Understanding Dimensions

Thirtieth Edition ; Dated: 15th October 2003

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1. DEFINITION OF A DIMENSION :

Dimension is that particular state of existence of a body whose increase or decrease (if dimension for that body be 'd') will increase or decrease (respectively) the body's capability of attaining more room for its accomodation at a limited amount of space with respect to an observer(or body) at a particular state of existence,which has it's Dimension Number greater than or equal to 'd'.

Note:

Increase in dimension with respect to a particular observer means increase in room of the body in the higher dimensions with the magnitude of the physical quantities of its existence (for eg. Length, breadth and height for a 3D object) in its earlier dimensions (at which the observer is present) remaining constant.



2. THE DIMENSIONS :




3. A GROUND BREAKING THEORY :

The Fourth Dimension : Time-Flow Rate

It is known almost universally that the Fourth Dimension is Time. But according to our research the 4D comes to be a different one : Time-Flow Rate.

Like simple quantities like length, breadth and height which can be theoritically zero in the 1st, 2nd and 3rd Dimensions respectively ; 'time' can never be zero in the 3rd Dimension. Time is a ever flowing stream of quantity. Time has a measure which can never be equal to zero in magnitude. Only the Time-Flow Rate (TFR) can be zero in Relativistic Mechanics. In a singularity, the Time never becomes zero, but it is the Time-Flow Rate which becomes zero.

Another proof that Time itself is present in every dimension is shown below:

We know that in our universe every body is in motion. So everything is moving and there is nothing called absolute rest. Now if we plot the motion of a point in one dimension in a position-time graph, we will require two axes. Similarly for two dimensional motion we'd require 3 axes and to plot the motion of a 3D body we'd require 4 axes, which can be managed theoritically. But if time is the Fourth Dimension, then the time axes would appear twice, which would be quite absurd.

Now it's time for some mathematical calculation:


From the Special Theory of Relativity we know that every body has its personal time.


The ratio of TFR to the space occupied dy a body is always constant, which is represented by � (called the Vivekaditya constant. Similarly a series of equations are formed in which the ratio with the different physical quantities like length, mass & time (which tends to change in relativistic mechanics) to the TFR, is a constant ( the Vivekaditya Constant ). But for different quantities the value is different. Please see the Appendix for more details. Hence the 4th Dimension is not Time but Time-Flow Rate.



4. DIFFERENT ESSENTIAL IDEAS ABOUT DIMENSIONS :

View from previous dimensions:




5. CURVED SPACE :

This is a very interesting topic to think about. Suppose a small One Dimensional Train runs on the letter 'L' with hypotenuse AC and the other vertex is B. To its passengers, the train would seem to run in a straight line, but in reality, their One Dimensional world has been 'curved' into the Second Dimension. The shortest distance to travel to the point 'C' in the above figure for that 1D train would be equal to (AB+BC). But to a 2D object the shortest distance would be along AC from A to C. So, we see that a 2D object takes less time to cover the distance than a 1D one.

Another illustration may be given :

Suppose the figure of a three dimensional life-saving tier. 'A' and 'B' are two fixed points on the interior side of it. To a 2D object, the shortest distance between A and B would be all along the surface of the tier. But to a 3D traveller, the shortest distance would be along the straight line joining the two points A and B. In this case the 2D world was curved into a 3D one.

Similarly, scientists say that our 3D world may also be curved to a 4D one, and to a living being of the 4D world, there may be some shorter distance to cover between you and this page !



6. MY NEW PERSONAL THEORY : We live in the Fourth-Dimension !!

Let us first grip the idea of the application of Dimensions by taking examples from our daily life :

Let us first review an account of a Two Dimensional drawing. When we draw a plane geometrical figure on a sheet of paper, we say it is in the Second Dimension. By saying this we mean that the figure has only Length and Breadth, but no height (or height = 0), or, we can also assume that the height of a Two Dimensional figure is constant while its length and breadth can be varied. Similarly, for this case we hold all the higher(>2) known and unknown dimensions constant (each equal to zero). Therefore, height, time(the accepted Fourth Dimension) have no effect on the plane figure.

Now, we place a solid cube on our palm and claim that it is Three Dimensional. Is it really so ?


The Proof of my Theory :

Now, as we see, for a Three Dimensional object, time has no effect on it i.e. the object is unchangeable with time. But in our daily life, we find that nothing is unchangeable with time.

For example, a person dies and after that (with advancement of time) it(the body) decomposes by the action of bacteria on it. So the body changes with time.

Again, when we strike a hammer on a fragile cup, it breaks immediately. Similarly, we can find billions of examples from our daily life. In fact, movement of anything in the universe cannot take place without time. Even light takes a considerable time to move.

So we see that time is not at all 'constant' in out universe, but it is ever-changing. Time only 'ends' after the Big Crunch Singularity or 'starts' after the Big Bang Singularity. So Three Dimensional objects, if any, can only exist after the Big Crunch or before the Big Bang. But this can never be possible, as all the matters in the universe gets 'sucked up' in both the Singularities.

By applying the similar theory, we can also prove that nothing 'real' can exist at a state/dimension below the Fourth Dimension. The lower dimensions can only exist theoretically, but never practically.


Note:

If the cup would be Three Dimensional, then the hammer could never touch it. Because, if the hammer touches the cup, it will pass on some kind of energy to the cup, violating the rules of the Third Dimension(which says that a Three Dimensional object remains unchanged with time.)



7. IMPORTANCE OF LIGHT IN THEORETICAL ABSTRACT PHYSICS :

Now, we will discuss why we pay so much importance to light in the determination of past, present and future.

The most important reason is that light has the highest velocity among all the other particles in the universe. The second reason is that our visibility, given to us by light, is the fastest and most convenient sensory process. These two reasons combined can make our discussion successful.

As we said, light has the highest velocity among all the things in the universe. Now, we know, we can sense an object when the impulse created by its mere presence is transported to our sensory organs by some transportive mediums (waves in case of visibility and hearing) and then to the brains by our nervous system. Again for the longitudinal sound waves are assisted by a particle medium and for transeverse electromagnetic light waves it is disturbed by a particle medium. We can see an object, when light rays coming from a particular source of light incidents on the object and reflected light rays fall on the retina of our eyes through the refractory mediums : cornea, aqueous humor, lens and vitreous humor respectively. The next work of transporting the impulse to the brain is done by some photochemical/photoreactive cells known as rod and cone cells and other optical cranial neurones. Again, when we a sound wave originating from the point of vibration strikes and vibrates the tympanic membrane of our middle ear and the impulse of vibration is modified by the three small bones of our body : incus, mallaus and stapes respectively and the next works are done by the Organ of Corti.

So we see, that in both the cases the two types of waves have to travel from the point of presence of the object to the point of our respective sense organs (i.e. to the point of presence of us). Hence their speed really matters and how fast we can sense the object depends on the speed of these waves. So faster the waves are, sooner we will perceive its presense. Now, we can understand why we rely on light so much. As light has the highest velocity, the impulse created by the light ray will be carried to us much much faster than the sound wave or than anything else.

We can definitely neglect the sense organs skin and tongue. Because we wont definitely like to go to the Adromeda Galaxy and then touch it or taste it to feel its presence !

That is why before we 'see' an object, we cannot determine its presence. And similarly, when a particle travels at a velocity equal to or greater than that of light, we generally say that it has gone into the future, as we cannot see the object, though it does its work. But in practical conservative crude scientific sense the body moving at a speed equal to or greater than that of light still remains in the 'virtual present' along with us. Its only the failure of light and our sense organs that sends it into the 'future' !!



8. 'VIRTUAL PRESENT' :

We all know that we are in the present, but you'll be surprised to know that this idea is completely wrong! With every nanosecond (1 nanosecond is an extremely small fraction of a second, here I mean a smallest fraction of time possible.) we step into the future. So, when we say, "we are in the present", while saying or even thinking, we have stepped into the future, and that 'present' has become 'past' now. So, it will be wiser to say that we are somewhere in between present and absolute future! That is why we are calling present as 'virtual present'.


Note :

For a body to move at a speed of light is absolutely impossible. Stephen Hawking says, "It (a body) can never reach the speed of light, because by then its mass would have become infinite ( there is a theory stated by Albert Einstein which says that the mass of a body gradually increases as it approaches the speed of light.) and by the equivalence of mass and energy, it would have taken an infinite amount of energy to get there.' Stephen Hawking also said, "Only light, or other waves that have no intrinsic mass, can move at the speed of light." - Thus no body can move at a speed equal to or greater than the speed of light.



9. APPENDIX :


Note 1 :

Density increases because we see from its previous dimensional field. But in reality when we see from a Superhigh Dimension then the density is always constant, considering the space occupied in all its dimensions.


Note 2 :

With incease in velocity, the TFR increases, and though the length, time and mass seem to change, they are always constant i.e.

(mass-1) / (TFR-1) = (mass-n)/(TRF-n) = �-1

(time-1) / (TFR-1) = (time-n)/(TRF-n) = �-2

(space-1) / (TFR-1) = (space-n)/(TRF-n) = �-3

(length-1) / (TFR-1) = (length-n)/(TRF-n) = �-4

Here the series of � is called The Vivekaditya Constant Series.The Values of the different � -s are not necessary equal.


Note 3 :

Most of the mathematicians or physicists working on the physical dimensions describe a cube as "an infinite number of squares piled upon one another" . Now I will try to explain the truth of this statement.

We know that a two dimensional square has no height i.e. height = 0. But then one may think that as any number multiplied by zero is zero then why do we get a cube (which has a definite height) by piling an infinite number of squares? Lets first review the maths equation and its proof below :



Proof of : 0 � [infinity] is finite

Let 'a' be a number such that a approaches 0.

Therefore,

0 � [infinity]

= Lt |a| � Lt (m/|a|) [ Both of these Limits exist ]

= Lt {|a| � (m/|a|) }

= Lt (m)

= m

Hence proved.
Here 'm' is any arbitrary real finite number.

(Proof developed by Vivek Panda )


Footnote:
Though here I have done a multiplication with infinity as one of the multiplicands, it must be borne in mind that it is not a number, just a symbol representing the number which is greater than the greatest possible number we can ever imagine. Conceptually here we have to accept infinity as an extremely great number.


Here we clearly see that multiplying a quantity, which is almost zero, almost an infinite number of times we get 1, i.e. it's dimensional number increases by one.

Similarly, by placing an infinite number of points(which has no dimension) one beside (with no space in between another it gets into a new dimension (length) and placing an infinite number of straight lines one beside another (with no space in between) it attains a new dimension (breadth). May be we can also define the fourth dimension in a similar way !!

The above result also explains why two straight line of lengths say x units and y units (where x and y are finite real numbers) are both consisted of an infinite number of points arranged adjacent to each other in a specific direction.



ACKNOWLEDGEMENTS :



Compiled and Written by : Vivek Panda

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© & ® Vivek Panda : June 2002