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Author Topic: Do dimensions really exist?  (Read 17058 times)

lyner

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Do dimensions really exist?
« Reply #25 on: 19/03/2009 14:23:02 »
Dimensions don't have to be 'xyz'. You can describe a position using polar coordinates just the same.
The point of having dimensions is that you can specify the position (and other conditions) of an object using a number of quantities which can be independent of each other. So you can change your x dimension without altering your y dimension by moving along a horizontal line on your ordinary graph paper. The x and y dimensions are independent (the posh word is orthogonal).  If you used polar coordinates you still have independent dimensions  so, for example, you can keep the radius constant and vary the angle  and the points will lie on a circle. Using r and theta, you can specify any position on a flat sheet of paper (a plane). Radius and two (orthogonal) angles can specify any point in simple space.There are other sets of coordinates you can use but you still need three dimensions.
When you calculate hard things like the Universe and all that, you can arrive at equations which involve more than just x, y and z. The other dimension which you get from String Theory, for instance, have to be there in order to explain, in one fell swoop, how objects will interact.

So, on a simple level, xyz are  enough to describe the position of objects. If you want to describe how they move about, you need to introduce time - a fourth dimension. If you need to describe the effects of electromagnetic fields and gravity all together, you can (they claim) do it using  extra dimensions  which, of course, we can't SEE. What they say is that moving along, say, the x dimension, we are, in fact moving through lots more dimensions. Although another object may be distant in the x dimension, its relation to us in its other dimensions may affect the way we move in the x dimension - i.e the other dimensions somehow explain how we experience the force of gravity from the Sun. String Theory replaces the theory which describes things in terms of Fields and masses. (Remember - Fields are not necessarily any more 'there' than anything else; we just use them as a model to predict and explain what goes on)
And, of course, when we talk of something with zero length, it may not have zero values for its other dimensions.
I am not too convinced that the two uses of 'dimension' are really that distinct from each other - except that Maths is a limited set of ideas (axioms). So, perhaps Mathematical Dimensions are just a sub set of Dimensions.
That's never stopped us from using all the rest of Maths (subset) to deal with the physical (complete set) World, though.
 

Offline yor_on

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Do dimensions really exist?
« Reply #26 on: 19/03/2009 15:12:45 »
Very nice description SC. It is this Idea that string theory seems to build on, that those 'dimensions' xyz are independent from each other. That makes it mathematically reasonable to see a 'one dimensional' string having qualities as 'vibration' aka 'mass' and 'tension. But that is if spacetimes dimensions really are independent isn't it?
 

lyner

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Do dimensions really exist?
« Reply #27 on: 19/03/2009 18:55:12 »
Those quantities could be functions of more than one dimension, of course, so it might be expected they could 'talk to each other'.
 

Offline DoctorBeaver

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« Reply #28 on: 19/03/2009 21:07:39 »
If a particle has momentum in an extra dimension but none in the 3 spatial dimensions we are used to, then that momentum will look to us like rest mass. Maybe particles that do have rest mass are free to travel in an extra dimension whereas photons aren't. Why that should be, I don't know. Maybe the answer lies buried somewhere in string theory.
 

Offline LeeE

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« Reply #29 on: 20/03/2009 11:54:42 »
That's an interesting idea Dr. B.

Instead of photons not being able to move in the 'momentum' dimension, they simply may not have any presence in it.

If it's not possible for something to exist in a limited set of dimensions, it must exist in every possible dimension, which brings us back to having to deal with an infinite number of dimensions again.  However, by allowing something to exist in just a limited set of dimensions, out of a possible infinite set, we don't have to worry about infinite dimensions any more; only the ones that are being occupied are relevant.
 

Offline DoctorBeaver

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« Reply #30 on: 20/03/2009 20:45:36 »
That's an interesting idea Dr. B.

Instead of photons not being able to move in the 'momentum' dimension, they simply may not have any presence in it.

If it's not possible for something to exist in a limited set of dimensions, it must exist in every possible dimension, which brings us back to having to deal with an infinite number of dimensions again.  However, by allowing something to exist in just a limited set of dimensions, out of a possible infinite set, we don't have to worry about infinite dimensions any more; only the ones that are being occupied are relevant.

Precisely. Less infinities=good news
 

Offline yor_on

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« Reply #31 on: 21/03/2009 10:55:31 »
Ethos discussed if the universe differed between left and right before. I don't think the universe uses our definitions at all. I'm not even sure that our definitions of a left or right handed spin have anything to do with what's really 'there'. We put on descriptions of 'stuff' like colourforce etc, but we can't see what we describe so it is quantitatively different than our macroscopic reality where a bike can be described as well as seen. At a QM level this type of definitions disappear and what is left is a mental guessing game where we find puzzle pieces that we label as being of certain properties. But there they may change shape, colour, and name at a moments notice, as a better theory comes.
« Last Edit: 22/03/2009 11:21:12 by yor_on »
 

Offline DoctorBeaver

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« Reply #32 on: 21/03/2009 11:05:29 »
yor_on:

That's absolutely correct. But without labels we wouldn't know what other people were talking about. Where spin is concerned, left & right are meaningless except for us to be able to differentiate between how the particles behave. We may just as easily have used up & down or backwards & forwards. I'm not sure how chirality entered the picture but I suspect it has to do with the terminology from polarity.
« Last Edit: 21/03/2009 13:57:18 by DoctorBeaver »
 

Offline LeeE

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« Reply #33 on: 21/03/2009 18:46:51 »
Yor_on & Dr B: these are examples of the abstracts you end up with as a consequence of any top-down analysis.  We assign them a quality and a value, but we don't really know what it is that we're dealing with, other than in abstract terms.
 

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« Reply #34 on: 21/03/2009 19:03:53 »
LeeE - I agree. But without labels we'd be buggered.
 

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« Reply #35 on: 21/03/2009 21:44:42 »
LeeE - I agree. But without labels we'd be buggered.

Yup - even if we don't know exactly what it is that we're talking about, at least we know we're talking about the same thing.
 

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