Category Archives: General Relativity and The Big Bang Theory

Can Mathematics discover unknown realities of Physical World?

Mathematics is quantitative extension of logic. It can move beyond logic only in exact quantitative terms. The basic realities are discovered through observations. Secondary realities are discovered through logic. Quantitative realities are derived from basic and secondary realities by using mathematics.


Unfortunately Modern Physics is built on assumption that mathematics itself is capable to discover unknown realities of Physics. We often read in science literature that physical fact ‘x’ was already ‘predicted’ by equations ‘M’ so physical fact ‘x’ is considered as a necessary consequence of equations ‘M’ and interpreted only within the context of same equations ‘M’.

In the Big Bang Theory, there is a deceptive claim that in year 1927, Georges Lemaître had ‘mathematically predicted’ physical fact of linear relationship of redshifts and distance whereas that mathematical prediction came true in year 1929 when Edwin Hubble experimentally found the same linear relationship. Only because the said relationship was already mathematically ‘predicted’, mainstream Physics did not feel the need to see whether that kind of relationship could be considered as physical proof of expansion or not. Only because already available mathematics was talking about ‘expansion’ so the newly found linear relationship was simply interpreted in terms of ‘expansion’.

Likewise, CMBR type radiation were already ‘mathematically’ predicted. When apparently same type of radiation were experimentally found, then again mainstream Physics felt no need to find the actual reason of those radiations and they were simply interpreted within the context of already available mathematics.

Right method should be Observation>>>Logical Interpretation of observed reality by evaluating all the possible explanations>>>Quantified Model using Mathematics. (This method implies that mathematics itself does not find unknown realities)

The actual prevailing method of Modern Physics is like Mathematics>>>apparent resemblance of later on found physical facts with already available mathematics>>>Hue and Cry that ‘mathematical prediction’ has come true>>>adaptation of already available mathematics (with few modifications) as final interpretation of newly found physical facts. (This method implies that only way to find unknown is the way of mathematics)

It is often stated that Einstein had found hard physical realities through the way of mathematics. Bending of light ray was experimentally confirmed during a Solar Eclipse etc. The thing to be noted in this case is that after reaching at ‘Equivalence Principle’ with the support of Eötvös experiment (Observed physical fact), First of all Einstein had logically evaluated the stuff. If acceleration due to gravity was independent of mass (a logical interpretation of physical experiment) then light also must accelerate under gravity (logic). But according to his own theory, speed of light could not be affected (logic). If speed of light could not be affected then there were two (logical) options; (i) Wavelength of light could be affected (gravitational redshifting) or (ii) light could change direction (i.e. other logical form of acceleration).

Thus logic took him to the idea of bending of light. Next stage was quantification i.e. ‘how much bending’. From this point onward the role of mathematics entered to the scene.

Therefore mathematics had not found unknown reality in this case. More specifically, if Solar Eclipse experiment had really confirmed anything then it was that (logical result out of observation) acceleration due to gravity was independent of mass.

However if we try to look at further details, then keeping in view the personality of Arthur Eddington who actually performed 1919 Solar Eclipse Experiment, the whole confirmation of General Relativity on the basis of this experiment sounds notorious and unreliable.

Arthur Eddington, within mainstream interpretation, had confirmed that mathematics really found unknown realities. Eddington again played a crucial role in 1931 when it was almost established that Georges Lemaître had already ‘mathematically predicted’ Hubble’s law in year 1927. However, later on, the same Arthur Eddington, in the case of Subrahmanyan Chandrasekhar, would refuse that mathematics can find unknown realities of Physics.

But since Chandrasekhar’s point of view was succeeded at the end so mainstream Physics ignored the confession of Arthur Eddington that Mathematics itself cannot find realities of Physics. 

Role of mathematics is also important to be clearly explained and limits be identified within the domain of Philosophy. Below I am quoting a relevant portion of my upcoming book “Descriptive Knowledge, Mind and Reality; a case of Epistemological Realism”:

“There is no a priori knowledge which is totally independent of sense experience and neither mind is a flat recipient of sensory information. Those general tendencies form a natural flow of expression of contents of framework of consciousness and tend to make it consistent, smoother, balanced and/ or more accurate. This is logical way of how external reality is perceived and then expressed and does not amount to a priori knowledge. To say that mind derives things or can calculate is equivalent to accept that there is no a priori knowledge. Mind derives or calculates means that mind has the ability to derive or calculate and does not mean that mind is already aware of correct answers. Certainty that we get from the results of mathematics is not real as most of the times it depends on suppositions. One plus one is always two because quantity of one is supposed to be fixed. Mathematics in its practical usage by mind is based on suppositions and thus not real; however there comes a real aspect of mind that mind is able to suppose fixed, unchanging, absolute or universal entities and then becomes able to get certain results by performing mathematical or logical operations on those supposed universals. Universals themselves are unreal but ability of mind to suppose them and perform mathematics and logic on them is real. Universals come from ability of mind to suppose and not from ability of mind to generalize. Generalization leads to ultimate categorization and not universalization. Simple analytic judgments are also not a priori. Judgment, basically being one or the other form of inference or conclusion, itself is a secondary thing. At the most it is a mold which gives the primary sensory information a different and useful shape such that all the ingredients of final product were already contained in that primary sensory information. In this capacity, again it is ability and not pre-existent correct answer. In analytic judgments where predicate is obtained by simply analyzing the subject, the pre-existent correct answer was contained in primary sense data and not created by mind through judgment. We take example of analytic judgment as provided by Lord Bertrand Russell[i] which is stated as: “a bald man is a man”. This type of analytic judgment was regarded in pre-Kant era, Bertrand Russell states, as example of a priori knowledge because in these judgments, predicate being part of the subject, we are certain a priori. As already mentioned, judgments themselves are secondary in origin therefore certainty connected with them is also secondary in character thus there is nothing a priori in analytic judgment. This is equivalent to say that it is certain that a tree is tree so knowledge of tree is a priori or at least this judgment is a priori. Knowledge of tree comes from senses and judgment is a secondary thing which tells us nothing wholly independent of sensory information.
Issue of analytic judgments, as Russell continues, is connected with principle of contradiction which asserts that nothing can at the same time have and not have a certain property. We should now examine the case whether this principle itself can be regarded as innate or a priori or not. The certain thing is that this principle in descriptive form is not innate. Even in the capacity of a logical mold machine, it is doubtful that this principle is innate of mind. However it is a fact that mind is not able to form mind images of self-contradictory things like impossible figures. But how an impossible thing can be regarded as innate just because mind remains unable to perform that impossible task? If principle of contradiction is innate of mind then inability of mind to see view of sun which is less than 8 minutes old is also innate of mind. The principle of contradiction is a general characteristic of outer reality which does not accommodate any object that at the same time has and not has a certain property. If we accept that this principle is innate of mind then next claim that outer reality is constructed by mind also becomes possible because then outer reality would be obeying this principle of mind and could well be a product of mind. In this regard, what is innate of mind is the ability of mind to remain consistent with outer reality though mind is able to stay away from facts of outer reality also. Basically human mind tends to stay away from facts and only after sufferings through mistakes then becomes able to keep itself consistent with outer reality. With the passage of this evolutionary process, mind has then captured this principle from the general behavior of outer reality through sense experience and through its own inability to form mind image of self-contradictory things. Then mind has given it absolute form through innate ability of supposition of universals. This principle talks of universal, unchanging and fixed entities; such things being non-extractable from general behavior of outer reality so this ability of supposition is innate of mind. But what things can be assigned universal attributes? The answer is only those things whose all component parts are traceable to sense experience, details thereof we shall see in chapter 5. Here we can proceed with our conclusion regarding analytic judgments and principle of contradiction that both are not innate and do not amount to a priori knowledge. However with regard to principle of contradiction, we do acknowledge that ‘inability’ of mind to imagine self-contradictory idea in the form of mind image is innate but at the same time this inability does not constitute any innate or a priori knowledge of mind which is independent of sense experience. Examples include impossible figures which cannot be imagined in the form of mind image and neither can be drawn on paper except in the form of illusory tricks. But this inability of mind is consistent with the inability of outer reality where also any impossible figure cannot exist. Self-contradictory thing is an impossible thing in itself and does not depend on inability of mind for its impossibility of physical existence. In simple terms, mind is not able to imagine what is impossible in itself so there is no involvement of any positive ability of mind. Positive ability of mind in this connection is the ability to conceive self-contradictory things only in descriptive format. It is possible for mind to conceive descriptive concept of impossible figure like a ‘square circle’ but it is not possible for mind to form mind image of same concept. Mere ability or inability of this sort does not constitute a priori or innate knowledge of mind. Our conclusion regarding ability of supposition of universals is that this ability is innate to human mind only since this ability seems not available to animal mind and that things that are supposed as universals ultimately had come from sense experience and thus there is no involvement of a priori knowledge.
If we take simple meaning of a priori knowledge as something we do not need to confirm in our routine judgments then yes we know a priori that a bald man is a man. Or that 7+5=12 is also a priori knowledge. But through this philosophy, we are examining our basic tools and infrastructure. In this realm, innately we are not even provided with any idea of 7 or 5. Children of pre-school age can learn counting only if they are taught by parents or guardians. Few months back I met a 10-11 years old boy who does not know counting more than 20 because his father died when he was so young and due to difficult domestic economic conditions, he might have attended school for only a short duration. Suppose he can do 2+2=4, which he cannot do in fact but suppose he can do, but how he will do 22+22=44? Suppose up to 20 figures are innate in him but why the simple figure 103 is not innate in him? It was a slip number which he could not read. My 4 years son who is studying in prep class can count up to 100 but he cannot do simple sum of 2+2=4 without my help and guidance that I provide using examples of concrete things. Lord Russell further states and affirms with reference to works of David Hume that 7+5=12 is a synthetic judgment as idea of 12 is not contained in 7 or 5; not even in idea of adding them together and also that knowledge of pure mathematics is a priori. Russell seems to point out that with this new problem, synthetic judgments also became a candidate of a priori knowledge. In fact David Hume has not discussed analytic or synthetic stuff at least in Enquiry Concerning Human Understanding. And in my humble opinion, David Hume has taken pure mathematics as a priori only in routine sense which I have described at the start of this paragraph. After discussing mathematics as a priori, then Hume moves to matters of fact such as someone is in Paris or not etc. that needs factual evidence for knowing the truth. Then he discusses cause and effect and concludes that cause and effect cannot be known a priori. His following sentence will make sense that basically he is talking about a priori knowledge in routine sense.
“I venture to assert, as true without exception, that knowledge about causes is never acquired through a priori reasoning, and always comes from our experience of finding that particular objects are constantly associated with one other.”[ii]
While discussing mathematics, his point was that reasoning alone could perform arithmetic or geometric operations and experience was not required. With the problem of cause and effects, his opinion is that reasoning alone is insufficient and experience is required. With further proceedings, more troubles will arise and he will say that past experience will also fail to predict future occurrences. Anyways, I here disagree that only pure reasoning can solve arithmetic or geometric problems as no pure reasoning which is independent of sensory experience exists at all because reasoning is the name of inferring process which is not independent of sense experience. However by saying that through reasoning, problems of arithmetic etc. will be solved, he is clearly taking routine meanings of a priori knowledge and same is the case with his later analysis. And perhaps Kant also has example of only mathematics with regard to synthetic form of a priori knowledge which we accept a priori only in routine sense and not in the sense of basic innate a priori knowledge of human mind. On the whole yes we are a priori certain that 7+5=12 but what about mathematical assertion that sum of series of odd numbers like “1+3+5+…” is always a perfect square? Only a person who already knows it through experience would be a priori certain about it. Any person who has not yet experienced it would tend to confirm it by adding 1 with 3 to get 4 which is a perfect square and then would add 5 with earlier answer 4 to get 9 which again is a perfect square and so on up to a reasonable limit to get a priority surety for the next times. David Hume had rightly pointed out (i.e. with only adjustment that pure reasoning is not independent of experience) that by examining only reasonable instances of mathematical assertions, we can get a priority surety for the future with regard to all the rest of un-examined infinite instances. But this is not the case with cause-effect situations where a priority surety for the future occurrences is not possible regardless of how many instances we already have examined.”

We get Redshifted light from all the directions. What are the possible interpretations?

We are getting redshifted light from everywhere.

Now there are two possibilities:

1- Space is expanding at every scale and universe is expanding like a balloon. (far fetched idea – we should expect such an idea from pseudoscience or flat-earth type people).

2- Only light is getting redshifted per unit of distance. (Sensible idea – should have been expected from mainstream).

Mainstream people of Physics accuse critics of the Big Bang Theory as ‘cranks’ and ‘crackpots’. They argue that discipline of Physics is prone to attacks from ‘cranks’ (for unexplained reason) whereas this is not the case with other branches of science such a Biology.

My response to them is that when mainstream Physics itself is ‘cranky’ then we feel the need to come forward. Other branches of science like Biology etc. are not ‘cranky’ themselves so we do not criticize them. It is modern Physics which has challenged human commonsense and at least my response to Physics is like answer to Modern Physics by the commonsense.

Anyways, to the above narrated two possibilities, I received following objection:

“If what you’re saying was true, then andromeda should also be redshifted, since it is far away from us, but it’s not, because it’s coming towards us.

We get the same thing with binary stars, when they are approaching they are blue, when they’re going away they’re red.

The same happens with spiral galaxies, the side spinning towards us is closer to blue, and the side going away is closer to red.”

My response was following to which I received no further reply:

“Light is getting redshifted per unit of distance.”

The rate of redshifting of light is very low. Within the range of local group of galaxies, the “light’s inherent redshift” can be lower than “Doppler’s Blueshift” due to actual approaching speed of galaxies of local group.

Same applies to binary stars where Doppler’s interpretation is correct.

But after a sufficient distance, inherent redshift of light always overcomes Doppler’s blue shift due to actual motion so after a considerable distance, we always get redshifted light.



What should count as ‘Physical Proof’? Why Redshifts and CMBR serve as ‘Mathematical Proof’ rather than being ‘Physical Proof’ of Big Bang?

Physical proof is simply the experimental proof. The redshifts that scientists have observed in light coming from far off galaxies are NOT due to Doppler’s effect thus do not amount to physical proof. That is a different kind of redshift which is called Cosmological Redshift.


This redshift is not proof of receding of anything. The only proof which Big Bang supporters have is a mathematical proof (FLRW metric). Its meaning is that the theory (Big Bang) is NOT developed out of experimental findings. It is NOT developed out of Doppler’s Effect. It is developed out of FLRW metric which only ‘explains’ or ‘attempts to explain’ the observed fact of ‘cosmological redshift’. Likewise, theory is also not developed out of experimental finding of CMBR. Only thing is that experimental finding has been ‘explained’ in terms of FLRW metric. At the most they got ‘prediction’ of CMBR from FLRW metric. In this way the maximum thing is that the Big Bang Theory becomes mathematical explanation of CMBR. But after all theory was not developed out of experimental finding of CMBR. At the foundation level, there is only mathematics. Observed facts are only at ‘interpretation’ level. It is possible to interpret both cosmological redshift as well as CMBR in some other way.

How idea of The Big Bang Initial Singularity Emerged?

In Modern Physics, there are two distinct forms of singularities which are (i) Black Hole Singularity and; (ii) Big Bang Initial Singularity. These so called ‘counter intuitive’ notions or concepts of ‘singularity’ are results of mistakes and misunderstandings rather than actual result taken from equations of mathematics. Development of scientific ideas is not outside the regime of epistemological principles. Scientific Knowledge is also evolved as progression of ideas. Ridiculous, non-sense or ‘counter intuitive’ ideas usually come from mistakes and not from genuine observations, deductions, inferences or mathematical derivations.

Ideas of above two kinds of ‘singularities’ are not older than early twentieth century though concept of ‘Black Holes’ can be traced to as early time as year 1783 when John Michell[i] first time pointed out the possibility of massive stars who could be able to trap light. He even provided the method to indirectly identify the presence of such ‘dark stars’ through the type of orbital motion of other visible stars in particular locality. Thanks to John Michell, he introduced genuinely possible concept of ‘black holes’ that was not based on ridiculous idea of ‘singularity’. The ‘super massive black holes’ that are now supposed to exist at center of galaxies are actually this type of non-singularity black holes. According to John Michell such ‘dark stars’ could have diameter as large as 500 times that of Sun. Therefore we see that original concept of black holes did not involve concept of singularities.

Following is a relevant quote from Wikipedia article on John Michell.

It was Michell who, in a paper for the Philosophical Transactions of the Royal Society of London, read on 27 November 1783, first proposed the idea that there were such things as black holes, which he called “dark stars”. Having accepted Newton’s corpuscular theory of light, which posited that light consists of minuscule particles, he reasoned that such particles, when emanated by a star, would be slowed down by its gravitational pull, and thought that it might therefore be possible to determine the star’s mass based on the reduction in speed. This insight led in turn to the recognition that a star’s gravitational pull might be so strong that the escape velocity would exceed the speed of light. Michell calculated that this would be the case with a star more than 500 times the size of the Sun. Since light would not be able to escape such a star, it would be invisible. In his own words:

If there should really exist in nature any bodies, whose density is not less than that of the sun, and whose diameters are more than 500 times the diameter of the sun, since their light could not arrive at us; or if there should exist any other bodies of a somewhat smaller size, which are not naturally luminous; of the existence of bodies under either of these circumstances, we could have no information from sight; yet, if any other luminous bodies should happen to revolve about them we might still perhaps from the motions of these revolving bodies infer the existence of the central ones with some degree of probability, as this might afford a clue to some of the apparent irregularities of the revolving bodies, which would not be easily explicable on any other hypothesis; but as the consequences of such a supposition are very obvious, and the consideration of them somewhat beside my present purpose, I shall not prosecute them any further.

— John Michell, 1784[13]

Then comes the twentieth century where Einstein induced new spirit to mathematicians by giving them opportunity to find ‘solutions’ to his General Relativity equations. One early solution that emerged was by K. Schwarzschild[ii] whose work has now become basis of all the singularity based black hole physics.

The English translation title of his 1916 paper is “On the Gravitational Field of a Mass Point according to Einstein’s Theory”. The paper itself is too complicated to offer solid and consistent sense. But title of the paper is simple. It is talking about ‘Mass Point’ and the first impression that at least I get is that he is going to discuss gravity field in abstract mathematical terms. From the title, I am not getting the impression that he is going to invent brand new idea of a physically ‘massive singularity’. There is also nothing in whole paper that could indicate that he was talking about ‘massive singularity’ type of thing.


Above is a more relevant point in this paper where he was giving an example of ‘point mass’ equal to mass of sun. Well, if I write a book on gravity, I will also use similar examples. But instead of using term ‘point mass’ equal to mass of earth, I will use phrase “hologram earth with nothing solid but real gravity equal to the gravity of earth.” It will make simple for me to explain what should be the behavior of falling body if there is no solid ground capable to stop motion under gravity. Schwarzschild was trying to explain gravity field in this sense. But since his paper was too complex … It was prone to interpretation errors. Apparently same thing happened. He died soon after publication of this paper while some other Physicists, excluding Einstein, started taking this ‘point mass’ with literally real meanings and eventually these concepts became the basis of all the coming singularity based black hole physics. However Big Bang Initial Singularity was going to emerge from a different source.

The Big Bang Theory acknowledges Alexander Friedmann as its founder. Friedmann must be unaware of misinterpreted concept of singularity that emerged in year 1916. In 1922, Friedmann founded a genuine (not misinterpreted) concept of ‘monotonic world’.


The ‘monotonic world’ of Friedmann was not ‘point mass’ at all. Simply, it was radius of universe at time 0. Friedmann’s model is actually consistent with Steady State Model though in the Steady State model there is no time 0. Just like Steady State model, radius of universe is to be increased with increase (creation) of matter such that total density remains the same. According to Friedmann, at time 0, mass was also 0. His monotonic world was not a point mass – it was like a singularity which is not consistent with Big Bang Model. Following point in Friedmann’s 1922 paper clearly shows that radius of universe increases or decreases with increase or decrease of both time and mass content of universe and this thing aligns his model with the Steady State Model rather than with Big Bang Model.


Here ‘M’ stands for total mass contents of universe and x4 is fourth coordinate and denotes time. Its meaning is that with increase or decrease of time, mass content (M) has to increase or decrease. This point is clearly in line with Steady State Model and thus Big Bang Model is actually not supported by Friedmann’s model. And with this setup where mass is getting reduced if we go back in time, then at 0 time there has to be 0 mass. Hence Singularity of Friedmann is not consistent with the singularity of Modern Big Bang Cosmology where there is infinite mass (or density at least) at 0 time, 0 radius. And actually Big Bang model has no other source of initial singularity which means that essentially Big Bang Model’s ‘Initial Singularity’ has come from misunderstanding of Friedmann’s actual model.

By 1927 when Lemaître published his French article, he was not aware of Friedmann’s work. In 1927 article, there is no concept of singularity at all. There is a ‘pre-expansion universe’ which was static Einstein’s universe. But then ‘pressure of radiation’ caused equations to change (cosmological constant modified) and universe came under the rule of revised equations (revised by Lemaître himself). Thus Lemaître was unaware of singularities by 1927. Then it happens that in a meeting at a conference, Einstein told him that Friedmann had already talked about expansion stuff. Now onwards, Lemaître would start studying Friedmann and would misinterpret and absorb his ideas of monotonic world. In year 1931, Lemaître would first time talk about Primival Atom i.e. singularity sort of thing. For further detail, please see A Philosophical Rejection of The Big Bang Theory.

[i] Acknowledgement – I got introduction of role of John Michell from Mr.Bill Gaede.


What is Evidence of the Big Bang Theory and how solid is that Evidence?

The only so-called evidence of the Big Bang Theory is that Georges Lemaître had derived Hubble type redshift-distance relationship in light coming from far off galaxies from relativistic (GR) equations in year 1927 whereas Hubble could experimentally find this relationship in year 1929. In this way, it is claimed that (GR based) mathematics had already successfully predicted that important relationship two years before its actual discovery.

But this so-called evidence of the Big Bang Theory is not acceptable because Georges Lemaître had not derived that relationship from (GR) equations. In year 1927, he had derived that relationship not from GR equations but from a method which he took from Hubble himself.

Georges Lemaître’s 1927 French article remained unnoticed until he, with the help of his former teacher Arthur Eddington, published English translation of his 1927 article. That English Translation was published in year 1931 i.e. two years after the experimental discovery of redshift-distance relationship.

There was huge blunder in the 1931 translation article. In the original French article, there was whole para under equation No.23 where Lemaître had clearly mentioned that he had data of redshifts of various galaxies and he also took method of finding distance of those galaxies from Hubble. But in the manipulated translation of 1931, this whole para was replaced by a single sentence.


This crucial omission was in the notice of Arthur Eddington and he was guiding Lemaître to present translation in that particular way. Yes, he is the same Arthur Eddington who already had authenticated whole General Relativity through his famous (may be notorious) 1919 experiment of confirming bending of light ray during solar eclipse.


And following is translation of omitted para under eq.23. This translation is given at the end of this paper.

revised translation

In 1931, the strategy worked and GR equations were projected, through a manipulated translation, as having extraordinary magical powers. But equations had no magical power as such. It was a trick. Arthur Eddington was already expert in those tricks.

For further details please see: A Philosophical Rejection of The Big Bang Theory