## Tuesday, February 13, 2018

### ON SPIN STATISTICS THEOREM

ON SPIN STATISTICS THEOREM.

A friend wanted to understand 'Bose -Einstein statistics’ in a simpler format. This is my reply to him.

'Bose -Einstein statistics’ follows from something called the Spin-Statistics Theorem. It requires relativity, to derive the Spin-Statistics Theorem. There are lots of attempts to justify the result without relativity, but they do not work in the mathematical formalism. As I have repeatedly written citing Prashastapaada, relativity is a wrong description of reality and there is much misunderstanding about the nature of bosons and fermions. One can Google “Anti-Relativity” and find huge support for my above statement.

It is said that exchanging the position of two fermions will change the sign of the wave function, while the wave function for bosons will remain the same. Why does this happen and what does spin has to do with it? No one understands. Some say Bosons’ are particles whose wavefunction is symmetric under such an exchange or permutation, so if we swap the particles, the wavefunction does not change. Fermions are particles whose wavefunction is antisymmetric, so under such a swap the wavefunction gets a minus sign, meaning that the amplitude for two identical fermions to occupy the same state must be zero. This is the Pauli Exclusion Principle: two identical fermions cannot occupy the same state. This rule does not hold for bosons. Too confusing.

Others say, Bosons’ wavefunctions do not change sign when you rotate them 360 degrees, while fermions’ wavefunctions do change sign when you rotate them 360 degrees. What happens if we interchange two bosons or fermions? Also, why fermions' wave functions change sign upon rotation of 360 degrees. Secondly, why two identical particles interchanged is equivalent to one being rotated by 360 degrees?

To understand the problem, one must understand what is spin and what is the nature of fermions and bosons. Think of a small cylindrical pipe and a candle. Place both on the table and rotate. When you rotate the candle by 360 degrees, it comes back to its original position. That is, by spinning once, it reverts to its original position. This is an example of Spin 1. Now rotate the cylindrical pipe. You do not have to rotate it by 360 degrees, it appears to come back to its original position after rotating 180 degrees – ½ of one spin. This is an example of Spin 1/2.

Now think of a glass and water filled in it. Water needs a container – here the glass tumbler. Overturn the glass by 180 degrees. All the water is displaced – occupy space in ‘another container’ – may be of different shape including the flat surface where it spreads. But if you rotate the empty tumbler by 360 degrees, it returns to its original position without being displaced. The solid glass tumbler behaves like a boson and the liquid water behaves like fermions.

Electricity is the flow of electrons and behaves like a fluid. You can picture these as a fish in water. The water surrounds the fish. We observe something only by contrasting its motion or radiation with its background. We observe the fish only because it radiates different wavelengths than water. We cannot differentiate one water molecule or a drop of water from another, because they radiate the same wavelength. If the fish moves, it creates a tip or a wave-front, which we could differentiate from the background. Similarly, what we call bosons (including electrons), are nothing but a part of the “electron sea”, in which some radiation from the protons (like the fish) creates a wave-front. We call each such wave front electrons.

For this reason, one cannot predict the position of an electron, but when one measures it, one finds it in a fixed position. How can one measure unless he/she first observe the wave-front? One cannot measure something without perceiving it first. “Scientists” up turn this logic and say that, though they cannot predict the exact location of the electron, an electron is always found in a place when it is measured. This way, they fool everyone with incomprehensible statements and “mathematical structures”.

There is no weirdness in the quantum world. I can explain each quantum phenomena with macro equivalents. Modern science needs rewriting and it must not be done by the “Scientists”, but rational people who do not fantasize.

The fallacy of modern science is imprecision in the name of precision. They do not define any term precisely, but give an operational definition, which is subject to change according to the context. Thus, they can use the same term to imply opposite features and make laymen believe that science is super magic and if one believes in God, then He is a magician.

What is space? Both space and time arise from our notions of sequence and interval (paratwaaparatwa). The intervals between ordered sequence of objects is called space and those of events (changes in objects) is called time. Since intervals have no markers to describe them, they are described through the alternative mechanism (vikalpana) of the boundary objects or events. Without boundary objects or events, space or time is meaningless.

Einstein defines space as that which we measure by a measuring rod. But it does not define space. It simply substitutes the word “space” by “which we measure by a measuring rod”. But what it is that is measured? No answer. From this he switches to manifold (such as four dimensional spacetime manifold), which is a collection of points forming a certain kind of set, such as those of a topologically closed surface or an analogue of this in three or more dimensions. This confuses everyone and they continue to extend this to a long array of different spaces and sub-spaces starting with Minkowsky spacetime, De-Sitter space and Hilbert space, etc. in n-dimensions without precisely defining dimension. If they precisely define dimension, all these “theories” including string theory or the other variant M-Theory would fall disgracefully as absurd. ALL modern scientists use these without defining space, time and dimension. If they define these precisely, ALL their theories will fall.

Now the other lie of modern scientists! Space or space-time is NOT expanding, as it is not evident in local scales. It is observable only in galactic cluster scales. Some “scientists” explain this by comparing space with a balloon and the stars and galaxies as rigid spots on it. If the balloon expands, the spots remain fixed – they say. But in that case, the balloon would burst. However, the universe is not bursting. Since space is the interval between objects and is described by the boundary objects only, it was indescribable before structure formation. However, since structure formation was an event, time existed before space. Thus, we can say space is emergent in time (kaalaat vyaapaka uchyate). Thus, time, as we know it, is emergent (aksharaat samjaayate kaalah) from the big-bang or big-bounce (minus its extensions and mathematics).

The fundamental nature of time is cyclic: measuring events from being as cause to becoming as effect, growth through accumulation, transformation through harmonious accumulation, transmutation due to dis-harmonious accumulation, and finally, change of form through disintegration and assimilation with other elements. This continues as a flow – a river flowing towards the sea (nadeeva prabhavaat kaachit). These cycles take two forms: individual (mrityu - death) and universal (yama – big crunch minus mathematics and extensions). The midpoint is the condition of maximum entropy. When all individual cycles become co-terminus at one point, they resemble the state before creation – beyond the quark-gluon plasma, which are derivatives of the primordial soup - but with some inherent instability. This inherent instability generates inertia of motion (vega) that moves at the fastest speed across the expanse in the state of near equilibrium. The background at rest responds by generating inertia of restoration (sthitisthaapaka) that decelerates the inertia of motion through something like a bow-shock effect (a boat being pushed back against its motion due to resistance by river water) to finally bring it to a halt (Maya). This cuts off a big spherical volume (hiranmaya anda), which is closed from the background at its periphery (naimishaaranya). This volume is called the universe (Brahmaanda).

From the boundary of the universe, the impulse of the initial forward motion reverses due to reconnection effect (like that seen behind a boat or in the magnetosphere). This incoming force (dhaaraa) leads to couplings that finally leads to structure creation (Jaayaa), due to accumulation in various proportions. I can describe the detailed mechanism separately. This process repeats continuously leading to slowing down the speed of light over time. This can explain the so-called dark-energy without esoteric and fancy ideas.

Like everything else in the universe, it itself is spinning around its axis. For this reason, the galactic clusters appear to move away from us (red-shift) at times to come closer (blue-shift) at other times, just like planets in the Solar system appear to move fast (atichaara) at times to become retrograde (vakra) at other times. There is no mystery, but lack of mastery in explaining physics.

Sequence is related to inter-se arrangement or relative positioning, which gives rise to direction. Without sequence, indicating a direction would not be possible. Interval is related to the inter-se arrangement of position, i.e., how far the objects are positioned from each other. It gives rise to dimension. Without interval, it would be impossible to define dimension.

Both space and time arise from our NOTIONS of sequence and interval means, it can only be perceived by using the concepts of sequence and interval. Perception is always about some external object. Thus, it is question of how we perceive it and not whether it is related to individual or universal perception.

All perceptions including that of space and time are sensory constructs. Its processing and comparison with memory are individual processes. Thus, we perceive the same thing differently – neither higher nor lower, as there is no yardstick for that. The individual perception is the notion for that individual. Intellectual disability is not a universal term. A person, who lacks the mechanism for perception of interval, cannot perceive space or distance, because distance is the interval of an object from some reference point.

Sequences could be ordered or random. Both space and time are ordered sequences. This gives time its “arrow”, because even undoing something is “another event” and not “undoing the event”. However, space is not bound by this principle. Hence there are different directions and no “arrow”.

If I pull your hand only, your body will also be pulled in the same direction, though inertia will try to resist the motion. Thus, local conditions affect global conditions – may be in a chaotic manner like the butterfly effect, where each step of the effect is not perceptible, though accumulated effects in the long run are perceptible. Expansion of the universe was postulated based on something called “red-shift”. Now, we have seen galactic mergers and collisions, which are not possible if the universe is expanding. Further, “blue shift” has been observed, which indicates that some galaxies are coming closer. Hence there is no reason to clutch to the earlier idea that the universe is expanding, even after the evidence showing its contrary, and when other cosmological phenomena like the planetary motions give a suitable explanation.

Analogy (udaaharana) is a thing which is comparable to something else in significant respects - a comparison between one thing and another, typically for the purpose of explanation or clarification (saadharmodaaharana). If it cannot explain or clarify the concept that is sought to be explained or clarified, it cannot be called an analogy.

Modern scientists cannot answer: “Into *WHAT* (if anything) is spacetime supposed to expand?” Thus, they say that is not important – I do not understand how it is not important.

Like everything else in the universe, it itself is spinning around its axis. By it, I mean the galactic center.

The galactic clusters appear to move away from us (red-shift) at times to come closer (blue-shift) at other times. This has been experimentally verified. However, our experimentation is highly insignificant in cosmic time scales. To observe both the Red-shift and Blue-shift for the same galaxies will requires a minimum of few million years.

Firstly, there is no book that is directly ascribed to Charvak. Even there is doubt as to whether there was a person by that name (some say he is the brother of Brihashpati) or it was a collection of palatable (charu) statements (vak). We gets bits of his views scattered in different places quoted by others. The terms used by you are used in Nyaya and the Buddhist philosophies, which are abridged versions of Nyaya. Diungnaga and Vasubandhu had discussed these in their books.

HETU (हेतुः): 1) In Vaisheshika, it is used as a determinant (ज्ञापकः). This can be of two types: true determinant (सद् हेतुः) or false determinant (हेत्वाभासः). 2) Cause (कारणम् or उत्पादकम्). 3. Independent inducer for an action (स्वतन्त्र प्रेरयन्). 4) An object that fulfills the need (फलसाधनयोग्यः पदार्थः). This is the Nyaya view that requires an analogy, based on which a statement is sought to be proved (उदाहरणसाधर्म्यात् साध्यसाधनं हेतुः). 5) Outcome (फलम्). 6) A type of simile (अर्थालङ्कारविशेष). 7) One of the five components of research methodology (न्यायावयवः).

SADHYA (साध्यम्). 1) Object to be accomplished or determined by applying logic (साधनीयम्). In your example, proving the existence of fire from smoke is Sadhya. 2) One of its variations is called Paksha (पक्षः) – When only a partial exposition in conformity with the proposition is presented (साध्यार्हः प्रतिज्ञेयः पक्षः). Here, the analogy given does not necessarily conform to the final statement. 3) The process of naming or describing an action (लिङ्गसंख्यानन्वयिनी क्रिया). 4) One of the various groups based on the gravitational effect (गणदेवता विशेषः). 5) A specific division of time (मुहुर्तनाम). 6) Capable of being easily performed (स्वानुकुलताग्राहकः पदार्थः).

VYAPTI (व्याप्तिः). It is a type of special relation (सम्बन्धविशेषः). It may extend one relationship or property or it may exclude such relationship or property. It is useful for drawing inference, which can be used to present one’s stand point (paksha). It is a vast subject with five branches. Gangesha has written a big book called Vyapti Panchak on this subject.

ON CERTITUDE (सिद्धान्त)

The issue of certitude can be approached from two different perspectives: 1) absolute perspective on the statement, which can also be called the abstract perspective, and 2) a more particular or as a special case. Let us discuss the absolute perspective first.

The word certitude is generally understood as: absolute certainty or conviction that something is “surely” the case. Thus, negative certitude would imply: absolute certainty or conviction that something is “surely” not the case. In either case, there is an “absolute certainty or conviction” or “surety” that one’s knowledge about something is validated by proof, aided by logic. Thus, the validity or otherwise of certitude – negative or positive – boils down to the validity of the proof submitted to justify it (siddhaanta). This can be examined from four perspectives.

1)      Everyone says something conclusively or with certitude only when he/she thinks it is “surely” true or useful in the particular context, which implies, ruling out its improbability. If the proof or logic advanced in its support of certain philosophy is accepted by all (there are several such concepts where all philosophers agree unanimously) and countered by none – the Holistic Truth or the Big Unitary Truth, then the certitude is positive and universal (sarva tantra siddhaanta).
2)      There are philosophies, which some consider as valid, whereas others contest its validity. If both groups could sit together and iron out the differences, then it becomes positive and universal certitude. But before such resolution, the competing philosophies remain as contrary or negative certitude for each other (pratitantra siddhaanta), because a third person cannot be certain, which philosophy is correct. They only “surely” know that one must be correct and the other wrong. Here, every theory has its own truth and truth standards, which cannot fairly be judged in the light of rival standards.
3)      There are certain foundational concepts, which, once established, leads to prove another concept. To give one example, the functioning of senses and consciousness are correlated. The senses are different and each perform a specific task – eyes can only see, ears can only hear, etc. But we perceive every sensory impulse uniformly as “I know…(I am seeing, hearing, smelling, tasting, touching)”. We may touch the thing we see, though the senses are different. Thus, the “knower” must be different from the “known” or the object of knowledge. But till the knower or Consciousness is established (i.e. a person is conscious), the individual senses have no meaning. The certitude like this, i.e., statements like “only conscious beings can utilize senses” is called foundational certitude (adhikarana siddhaanta).
4)      There may be cases where we do not have a clear stand on any subject, though other philosophies have a specific stand on it. We can temporarily accept that proposition as true and then apply logic to determine related aspects. In such a case, if we come to a conclusion based on an uncertain proposition, the certitude is called directed certitude (abhyupagama siddhaanta).

I am unable to make any sense of it. Kindly remove my doubts by explaining your comments.

a)            How does your statement at a) harmonize with the measurement problem of QM? Zeno effect is a wrong description of reality, where the principle of measurement cannot be applied. Measurement is a comparison between similars, out of which one is the unit, with which the other is scaled up or down. Hence, measurement always returns scalar quantities. In Zeno effect, reduction of remaining distance by half is compared with a constant velocity in each step. Both being finite quantities, the answer should be finite and not infinite. Otherwise the definition of motion itself would be wrong. Any reduction must imply a scalar quantity by which the objects are scaled down. This would necessitate a gradual change in the system. If “conscious entity would be a sequence of state function reductions”, the state cannot remain invariant. Your comparison of this with Maya may not be proper. Mostly, people have no understanding of Maya, which, by definition, is related to measurement and superposition – not illusion. Some, who do not know about its mechanism, speak vaguely about it.
b)            ) In zero energy states, there cannot be any motion, as all motion requires energy. Time evolution implies change of state in time. Thus, there cannot be zero energy states – these can only be states at equilibrium – or zero net energy. There is much confusion about super-position of states. Suppose in a sea beach, two waves come from two angular directions, where the crest of one interacts with the trough of the other, so that both flatten out. Before their interaction, we could differentiate between the two waves. After the interaction, we can never identify each wave – they have gone into a superposition of states. This is not a uniquely quantum phenomenon, but is happening regularly every moment in the universe. Water from the ocean goes up to come down as rains. We die and our bodies are assimilated in Earth or the atmosphere to reappear in different combinations. It is our inability to point out the “position” of something that we knew earlier – it has a different position now, may be by distribution in parts scattered all over, making it impossible for us to specify its earlier specific position, but known to be present in different positions by part simultaneously. For this reason, it is called superposition of states. Light cone is fiction. If a light pulse expand in time in a two dimensional field, it would generate concentric circles of higher radius in the same plane – not in different planes (that would make it three dimensional, but unlike the images given by Hawking and others, which show it as conic sections). In three spatial dimensions, the light pulse expanding in time, would make it concentric spheres of increasing radius – not cones. “Opposite boundaries of causal diamond (CD) obtained as intersection of future and part directed light-cones” are nothing more than meaningless words. Thus, kindly explain what exactly you wanted to convey, because, rest of your comments are based on these.
c)            Death, just like birth, is a feature of time evolution related to superposition of states. Time, like space, arises from our concept of sequence and interval. The ordered internals of two sequential objects is space and that of events is time. Since intervals have no markers to describe them, these are described by using alternative symbolism of the boundary objects and events. The boundary objects and events are not space and time, but are the digitized versions of arbitrarily chosen segments of analog space and time. Unlike space, time is cyclic. Existence involves six stages from “being” as a cause to “becoming” as effect, to “growth” by accumulation to “transformation” by accumulation of harmonious elements to “transmutation” by accumulation of non-harmonious elements to “change of form” by disintegration and dispersal. This is one cycle for any object. There are infinite interrelated cycles. The beginning of a cycle is called its birth and the end is called death. But these do not define life. There is no proof to show that “Self re-incarnates at opposite boundary as time-reversed self”. Rather your statement raises questions on re-incarnation, arrow of time, and self. What is the proof for re-incarnation and time reversal? WHAT is “SELF”. What are sub-selves? What is geometric time? What is sleep?

There is much confusion about freewill. It is limited freedom of thought and consequent action. All our actions are guided by two factors: 1) any external impulse that stimulates our senses, and 2) our memory that retains the earlier experiences in yes/no/neutral format. If the incoming impulse is harmonious with our stored memory of experience, we get attached to the object. If it is not harmonious, we are repelled by it. If it is the first time or indeterminate experience, we ignore it. Thus, our reaction is shaped by a) our past experience that shapes our mental preparedness b) our ability to respond physically to the mental preparedness. Freewill is subject to these limitations. In case of conceptual issues, it is our ability to understand natural principles based on our early experience (knowledge) and relate it to other aspects of the physical world, guide our thinking process. Mostly people approach the same subject from different angles based on their past experience, which operates on the principle of inertia of limited motion. This inertia is known as the thought. This is continuously updated. That might be called the evolutionary approach.

The idea of Truth must have some perfect correlation to the state of reality. Truth is based on some central theme, around which, we build a field of related experiences, which is confined by our “total knowledge”. This is the same as in the quantum world: a nucleus, surrounded by an intra-nucleic field, and confined by the electron sea. Hence, it is not correct to say that reality prevents us from acquiring such knowledge. Suppose we see a rope in the darkness and mistaken it for a snake. We may not have the knowledge of the rope, but we must have knowledge of the snake. If we start from their and examine it closely, the motionlessness would first give us the impression of a dead snake. Then if we get bold and examine it from close quarters, we can finally come to the conclusion that it is not a snake, but something else, to which we give a name. Later we can have knowledge about the rope. Here we must differentiate between two types of “total knowledge” – individual and universal. Whatever we come across, if we have a knowledge about its reality – conceptual and functional mechanism that is perceivable and communicable – it is “individual total knowledge”. The maximum extent of this “total knowledge” is Omniscience.

Regarding "probabilities are quantifying OUR degree of UNCERTAINTY about reality", there cannot be any standard candle. The effects can be devastating (the 1 % probability of a bullet hitting a person) or marginal or negligible (99% probability of getting a few rotten wheats in a sack of wheats). In the former case, the 1% probability can become vital (or interesting), whereas in the latter case, even 99% probability is trivial. The same applies to scientific research. Most of our so-called theories are fallacious or are based on unproved or non-existent concepts or particles. The list is never ending, one of which related to the so-called dark energy is dubbed the biggest mismatch in history. Modern science thrives only on technology. Here even there is no probability of 1% of the “theories” standing the test of scientific proof. Scientists cover is up under the cloak of incomprehensibility and reductionism – and the latest trend of cocktail science. Knowledge is never new, because it is our ability to understand some existing function. It is always a discovery.

If meta-truth means the descriptive properties of terms such as "good", "bad", "right", and "wrong" do not stand subject to universal truth conditions, but only to societal convention and personal preference, then you are correct. What is good for one can be bad for the other. These are relative. But there are a few universal truths like death for everything that was born, seasonal changes, etc. These are neither good nor bad universally. To that extent, your statement: “Reality … requires some sort of balance between order and chaos at all levels (both physical and abstract), which seems to demand of us successive levels of both humility and acceptance of diversity in ways that may not be at all comfortable”, is correct.

Though you are talking sensibly, are you not mixing two things? When you talk of numbers, we have to differentiate between the concept of numbers and its application. Number is a property of all substances, by which we differentiate between similars. If there are no similars, it is one. If there are similars, it is many, which can be 2,3,4,…n, depending upon the sequential perception of “one’s”. The number game applicable to many. But can it be applied to something like consciousness? The objects of our knowledge may be different, but in all such perceptions, the knowledge: “I know ….” Remains invariant. Without the common “I know ….”, there can be no meaning to anything.

When you talk about the pixels or colored dots, you are talking about the process of the “many”. But unless one possesses the “eyes”, you cannot interpret it. You analyze the external impulse in the brain and decide what you want to do. But as I have explained earlier while discussing freewill, you are really not independent, but are guided by your memory of past experiences and physical capabilities. You are also telling the same thing in a different language. The only difference is you are mixing up brain and the consciousness. Functioning of the brain is a conscious process, but brain is not the “consciousness”. There is a difference between the knower, the known and the mechanism of knowledge. You are talking of the last two, but leaving out the first.

Does “quantum mechanics chipping away at one side, and AI and virtual reality approaching from a completely different paradigm space”? I have shown while discussing truth that both have a similar format. Only we have to see it in the contextual perspective. “Complexity theory, maximal computational complexity, and notions like density matrices” etc. are related to mechanism of observation or knowledge.  There may be “a great many limits to our ability to ‘know’ anything at any level beyond some sort of ‘useful approximation’ relevant to the context”. But even there, the “I know ….” Part remains invariant.

“Science, logic, computation, abstraction”; do not change the knower or the object to be known. Humility “that accepts a sort of fundamental ignorance that no AGI (Artifical General Intelligence) is a sign of higher intelligence.  Non-computable approximations are working arrangements within our limitations.

But does the description “one spec of dust” has any meaning in isolation? You must differentiate dust from everything else to make any sense for the word “dust” (differentiation from dissimilars) and differentiate all other dust specs from the “one” you are talking about (differentiation from similars). Thus, your perception depends upon these two differentiation (there is also the differentiation of parts from the whole). Eyes and light are only subsidiary instruments for perception of objects. For example, consider something placed in a room. If one is blind or there is no light, one cannot perceive anything. But if there is light and the person has healthy eyes, he/she can see clearly and describe such object. Mere placement of objects before our eyes cannot ensure perception – or information. This is my scientific training.

Can you count 10^10 molecules at a time? No. We count one by one. We may make units of thousand or million or billion in this process. Then we have a mental picture of the total unit. That was only we could count or know or measure 10^10 molecules. That is the only scientific explanation. It applies for everything universally – be they molecules, atoms, nucleons or quarks. We never utilize the full capacity of our brain, but use only a small fraction of its total capacity. That is our inability – bot brain’s failure.

How do you “take a snapshot of all the atoms in our bodies, and blow it up to a size we can see”? Magnification distorts. We observe only the present at here-now. Can we meet our ancestors or progenies if we move fast enough? This is fiction – not science. Does the pulse of light that radiated by a galaxy a billion light years away reach us undisturbed by anything in its flight path? Not likely. Then how can we say that we are looking at the past? How does relative speed affect perception? In the laboratory, we measure wavelength of light. Since light moves at constant speed, while our instruments are stationary, should we apply length contraction to the wavelength? In that case, the result will be zero or infinity depending upon how you interpret it. Will that be scientifically correct? My 50 years of experience in this field tells me NO. Could we take a movie of a single active enzyme site within one of our cells, for just one second of real time, then slow it down enough so that we could actually see the movement of the water molecules? The mismatch you say is proof enough for its scientific validity.

Your view that “to know something means simply to have some sort of approximation that is useful in context” is a practical one and is often used by everyone.