Space and Dimensions

[JimA]

Space - with its 3 dimensions (+ time) is distorted by mass --- no mention of changing dimensions.

Possible extra dimentions (beyond the 3 +1) are considerred to only make sense if the dimensions are "wrapped up small" --- no mention of changing space.

Why the different approach ?

[Phi for All]

32 minutes ago, JimA said:

Space - with its 3 dimensions (+ time) is distorted by mass --- no mention of changing dimensions.

Possible extra dimentions (beyond the 3 +1) are considerred to only make sense if the dimensions are "wrapped up small" --- no mention of changing space.

Why the different approach ?

Scale. The higher dimensions predicted by string theory are Planck-sized.

You aren't "changing" either space or dimensions. If you were, I think there would be more support for string theory.

[studiot]

2 hours ago, JimA said:

Space - with its 3 dimensions (+ time) is distorted by mass --- no mention of changing dimensions.

Possible extra dimentions (beyond the 3 +1) are considerred to only make sense if the dimensions are "wrapped up small" --- no mention of changing space.

Why the different approach ?

They are not dimensions in the same sense as length or time.

They belong in a virtual space called phase space.

 

[JimA]

On 4/9/2021 at 9:21 PM, Phi for All said:

Scale. The higher dimensions predicted by string theory are Planck-sized.

You aren't "changing" either space or dimensions. If you were, I think there would be more support for string theory.

 

On 4/9/2021 at 9:21 PM, Phi for All said:

Scale. The higher dimensions predicted by string theory are Planck-sized.

You aren't "changing" either space or dimensions. If you were, I think there would be more support for string theory.

 

(I'm still floundering with the website)

I don't see "scale" as relevant. I agree - the normal dimensions can be of any size, and the higher dimensions are shrunk (as you say) down to very small.

The normal space is said to be changed by mass - particularly large concentrated masses (forming black holes).

The higher dimensions are talked about as shrunk --- from any size down to Plank sized

[studiot]

1 hour ago, JimA said:

 

 

(I'm still floundering with the website)

I don't see "scale" as relevant. I agree - the normal dimensions can be of any size, and the higher dimensions are shrunk (as you say) down to very small.

The normal space is said to be changed by mass - particularly large concentrated masses (forming black holes).

The higher dimensions are talked about as shrunk --- from any size down to Plank sized

 

scale is really the wrong word as is size, since they both refer to measurements in our normal 3 dimensions of space.

consider the following sequence

[math]\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + \frac{1}{{32}} + \frac{1}{{64}}..........[/math]

 

The sum to infinity of this is 1.

That is using successively smaller and smaller intervals as marks on a coordinate axis allows you fit an entire infinite 'dimension' into a length of 1 unit of one of our normal space dimensions.

You could say the 'scale' is different or shrunk etc but there is much more to it than this.

The lesson to be learned from this is that we are dealing with ratios (of two numbers one from each system), not simple numbers on their own.
I will return to the significance of this after my next comment.

 

Now consider a standard trio of three dimensional axes, say x,y,z. 
This trio of axes can be right handed or left handed, but there is no movement in 3D space (ie any combination of rotations and translations) that can turn a left handed set x,y,z into a right handed set x,y,-z.

But if we had a fourth space dimension like the other three we could do exactly that ie we could move our trio about in 4 dimensions and turn a left handed set into a right handed set.

So there is something to gain from this if it were tue. Of course observations suggest that we cannot do this and thus suggest that there are only 3 space dimensions available.

So what do we have to gain by introducing string 'dimensions' ?

Well consider the following again in normal dimensions, just 2 D will do this time for the example.
A ship is observed from 3 observing stations and their lines of sight plotted on a chart thus.

In theory the intersection of any pair of lines of sight should give the exact position of the ship.
So all three lines should meet at one single point.

But it can be seen that in my sketch, as in reality, they do not meet like this but form a small triangle pqr, the centroid of which is taken as the actual position.
Notice I said small triangle. With better optics we can determine our line of sight more accurately.
But there comes a point where the dimensions of triangle pqr are less than a planck length and we cannot do better than this.

We then have here a situation where we move from an exact position to a most likely position and probability of position.

 

What is meant by saying that the 'strings' are smaller than the planck length is that we are in the same position as the observers of the ship.
Yes we can propose mathematical structures within the string similar to series I showed earlier to give us desirable properties las we did with the extra fourth dimension for our trio of axes.
But as with our series we are talking of ratios.