當哲學被藐視之後。。。。

戴榕菁

2022年8月我在英文網站貼出一篇題為“When Philosophy is Disparaged in World of Science”的文章舉出我在2021及2022年所討論過的在數學和物理學科裏因為藐視哲學而出現問題的幾個例子。後來正好收到ICSS XXXI Luxembourg 2022的投稿邀請，我就將該文寄給他們。該文被錄取了。他們希望我能去參加會議，我告訴他們我沒錢去，他們就讓我參加網上發言，我也因為家境貧寒購買不起網上視頻設備而沒發言，隻答應在網上參加會議，因為他們的時間與美東不合適，所以我也隻聽了一個人的發言。後來我的文章的摘要出現在了他們的proceedings上【[1]】的倒數第二篇，但本來說好了的要出的會議雜誌一直就沒了音訊，但願不是我的文章拖累了大家。

關於ICSS XXXI Luxembourg 2022我有必要多說兩句。首先，他們對於根本不在主流學術圈的我不但發邀請而且當我說家境貧寒後，在已經看到我的文章對現有學術體製之“大逆不道”的反叛的情況下，更在我明確告訴他們我的那篇文章不久前投給西班牙Valencia的會議向我約稿時未被接受的情況下，還非常友善地免去了我的幾百美金的會費。另外，之後在評審員（reviewer）對我的文章提出異議時他們居然仍堅持要接受我的文章。應該說那是主流學界對現有體製（我一直高度懷疑有外星勢力存在於現有體製背後）的一次小小的反抗。但是，從最後會議雜誌泡湯這一點來看，這仍然隻是一次失敗的反抗。但至少是一次華人社區根本不可能有的對於現有學術體製的反抗。

會議結束後不久我收到Global Journals Research In Engineering的約稿。盡管他們沒有提與ICSS XXXI Luxembourg 2022有什麽關係，而且我也經常收到各種收費的open access雜誌的約稿，但我感覺這次Global Journals Research In Engineering與ICSS XXXI Luxembourg 2022的組織者之間存在著某種聯係。我有這種感覺不但因為當我一如既往地回複說我家境貧寒付不起發表文章的費用後他們馬上免去我的費用，而且因為ICSS XXXI Luxembourg 2022的組織者曾在email裏和我提到他們有一個engineering的雜誌，問我是否願意在那裏發文章（但當我說願意後，對方又沒了下文），更重要的是在他們發表我的文章之前還出現了一次超自然的前兆。

我並沒有將“When Philosophy is Disparaged in World of Science”一文寄給Global Journals Research In Engineering雜誌，因為它是一個engineering雜誌。我將一篇與engineering看上去有些沾邊但又不屬於要推翻狹義相對論或推翻能量必須守恒那麽反主流的文章，“The Dynamics of the Chain Fountain”寄給了他們，這篇文章之前也同樣已被其它大雜誌封殺的。

他們一開始也向我收費說可以discount，我說因為從未有人給我的研究花過一分錢，我也沒義務給任何雜誌付錢，當然家境貧寒忍饑受凍的我也不可能花幾百美金發表文章。他們馬上回複說因為是他們向我約稿，所以一分錢也不要。他們的grammar checker很厲害，一下子找出了我文中很多我忽略了的語法問題。我收到他們的報告的當天就心服口服地進行了修改馬上寄了回去。

之後他們可能認為我的那篇文章與科學更沾邊，於是我收到email說我的那篇文章被Global Journal of Science Frontier Research接受了。之後好長一段時間就沒有音訊，我以為又是一如既往地泡湯了。但是在聖誕節過後的某天我突然做了一個很奇怪的夢，該夢非常清晰，告訴我在12月30日的聯合世界報有重要的文章。夢醒之後我還以為台灣的聯合報會有什麽重要的文章，因為他們在美國的報紙叫世界日報。但結果我在12月30日收到Global Journal of Science Frontier Research的Email說我的文章馬上就要發表，且給了我預備發表的鏈接。我點擊他們提供的鏈接，看到他們的22卷第八期的物理與空間類的第一篇就是我的文章，幾天後改期雜誌正式發表【[2]】。之後他們沒再向我約稿，我也沒再給他們投稿因為我知道如果不是他們約稿就不可能免去那幾百美金的費用，而勒緊褲帶過日子的我是不可能有錢來發文章的。

回到“When Philosophy is Disparaged in World of Science”，這篇文章舉的是2022年8月以前所作分析的例子，所以很多之後與相對論及量子論的工作都未涉及。既然沒有被雜誌正式發表，我會在今後繼續擴充該文，將去年8月以後，特別是與量子論有關的內容陸續補充進去。下麵就是該文在去年的版本正理後的內容：

When Philosophy is Disparaged

Rongqing Dai

 

Abstract

Human beings are paying a dire price for disparaging philosophy in all facets of life, especially in the field of natural science where the most intelligent explorations of nature for the survival and advance of Homo sapiens species are supposed to be conducted. This writing will demonstrate through examples how philosophically erroneous mistakes in mathematics and physics that were made at the turn of 20^th century could last for more than a century without being identified, as well as an issue that has lingered for several centuries and still confuses the whole world with its philosophical complexity. In those examples, we could see that scientists with the aura of the smartest people on earth could easily be convinced by “simple, straight, and brilliant ideas”, which could bring aesthetically attractive convenience but would lead to various kinds of false knowledge and wrong practices, and then defend those ideas with all their lives for a long time, simply because the scientific community has not been prepared with strong philosophical capacity of reasoning.

Keywords: Philosophy, Hilbert First Problem, Special Relativity, Energy Conservation, Metaphysics

1. Introduction

Since ancient times, scientific researches have operated as a tripod engine with observation (experiment), mathematics, and philosophy as its three supporting legs to enrich the repository of knowledge, among which philosophy as the steward of logic is supposed to be the agent to digest the knowledge acquired with math and lab and thus becomes the tie to bind all scientific works together. The basic reason why philosophy can do its job is as Aristotle pointed out more than two millenniums ago in Metaphysics (Aristotle 350BC) that all beings share common logic for being qua being.

Sadly, as science advanced into the era that is now tagged as modern, it no longer operates as a balanced tripod machine, but instead a severely tilted bipedal robot with a shrunk philosophical tail. A quick survey of the evolution of scientific writing style since the turn of 20th century, we might easily identify the gradual vanishing of metaphysical reasoning or speculative discourse in the writings over the past century.

Although varieties of hypotheses are certainly not scarce in nowadays scientific papers (especially those of theoretical physics), even the best of them can seldom be counted as good philosophical speculations since generally they are not the outcome of profound metaphysical reasoning but mainly out of imaginations, and human imaginations are often disconnected from reality.

In fact, even the scientific literature with philosophical style discourses around the turn of 20^th century as historical records were already at the end of the inertial flow of the ancient philosophical stream. That was the time period when scientists began to put their faith mainly in math modeling and lab data. Besides, the drastic decline of academic philosophy started almost right before the end of the era of the so-called classic science and the beginning of the so-called modern science. Consequently, humans as a whole are paying the price for disparaging philosophy since then.

On the other hand, human scientific advances have never been perfect at any historical stage, and thus always leave some critical unfinished tasks to the new comers.

It was the metaphysical style speculations that helped giving birth to the iconic modern fields of physics --- the theories of relativity and quantum physics. Naturally, those endeavors have left some confusions or mistakes that would require later generations to further clarify or correct. However, the heavy mathematical and experimental reliance of those new scientific fields created the impression that math plus lab are the only things needed for science, and philosophy is just an excessive appendix.

As a result, while the destitute of the capacity of high quality speculative thinking obviously accounts for the current stalemate status of the frontier physics as well as many other scientific fields, scientists are still collectively despise the role of philosophy in scientific endeavors simply because they have no idea what good philosophical thinking could do in scientific researches since they never tasted it since their school times. This has created an awkward situation as would be illustrated in this writing through examples that errors resulting from defective or wrong philosophical thinking could linger for decades or even centuries without being spotted by the whole academia of science. To make matters even worse, nowadays scientific workers would often try their best to defend some logically evident errors left by their antecedents, simply because of the dearth of the required philosophical capacity to make full sense of the logical complexities behind the pages of fancy mathematical expressions and observational data.

In this writing, I will demonstrate how philosophically erroneous mistakes in mathematics and physics that were made at the turn of 20^th century could last for more than a century without being identified, as well as an issue that has lingered for several centuries and still confuses the whole world with its philosophical complexity.

2. The Shocking Acceptance of the Continuum Hypothesis

In 1870’s Georg Cantor developed his set theory by establishing the notion of the equal size of two infinity sets based on one-to-one correspondence between the sets: if we can find a one-to-one correspondence rule between two sets (i.e. matching the elements of those two sets through a seamless one-to-one correspondence), then they are considered to be equally long or have equally many elements, which means that they have the same cardinal number; or otherwise they are not equally long, but of different cardinal numbers. Along this Cantorian philosophical line, in 1878 Cantor proposed the continuum hypothesis (CH for its acronym) (Koellner 2019), which could be expressed as "There is no set whose cardinality is strictly between that of the natural numbers and the real numbers." In 1900 Hilbert listed CH as the first of his 23 open problems, which has been considered unsolved by the academia of mathematics to today.

However, as discussed by Dai (2022a) , the real cause for the mathematical academics including the most famous ones to have failed to solve the Hilbert first problem is the illusive nature of the above mentioned Cantorian philosophy of measuring the length of an infinity set, or the Cantorian cardinal system.

In 1873, Cantor provided a proof (Veisdai, 2021) that there are as many rational numbers as natural numbers, which can be briefly presented as follows:

Let us arrange all the rational numbers (ratios of natural numbers) in an infinite table as such:

1/1  1/2  1/3  1/4  1/5  ...                                                                                        

2/1  2/2  2/3  2/4  2/5  ...

3/1  3/2  3/3  3/4  3/5  ...

4/1  4/2  4/3  4/4  4/5  ...

5/1  5/2  5/3  5/4  5/5  ...

...    ...    ...    ...    ...

Next, starting in the upper left hand corner, move through the diagonals from left to right at 45 degrees, starting with 1/1, then 1/2 and 2/1, then 3/1, 2/2 and 1/3 and so on, write down every new number we come across. We will obtain the following ordering:

(1) 1/1,                                                                                                               

(2) 1/2,

(3) 2/1,

(4) 3/1,

(5) 2/2,

(6) 1/3,

(7) 1/4,

(8) 2/3,

(9) 3/2,

(10) 4/1,

….

which is not just well-ordered, but also in one-to-one correspondence with the natural numbers in their natural order. This proves the countability of the rational numbers by natural numbers, and thus according to Cantorian philosophy, he proved that there are as many rational numbers as natural numbers. Based on the same philosophy of counting infinite sets by one-to-one correspondence with natural numbers, in 1874 Cantor proved that real algebraic numbers are countable (by natural numbers) as well.

In 1874 Cantor also provided a proof showing that real numbers are strictly more than natural numbers. Therefore, up to that point he had effectively divided the infinite series within the domain of real numbers into two categories, one is of the same size as natural number, and another is with all real numbers, and the continuum hypothesis says that there is no other infinite set strictly sitting between these two categories.

Once we accept the above conclusions of Cantor, it is then very hard for anyone to find an infinite set with its cardinality strictly greater than natural numbers but strictly smaller than real numbers. This is the reason why Hilbert’s first problem has been lingering for such a long time.

2.1. The trick of abusing the abstract notion of infinity

In the time of Johann Bernoulli and L'Hopital, humans already knew that the so-called infinity is not an empty abstract logo, but with real meanings that we can use to compare the magnitudes of different infinities (e.g. Wikipedia, 2022a). But Cantor used the notion of “infinity” as an endless repository for him to withdraw numbers whenever he needs for his schemes. By doing this, he effectively eliminated the difference in the speed to go to infinity as Johann Bernoulli and L'Hopital noticed.

If we actually count the series of rational numbers following the above Cantorian procedure, no need to go too many steps we will find that the natural number that is used to mark the largest rational number would be much bigger than its rational counterpart. This tells us two things:

1) if we count the numbers of elements for a given magnitude, the rational would go to infinity much faster than the natural; but 2) if we count the numbers one by one then the natural would go to infinity much faster than the rational.

Both of these two facts tell that rationals are much more than naturals, instead of being equal to naturals as Cantor demonstrated with his trick.

Obviously, the trick of the Cantorian scheme of measuring is to borrow from future for the current spending, and he did not have the need to worry about running out of resources as economists would do when dealing with deficit economies, because he had an endless repository of supply for his expenditure whenever dealing with infinity, even though obviously his expenditure would potentially outrun his storage whenever the infinity line of supply is cut off.

Then the audience might ask such a question: “does the Cantor's scheme of abusing the notion of infinity make any real sense?” The answer is “no” except for playing brain-burning games for fun or for idiotizing youngsters with meaningless tricks. In fact, we might expose the absurdity of the deficit spending that Cantor conducted for his counting game by cutting the series of rational numbers at a randomly large value, e.g. 1 quadrillion, and we will see that there are far great more rational numbers than natural numbers. This tells that the Cantorian counting scheme is meaningless for any real world thing except for his fictitious infinity, because all numbers involved in real life issues, no matter the count of money, population, or the particles in a block of matter, or the toners used to print a drawing etc are all finite instead of infinity, no matter how big the number is, and thus you will always find that rationals are way much more than naturals. Further, as demonstrated by Dai (2022a) [3], even for any two given natural numbers we can find infinitely many rational number between them. In fact, we can easily see this by picking up 1 and 2, then we can find that there are infinitely many rational number between them (e.g. 1.1,1.2,1.3,…,1.999999,….).

3. The Baffling Ignorance of the Irreversibility Entailed by the 1^st Postulate of Special Relativity

For the past century, people have become familiar with basic features of the relativistic effects of motions prescribed by the special theory of relativity; but one important aspect of the effects that would be entailed by the theory of special relativity has been basically missing, which is the irreversibility of the relativistic processes. According to the mainstream claim of relativity, when the relative speed of two system decreases to zero, things would go back to the status at rest based on the Lorentz transformations. However, as discussed by Dai (2022b), the first postulate of the special theory of relativity would logically dictate irreversible physical as well as chemical changes in the remote system, which is logically unreasonable and naturally impossible.

The first postulate of the special theory of relativity is also called as the principle of relativity, which states that all inertial coordinate systems are equivalent in describing natural laws. In the meantime, according to the two most important icons of the special theory of relativity, the Lorentz transformations and the Einstein energy-inertia relationship, we know that when an object is in motion, it would contract by a factor of (1 - v²/c²)^1/2 in the moving direction while the sizes in the other two spatial dimensions remain the same:

L’ = L (1 - v²/c²)^1/2,     (1)

and also acquire an increase of mass as:

?m = ?E/c²,                (2)

where ?E is the acquired kinetic energy for the motion.

The increased mass and decreased volume would logically lead to the following conclusion:

[The density of the moving object increases as the result of its motion.]       (*)

The most troublesome thing is that according to the first postulate of special relativity, the above statement (*) is not pure imagination but rather physically real. This would entail irreversible physical and chemical changes that are impossible to happen in nature as demonstrated in the following two thought experiments:

Experiment one: Permanent plastic change of a cuboid of plasticine

Suppose we have a cuboid of plasticine with a longitudinal length of L and sectional area of A in a frame of reference K and there is an observer O’ in a frame of reference K’ that is moving at speed v relative to K in the direction parallel to L. Now according to FitzGerald–Lorentz contraction hypothesis (1) and Einstein energy-inertia relationship (2), we would have a volume reduction AL and a mass augmentation of m, and thus a density increment of

 ?ρ = (?Lm+L ?m)/AL2 (3)

where both L and m are positive. However, according to the theory of solid mechanics, the deformation of a solid in one dimension would also cause the deformation of the solid in the other two dimensions (e.g. Wikipedia, 2022b; Wikipedia, 2022c); but in the case of a cuboid of plasticine, the non-relativistic deformation in the other two dimensions would be permanent and would not disappear even though the length in the moving direction could be assumed to restore to the original L after the relative motion stops according to special relativity.

Experiment two: Melting wax

Suppose we have an insulated box filled with air consisting of molecular nitrogen and oxygen only (Based on example from Wikipedia, 2022d) at 38?C and also containing a wax bar that will melt at 40?C. Now a spaceship at a distance away is launched and a while later it reaches the speed about 18% of the speed of light c. Then according to the special theory of relativity, the astronaut O’ in the spaceship who is knowledgeable of the insulated box would estimate that the density of the box and everything inside would have increased more than 1.6% due to the reduction of the volume and the addition of mass, and thus the temperature within the box should have adiabatically risen to exceed 40?C, which means that the wax bar is melting. Since the melting of wax is thermodynamically irreversible, the melted wax in the insulated box “observed” by the astronaut O’ will never come back to its original intact state again. Then the astronaut returns to the launch site and go to check the insulated box after he has landed. When he opens the box, if the wax is melted as he “observed” in space according to the special theory of relativity, then the whole universe would be in a complete mess. But fortunately, as we can say with confidence, the wax in the insulated box would not melt simply because of the motion of some irrelevant spaceship faraway.

It is important to notice that in each of the above two examples, the observer O’ does not have direct connection with the observed object which could justify a cause and effect relationship, and thus O’ and the observed object could be just two randomly moving objects in the universe.

4. The Surprising Denial of the Rule of Velocity Superposition for the Sake of the 2^nd Postulate of Special Relativity

The second postulate of special relativity states that the speed of light in vacuum is constant to all observers. Because of this postulate, the speed of light has become one of the fundamental physical constants with a value that is exactly equal to 299792458 meters per second. It is exact because, by a 1983 international agreement, a meter is defined as the length of the path travelled by light in vacuum during a time interval of 1⁄299792458 second. This particular value was chosen in order to provide a more accurate definition of the meter that still agreed as much as possible with the definition used before. The time unit second is in turn defined to be the interval of time occupied by 9192631770 cycles of the radiation emitted by a caesium-133 atom in a transition between two specified energy states. (e.g. Wikipedia 2022e; NIST, 2019)

However, as discussed by Dai (2022c), this postulate of invariant speed of light in vacuum is not only logically defective for its entailment of impossible results as demonstrated with a recently designed thought experiment, but also has been experimentally proved wrong more than a century ago by Sagnac and others.

The fate of Sagnac experiment and the corresponding Sagnac effect is worth our special attention because of its exemplar role for illuminating the importance of philosophy in scientific practices.

In 1913 French physicist Georges Sagnac conducted an experiment which substantially challenged the second postulate of the special theory of relativity. During the experiment, a beam of light is split into two beams which are made to follow the same path but in opposite directions, and on return to the point of entry the two light beams are allowed to exit the ring and undergo interference as recorded by an interferometer. When Sagnac (e.g. Wikipedia, 2022f; Sagnac, 1913) let the table on which the light paths were established to rotate slowly (1 to 2 revolutions per second), he recorded the difference between the paths of those two beams, which was a clear indication that the speed of light relative to the observers obeys the classic Galilean rule of superposition. The mechanism of the Sagnac experiment has been named as Sagnac effect and devices built with Sagnac effect are routinely used in guidance and navigation systems for commercial airliners, nautical ships, spacecraft, and in many other applications.

However, the physical revelation of the Sagnac experiment has been surprisingly misinterpreted for the past more than a century period of time as a typical example of the correctness of relativity. The most hilarious part of this is that the relativistic derivations of Sagnac effect would normally share the commonplace of first admitting that the speed of light of those light beams in opposite directions equal to c - v and c + v, and then managing to prove that the constant speed of light in vacuum makes sense in Sagnac experiment by citing the Lorentz transformations, as we might see in the work of Mathpages (2022) when the author even admits that devices made of Sagnac effect are capable of detecting rotation rates as slight as 0.00001 degree per hour. Obviously, these people do not seem to realize that by assuming the speed of light of those beams in opposite directions to be c - v and c + v, they already deny the constancy of the speed of light in vacuum and thus deny the value of special relativity. This is a typical example how things could go wrong for a long time (more than a century) after the whole society losing the capacity of thinking in philosophically correct ways.

4.1. The influence of Sagnac’s goal and claim upon the misinterpretation

Respecting truth and denying untruth should always be the ultimate principle for scientific explorations and thus humans do not have any excuse for making collective mistakes such as misinterpreting the outcome of Sagnac experiment for more than one hundred years. Nevertheless, it might also be meaningful for us to notice the distractive effect of Sagnac’s goal for his experiment and correspondingly his claim of what his experiment proved.

Sagnac was trying to prove the existence of the luminiferous aether and claimed that he succeeded in doing so while the connection between his results and the existence of aether was not soundly convincing. As we could see from the above discussions, the need to assume the velocities of light to be c + v and c - v by the relativistic scholars has already proved that the constancy of speed of light in vacuum is wrong. That is to say, the result of Sagnac experiment could be well explained without the need of the superfluous notion of aether that is attached to extra unneeded attributes. However, more than one hundred years ago, when the scientific focus was still not completely off the topic whether space was filled with the luminiferous aether, Sagnac’s goal of searching for aether and his claim of having found it could have practically played a role of distracting the attention of scientists and caused them to ignore the fact that Sagnac experiment had offered a good example that speed of light in vacuum is not constant to all. 

4.1.1. More profound causes

But on the other hand, humans should not use any excuse to shed off the collective responsibility for such a long-lasting mistake, just like that a failed student cannot blame some intentional distractions of tricky questions in a test. We need to introspect about our worldwide culture in the scientific community to find more profound social cultural causes behind this phenomenon. By looking into the century long misinterpretation of the Sagnac experiment, we might find at least three profound philosophical causes behind.

First, we might see from this phenomenon that people often defend something simply because the big name of the thing makes them feel that they should defend it instead of that they really understand what they are defending. This mindset of placing social benefits above truth is against the fundamental principle of philosophy which values truth above utilitarian needs.

Second, despite that human intelligent capacity (especially the intelligent capacity of scientific elites) is often unrealistically exaggerated, intellectually humans are indeed quite weak in general, vulnerable to various kinds psychological distractions, and could even be collectively under some distractions for very long time without being able to pull out from the social psychological trap.

Third, more importantly, the misconception of the separation of science from philosophy has sadly caused the social disparagement of philosophy in the scientific community for the past centuries, which has severely crippled the human collective scientific capacity in general while human self-puffing-up confidence in human scientific capacity has reached its pinnacle. This issue is at the root of the above two issues.

5. The Jaw-dropping Relativistic Chronology

At the core of special relativity lies the peculiar light-seeing-based philosophy which claims that the happening of event P is meaningful to event Q only when the (imaginary) light emanating from the spot of P could reach the spot of Q according to the speed of light in vacuum c; vice versa. According to this special logic, to anyone in the spot of Q, P never happens until the light emanating from the spot of P could reach the spot of Q. If event P and event Q cannot “see” each other, they are considered as irrelevant in the universe. Both relativistic simultaneity and relativistic causality are established on top of this peculiar philosophy of determining the mutual reality of things. We might call this philosophy as relativistic chronological logic because it determines how a relativistic scholar should think of the sequential influence between things, including how to determine simultaneity and causality.

The most famous manifestation the relativistic chronological logic might be the definition of light cone that was conceived by Minkowski (e.g. Wikipedia, 2021a), which describes the path that a flash of light, emanating from a single event at a single point in space and a single moment in time and traveling in all directions, would take through spacetime; but the most astonishing application of the relativistic chronological logic could be found in cosmology where we often hear claims that it is meaningless to even talk about the happening of a cosmological event before we can virtually see it (according to the calculation based on speed of light).

This would lead to the hilarious conclusion that the explosion X of a celestial body of 1000 light-year away 999 years ago happened later than the explosion Y of a celestial body of 5 light-year away 5 years ago, despite that the relativistic cosmologists would still study the explosion X as 994 years earlier than the explosion Y because they know that if they do not do so, the whole cosmological causality chain network would be messed up so that it would be impossible for them to correctly study the cosmological history and dynamics.

Obviously, the light-seeing-based relativistic chronology creates a cracked logical framework that cannot be consistent with itself or with the logical and semantic systems of the general culture. As a matter of fact, even from the most utilitarian point of view, the abovementioned relativistic causality view is problematic because even before the observer sees the light from a cosmological event, physical events within each celestial body and interactions between all celestial bodies never cease to happen, which is not determined by whether it is possible for an observer to see anything of them at all. On the contrary, only if the observer respects the objective happenings before he could see them he could possibly understand them correctly.

6. The Misleading Diagnosis for the Apparently Longer Lifespan of the Muon

In this section let’s look into a famous claim among the so-called experimental testing of time dilation that the apparent elongated lifespan of muons travelling through the atmosphere is the result of time dilation. The theory normally goes like this (e.g. Wikipedia, 2022g):

The emergence of the muons is caused by the collision of cosmic rays with the upper atmosphere, after which the muons reach Earth. Suppose T is the lifespan of the muon measured in the earth inertial frame S, and T’₀ is the lifespan of the muon according to the proper time of a clock in the inertial frame S’ comoving with the muon, corresponding with the mean decay time of the muon in its proper frame, then because of time dilation we have

 T = γT’₀ > T’₀,                                                (4)

where γ = 1/√(1- V²/c² ), from which the relativistic scholars conclude: the reason why the muon can pass through the thickness of earth atmosphere within its supposedly very short lifespan is because when observing from the earth inertial frame S its lifespan becomes longer thus it can move farther with the same value of the supposed lifespan at the same relative speed v.

Then when stepping from S into S’, the relativistic scholars would use time dilation no more but shift to length contraction as follows

 L = L’₀ /γ < L’₀,                                              (5)

where L’₀ is the proper distance in S’ that the muon could travel within its lifespan, and L is the distance that the muon can travel in S when calculated in S’, from which the relativistic scholars conclude: the reason why the muon can pass through the thickness of earth atmosphere within its supposedly very short lifespan is because when observing from muon’s inertial frame S’, the earth atmosphere becomes thinner thus muon needs shorter time to pass through it at the same relative speed v.

Here we should take heed of the typical asymmetric uses of the Lorentz transformations: time dilation is cited when the discussion is based on the observation from S while length contraction is cited when the discussion is based on the observation from S’.

This asymmetric uses of Lorentz transformations in S and S’ when explaining the seemingly longer lifespan of the muon is not accidental but due to inevitable causes:

If they continue to use time dilation when stepping into S’, since the relative speed v would not change with the Lorentz transformation, we would have

L = vT = vT’₀/γ = L’₀ /γ < L’₀                                           (6)

Although (6) and (5) look exactly the same, they actually read very differently because with (5) we are focusing on the relativistic change of spatial span while with (6) we are focusing on the relativistic change of temporal duration. More specifically, (5) reads as “the thickness of the earth atmosphere in S that the muon needs to pass through becomes thinner when observing from S’”, but (6) reads as “the distance L that the muon can travel in S within its lifespan is shorter than the distance L’₀ that the muon can travel in its own frame S’ within its lifespan”.

Obviously, the effect indicated by (6) would logically cancel out the effect indicated by (5): even though now the muon only needs to travel a shorter distance in order to pass through the earth atmosphere, it would also die within a shorter distance therefore it might still not be able to pass through that shorter distance.

Here the catch that causes this confliction is that the speed v and the lifespan T’₀ of the muon in S’ are two constants for the analysis. Therefore, when we make observation from S, we might conclude that the muon can travel a longer distance at the same speed v because the earthly observed lifespan is longer than T’₀, but when we make observation from S’, we would find that a shorter period of time T in S would be corresponding to T’₀ in S’ according to Lorentz transformation for time dilation, which entails that the muon would only travel a shorter distance in S within its lifespan T’₀. Obviously, these two conclusions contradict each other.

This need of asymmetric treatment due to the difficulty of symmetric treatment is a common problem with special relativity. In fact, if we cite length contraction instead of time dilation when observing from S, it would right away lead to the opposite conclusion of a longer lifespan for a moving muon: we might find that when observed in S whatever distance the muon travels would become shorter and thus the muon would die within a shorter distance than calculated in S’.

6.1. Reasonable considerations for investigating the muon lifespan issue

Obviously, it is logically unsound to assume that time dilation is the cause of the apparent longer lifespan of muons in the earth atmosphere. Philosophically speaking, the reasonable approach to investigate the said phenomenon should be conducted by taking into consideration of the following two aspects:

1) Given that air density is much higher in the lower atmosphere than the  upper atmosphere while cosmic rays are constantly penetrating the atmosphere with high magnetic rigidity (Viel, 2021), it would be more reasonable to question the validity of the assumption that muons in the atmosphere are solely created at the upper atmosphere. This is because the increase of air density near the ground compared to the upper boundary of atmosphere is tremendous while the reduction of cosmic rays due to the influence of earth magnetic field is only a small portion as pointed by Viel (2021), and thus there would be more chances for the cosmic ray to create muons in the lower region with higher air density.

2) It would also be meaningful to investigate the impact of the dynamics of moving in the earth gravitational field upon the lifespan of muons until some definite knowledge can be obtained for the issue.

7. The Interesting Process of Denying the Absolute Space and Time

In 1687, Isaac Newton formally put forth the notion of absolute space and time in his masterpiece Philosophiæ Naturalis Principia Mathematica, it then became the backbone of the classic mechanics until it was banished and replaced by the relativistic spacetime at the turn of 20^th century. The failed efforts of searching the luminiferous aether and the cosmic center played an important role in the process of denying the absoluteness of space and time (Dai, 2022d); however, the logic behind this process is very amusing and thus philosophically interesting as we might see from this section. Nevertheless, in the end of this section we will also learn the unintentional role of this process in a semiotic scaffolding practice that helped humans to reach a meaningful destiny of knowing the nature of space and time.

7.1. The amusing roles of the most famous failed experiment and the nonexistent cosmic center

19^th century was the time when physicists were exploring the electromagnetic world by making analogies to the classic mechanics. Naturally, they had the idea of supposing a medium to support light just like air or water as media to carry sound waves or surface water waves, and they called that medium as luminiferous aether as an analogy to the ancient notion of aether for the medium of gravity (van Lunteren, F.H., 2002). This idea instigated a surge of researches trying to prove the existence of the luminiferous aether or even to find a way to measure it. This goal failed badly, and the most famous of those efforts was the experiment conducted by American physicists Albert A. Michelson and Edward W. Morley in 1887 and published in November of the same year (e.g. Wikipedia, 2022h). Since then the Michelson-Morley experiment has been called the most famous failed experiment in history because it became an important catalyst for the birth of the special theory of relativity.

Starting from 1880’s, a peculiar aesthetical fondness drove scientists to demand that the Maxwell equation should look the same in all inertial frame of references, which is undoubtedly the origin for the first postulate of the special theory of relativity, i.e. the principle of relativity, which could be deemed as an extension of the Galileo's principle of relativity (e.g. Wikipedia, 2021b).

But even if the Maxwell equation looks the same in all inertial frames of reference, the need of a media for light to propagate might become an important reason for people to think that the actual speed of light could change with respect to the observers of different velocities. Therefore, the missing of aether shown by the failed Michelson-Morley experiment made many to believe that it was the straw that broke the camel’s back because they thought that the missing aether is the proof that the speed of light should be constant in vacuum to all observers, which became the second postulate of the special theory of relativity.

The establishment of the special relativity in turn caused the denial of the notion of absolute space and time by claiming that space and time are relatively relating to each other through the Lorentz transformations. As we have seen in the past months, the special theory of relativity is wrong and the failed outcome of the Michelson-Morley experiment could be easily and definitely explained by the following equation based on the revised postulate of speed of light in vacuum (Dai, 2022e):

c_ab = c + ?v                              (7)

where c_ab is the speed of light in vacuum between two objects a and b, c is the speed of light in vacuum given by the Maxwell formula, and ?v is the relative speed between objects a and b. From (7) we can see that the reason why the Michelson-Morley experiment failed is because with their experimental set up, ?v = 0, and thus in theory we should have c_ab = c; of course, since the surface of earth is not in pure inertial motion but with slight acceleration, with high precision Michelson-Morley style experiments, we might still detect the tiny ?v caused by the acceleration of earth.

Another important reason for the notion of absolute space and time to be banished at the turn of 20^th century accompanying the birth of theories of relativity, as indicated by Einstein (1916), was the thought that Newton’s absolute space and time would require a centre of universe with a maximum density of stars. The failure of identifying such kind of cosmic center became another reason for denying the notion of absolute space and time.

However, as discussed by Dai (2022d; 2022e), we do not need any coordinate system, not to mention a universe center, for us to make sense of absolute space and time.

Now when we look back to the whole thing, we might find that the above logic of using the failed Michelson-Morley experiment and the unfound cosmic center as the reason of denying the absoluteness of space and time is amusingly ill-founded. Here we see such a strange role of the failed Michelson-Morley experiment and the unfound cosmic center in the banishment of the notion of absolute space and time: people first artificially fabricated the concepts of aether and cosmic center and tried hard to prove their existences, then the failures of proving their existences were used as the evidences that the space and time should not be absolute but rather relatively relating to each other. In other words, scientists first created some nonexistent things so that they could prove their nonexistence and then used those proofs to conclude that space and time are not absolute. If this type of logic is allowed in everyday life, we could imagine what might happen to this world.

7.2. The accidental help to the knowledge of softly absolute space and time

Now as we know that special relativity is incorrect because both of its postulates are wrong, we seem to have come back to the old Newtonian absolute space and time. But the truth is that we indeed are not coming back to the old rigid Newtonian space and time, but rather entering a new era of the soft absolute space and time that would conform to the general theory of relativity.

Up to this stage, we humans have finally come to a staging area after the centuries long journey from Newton to Einstein to now, and learned that space and time are neither rigidly absolute nor softly relativistic, but rather softly absolute. One thing that we need to take special heed is that in this softly absolute space and time, space and time are independently separate from each other instead of correlating with each other through Lorentz transformations as required by the special theory of relativity.

7.2.1. Inertial coordinate systems as the absolute coordinate systems

Traditionally, the notion of absolute space and time was deemed to be tied to the notion of absolute coordinate system or preferred coordinate system. After we enter the new realm of soft absolute space and time, the issue of absolute coordinate system might resurface again. As pointed out by Dai (2022e) [23], we do have the liberty to claim an absolute coordinate system now, but once we do that, we will find that all inertial systems that move with regard to each other at constant speeds without the impact of gravity are absolute coordinate systems. Further, in the soft absolute space and time, light would still travel rectilinearly in all inertial systems (i.e. absolute systems) and the speed of light in vacuum between two moving objects would also be the same to all inertia systems. This might sound a lot like the second postulate of special relativity, but it differs from the latter in that the speed of light between two objects varies with the relative speed between those two objects.

8. The Over-Confidence Resulting From the Ignorance of What Energy Is About

Over-confident of the existing textbook knowledge is a common philosophical error over human history. One typical example is about the notion of energy conservation, which was first established by Émilie du Châtelet in 18^th century based on the transfer between kinetic energy and potential energy in mechanics, and was later extended to all forms of energy and the transfer between different forms of energy (e.g. Wikipedia, 2022i).

While the notion of energy conservation and the corresponding equations have been one of the critical composing part of scientific derivation in any branches of modern science (especially physics), scientists are not as sure about the meaning of energy itself as the public might have supposed. So far the scientific notion of energy has been completely constructed on top of the concept of conservation established by Émilie du Châtelet, and thus it is almost impossible for scientists to think about energy beyond the conservation of that invisible and intangible natural vigor. Nevertheless, nature could always surprise us by going beyond the best imaginations that humans can have. As discussed by Dai (2021a; 2022f), while energy seems always conserved in the subatomic world explored by quantum physicists where boundary configurations for the potential energy are always simple, in the complicated macroscopic world, energy conservation could be violated under certain special dynamic configurations of the system. Further, as discussed by Dai (2021b), the common familiar natural phenomena like redshift and blueshift are constantly violating energy conservation with or without the influence of the expansion of universe.

Therefore, the claim that the law of energy conservation can never be violated is incorrect; but since the scientific notion of energy has been constructed based on the concept of conservation and transfer, the above mentioned discoveries of cases in which energy is not conserved have exposed the ignorance of the scientific community about either the true essence of energy or the mechanism of its creation and annihilation which has not been clearly taught in textbooks.

9. Discussion

Human beings are paying a dire price for disparaging philosophy in all facets of life, especially in the field of natural science where the most intelligent explorations of nature for the survival and advance of Homo sapiens species are supposed to be conducted. In the examples discussed above we could see that scientists with the aura of smartest people on earth could easily be convinced by “simple, straight, and brilliant ideas” that would lead to various kinds of false knowledge and wrong practices, and then defend those ideas with all their lives for a long time, simply because they do not possess the capacity to discern simple philosophically wrong ideas.

Very often those “simple, straight, and brilliant ideas” could bring aesthetically attractive convenience with its logical defects hidden in various camouflages that could be easily identified if the society has been prepared with strong philosophical capacity of reasoning.

In the case of Cantor continuum hypothesis, its defect is almost as simple and straight as the Cantor measuring scheme for infinity sets once we identify his trick of abusing the endless repository of infinity set by running a deficit economy in counting the number of the elements in an infinity set.

In the case of the first postulate of special relativity, as a mathematical expedient, even without any reason to believe that it should actually happen in nature, one might still assume the contraction of the whole space in the direction of the motion in order to make the Maxwell equation look symmetric without worrying about the impact to the perpendicular spatial dimensions. However, when that mathematical expedient is extended from the electrodynamics to the classic mechanics in an effort of replacing Newtonian mechanics, a simple mathematical common-sense error was committed: while it is reasonable to assume that the postulated contraction of the scale of the electromagnetic wave in the direction of motion would not affect the physics in the other two perpendicular directions, when the same postulate is applied to a macroscopic moving object, it would be immediately problematic due to the inevitable violation of the 2^nd Law of Thermodynamics.

Once again, the defect here is as simple and straight as the convenience the Lorentz transformations could bring: it is a simple mathematical common-sense error of ignoring that the increased number of elements (particles) would tremendously increase the complexity of the involved math.

In the case of the second postulate of special relativity, although it might take some deep insight to logically expose the erroneous result which the postulate would lead to, as presented by Dai (2022c), the defect of defending relativity by twisting the significance of Sagnac effect is as simple and straight as the psychological comfort it could bring to those with firm faith in the special theory of relativity.

In the case of the light-seeing-based relativistic chronology, with a simple logical reasoning for one more step further from the seemingly reasonable claim that if A could not “see” B then B is meaningless to A, one could easily spot its chaotic consequence of dictating that new events could happen earlier than old events.

In the case of the false claim of time dilation for the apparently longer lifespan of muons, it only needs a trivial step of asking why the time dilation and length contraction cannot be applied in a symmetric manner when changing the inertial frames in order to debunk the myth.

As for the amusing roles of the failed Michelson-Morley experiment and the unfound cosmic center in denying the absoluteness of space and time, it is one of the best examples in history showing how wrong philosophical thinking could lead the whole world go astray for a very long time; besides, it might also suggest that sometimes we need to have some humor to look at how wrong philosophy operates in human history.

The apparently most complicated case (and thus the most lingering issue) discussed above would undoubtedly be the over-confidence based on the textbook knowledge that energy conservation can never be broken. Nevertheless, if we carefully examine the history of establishing the energy conservation law as described in textbooks, it is not hard for us to find that human efforts of defying that law have never been ceased since the time when the conservation law was proposed but unfortunately all unsuccessful (at least according to the literature records).

However, one important reason that should account for the failures of the past attempts to defy the energy conservation law is the worldwide crackdown of any attempt of doing so, through political and cultural means by smearing those defiant ones as morally or mentally unhealthy or unworthy. But the problem is that the officially pronounced reasons why perpetual motion machine is impossible (which is a slogan equivalent to the claim that the thermodynamics laws cannot be violated, where the thermodynamics first law is the energy conservation law) are themselves normally versed in a manner of sophistry as shown in the following typical layout (e.g. Wikipedia, 2021c):

• A perpetual motion machine of the first kind produces work without the input of energy. It thus violates the first law of thermodynamics: the law of conservation of energy.
• A perpetual motion machine of the second kind is a machine that spontaneously converts thermal energy into mechanical work. When the thermal energy is equivalent to the work done, this does not violate the law of conservation of energy. However, it does violate the more subtle second law of thermodynamics (see also entropy). The signature of a perpetual motion machine of the second kind is that there is only one heat reservoir involved, which is being spontaneously cooled without involving a transfer of heat to a cooler reservoir. This conversion of heat into useful work, without any side effect, is impossible, according to the second law of thermodynamics.
• A perpetual motion machine of the third kind is usually (but not always) defined as one that completely eliminates friction and other dissipative forces, to maintain motion forever due to its mass inertia (Third in this case refers solely to the position in the above classification scheme, not the third law of thermodynamics). It is impossible to make such a machine, as dissipation can never be completely eliminated in a mechanical system, no matter how close a system gets to this ideal (see examples in the Low Friction section).

The defect in the above commonly accepted official reasons of why perpetual motion machines are impossible is as simple and straight:

The above three reasons all use extreme scenarios to cause the audience to ignore the possibility of the logical middle, i.e. cases that are not completely void of energy, are not completely void entropy increment, and do not completely deplete dissipations caused by friction or any other causes, but still violate the energy conservation law as discussed in above section 8.

The fact that the whole world could have accepted the above reasons for the impossibility of perpetual motion machine for centuries is once again an excellent example of how things could go wrong when the whole society is deprived of quality capacity of philosophical thinking.

History is full of coincidences. A few decades before the academic world accepted Cantor’s set theory, Danish author Hans Christian Andersen published his famous writing “The Emperor's New Clothes” (e.g. Wikipedia, 2022j) , and then a few decades later, as we have witnessed from the examples discussed above, the community of scholars in mathematics and physics, a group of elites that would be least possible to be connected by the public to that folktale of Andersen, started to put on the real life show simply because of their collective dearth of strong capacity of philosophical thinking.

10. Remarks for the Future

The academic capacity of philosophical thinking has been severely crippled by the collective misunderstanding and disparaging of the role of philosophy for the past few centuries. It is the outcome of complicated historical developments of both academic philosophy and academic science with profound causes in both prescribed and accidental forms. Obviously we cannot go back in history to fix the historical causes but rather have to face the current challenges coming with it if we do want to have a change of the status quo with the academic philosophical weakness.

10.1. The need for the change of attitude

One of the biggest challenges at this point of history for the world to deal with the fallout of disparaging philosophy for a long time is to admit that collectively disparaging philosophy has done huge harms to the civilization. This would be much more difficult to the academia than it might sound because it is always a popular tendency for people to focus on particular technical or conditional reasons for their mistakes or failures instead of the defects in their fundamental ways of thinking (i.e. their philosophical thinking) since hardworking people would always think that they have tried their best to muster up their good logical ability to take care of all the necessary aspects. Consequently, although due to the undeniable directional errors when we look back over the century-long course it would be very hard for serious readers to deny the philosophical causes behind the mistakes discussed in this writing, when similar situations occur in the future practices, people would most probably repeat the same mistakes if the negative societal mindset about the role of philosophy remains the same.

A change of the mindset of disparaging philosophy by admitting the important role of philosophy in scientific endeavors is of the utmost importance for us to improve human societal capacity of philosophical thinking. We need not only personal willingness of taking philosophy more seriously but also the same kind of societal willingness; personal willingness is important since every discipline is made up of individuals while societal attitude would be critical for the resource granting and platform allocation (e.g. paper publication).

10.2. An awkward situation

Even if the whole academia of science is now willing to admit the important role of philosophy in scientific endeavor, we would face the general awkward situation that philosophers do not know science and scientists do not know philosophy. To make matters even worse, as declared by Heidegger in last century that the academic philosophy is pretty much dead. Some typical symptoms of the ailing academic philosophy include: 1) collective poor capacity of reading (see Dai, 2019, 2020 a-b, 2021c); 2) the widespread abuse of empty isms as the substitutes of real life logical issues; 3) lacking the knowledge of what philosophy is meant to be; 4) lacking the capacity of metaphysical analysis of real life dynamics and accordingly having lost one of the most important functionalities of philosophy which is the diagnoses of problems for social practices; 5) lacking the knowledge about why the academic philosophy is pretty much dead.

Obviously, this stalemate situation would discourage scientific workers to take philosophy seriously or give them (wrong) excuse to continue disparaging philosophy; in the meantime professional philosophers cannot provide much help to scientists even if they think they can or claim they can.

10.3. An acute disorder without a quick solution

With or without the relevant human awareness, the collective societal poor capacity of philosophical thinking would continue to take its toll on the wellbeing of human civilization in all areas such as science, economy, politics, environment, etc. Practical issues that are deemed as urgent in everyday life might very well be rooted in the unhealthy status of general societal capacity of philosophical thinking. That is to say that we have an urgent task of mending our societal capacity of philosophical thinking instead of assuming that the impact of philosophical development is always a long term bet without the hope of helping the pressing issues and thus without the need of urgent treatment.

Nevertheless, we do not have much in hand to solve this dilemma. Obviously, this situation cannot be changed by a single-task project in any single discipline of culture. This demands a collaborated action across disciplines and across the world and requires generous investment without utilitarian financial expectations for immediate paybacks.

10.4. The need of a new specialty of advanced applied philosophical (metaphysical) analysis  

The long term solution for boosting the global societal capacity of philosophical thinking would undoubtedly involve revolutionary changes in philosophy education at all levels (from grade to graduate). However, fundamental educations would not suffice for meeting the global demands for advanced philosophical capacity in helping with practical needs in scientific, economical, political, environmental, and all other cultural areas. We need to have professionals of advanced capacity of metaphysical thinking in various decision making bodies to help avoiding detrimental actions.

The challenge here is that we need a new specialty to help the world with widespread demands while it is impossible for us to train people with this specialty like we train other professionals. This new specialty would require its professionals to be not only proficient in math and science but also in philosophy (metaphysics). This requirement determines that it would be like building another ivory tower in the academic world. Nevertheless, since we need it we have no other choice but start to build it so that we might get over the barrier of societal weak capacity of philosophical thinking.

 

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