This post is in response to a point of view that starting point of Western Philosophy is Socrates because this era was the start of reason and that study of Philosophy should be started from this era.

My response is that Philosophy makes no sense if we do not start with earlier period that was characterized by superstitions and mythology. Age of reason has come as response or reforms to those earlier unreasonable practices. Following is a summery of different stages up to Aristotle:

———-

Scene-1:

Dionysus … the god of vine.

Orpheus … The proponent of Dionysism …

According to him matter is prison of soul.

Soul must meet the ultimate reality (might be the same god Dionysus).

The method is drinking vine and inducing the spirit of Dynonisus in them.

So purpose achieved…!!!

———-

Scene-2:

Pythagoras … a REFORMER of Dionysism.

Purpose is same.

There is AMENDMENT IN METHOD.

Now method is NOT drinking vine.

Now method is using Intellect and intellectual thought.

That is BIRTH of REASON.

———-

Scene-3:

Parmenides.

A follower of Pythagoras and devotee of reason.

matter was previously the prison of soul.

Now again … matter is a bad guy. ILLUSION.

According to REASON, reality is not in observable matter.

Only reason can find the UNCHANGABLE reality.

———-

Scene-4:

Reaction to Parmenides using same reason.

Atomism. Reality of matter affirmed.

———-

Scene-5:

Reason becomes a standard method of inquiry.

Sophists and Sophistry.

———-

Scene-6:

Sophistry method is not clear. In order to refer to things or phenomenon, we must use definitions and concepts.

An important concept added to reason by SOCRATES.

———-

Scene-7:

PLATO … reality is in reason. The point of Prmenides.

Parmenides said whole reality is UNCHANGEABLE and matter is ILLUSION.

PLATO said every individual thing of experience has UNCHANGING IDEAL ‘UNIVERSAL’ counterpart.

Those ideal universals are real. Observed things are shadows (a form of illusion).

———-

Scene-7:

Aristotle

…. Method of reason must be refined. There must be rules of accuracy. Theory of Logic.

What I want to say … reason itself was not discovered at this stage. Rules of accuracy of reason were discovered at this important stage.

The question is what is the purpose of reading Philosophy?

Is the purpose to understand Philosophy?

Or to understand reality?

If understanding of philosophy is pursued, then my be, studying 2400 years of philosophers from the time of Socrates should be the approach.

If understanding of reality is the task … then we can even start from Frazer. Who will take us to most ancient times where humans started using brain in whatever form. Off course, that path will lead only towards reality of consciousness and mind.

Reality of matter must be judged from personal experiences and reflections and off course by taking help from reading previous or present relevant Philosophers and scientists.

The question was can you define Immanuel Kant in one sentence?

Immanuel Kant

So following was my one sentence definition of Kant:

One who accumulated jumble of shallow details to legitimize metaphysics by attributing it to intelligible knowledge, by not treating it but by calling it ‘a priori’ knowledge and by saying that sensible world is created by that ‘a priori’ knowledge.

Big Bang Theory is invalid theory in the capacity of a “scientific theory”.

Modern cosmologists now try to get rid of the term “big bang” by saying that it was derogatory term coined by Fred Hoyle etc.

They do affirm at least two things and insist that these two things are scientifically valid. Following are the two points:

  1. That Universe is Expanding and;
  2. Early Universe was hot and dense.

‘Big Bang’ is not a recognized theory as such. But above two points constitute a recognized theory which, in detailed mathematical form, is often termed as “Lambda-CDM Model”.

Both of these two points are actually without any scientific proof. Expansion is said to be derived from observed redshifts. The point is that the observed redshift is not Doppler’s Effect. It has different name i.e. Cosmological Redshift.

Unlike Doppler’s effect, Cosmological Redshift itself does not constitute the proof of receding of anything from us. In the absence of clear Doppler’s Redshift, there is need of direct evidence that galaxies are in fact moving away. But there is no direct evidence. For example they say that galaxies are moving away and at greater distance, same galaxies will become more redshifted.

Now direct evidence can be in the form that we may note increase in redshift over time. We have 100 years old data of redshift of many galaxies and increase in redshift over the period of 100 years has not been recorded. Let’s say the farthest visible galaxy is moving away at speed of light and its redshift value now indicates distance of 13.3 billion light years. After one million years, we shall be able to note slight increase in redshift that will indicate a distance of 13.31 billion light years.

Fact is that … direct evidence of receding of galaxies is not available now and it can be available, if galaxies are really moving away, only after hundreds of thousands of years.

My point is that … till then please call it a philosophical theory. When after many hundreds of thousands of years you will eventually get the direct evidence, then I also will call it a scientific theory. But before that time, it is Philosophical or even Mythical.

They also say that CMB is proof of expansion. I say CMB is not the proof of expansion. They only have ‘interpreted’ CMB in terms of expanding universe.

CMB can also be ‘interpreted’ in terms of non-expanding infinite universe. In this case, there should be daytime brightness in terms of Olber’s paradox. I say that CMB is that daytime (redshifted to invisible spectrum zone) brightness and thus it is proof of infinite and static universe.

They do not even have any explanation of CMB if universe is not expanding.

They also say that abundance of light elements in far-off (early) universe is also proof of expansion.

I say this is also not the proof of expansion. Let’s say Universe was infinite and by the time of their so-called Big Bang there was only universal fog of Hydrogen (may be including other light elements). In that case, first galaxies started to emerge by way of gravitational condensation of already existing fog at the standard accepted time and thus again abundance of light elements has been explained in a non-expanding universe. In fact, abundance of light elements is not any proof of expansion. If correct, then it is only proof to the fact that at earlier time, everywhere throughout infinite vastness, there were only light elements.

In short, fact is that so-far there is exact zero proof of this expanding universe theory. When after many hundred of thousands of years they will get the direct evidence, then I will be the first to accept that yes expanding universe theory is a scientific theory.

Thanks to Encyclopedias and other secondary sources through which we may know what Wilhelm Friedrich Hegel was saying. His original writings are almost not readable.

My assessment is that Hegel does not expect anything from or care anything for the reader. He is himself expert of Socrates, Plato, Aristotle, Descartes, Spinoza, Locke, Leibniz, Hume and Kant etc. and he is talking to himself. He is not even trying to explain his points to readers. His context is his own mind and only he knows where he is talking from. It seems like he was writing diaries for record of himself alone and then published those diaries.

Off course it may be possible to reach to his context by first becoming expert of all those Philosophers as stated above. It also may be equally correct to say that he is writing only for top experts of the field or for advanced students. But he himself does not state this ambition. Based on my attempt of reading him from translation of original writings coupled with what secondary sources inform us about him, my understanding is that he is idealist and talks in terms of universals. His dynamics are dynamics of ideas alone. Progress in ideas has nothing to do with observation of Phenomena though title of one of his books is “Phenomenology of Spirit”. Progress in ideas takes place only due to internal conflicts of ideas. Sometimes it seems that he also favors empirical approach and talks about real things that exist around us, but a closer look may reveal that he talks about them in the sense of “universals”.

Hegel’s Dialectic is a closed Rationalist Idealism. There is already an idea, a ‘thesis’ (thesis_anti-thesis are perhaps interpretations to be found only in secondary sources but do offer convenient approach for describing what Hegel was actually saying). Progress in ideas will come from within this thesis as the same thesis will give rise to anti-thesis. This is closed system because there is no role of outsider fresh information in the process of up-gradation of ideas. There is no role of phenomena as well. This is Idealism because ideas alone give rise to further ideas and there is no role of material world. It is Rationalism because only an internal logic of ideas i.e. meta-logic determines the direction of ideas. This is extreme Rationalism like of World of Ideas or Universalization that of Plato.

There are lot of fishy things going on in Modern Physics. Textbooks on Physics as well as all the official sources of Physics inform us that second law of Newton is F=ma (or modern form of F=dp/dt).

Anything questioning this stance is straight regarded as crack-pottery. But I dared to question this. I have had intense debates with experts on this topic many times.

Here I choose to not go into the details. Topic is lengthy and I should write a book on this subject. Here I am only telling that recently I had debate with a PhD Physics person. When I sufficiently showed to him that in fact Newton did not say F=ma and that what actually he was saying can be described as F=mv.

That PhD Physics person then had to say following:

The fact is, Newton was not quite as careful and precise with words and definitions in 1687 as modern science and mathematics (and yes, textbooks) demand.

09-07-2019 – By a person “PhD in Theoretical Physics”.

The brief background is that I confronted him that Newton did not say F=ma; instead he said F=mv.

Now he tried hard to prove that Newton in fact said F=ma.

But I sufficiently proved my stance that in fact Newton was saying F=mv instead of F=ma.

At this point … not only he … the experts in general tend to unduly favor textbooks stance. They do usually come to the point that … so what if Newton carelessly stated his law in a way that cannot be mathematically described as F=ma. But Textbooks reached to the better truth of F=ma which has passed ‘all the tests’.

My demand from them is that then please stop calling second law of motion as ‘Newton’s Second Law of Motion’.

If task is to present correct information in textbooks, then please inform the students that originally Newton presented F=mv. But textbooks reached to the better position of F=ma.

Above is their accepted truth that they do not openly present.

What they do not accept so far is that Newton was right in saying that F=mv and textbooks are wrong in the formulation of F=ma.

Yes … in my opinion … Newton was right. F=ma is a wrong formulation.

My demand from Science authorities is that please rename this law as “Euler’s Law of F=ma”.

I share following quote from Stanford Encyclopedia’s entry about Newton. The quote is saying that F=ma formulation is not traceable from within Principia. This quote also tells the name of person (Euler) who made this formulation F=ma as part of academic culture. This quote is also saying that textbook “Newtonian Physics” is actually “Euler’s Physics”.

Therefore my demand is … Instead of calling it (second law) Newton’s Law … Please call it Euler’s Law.

Isaac Newton (Stanford Encyclopedia of Philosophy)

Euler was the central figure in turning the three laws of motion put forward by Newton in the Principia into Newtonian mechanics. These three laws, as Newton formulated them, apply to “point-masses,” a term Euler had put forward in his Mechanica of 1736. Most of the effort of eighteenth century mechanics was devoted to solving problems of the motion of rigid bodies, elastic strings and bodies, and fluids, all of which require principles beyond Newton’s three laws. From the 1740s on this led to alternative approaches to formulating a general mechanics, employing such different principles as the conservation of vis viva, the principle of least action, and d’Alembert’s principle. The “Newtonian” formulation of a general mechanics sprang from Euler’s proposal in 1750 that Newton’s second law, in an F=ma formulation that appears nowhere in the Principia, could be applied locally within bodies and fluids to yield differential equations for the motions of bodies, elastic and rigid, and fluids. During the 1750s Euler developed his equations for the motion of fluids, and in the 1760s, his equations of rigid-body motion. What we call Newtonian mechanics was accordingly something for which Euler was more responsible than Newton.

Stanford Encyclopedia is acknowledging that F=ma formulation appears nowhere in Principia.

Anyways, when experts do say that Newton was careless as he should have said F=ma which he failed and they say this thing only after finding that there is no way to escape, then my genuine demand is that please rename this law as Euler Law and stop calling it Newton’s law.

If they do not rename this law and keep calling Newton careless when they themselves fail to defend the stance that Newton has anything to do with F=ma thing … then their act of calling Newton as careless is kind of “Cat out of Bag Situation”.

Relativity Theory has survived more than 100 years and Big Bang Theory will also somehow complete its century. How powerful these theories are! We are told that scientists always struggle to device (costly) methods to prove them wrong but every time these theories pass the test with flying colors.

Here I only say that they did not devise multi-million LIGO project only to disprove Einstein. There is no “Einstein was wrong” business in market. It is “Einstein was Correct” business which exists in market. Here I present two examples of my own interactions with representatives of science authorities that show that actually they have imposed an impassable barriers to ensure that their beloved theories may not be proven wrong by anyone.

First example is my interaction with a National level scientist (or representative of science) of my country in year 2007 when he told me that Editors of renowned science journals do not even bother to read any submission critical of Relativity Theory. Those submissions straight go to dustbin without anyone even read them:

Special Relativity is a closed case. We teach it to high school kids these days. The editor of the American Journal of Physics told me 30 years ago that he receives 10 attempts a month to question SR and dumps one as soon as he sees it.

Feb-04, 2007.

Yes above discussion related to only Special Relativity. But we can guess that they might have done the same for any criticism of GR as well. But so far there is no hint for the “impassable barrier” which is the topic of this blog post. This hint mainly comes from personal experiences – when you try to criticize these official theories. However, my following interaction with a NASA Information Officer is capable to convey this hint to the general readers as well.

Sometime back I had conversation with a NASA Information Officer.

NASA Information Officer:

Nobody stops you from throwing GR and QM out if the window. But if you do so you have to cone up with an explanation fir ALL things these twk theories explain perfectly.

(This NASA officer was occasionally writing incorrect spellings. But this is not the point.)

My response:

Obviously all things cannot be thrown out with a single published paper. Now logic becomes.
Since a single paper cannot throw out all the things so that single paper will be rejected. Therefore second paper will also not be published.
And thus … actually no criticism of basic frameworks can ever be published through this peer review system

.
NASA Information Officer:

The big bang theory made many predictions which were all observed and confirmed. If you provide a new theory it is therefore necessary to explain all these observations. You can write a paper on a static universe.
You only have to explain redshift, cmb, finite age of stars, galactic evolution, absent of black dwarfs, elemental abundances, large scale structures,… and yes, in one paper.

My response  was:

This is unfair. Standard model has not developed all these concepts through a single paper. Secondly all these things are ‘confirmed’ only through particular interpretations.
All these things can be interpreted in better way. But it is not fair to demand all the reinterpretations from a single paper. ……..

Thus apparently they do tell us that they devise expensive experimental projects to critically test these theories but actually they only intend to prove these theories correct. Apparently they do tell us that a single falsification will render these theories to dustbin but actually all the attempts to falsify straight go to dustbin without anyone actually read them. They have constructed (in their minds) sort of impassable barriers that any critique must pass. And I confidently assert here that even if it is done by anyone, they will come up with additional excuses that this or that thing is not covered etc.

And … do I intend to pass this impassable barrier?

Well, I do not intend to write a single paper or book which will falsify all the aspects of their beloved theories. Their theories do contain partial truth due to which apparently they do pass all those tests. But “Universe is Expanding” is not truth. “Dark Matter” and “Dark Energy” also do not exist. Gravity is not curvature of spacetime. Actual Newton is different from textbooks Newton such that actual Newton is more accurate. I am not going to explain all these things in a single paper or book. But I do will explain all these things here and there somewhere. I do not intend to pass any impassable barrier. Let them try to throw me in dustbin without even reading me. And let me try to survive those dustbins.

We live in a physical world that behaves mathematically. We do not live in a mathematical world that manifests itself physically.

Physical reality comes first. Equations do not govern physical reality. The physical reality can be approximated into the form of equations. Physical reality also can be approximated into the form of logical propositions like Newton’s first and third laws of motion. Newton has described even second law also in the form of logical propositions and without mathematical formulation.

We start from Wikipedia’s explanation of ‘Metric Expansion of Space’:

“The metric expansion of space is the increase of the distance between two distant parts of the universe with time. It is an intrinsic expansion whereby the scale of space itself changes. It means that the early universe did not expand “into” anything and does not require space to exist “outside” the universe – instead space itself changed, carrying the early universe with it as it grew. This is a completely different kind of expansion than the expansions and explosions seen in daily life. It also seems to be a property of the entire universe as a whole rather than a phenomenon that applies just to one part of the universe or can be observed from “outside” it. Metric expansion is a key feature of Big Bang cosmology, is modeled mathematically with the Friedmann-Lemaître-Robertson-Walker metric (FLRW Metric) and is a generic property of the universe we inhabit. However, the model is valid only on large scales (roughly the scale of galaxy clusters and above), because gravitational attraction binds matter together strongly enough that metric expansion cannot be observed at this time, on a smaller scale.”

In short, according to official sources, ‘Expansion of Space’ stuff is rooted in FLRW metric. It is said that before the discovery of ‘redshift-distance’ relationship in light coming from far off galaxies in 1929 by Edwin Hubble, (F) Friedmann (1922) and (L) Lemaître (1927) already had described ‘Expansion of Space’ in their respective works.

Before presenting the actual points of (F) Friedmann (1922) and (L) Lemaître (1927), let me first share point of view of a famous Internet Physics writer Mr. Victor T. Toth on this topic. Following was his reply dated December 01, 2017 to a question:

Big Bang theorists do not claim that space is “created physically”, whatever that means.

Big Bang theorists do claim that things, on average, recede from each other; that the distance between things is therefore increasing, on average; and that correspondingly, the metric of spacetime evolves as governed by Einstein’s field equations.

None of this implies space being created, “physically” or otherwise. (For starters, space is not a measurable, tangible concept, nor is it a conserved physical quantity. When you measure “space”, what you actually measure is the distance between things, not space itself, which is intangible.)

In above answer, Mr. Victor T. Toth is saying that Big Bang Theorists do not claim that space is expanding or being created or anything like that. But in another recent answer, he is accepting that Big Bang Theorists do say like that and thus he is showing his disagreement with those Theorists:

Not for the first time, allow me to be the contrarian here and challenge my esteemed colleagues who are telling you that space is expanding, by making three (to me) rather important points: (i) What is this “space” that is expanding? How do you measure it? Where are its little markers to which you can attach your measuring tape? And exactly how is this “space” represented in the Friedmann equations? (ii) Speaking of which, if it was space expanding, how come I can derive (see, e.g., books by Weinberg or Mukhanov) the aforementioned Friedmann equations purely in the context of Newtonian physics, with its concept of absolute space and time? (iii) Last but not least, when gravity brings expansion to a halt, how does it do that? Is it somehow acting on “space”, as opposed to acting on matter? (See also Peacock’s Cosmological Physics.)

No, space is not expanding. It’s not even something we could measure if it did. The Friedmann equations contain two entities: matter (represented by its density and pressure) and the gravitational field (represented by one component of the very special, homogeneous and isotropic FLRW metric.)

Galaxies are moving further apart. If you could stretch a measuring tape from the Milky Way to a distant galaxy, the distant galaxy would be zipping alongside that measuring tape at quite a clip (probably several hundred kilometers a second, at the very least.) And when, in a region where matter is denser-than-average, gravity prevails, it stops those galaxies from moving away from one another.

The purpose of presenting quotes of Mr. Victor T. Toth was to show that some big bang cosmologists are already against the idea of Expansion of Space. However here Mr. Victor T. Toth is not representing the dominant opinion of mainstream big bang cosmologists who overwhelmingly think that Space is Expanding and that this notion of Expansion of Space is rooted in the works of (F) Friedmann (1922) and (L) Lemaître (1927).

Therefore, now I will show that both (F) Friedmann (1922) and (L) Lemaître (1927) did not actually talk anything about Expansion of Space and that this notion is deceptively being attributed to them by the mainstream cosmologists. Mr. Victor T. Toth already has given a hint that Friedmann equations contain two entities which are (i) matter and (ii) gravitational field and thus there is nothing like Expansion of Space in the works of Friedmann (1922).

So let us first check the Friedmann’s actual concept of space. The English Translated title of his 1922 paper is “On the Curvature of Space”. He uses terms ‘space’ synonymous to ‘radius of universe’. By the term ‘radius of universe’ his meaning is that mass contents of universe would cause gravitational boundary of universe that a straight line universal journey of a physical object would be a complete circle and would reach back to the original point. ‘Radius of universe’ is radius of this universal ‘straight’ line which is actually circular. Within this meaning of ‘space’, it is physically valid to say that space may expand or contract. Within mathematical model of Friedmann, space is really expanding or contracting according to this meaning. Following are some examples in Friedmann’s paper of usage of term Radius R as curvature of space:

“Here R depends only on x4 and it is proportional to the radius of curvature of space, which may therefore change with time.”

While deriving constant universe model of Einstein within his own general scheme,

Friedmann writes: “whereby R signifies the constant (independent of x4) radius of curvature of space.”

“If we restrict our consideration to positive radii of curvature”.

“Let the radius of curvature equal R0 for t = t0.”

“Positive or negative depending on whether the radius of curvature is increasing or decreasing for t = t0.”

“by choice of the time it can always be arranged such that the radius of curvature increases with increasing time at t = t0.”

It is now clear that yes space is contracting or expanding in Friedmann’s model but it is contracting or expanding within above physically valid meanings of contraction or expansion of space. But Big Bang Cosmologists tell us a whole different and misleading thing and they attribute their own faulty model to Friedmann. They call their own misleading model of ‘expansion of space’ as ‘metric expansion of space’ and wrongfully attribute this faulty physical model to Friedmann.

After checking the actual position of Friedmann (1922), now we come to see the actual position of Lemaître (1927) with regards to the notion of Expansion of Space.

Modern concept of Expansion of Space has actually come from manipulating Equation No.23 of Lemaître (1927) paper. Following is the snapshot of Equation No.23:

This equation can be written as V/C = (R’/R)r

The above form of equation No.23 superficially resembles to Hubble Law which is V = HD

In Equation No.23, V/C is ‘Redshift’ and in Hubble Law, V is ‘Redshift’; thus LHS of both equations are equal.

Moreover, in Equation No.23, r is Distance, so ‘r’ and ‘D’ of RHS of both equations are also equal.

Therefore, if we use the notation of Hubble Law, we can write Equation No.23 as following:

V = (R’/R)D

R means radius of whole Universe … (Radius of ‘whole’ universe itself should have been regarded as ‘cranky idea’ in first place).

Anyhow ‘R’ means radius of whole universe.

What Lemaître stated was like V=(R’/R)D

What standard ‘interpretation’ goes in every official source … books/papers etc. that is V=(S’/S)D

In short Lemaître was saying in his equation No.23 (1927) that redshift (V) is caused by increase of radius of whole universe. While distance of galaxy (D) remains constant.

Actual equation No.23 is not exact this one. If we use notation of Hubble law then equation No.23 becomes like this and superficially does resemble with Hubble law.

But unlike Hubble law where H is constant … here we have distance of galaxy (D) as constant.

R’/R … does it mean H or not?

Whether or not it mean H … it is not constant like H

This is the actual position of Lemaître .

What FLRW metric attributes to him?

FLRW metric makes this thing into V=(S’/S)D where S means ‘Space’.

Here conversion of R into S is a simple manipulation.

Lemaitre here did not say increase of Space or even increase of distance of galaxy… according to equation No.23, distance of galaxy remained the same.

This thing has been ‘interpreted’ in FLRW metric that ‘coordinate’ of galaxy remains the same and space is increasing.

In the end … after all this is a deceptive manipulation. V=(R’/R)D is NOT equal to V=(S’/S)D.

Thus we have seen and confirmed that both Friedmann (1922) and Lemaître (1927) had not coined the term or concept of Expansion of Space and that this concept or notion is only deceptively being attributed to both of them by the so-called FLRW metric.

Position is that without the notion of Expansion of Space, the Standard Model of Cosmology (Lambda-CDM) does not work and this notion itself is unreal, illogical, non-physical as well as deceptive.

For further details, please see my book “A Philosophical Rejection of The Big Bang Theory”.

There is reality in gravity having its effect distinct from electric effects. But it is also fact that effects of electricity and magnetism start well before reaching to so-called singularity only where according to ‘legitimate’ scientists, theory of gravity fails.

Earth-moon system works differently than the known effects of electricity. So Solar system, galactic system and larger structures are likely being operated by gravity rather than electricity or magnetism. But small scale contributions of forces other than gravity also cannot be denied. Stars are made of plasma therefore within stars major contribution of electric or magnetic effects make sense.

More importantly, mainstream point of view that early universe was hot and dense yet only gravity was the major player in the dynamics of such dense and hot environment makes no sense.

Overall electric and magnetic dynamics are more complex and beyond my satisfactory comprehension ability. Mainstream scientists also avoid indulging themselves into the complexities of electric and magnetic effects at larger scales. Mere presumption that these effects just get neutralized is over simplification. Overall I also assume that larger structures are mainly operated by gravity. I just accept possibility of minor contribution of electricity and magnetism at such scales. Plasma stars are localized structures and major contribution of electricity and magnetism within plasma based local structures cannot be denied. It is also possible that some astronomical effects which are presently regarded or understood to be the effects of gravity might actually be the effects of electricity/magnetism.

By 1916, Einstein had successfully presented his Field Equations of Gravity i.e. General Relativity (GR). In year 1917, he attempted to apply his GR equations to describe whole Universe. Following is the link to English Translation of Einstein (1917) paper:

Cosmological Considerations in the General Theory of Relativity.

Einstein starts by evaluating compatibility of General Relativity with an infinite Universe and he does evaluate by going into technical details. Basically he was trying to set ‘boundary condition’ for a spatially infinite universe.

At the end he admits that he failed in doing so:

From what has now been said it will be seen that I have not succeeded in formulating boundary conditions for spatial infinity.

Einstein (1917)

Einstein was more interested in ‘boundary condition’. He failed in determining the boundary condition for spatially infinite universe. But he would ‘successfully’ determine the same for a spatially finite universe.

So how did he ‘derive’ the idea of Finite Universe? Well … he did not derive. He just introduced this idea as a commonsense alternative. Only one extra thing i.e. Cosmological Constant was needed and every problem would be solved. So let’s see how actually the idea of Finite Universe was introduced and what problems were solved through cosmological constant:

Nevertheless, there is still a possible way out, without resigning as suggested under (b). For if it were possible to regard the universe as a continuum which is finite (closed) with respect to its spatial dimensions, we should have no need at all of any such boundary conditions. We shall proceed to show that both the general postulate of relativity and the fact of the small stellar velocities are com- patible with the hypothesis of a spatially finite universe; though certainly, in order to carry through this idea, we need a generalizing modification (i.e. Cosmological Constant) of the field equations of gravitation.

Einstein (1917)

“For if it were possible to regard the universe as a continuum which is finite (closed) with respect to its spatial dimensions …” This sentence clearly shows that finite universe idea was not derived from equations. It was annexed to theory as a commonsense alternative where complexities of infinite option remained unsettled.

How boundary condition was determined? “we should have no need at all of any such boundary conditions.” So problem with regards to boundary condition is solved in a spatially finite universe as now such a boundary condition is not even needed.

And … what were the problems whose solution was the ‘cosmological constant’?

The above quoted paragraph shows that there were two problems:

(i) Finite Universe itself and; (ii) Fact of the smaller stellar velocities.

So the problem was associated with the idea of finite universe. If universe is infinite then there was no need of cosmological constant. With finite universe, Einstein feared that it should be collapsed under gravity.

Generally orbiting objects do not collapse under gravity and Einstein was fully aware of this fact. But why do objects orbit? They orbit due to side-way velocity. Einstein knew this fact also as it is clear from following quote out of same paper:

According to the general theory of relativity the metrical character (curvature) of the four-dimensional space-time continuum is defined at every point by the matter at that point and the state of that matter.

Einstein (1917)

But Universe even if finite must have been very big. Einstein was thinking that at cosmic scale matter must be at permanent rest. In following quote, he is saying that at cosmic scales, the relative velocities of stars are very small:

The most important fact that we draw from experience as to the distribution of matter is that the relative velocities of the stars are very small as compared with the velocity of light.

Einstein (1917)

On the basis of ‘fact’ that relative velocities of stars are very small, he then concludes that at cosmic scales, all matter must be at permanent rest:

There is a system of reference relatively to which matter may be looked upon as being permanently at rest.

Einstein (1917)

“Stars are relatively at rest” … and therefore (finite) universe is at “permanent rest” … Einstein reached to this conclusion and need for introducing ‘cosmological constant’ was invoked.

Because in a finite cosmos, only orbit moving stars could prevent gravitational collapse … since stars were at “rest” … there was no orbiting going on … hence an anti-gravity agent “cosmological constant” was needed to prevent gravitational collapse.

We have seen that basic idea of Einstein was that since stars are relatively at rest therefore finite universe must be at permanent rest. In year 1917, Einstein was definitely not aware that finite island universes (galaxies) do exist where not only that stars are not relatively at rest but they are rotating at faster speed than could be (officially) expected for such galaxies.

Thus in a real finite universe, there was no need of cosmological constant. It was needed only for a flawed hypothetical infinite universe which is at permanent rest.