Are Extra Dimensions Just Mathematical Mumbo Jumbo?

[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 disappear 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

 

[Noone]

Could that be what the big bang was? just a huge out burst of madder from the other end of a black hole? wonder if there would be a way to prove it? well i do know the people don't know if the big bang was spontaineus or if it slowly grew from one point in orgin :/ if you beg to difer please place a like to some info