We have several members strugglings with various concepts of dimension at the moment and this seems to come round again and again.

So here, (hopefully) is some clarification by analogy.

Consider an old fashioned torsion suspension meter and pointer.

When the wire supporting the pointer twists about its longitudinal axis the pointer sweeps over the scale, giving us a reading measurable in one or two dimensions on the flat scale., as an angular deflection or as a pair of x, y coordinates like a graph on the scale.

In principle the wire is of zero thickness so the twisting itself is not measurable in terms of the axis of the wire.

That is the twist takes place in a (phase) space entirely different from the dimensions we measure the meter reading in.

We can translate or rotate the meter as a whole in any of the normal 3 D, but the twist must occur independantly of these as the reading will (should) be the same.

So a full specification of dimensions to state the condition of the pointer would include all three standard x, y and z coordinantes plus the twist of the wire.

String theory postulates additional 'dimensions' like this to accomodate property activity of fundamental particles.

 

Sorry it's a bit rambling and I know some diagrams would help but please feel free to pick over my analogy.

9 minutes ago, studiot said:

When the wire supporting the pointer twists about its longitudinal axis the pointer sweeps over the scale, giving us a reading measurable in one or two dimensions on the flat scale., as an angular deflection or as a pair of x, y coordinates like a graph on the scale.

Could you find or draw a diagram of this. I can't visualise what this means. (I am about to google "torsion suspension meter" to see if that helps...)

Edit: no, Google didn't shed any light on it ...

Edited August 18, 20187 yr by Strange

5 minutes ago, Strange said:

Could you find or draw a diagram of this. I can't visualise what this means. (I am about to google "torsion suspension meter" to see if that helps...)

Edit: no, Google didn't shed any light on it ...

I was afraid of this so yes I will draw a sketch, but not till tomorrow as it's half past midnight here.

You don't really need the torsion wire to consider what I am saying, that was an attempt to link  the differential geometry of the isuue to the phyiscal implementation.

You can have the meter on the floor, on the table, in the next room, facing North, South, East or West, upside down or whatever.

Each of these will involve unique x, y z coordinate.

Yet none of those x, y and z values will give you the reading on the meter;

You need a fourth value -the angular deflection to specify that and this is therefore independent of the x,y,z coordinates.