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.
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