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# Archive for the ‘Physics’ Category

## What is Aristotle’s law of motion? What are its applications?

Posted by Magellanic Cloud on December 14, 2016

What is Aristotle’s law of motion? What are its applications? by Khuram Rafique

For Aristotle, there are four objects (i) earth, (ii) water, (iii) air and; (iv) fire.

First two are heavier objects and last two are lighter objects.

Natural tendency for heavier objects is to move downside due to ‘gravity’.

Natural tendency for lighter objects is to move upside due to ‘lavity’.

Law of Motion: Natural tendency for the moving objects is to stop. If motion is to be continued, force is required.

Aristotle knows that objects move in resistant or viscous medium that’s why they eventually stop.

But Aristotle also thinks that objects cannot move in vacuum. For Aristotle, resistant medium is required for the motion to occur.

For example, a projectile is thrown with hand … after the contact of hand is removed then how motion is continued? Aristotle’s answer is that projectile is moving through resistant medium which is air. When it is moving forward, there will be sudden vacuum at the back side of object and then this vacuum will be suddenly filled by the surrounding air. This sudden vacuum filling by the surrounding air will generate a forward thrust and object will be able to move forward even at time when contact of throwing hand is removed.

However the resistance force of resistant medium will eventually overcome the forward thrust and at the end object will stop.

For Aristotle, first of all any motion in vacuum is not possible due to missing thrust. Secondly, if we accept any motion in vacuum then it would lead to absurdities that object will acquire infinite motion due to absence of resistant medium.

So what was absurd in view of Aristotle, that thing was finally shown as natural by Newton.

What is Aristotle’s law of motion? What are its applications?

## Simple Thought Experiment to Disprove Relative Constant Speed of Light.

Posted by Magellanic Cloud on October 5, 2016

Light Speed is said to be constant irrespective of relative motion of observer.

Moon is about 1.3 light seconds away from us. Suppose moon is looking like a clock such that moon clock is behind your watch by 1.3 seconds.

Now you start moving towards moon with a normal speed of 100 km/hr. Moon is 384400 KM away so your journey will take about 160 days.

Normal speed is assumed so that there should be no alleged effect of time dilation due to ultra high speed.

So after 160 days you will be on moon and what will be the difference in time of your watch and moon clock…???

There will be no difference. Means that due to your relative motion, light of moon clock has traveled up to you at speed c+100 km/hr i.e. with speed c+v.

If you are still reading moon clock as 1.3 seconds behind your watch then it means that from an ordinary distance, light is taking 1.3 seconds to reach you so again constant speed of light postulate is disproved.

Above is only a thought experiment. Now we do a real experiment. So now moon is looking like normal moon and not like a clock. And from earth we see moon which is 1.3 seconds younger than its actual age.

Now we do not suppose, we actually start moving towards moon at normal speed of 100 km/hr. And after 160 days we reach at the surface of moon.

By standing on surface of moon we are looking at moon which is not younger by 1.3 seconds but are looking at moon that exists right now. It means that during whole of our journey we had been receiving light of moon with c+v formula.

If by standing on surface of moon we are watching moon which is 1.3 seconds younger than its actual age, it means that light is taking extra 1.3 seconds to reach our eyes and again constant speed of light postulate is disproved.

## Issue of larger brain size of Einstien:

Posted by Magellanic Cloud on July 20, 2009

People believe in scientific myths that Einstien got some extraordinary brain:)

Was really E=mc2 anything new???

Not at all…!!!

So, in a sense, there was nothing new in “energy-mass equivalence”.

“c” is only the so-called absolute form of “v”.

When talking in absolute terms (i.e. not in half terms where K.E is half of Total Energy), then we don’t need “1/2” in the equation of K.E.

We simply get “E=mc2”

It is said that this wonderful formula describes energy equivalent of mass at rest. Since value of c is so high so an ordinary mass at rest will be possessing huge quantity of energy. It is also said that this formula rightly predicted such things as Nuclear Bomb.

Whereas fact is that this formula only describes such an hypothetical situation where velocity “v” of a mass has reached to the standard maximum value i.e. “c”. So actually this formula has nothing to do with state of rest of mass.

It is so assumed that this formula describes energy equivalent of mass at rest because “c” has been considered a “universal constant”. Again, fact is that within the context of matter having mass, “c” is not any “universal constant”. “c” is just the standard maximum value of a “variable” which is velocity “v”. Despite official claims of Science, there are so many unofficial counter claims that speed of light “c” is not constant or even the maximum possible speed. But here we don’t need to go against official claims. Let us accept that speed of light may be constant and may it be the maximum possible value of “v”. But point is that even then “c” cannot be regarded as “universal constant” when talking in terms of matter and mass. Because after all then it is only a value of a variable “v”. So in this sense, if “c” is not a universal constant, it means that formula E=mc2 is not describing state of rest of mass. It is only describing an hypothetical situation where value of speed (i.e. a variable “v”) of certain mass has reached to the standard maximum value which is “c”. In this right context, actually formula E=mc2 is just worthless. It is only the case of such a K.E which, due to the mass having been reached to the maximum value of velocity (may be just hypothetically), has become Total Energy.

Nuclear Bomb was the result of later discoveries of hidden Nuclear forces and was not the result of this formula. Neither this formula has anything to do with those nuclear forces. It is the nature of Nuclear Structure of any atom which determines energy contents of that element. Mere “mass” does not determine it. If it were the case then Scientists should not have needed Uranium etc. because they could get mere mass from other common elements like iron etc. also, for making Nuclear Bomb.

“Professional scientists” are making us fool by saying Einstien had some extraordinary brain…!!!

## Nature of Science – Rational or Empirical…???

Posted by Magellanic Cloud on August 24, 2007

Nature of Science – Rational or Empirical…???

There is widespread misconception among many supporters of modern established science that scientific facts and theories are all empirical in nature and this so-called “empirical” knowledge is superior to any kind of “rational” knowledge. Sometimes back, I had a little debate with supporters of the idea of so-called “empirical science”. In that debate, I pointed out that modern science’s over-emphasis on “empirical methods” is based on following false and misleading point of view:

“The sense-perception information is gained using our basic senses. It is opposed to the information that one develops by pure rational reasoning.”

In my opinion, the above-quoted point of view is misleading. First of all I do not accept the idea of “pure rational reasoning”. For me, the idea of a Rationalist that mind can find the first principle without any involvement of sensory information is WRONG AB INITIO.

In this connection, for me, point of view of John Locke is true that all basic knowledge comes only through the channel of senses. Mind cannot reach to any first principle without involvement of sensory information.

A Rationalist like Descartes or Hegel says that mind, at its own, can reach to first principle. All other knowledge of reality then can be deduced out of that first principle. Thus this form of Pure Rationalism works on deductive logic.

Now I try to explain that this “Pure Rationalism” is deductive logically inaccurate. Consider the following simple deductive argument:

All A is B
All B is C
Conclusion: All A is C

Now I try to analyze this “conclusion”. This deductive conclusion consists of four words which are (i) All, (ii) A, (iii) is (iv) C

In this conclusion, not a single word is anything new. All these four words are already contained in the premises. So in any deductive conclusion, all the contents of conclusion are already contained in the premises. In the conclusion, only the arrangement of words is changed.

Now take the example of a renowned first principle i.e. “Cogito Ergo Sum”. Descartes claims that this is the first principle of his philosophy. In the Pure Rationalism, all other contents of philosophy must have to be deduced out of this first principle.

Now we know that in any deductive conclusion, only the arrangement of words is changed. What it means? If Descartes` philosophy is really a Pure Rationalism, then there should not be more than three words in his whole detailed philosophy.

Pure Rationalism is logically wrong….!!! because actually there are so many words in the philosophy of Descartes. Descartes is having a false claim that he is pure Rationalist Philosopher. In the real sense, his Philosophy could not go against the basic idea of John Locke. That`s why his detailed philosophy is having so many words … which are although seeming to be the part of reasoning … but actually have come from sensory information.

Now I again come to the above-quoted statement, which, in my opinion, is a completely misleading point of view. I reproduce that statement below:

“The sense-perception information is gained using our basic senses. It is opposed to the information that one develops by pure rational reasoning.”

In this connection, my opinion is that sensory information is considered to be opposed to rational reasoning by the “Pure Rationalist Philosophers”. Pure Rationalists` point of view is logically wrong so this statement is also logically wrong.

Fact is not that reasoning is opposed to sensory information. Fact is that reasoning is actually a RE-ARRANGEMENT of sensory information.

My opinion is that all knowkledge is basically empirical … because point of view of John Locke i.e. an Empiricist, was right, in my assessment.

But in my opinion, there is no clash between “empirical knowledge” and the so-called “rational knowledge”. Rational Knowledge is actually just a re-arrangement of empirical knowledge. This point of view, basically, was originated by David Hume.

Here, an objection can be raised that point of view of modern science is not akin to the philosophy of “Pure Rationalism” because modern science doesn’t work on any given “first principle”.

My point of view is that mere fact that science doesn’t work on any given first principle doesn’t make it purely empirical in nature. Modern science is still very much “rational”, in my opinion. But modern science is not “rational” in the sense of “pure rationalism philosophy”. Modern science is “rational” only in the true sense of rationalism. And the true rational sense is that product of reasoning has to be a “re-arrangement” of sensory data. So in this right sense, we should not find any clash between product of reasoning and any empirical knowledge. If we try to look more closly, we shall find that product of reasoning, being the “re-arrangement” of sensory information, can be considered to be the final product. Mere sensory information can be regarded as just raw material in this right sense. In this way, rational knowledge i.e. the product of reasoning, should be considered to be superior form of knowledge because of being the final product in essence. Mere empirical knowledge is actually inferior because it is just like raw material which still has to go through the process of rational reasoning. The mistake of modern science is that it considers itself only empirical in nature. It is important to highlight that modern science, mistakenly, not only disowns, but also degrades all the forms of rational reasoning. As a collateral mistake, modern science considers only empirical knowledge to be the superior most form of knowledge. And as a result of this kind of mistakes, modern science doesn’t officially recognize any valid role of logical reasoning in it’s research procedures. It’s proof is that theory of logic is not the part of syllabus of study of science at any level.

I have mentioned earlier that in the “true rational sense”, product of logical reasoning has to be a “re-arrangement” of empirical knowledge. I have no objection against a True Rationalist. I have objections against only Pure Rationalist. A True Rationalist knows the importance of sensory or empirical information. But he doesn`t confine himself to just empirical procedures. The procedure of a True Rationalist can be stated like:

Sensory Information >>> Logical Conclusions >>> Empirical Verification>>>Logical Interpretation of Empirical Verifications

I have objections against “established” scientists also. They are Not True Rationalists because they ignore the LOGIC part of this true procedure. If anyone is a PhD. in Physics, I am hopeful that he/ she migh not have seen Theory of Logic as a part of his/ her syllabus.

Here I am in need to clearly differentiate between “True Rationalism” and “Pure Rationalism”. Accepted definition of Pure Rationalism is “such a Philosophical view that accepts the possibility that mind can reach to first principle (i.e. axiom) without help or involvement of sensory information.” This form of Pure Rationalism downgrades sensory information, by assigning superiority to only Pure Rational Knowledge. All the detailed philosophy of reality is supposed to be rationally deducible out of that first principle. In this way pure rationality can find everything about reality even in complete absence of sensory information. This philosophical view has created a misconception as if there is some clash between sensory knowledge and rational knowledge.

In the times of Galileo, Johannes Cappler and Newton etc. when Old Greek “rational” (i.e. pure rational … as supposed) theories were found to be wrong as per experimental tests, then sensory or empirical data/ information got superiority over the so-called pure rational knowledge. Then scientists started degrading all the forms of rational knowledge because no one bothered to see that actually rational knowledge was not any entity which could exist independently of empirical knowledge. General idea was that empirical knowledge and rational knowledge were having separate and independent sources of origin and that now onwards, only empirical knowledge became standard of truth. Newton’s laws of Motion were declared to be Empirical Laws whereas fact is that let’s say First Law of Motion is a complete Logical Law. My question is that what is the empirical proof that an object shall always remain in the state of rest until and unless it is impressed upon by a net positive force? What could be the “empirical proof” for such a law? Obviously such a law can only be empirically tested in the time-scale of infinite period because the thing to be empirically confirmed here is that the object shall ALWAYS remain in the state of rest. So the complete empirical test can be performed only over an infinite period of time. Not only that this law cannot be empirically tested, it is also not the product of any empirical test but is the product of Logic. In order to develop this law, Newton himself had not conducted any experiment. This law happened to be the Logical Conclusion of those experiments which Galileo had performed on inclined plane. Galileo had found that a ball, in a double inclined plane, when moves downwards on downside plane, it accelerates. And the same ball when moves upside, on the other upside plane, the ball decelerates. Galileo reached to its logical conclusion that if ball is neither moving downside, nor upside; then it would neither accelerate nor decelerate. The logical conclusion, to which Newton reached was that if a ball is neither accelerating nor decelerating, then the ball shall be in the state of rest or uniform speed. And since Newton knew the concept of Force of Gravitation, so he drew another logical conclusion that downside acceleration and upside deceleration of ball was due to net downside force and net upside force respectively. The next logical conclusion was that in the absence of any “force”, the ball shall neither accelerate nor decelerate. And the other logical conclusion was that a ball, if neither accelerating, nor decelerating, it means that either it is at rest or it is moving with uniform speed. And the final logical conclusion was a simple generalization that any object, as long as it is not impressed by any net positive force, it shall either remain in the state of rest, or shall remain in continuous straight and uniform speed motion.

So despite this complete logical construction, this law is still considered to be an “Empirical Law”, and therefore, a part of “Empirical Knowledge”. Any “Rational Knowledge” is still disregarded, as scientists believe in the erroneous idea of some clash between empirical and rational knowledge. Although the scientists do sometime talk of ‘rationality’ as well and it is also true that their concept of ‘rationality’ is not akin to the philosophy of Pure Rationalism, but still their concept of rationality cannot be regarded as true rationality. It seems that scientists are not clear on the issue of type and nature of ‘rationality’ that should be the part of their procedures. In above discussion, I mentioned the True Rational Procedure in following way:

Sensory Information >>> Logical Conclusions >>> Empirical Verification>>> Logical Interpretation of Empirical Verifications

Currently, scientists are disregarding “Rational Knowledge” and “Theory of Logic” as well. The true rational procedure, as identified above involves application of the theory of logic at two important stages.

Just the “Empirical Verification” cannot become a solid proof until and unless such “Empirical Verification” has been logically interpreted and explained. Those who are not scientists may not believe in the just simple truths of scientists. I believe that many illogical and inaccurate theories are still the part of established science.

Modern science emphasizes on its so-called “empirical methods” so much that it tends to almost completely deny any valid role of logical reasoning or the theory of logic in the process of development of new scientific theories. This position of modern science can be described in the words of a so-called scientist in following way:

“While all credible scientific theories are logically consistent, logic by itself has seldom, if ever, discovered any scientific theory.”

It is a super false idea. I already had discussed the complete logical development of first law of motion by Newton in the above discussion.

So previously, I had shown that first law of motion was the product of “LOGIC”. Now I try to show that second law also had come from the door of LOGIC. As first law was stating the logical results of the complete absence of force, second law just stated the logical results of presence of force. In the first law, the logical result of the absence of force was non-acceleration. This non-acceleration had two logical states which were (i) complete rest and; (ii) uniform velocity motion.

Now come to see what was the second law in fact. Second law just had introduced the element of “force” in the same situation of first law. In the first law, the absence of force had given the result of “non-acceleration”. So the LOGICAL result in second law, of the “presence” of “force” was the “acceleration”. Second law of motion was outcome of just mere logic up to this point. The next problem was that ok there had to be “acceleration” in the presence of “force” … but how much acceleration…??? The issue of “how much acceleration” required experimental works as well as application of mathematics. For the development of second law of motion, logic played primary role whereas experimental and mathematical works had secondary function.

Perhaps science is having complete pragmatic self-conception, which may be useful but may not be acceptable to True Rational Philosophy because of being inconsistent with facts. Science only sees if “outcome” is useful or profitable or not. Science focuses only on end results and doesn`t bother to see or evaluate the sources of origin of scientific theories.

Was Mendeleev`s “Periodic Table” not the outcome of logic? He had constructed that table on the basis of “consitent” or “ordered” properties exibited by certain elements. Is logic not the name of consistency and order? He had placed even some unknown elements of his time in their proper order. The act of placing an unknown thing on its right place was a logical act and cannot be regarded as “empirical” act in any way. It is just like as premises come from sense experience whereas right logical conclusion is formed without direct sense perception.

Even the John Dolton`s theory of atom was also logical. Original theory of atom was just the logical answer to such questions as why only specific quantitative combination of different elements result in chemical compounds.

Uptill now I have discussed only the role of deductive logic in the process of development of scientific theories. Actually role of deductive logic is really limited. Most ideas or scientific theories are actually the outcome of ANOLOGY, which is a form of inductive logic. To understand the role of analogy, readers will have to go through my following article in complete:

In my opinion, Newton had reached the concept of Gravitational Force of earth through the process of analogy. If anyone asks, I can write about it in details as well. Coulumb`s law is very much similar to Newton`s Law of Gravitation. Role of analogy cannot be overlooked in the process of development of Coulumb`s law because analogy works on the basis of “similarity” between processes or phenomena or things. Many of the theories of Einstien were “analogical” in nature like the idea of “similarity” between field of gravitation and an accelerated system. The idea that if accelerated system could bent ray of light then a gravitational field also could bent ray of light, was also analogical idea. And remember that it was this idea which was experimentally verified to be true in 1919 during the time of a solar eclips.

I am having the opinion that more than 95% new ideas come through the process of analogy, i.e. a form of LOGIC. I have given link to my related article for its details.

So science should not be restricted to just “empirical procedures”. There is valid role of rational reasoning in the process of discovery of new scientific facts. So there is need to include theory of rational reasoning in the research procedures of science as well as in the syllabus of science education.

## Space – as a form of ‘Nothingness’:

Posted by Magellanic Cloud on June 29, 2007

Our Universe is considered to be made up of matter, energy and space. At the level of sub-atomic particles, Quantum Physics has found that both matter and energy behave like ‘waves’. There are some modern scientists-cum-philosophers who assert that ‘space’ is also composed of waves. They actually think that all the reality is made up of just ‘space’ and ‘space’ itself is made up of ‘waves’. Here, I disagree to the idea that ‘space’ is made up of waves. My contention is that space is NOT ‘composed’ of waves but actually space just ‘holds’ waves. Space is the name of nothingness. Space is the name of complete non-resistance for physical entities (waves: matter + energy). Space has no dimensions. Space has no measurements of its own. Space has no vastness. It is not right to say that space is finite or infinite. Because Space is ‘nothingness’. Space has no positive ‘existence’. Space, being complete non-resistance, neither attracts, nor repels anything. Those modern scientists-cum-philosophers also show amazement that how comes that matter is ‘suspended’ in space. For me, it is just due to the simple fact that space itself neither attracts, nor repels anything. So there is nothing to wonder for why objects are suspended in space.

We never measure ‘space’. We only measure ‘material entities’. For instance, 3 meters of ‘space’ is not 3 meters of ‘space’ in the real sense. 3 meters of space is actually just equal to 3 physical meters. In this way, neither we ever measure space, nor space can be measured. Only material entities can be measured. And since ‘space’ is the name of complete non-resistance, so space offers no resistance even to the measurements of material objects, to their mutual distances or to any other form of their mutual interactions. And if there is ‘distance’ between two material objects, it does not mean that any space of particular measurement ‘exists’ between those two objects. Those two objects are away from one another with distance, which is equivalent to particular number of times a physical object such as a meter. As space is ‘nothingness’, so it should have no ‘dimensions’ as well. We know of ‘dimensions’ also only in terms of material objects. It is the ‘geometry’ of physical objects, which makes us think as if space is having 3 (Some modern theories of Physics are advocating for even n-dimensions) dimensions.

So I have this type of objections in mind. For me reality is not space because it is a non-existent entity. Reality should be seen in those entities that positively exist. There are two things which are known to have positive existence which are: (i) matter and; (ii) Energy. And since both these things have been found to be made up of single entity i.e. ‘waves’, so instead of considering ‘space’ to be the source of all reality, I think it better to consider ‘waves’ as the source of reality. But we also should properly distinguish between existing entity and non-existing entity.

If waves only have discrete motion (as per Quantum Physics), then why to even talk of any kind of continuous physical motion at all? For me, all physical motion, including physical motion of ordinary objects is not continuous at all. All physical motion is discrete. Consider a simple situation. My car is moving at the speed of 100 Km/hrs and it is raining outside. Suppose vertical velocity of a raindrop was 10 Km/hrs whereas that drop had zero horizontal velocity. Now when that drop shall collide with my windscreen, it will at once acquire horizontal velocity of 100 Km/hrs. So obviously there has been a sudden change in the velocity of that drop. I can give many other simple such examples. Since the examples are too simple so I assume that readers shall understand at their own. However, I shall elaborate this point in further details in my next posts. Here, I can confidently proceed that all physical motion is only discrete. Here Zeno’s famous paradox also can be very easily solved. Zeno had argued while assuming continuous physical motion and physical existence of ‘space’. But since space has no positive existence at all and the motion of physical objects is only discrete, so logically it is possible that material objects can cover distance and so reality is not static but reality is there in variations.

## Some Points About Nature of Infinity:

Posted by Magellanic Cloud on May 6, 2007

Some Points About Nature of Infinity:

Issue of the nature of infinity is quite confusing. There are theories in Mathematics, which suggest that a finite line and an infinite line, both will be having one to one, and onto correspondence between their respective points. It means that as per these theories (e.g. Georg Cantor; 1845-1918), number of points of a finite line has to be exactly equal to the number of points of an infinite line. Apparently, this theory made no proper sense to me. Actually I believe in the “discrete” nature of reality rather than considering it to be “continuous”. Soon I shall try to explain this point in my next posts. For the purpose of this post, we can just assume that reality is “discrete” and is not “continuous” in any way. Keeping in view this assumption, below I try to discuss some of the supposed characteristics of infinity:

1. The set of all positive integers (i.e. infinite) is smaller (in cardinality) than the set of real numbers between 0 and 1.

May be true. But I doubt in the “real” existence of real numbers. As I assume (which I shall prove later on) that reality is “discrete” and not “continuous”, so what I think is that continuous numbers can exist only in certain abstract mathematical relations but any such kind of continuity cannot exist in our Physical world. There cannot be infinite discrete numbers between 0 and 1.

2. The set of real numbers between 0 and 1 is equal (in the sense that there exists a one to one and onto mapping) to the set of real numbers between 0 and 2.

Actually this one to one and onto mapping of points is considered to be existing even between a finite line and an infinite line. It means that according to mathematics (theory of Georg Cantor; 1845-1918), the numbers of points on a finite line have its number of points exactly equal to the number of points of an infinite line.

It can be seen that this theory is older than the emergence of Quantum Physics. I no more consider this theory to be valid. A finite line must be having finite number of discrete points and an infinite line must be having infinite number of discrete points. There cannot be one to one correspondence between finite points and infinite points. Quantum Physics has even calculated the minimum possible (or absolute minimum) distance. There is no anything like perfect continuity in our physical world.

Secondly, Geometry still uses old Greek concept of point. It is defined something like an abstract point, which occupies no space. The same Geometry defines ‘line’ something like as a “combination of points”. What I think is that this pure abstract mathematics cannot be applied to the physical world. If a ‘point’ has no space at all then how any ‘line’ (i.e. combination of points) can have any space…??? I think that a combination of ‘space less’ points cannot have any length. Abstract Mathematics says that a ‘line’ has length but it does not have any width. Anyways, there is need to have a Quantum or Discrete Geometry as well.

Basic forms, and a definition of Infinity:

A line can be started from a definite point and can be considered to be extending to infinity on one direction. Such a line can be considered to be ‘infinite’ line. But remember that this ‘infinite’ line has a ‘definite’ origin. This line is infinite only on onward side but this line is not infinite on backward side.

On the other hand, there also can be a line, which can be considered to be extending infinitely towards both sides. This line is also infinite. But this line is infinite towards onward and backward sides both. So there can be one directional infinity as well as there can be two directional infinity. Similarly, there can be multiple directional infinity as well and in the same way, there can be an all-directional infinity also.

One type of infinity can be smaller or larger than other one. Meaning of infinity is Never Ending on one or more sides. A thing which can end on all sides (like a finite line), cannot have never ending points in it.

What is meaning of 1/0?

If you have to divide \$100 among zero people, it only means that you are not going to disburse any sum to anyone at all. You can distribute \$100 to as many (i.e. never ending) zero persons you like. 1/0 is only Abstract Mathematics. It is good only in abstractions. It cannot be as it is applied to real physical world. More precisely, 1/0 is not the case of “never ending”. Actually it is the case of “never happening”.

The following objection was raised on my above-mentioned points:

“There cannot be infinite discrete numbers between 0 and 1”. You may well be right. But if I take rationals to be discrete, as I can count them through a one to one and onto mapping with the set of integers, then there are indeed infinite discrete numbers between 0 and 1. So your frame of reference and mine are very different. We cannot discuss much and can only agree to disagree on our frames of references.

My response was:

I already have dealt with the issue that a smaller and a larger “line” have exact one to one correspondence between their respective number of “points”. I made diagrams to see if really there was such one to one and onto mapping of points or not.

The actual mistake in official theory lies in the definition of “point” in Geometry. Geometry considers “point” as a “space less” particular location. Since this “point” is space less, so it is having no “length” at all. The same Geometry considers “line” as a linier combination of “points”. The same Geometry also considers that a line possesses a non-zero length but it doesn’t possess any width. But if the constituents of line i.e. “points” had no length at all then how just the combination of those “points” could result in any non-zero length…???

Anyways, this definition of “point” may be right definition in pure Abstract Mathematics. But this is not right for our physical world because there can be no space less physical entity in our spatial world. A “physical point” would be having some “space”. In fact, all the “points” would be having same or uniform non-zero space. Let’s say the length of one point is 1 and the length of a finite line is 100. It means that this line has only and only 100 (discrete) points. Points of this line CANNOT have one to one and onto mapping with the points of that line whose length is 200 or infinite.

What is the mistake of official theory…???

The official theory actually draws one to one and onto mapping not between the individual points of a shorter and a longer (or infinite) line. It actually draws one to one and onto mapping between fractional parts of individual points of shorter line with the complete individual points of longer or infinite line.

Now I give you a task. Consider the “length” of a “point” to be 1. Now take two lines. First line being shorter and second line longer.

Length of first line = 100

Length of second line = 200

In this way, there are 100 “points” in first line and there are 200 “points” in second line. Now try to draw one to one and onto mapping between all the points of first line with all the points of second line. Be careful that do not take fractional or overlapping parts of individual points of shorter line!

Believe me, you will not be able to do it, because it is an impossible task. So come out of the fantasy of old Abstract Mathematics where length of “point” is zero and sum of many zeros (i.e. a “line”) is non-zero positive length. In a physical world, any real “point” will be having non-zero positive length.

This is not the case of just difference of frames of references. It is a matter of clear-cut mistake of 0 + 0 + 0 = 3