* but logic can :)

 

[Noone]

I mean a Black hole within a black hole that is a black hole