The 91243443243th dimension?

[anglepose]

Just how many dimensions are there

[Pyrotex]

Just how many dimensions are there

Somewhat fewer than 9X10^10 :eek: :cup:

Well, lessee...

What kind of dimensions would you like?

There are three (3) spatial dimensions that we can experience. Our lab experiments also detect only three.

 

Time is considered a 4th dimension sometimes, so there are four (4). However, this is not an equivalent dimension to the other three. For Time to be mathematically combined with spatial dimensions, Time has to be multiplied by c (the speed of light) and i (the square root of minus one). So, in effect, it's not T that is a 4th dimension, but Tci. Since it is impossible for most people to even imagine what "i" really means, it is just as impossible to image a 4th dimension where "length" is equal to Tci. :hihi: But the math works.

 

One can create equations with any number of dimensions, it's arbitrary. The problem is, do these equations do anything or explain anything that our normal 3-D (or 4-D) equations do not. There is research in an area called "string theory" which uses either 10-D or 11-D equations, and it appears that they behave in such a way that it helps our understanding of what space and time are "made of" (if such a phrase makes sense at all). But that does not mean that there REALLY ARE 10 or 11 dimensions. Math using 8 dimensions was popular for a while, but not any more that I hear of.

 

So, the proper answer is probably 3 dimensions. So far as we know for sure, all other "dimensions" are math structures that we use to aid our understanding.

[anglepose]

yes ive heard about string theory still getting to grips with it thanks

[ughaibu]

Didn't Pythagoras come up with string theory?

[Pyrotex]

Didn't Pythagoras come up with string theory?

Very Funny :hihi: :cup: :cup: :eek:

Yes he did. The "strings" being those of a stringed instrument, and his theory being the relationships between tone and length, and tone and tension.

But there is not a PARTICLE of evidence that he was discussing the nature of space and time.

[Vending]

i think there are an infinite amount of dimensions.

 

Now, how many dimensions are there that have a physical interpritation? That is a whole 'nother question :hihi:

[Qfwfq]

The set of functions of a single real value is a linear space of infinite dimensions. There are even far "smaller" but infinite-dimensional spaces, even of importance in representing physical facts.

 

What we call space is just one example of "space".

[Boerseun]

Interesting, Pyro - but don't we assume a little too much in maths?

 

How can we say that the math works out using Tci, when there is no way to define i numerically? You are stuck with a symbol denoting an impossible number, so how can the math 'work out' for it? This can't be tested, surely, and using i for anything must be an assumption of the validity of the formula, no?

[Qfwfq]

What's impossible about i Boerseun? :) I eat a bit more than 16i grammes of chocolate every morning before coming to work. :eek2:

 

BTW, Pyro, the only text I've ever seen using the i trick for Minkowskian geometry is Landau-Lifschitz. Everybody else uses the g metric tensor and indices being either covariant of contravariant.

 

Because of the (pseudo)metric being anisotropic, time sure isn't exactly the same thing as space. It is however certain that they are but different directions in space-time. A direction may be spacelike, null or timelike. Of all the timelike ones, which is the "true" time axis? :)

[Doctordick]

Just how many dimensions are there

Just how many independent things do you want to keep track of? Dimensionality is a way of keeping track of information. It is your subconscious mind which first comes up with a visual representation of reality (what there "is"). That representation could have been one dimensional, but analysis of the information from a one dimensional perspective is somewhat limited; only a few concepts seem to have any real value: backwards and forwards and perhaps limits in those two directions. Just what could your subconscious do with that?

 

So the human mind clearly requires a more complex view. Look at a two dimensional perspective. Well we can define a few more concepts. Backwards and forwards can be associated with the two dimensions. In fact we can introduce the concept of direction and associate backwards and forwards with any direction. Plus that we have a new concept, rotation, changing direction. And, with regard to limits in directions, we can associate different limits with every direction. In fact, we can even conceive of a closed area with an open exit together with going out and coming in. That brings up all kinds of structures which can be represented and lots of behavior.

 

Though a two dimensional picture can represent a much more complex universe than can be represented in a one dimensional picture, it is still a rather confined representation. Try designing simple machines in two dimensions and you will begin to comprehend the simplicity of the view. So step up to a three dimensional perspective. Now there are all kinds of complex relationships and behavior which can be represented. In fact, at this point, your subconscious has a sufficiently complex picture to explain most everything it encounters. So what does it do? It quits! It comes to the conclusion that you live in a three dimensional universe and simply never worries about going farther.

 

It is thus the assumption of the human race that everything can be represented in a three dimensional perspective. On an anthropomorphic level that certainly appears to be the case. Now, higher dimensional analysis can be handled from an analytical perspective and scientists have found that some phenomena are easier to explain with a universe of more dimensions. So we have people talking about dimensionality of ten or twelve as being real. Who knows, maybe things get more complex than that.

 

Maybe the universe is n dimensional where n is three times the number of fundamental particles in the universe (such a circumstance could be seen as n three dimensional objects). If that is the case then the universe would actually consist of one particle. Now what kind of complex behavior could such a representation allow? I know one resultant concept which is somewhat interesting (among the many others I have considered). That single particles wave function in this n dimensional space could be written in a spherical form. That would yield angular quantization in all arguments except that single radial component. The total number of angular quantum numbers necessary to describe the universe is an interesting number. We end up with exactly n/3 additional quantum numbers: exactly one for each of those represented three dimensional entities. What might this extra quantum number correspond to in our picture?

 

What I am trying to point out is that dimensionality is in one's head and has nothing to do with reality.

i think there are an infinite amount of dimensions.

 

Now, how many dimensions are there that have a physical interpritation? That is a whole 'nother question :)

I would have to go with Vending! :eek2:

 

Have fun -- Dick

[Pyrotex]

Interesting, Pyro...How can we say that the math works out using Tci, when there is no way to define i numerically?...?

Well, the use of "i" in multi-dimensional math can be looked at as a "useful trick". (Though I am sure Qfwfq could explain this better)

 

If you want to "create" a 4th dimension that is indeed perpendicular to the spatial 3, then slapping "i" on it is a quick and dirty way to accomplish this. Any vector that has "i" in its expression, obviously has a component in this 4th dimension. The fact that i*i = -1 means that the cross-product of two 4th-D vectors will produce results that are (at least partially) in the real 3 dimensions.

 

And why have the "c" in Tci? Easy. Multiplying Time by any velocity gives units of length. Using "c" rather than any other velocity gives you the length that light would travel in time T. Therefore, Tci becomes a "length" just like the real 3 dimensions.

[Pyrotex]

...BTW, Pyro, the only text I've ever seen using the i trick for Minkowskian geometry is Landau-Lifschitz. Everybody else uses the g metric tensor and indices being either covariant of contravariant....A direction may be spacelike, null or timelike. Of all the timelike ones, which is the "true" time axis? :eek2:

Er...ah...sputter...uh...

Yes. YES! Of course! Er...ah...I was going to say that! Yeah!

And which is the "true" time axis? Well...er...ahhhh...that would be...

the axis that ticks the loudest?

[Erasmus00]

BTW, Pyro, the only text I've ever seen using the i trick for Minkowskian geometry is Landau-Lifschitz. Everybody else uses the g metric tensor and indices being either covariant of contravariant.

 

Its an old and somewhat outdated notation. It was scrapped in favor of using a non-euclidean metric, as that makes the difference between the space and time dimensions more immediately apparent. You'll see it a lot in older books that don't focus on GR.

 

Kleppner and Kolenkow's excellent introductory mechanics uses this unfortunate notation, for instance. As does Heald and Marion's excellent (though often ignored) classical radiation book (though perhaps it may have changed with later revisions).

-Will

[HydrogenBond]

Could that multi-dimensional ability of math indicate that math can used to play tricks and create illusions. This could be an important point for our understanding of the practical limits of math.

[Qfwfq]

the axis that ticks the loudest?

:eek2: Wow I hadn't thought of that!!!! Maybe with this idea we can finally find Absolute Rest... :)