Difference in the geometrics of multi-Dimension objects and 3D objects

As long as we work in the environs of three dimensions and three coordinates, it did not make any difference even if we called a dimension – a coordinate, or a coordinate – a dimension.

But we have to be cautious if we enter the environs of multiple dimensions and multiple coordinates.

It is so because if we designate the number of the dimensions of a multiple dimension object as “m” and the number of the coordinates of a multiple-coordinate object as “n”, we may say – “m:n ratio” of 3D objects is 1:1.   

But this ratio is no more 1: 1 if the value of m or n is more than 3. 

The fact is it was not till it did not dawn on us that an object could have only three coordinates or three dimensions only if something is  stationary when viewed from the designated origin but not for the things such as electrons that revolve around the nuclei of the atoms, the celestial bodies that revolve in the space around our galaxy or the light waves emitted by the suns.

Though how we decide what type of dimensions such objects may have – is still not very clear, we may assume that we may assign such dimensions to the light waves, as is shown in the following diagram.

 

I would not contest if you think we can’t call D1~D5 – dimensions.

But I hope you would not mind listening to me why I don’t want to contest.

Here are the reasons – why I don’t want to contest.

Reasons why I don’t want to contest

As you would have noticed, four dimensions (D1, D2, D4 and D5) are linear dimensions and one angular dimension (D3) is an angular dimension.

As regards the wavelength and the amplitude, clearly wavelength and amplitude are for a wave what width and height are for a cube. So, it would be being too orthodox to apprehend that wavelength and the amplitude should not be treated as dimensions.

The same way, if you have an apprehension why Θ° should have been taken as a dimension, dimensions may be only linear – not angular; though it is true that all dimensions happen to be linear in the Cartesian system, in the Spherical system – only one dimension (radius) is linear, the other two dimensions happen to be angular. Likewise in the Cylindrical system – though, two dimensions (radius and height) happen to be linear everyone knows that one of the dimensions, very much, happens to be “angular”. So, it calls for changing the very perception that a dimension has to be only linear, not – angular.

It has been taken as a dimension – based on an assumption that waves of each wavelength may be travelling in a different plane of their own instead of waves of all wavelengths travelling in the same plane.

If you have an apprehension, how the gap between adjacent photons should be a dimension, gap between the photons is a unique characteristic of light waves that so well explains – even though almost 100 per cent of space is fully soaked with light (since hardly a tad of the total light emitted by the sun gets intercepted by the planets etcetera the rest of it fills up the space), why we are not able to notice the presence of the light waves even though when photons move forward the preceding photons immediately fill up the void created by the leading photons, as follows.

If the gap between the adjacent photons may be as large as half the wavelength – the trailing photon would be out of phase by 180° due to which, when the wave formed by it overlaps the wave formed by the photon that may be leading it, it geometrically neutralizes the wave formed by the leading photon.  

Anyway, instead of getting stuck up here, we may end up this discussion here and start looking into the number of coordinates the light waves – may have.

Number of coordinates light waves may have  

So long as the photons are moving along a straight median, they may have only three coordinates (C1~C3), as follows.

C1 = their distance from the origin (If we treat the sun as the origin, distance from the sun).

C2 = the phase 1, 2, 3 or 4 – as follows.

1   if they are climbing upward away from the median toward the crest.

2  if they are descending from the crest toward the median.

3   if they are descending from the median downward.

4   if they are ascending upward from the bottom of the wave toward the meridian.

C3 = inclination of the plane (in which they are travelling) to the vertical plane.

But, as we know, light waves have a chance of getting deflected on their way, as shown in the following diagram.

Since, while the wave is getting deflected, it would be travelling along a curved path – as long as it does not get fully deflected, it shall have some additional coordinates (C4~C6), as follows.

C4 = the distance of the green star from the light wave.

C5 = the major abscissa of the curved median.

C6 = the minor abscissa of the curved median.

Once the wave has turned around, it would again have the same three coordinates as when the wave was moving along a straight median.

So we may say the value of n of the photons may be either 3 or 6.

If it is 3, the m:n ratio of the light wave would be 5:3 – otherwise, it would be 5:6.  

So, beyond any doubt,

• We should stop using the terms “dimensions” and “coordinates” interchangeably, if m and n are more than 3.
• Though we may use the “4D” or “5D” notation if the value of m may be 4 or 5, we should use the “4C” or “5C” notation if the value of n may be 4 or 5 – likewise, for the other values of m and n.