Is Reality Digital or Analog

The Scientific American and Peter & Patricia Gruber Foundation with FQXi’s had organizing an International essay competition on the theme: “Is Reality Analog or Digital”. The phraseology of the topic is symptomatic of the malaise of reductionism that is endemic in modern science. It is like asking: “Whether observation by the Schrödinger’s cat can collapse the wave function”, without defining the observer and the precise mechanism of wave function collapse. Such open-ended questions leave ample scope for manipulation and diverting the topic into various directions not consistent with each other. There are a large number of different approaches to the foundations of Quantum Mechanics (QM). Each approach is a modification of the theory that introduces some new aspect with new equations which need to be interpreted. Thus there are many interpretations of QM. Every theory has its own model of reality. There is no unanimity regarding what constitutes reality. We will first define the ultimate nature of Reality and then show that there is a deep, foundational reason why reality must be purely analog and digital descriptions can be derived from continuous symmetries.

Quantum effects exist in the macro world also but are generally overlooked. Though some features appear to be exclusively quantum features, the synergy between quantum theory and classical theories are gradually emerging. The American Mathematical Society in October 2005 reported that the Theory of Dynamical Systems used for calculating the trajectories of space flights and the Theory of Transition States for chemical reactions share the same sets of mathematics. This proves that both microcosm and the macrocosm replicate each other. Example: the internal structure of proton and Planet Jupiter is similar. Like protons, there is an abundance of Jupiter like planets in the universe.

Everything in Nature can be broadly categorized into fields, particles and strings. There is no single description that explains all phenomena on its own. A field is a region of space characterized by a physical property having a determinable value at every point in the region. If we put a body in a field, we can notice something else out of that field which makes the body interact with it in specific ways that can be measured. This something else is a type of force that interacts with the confined body as a whole. Quantum Field Theory can’t be imagined without particles which are accelerated and scattered in colliders. Particles and fields are temporally different but inseparable conjugates bound by a common thread like the diameter and circumference of a circle. This has given rise to the idea of strings with many unanswered questions1. High temperature particles are confined by low temperature fields giving them fixed dimension. Energy confined around a point generates externally directed pressure that is felt as mass. These are digital entities. The field is analog space. The four way bonding2 between particles and fields are perceived as reality.

All bodies are created from the same fundamental particles. Only the numbers of these particles and the pattern of their coupling make each body different from others. Quantum particles are like compounds (strong coupling) of fundamental particles and macro particles are like mixtures (weak coupling) of quantum particles. These are nothing but accumulation and reduction of particles in the field in specified ways with a countable set of discrete values. This implies that Nature or Reality is mathematical but only in specified ways.

Mathematics is said to be the language of nature. Language is a created vibration or sign that is meaningful only if it follows a fixed pattern and a fixed meaning is ascribed to each specific combination of vibrations or signs. Mathematics is a tool with specially created sets of symbols and operations that is meaningful only if the accumulation and reduction in numbers follow a fixed pattern to make it logically consistent. To be a language of nature, mathematics must be logically consistent in specified ways. Thus there is physics beyond known mathematics and all mathematical statements are not physics. Mostly they perpetuate incomprehensibility. Example: if the cost of 5 bikes equals the cost of 1 car, then the cost of 1 bike equals the cost of 1/5th of a car. But 1/5th of a car is a meaningless statement. Most of the so called mathematics used to describe events are unphysical and unmathematical3.

There is no equation for the observer. Can any equation ever describe the fragrance of the wild flower, the cacophony of the birds in the morning, the musical rhythm of the flowing fountains or the enchanting smile on the lips of the beloved? Can there be an equation for love, happiness, devotion or other sublimate emotions? Are they not real?

Mathematics is related to numbers, which is a property of particles by which we differentiate between similars. Fields have no numbers because we can’t differentiate between similar fields. Fields have no rigid boundary. If we add two volumes of water, we get a higher volume (mathematics); but now we can’t differentiate between the two volumes (physics). Fields reveal different forces that co-exist but unlike mass, they are not linearly additive4.Their interaction is in the realm of the quantum.

Measurement is a process of comparison between similars. Thus the result of measurement is always a scalar quantity. Measurement processes for particles and fields are different, just like measurement processes for space, time and space-time5 are different. The result of measurement is the description of the state of the object measured at a designated instant. The state of the object was not the same before nor will be the same after the measurement as it continues to evolve in time independent of our observation. We freeze the description of the state at a designated instant and call it the result of measurement at subsequent times. All other unknown states together are called superposition6.

Everything in the Cosmos is confined and ever moving. Quarks move within the confinement of neutrons and protons. Nucleons and electrons move within the confinement of the atoms. Atoms move within molecules that are confined in the body. Planets move confined within the Solar system. Sun and the stars move within the Galaxy. Galaxies are said to be receding from each other. But the expansion is not uniform. It is apparent only at clusters and super clusters of galaxies, but not in the solar system or even the stars within the Galaxy. The solar system is not expanding but the planets appear to be moving away from each other periodically to come closer again as they orbit the Sun. Thus the only explanation for the expanding universe is that the galactic clusters are spinning around a common center at different velocities, which appear as receding from each other. The universe is a closed system that spins. Spin is a common feature of all bodies from atoms to stars to galaxies. It is also a feature of the universe.

REVISITING UNCERTAINTY

While the particles are constantly changing their alignment within their confinement, these are not externally apparent. Various circulatory systems work within our body that affects its internal dynamics polarizing it differently at different times which are not apparent in our interaction with other bodies. The elementary particles have intrinsic spin and angular momentum which continually change their state internally. The time evolution of all systems takes place in a continuous chain of discreet steps. Each body acts as one indivisible system. This is a universal phenomenon that creates the uncertainty because the internal dynamics of the field that creates perturbation are not known to us. We may quote an example. Imagine an observer and a system to be observed. Between the two let us assume two interaction boundaries. When one medium ends and another medium begins, the interface of the two media is called the boundary. Thus there will be one boundary at the interface between the observer and the field and another at the interface of the field and the system to be observed. In a simple diagram, the situation is like:

O represents the observer and S the system to be observed. The vertical lines represent the interaction boundaries. The arrows represent the information exchange in the act of observation.

All information requires an initial perturbation as perception is possible only through interaction (exchange of force). Such application of force is preceded by freewill or a choice of the observer to know about some aspect of the system through a known mechanism. The mechanism is deterministic – it functions in predictable ways. To measure the state of the system, the observer must cause at least one quantum of information (energy, momentum, spin, etc) to pass from him through the boundary to the system to bounce back for comparison. The quantum of information (seeking) or initial perturbation relayed through an impulse (effect of energy etc) after traveling through (and modified by) the partition or the field is absorbed by the system to be observed or measured (or it might be reflected back or both) and the system is thereby perturbed. The second perturbation (release of energy) passes back through the boundary to the observer (among others), which is translated as the quantum of information. The observation is the observer’s subjective response on receiving this perturbation.

The system being observed is subject to various potential (internal) and kinetic (external) forces which act in specified ways independent of observation. For example chemical reactions take place only after certain temperature is reached. Observation doesn’t affect it. We measure the outcome – not the process. The result of measurement will depend on the totality of the forces acting on the systems and not only on the perturbation created by the observer. Thus the other influences affecting the outcome of the information exchange give rise to an inescapable uncertainty in observations.

The observer observes the state at the second perturbation – neither the state before nor after. If ∑ represents the state of the system before and ∑ ± ∑ represents the state at the instant of perturbation, then the difference linking the transformations in both states (other effects being constant) is minimum if ∑ << ∑. If I is the impulse selected by the observer to send across the interaction boundary, then ∑ must be a function of I: i.e. ∑ = f (I). Thus the observation is affected by the choices made by the observer also. Observation records only a temporal state and freezes it as the result of observation. Its true state at any other instant is not evident. Quantum theory takes these uncertainties into account. However, the mathematical format of the uncertainty principle is wrong.

The inequality: δx. δp ≥ h permits simultaneous determination of position along the x-axis and momentum along the y-axis; i.e., δx. δpy = 0

Position has fixed coordinates and the axes are fixed arbitrarily so that the dimensions remain invariant under mutual transformation. Position along x-axis and momentum along y-axis can only be related at the origin (0,0). If one has a non-zero value, the other has zero value. Multiplying both, the result will always be zero. Thus no mathematics is possible between position (fixed coordinates) and momentum (mobile coordinates) as they are mutually exclusive.

Uncertainty is not a law of Nature. It is a result of natural laws relating to observation that reveal a kind of granularity at certain levels of existence that is related to causality. The left hand side of equations represents free-will, as we are free to choose the parameters. The right hand side represents determinism as the outcome is based on the input in predictable ways. The equality sign prescribes the special conditions to be observed. For example, we can’t create a molecule from any combination of atoms – it has to follow certain rules. The conditions may be different for the initial perturbation sending the signal out and the second perturbation leading to the reception of the signal back for comparison because the inputs may be different like c+v and c-v. The “special conditions” and external influences and not the process of measurement create uncertainty.

REALITY DEFINED

Some say reality must be well defined according to nonhuman entities that lack any understanding of human concepts like particle, observation, etc. For some there are two views of reality: external or the bird’s eye view like the overview of a physicist studying its mathematical structure and inside or the frog in the well view of an observer living in the structure. They confuse the external factors affecting reality with the first view and the functioning of the instrument or sense organs with the second view. Ever-changing processes can’t be measured other than in time. Since we observe the state and not the process during measurement, objects under ideal conditions are as they evolve independent of being perceived. What we see reflects only a temporal state of their evolution.

Reality is related to perception which has three components: the object of perception, the observer and the mechanism of perception (includes instrument). The mechanism of perception is affected by two factors: its mechanical functioning and the external factors that introduce uncertainty. Since the external factor is as important as the mechanical functioning of the measuring instrument, reality has to exist independent of observation. Process malfunctioning distorts reality. For example mirages are seen, but are not real. Color blind persons do not perceive some colors. To know their true state, we must consider a large number of observations and accept the mean value as representative of reality. This is done in most measurements – especially in time keeping measurements. The same principle should apply to reality. Reality is the description that remains invariant under similar conditions during proper perception at all times. This description is possible only if it satisfies three conditions.

A description of objects can’t be completely abstract because reality has no meaning unless its existence is perceived as such. The relationship between objects is secondary and can be purely imaginary. When we describe imaginary objects, each individual component of it must exist and have been perceived by us even though a combination of such components may not be possible. If we imagine a flying horse, we must have seen a horse and something flying. Thus independent discreet existence, i.e. confinement is a criterion of reality. When the field set up by our sense organs interacts with that of any object, the impulse is measured - compared with the memory in our brain. If there is a similar previous experience, we describe the experience as similar to the other. In other words, the content of our perception is: “this is like that”. If there is no previous experience, we store the information (without perceiving it clearly) for future reference. The this is like that part, i.e. knowability is a criterion of reality. It plays an important role in the double-slit experiment and entanglement.

Perception is a matter of personal experience. We can describe the object that we have perceived through speech form for comparison with other’s perception. The “that” in the above statement is described through speech form. Thus confinement, knowability and describability are the three essential conditions for judging reality.

DIGITAL OR ANALOG

Something that exists, can be known and described, implies it has both digital and analog components, as all measurements are done in present, which has a fleeting existence. We use the result of this measurement at a time that is in future with reference to the time of measurement. We use the information when the time of measurement is in the past. We compare the result of present measurement with that of the past memory to perceive it. Thus, perception is time invariant – hence analog. Yet, each individual perception is digital like separating a pot of water from the ocean.

Both time and space are related to sequence. We fix some unit of time and space from an intelligible repetitive interval. We call the interval between objects as space and compare it with a fixed interval unit to measure space. Similarly, we call the interval of the events as time and compare it with a fixed interval unit to measure time. But these are small segments of the infinite expanse that is described as space or time. Every unit of space and time is just like every other unit and they are indiscernible. We mark them with particular objects or events and superimpose this description over space and time as a matter of convenience. Curvature of space is actually curvature of the objects that define space. Space, which is the interval, can’t be curved. Like a fluid it assumes the shape of the object. No one knows when space or time started or where it will end. However, there is no ambiguity about their segments measured by us. This has important implications for relativity7.

Space is related to objects that are associated with numbers and time is related to changes in them. When there are no other similar objects and the dimensions of the object is fully perceptible, we call the number associated with it as one. But in the case of one, if the complete dimensions are not perceptible, then we call the number associated with it as infinity7. Infinity is not a very big number. Since we can not perceive other entities similar to space and time, they are like one. But since the complete dimensions of space and time are not perceptible, they are infinite. Any non-linear accumulation or reduction (multiplication and division) of 1 or ∞ is mathematically void. Since their complete dimensions are not perceptible, linear accumulation or reduction of ∞ is also void. Hence renormalization is mathematically void.

Objects change with time, which is possible only with successive application of external force for which there must be some interval. This interval is not void. It is the field and the charge transmitted through it. In space measurement, we use the perception of the number of steps the unit takes to cover the interval between objects. Since these units are discrete, the result of space measurement is digital. In the case of time measurement we compare the interval between changes with a standard interval. Yet these are segments of the infinite space and time respectively making discreteness evident even though they are segments of a continuum.

This explains the implications of minimal length, time or energy. Since objects occupy some position, unit change of position implies total movement from the space occupied by it to the adjacent space. Since particles are confined in space, we can use the space occupied by the smallest perceptible particle as the unit length. That is the minimum length. The interval between successive movements over the minimum length is the minimum time. The energy required to move the smallest particle to the adjacent position is the minimum energy.

In addition to space and time, the universe is analog (infinite) in two different ways only: order of arrangement (direction) and consciousness, as only these two fit the description of infinity. We can perceive what is described as any specific direction with reference to the order of placement of any object with reference to another object. But by changing the order of arrangement we create a new sequence which changes the relative direction of the object without changing the axis. For example, if two objects P1 and P2 have placement values of x = 3 and x = 5 respectively, we say that P1 is in the -x direction from P2. But by changing the placement of P1 to x = 7, we create a sequence, where P2 is in the -x direction from P1. Though our description of their relative direction has changed, the axis has not changed. Since there is no other sequence like direction and we cannot perceive the full extent of any axis, it has infinite dimension like an analog field. We use only particular segments of it by devising a relative unit, which is a digital description.

The same logic applies to consciousness. In the content of conscious perception: this is like that, the term this refers to the interaction between the field set up by the object with the field set up by our sensory organs. The term is refers to time invariance, because the interaction that happened at now has been associated with past at the instant of consideration, which is future with reference to the instant of measurement. The term like refers to comparison with similars, i.e., measurement. The term that refers to the constancy of values assigned to the objects of perception. In such exercises, the conscious Self as differentiated from others (this leads to empathy), remains invariant as I perceive. Since there is no other mechanism like perception and since we can’t perceive the full extent of perception, it is infinite like an analog whole. Yet, we use only particular segments of perception for our purpose, which is a digital description.

This description is consistent with flow of time. Since objects in space don’t continuously change their position, space is differentiated from time, which is associated with continuous change of position, i.e. application of external force. If we measure the spread of the objects from two opposite directions, there is no change in their position. Thus the concept of negative direction of space is valid. Time is related to change, which materializes because of the interaction of bodies with forces. Force is unidirectional. It can only push. There is nothing as pull. It is always a push from the opposite direction. (Magnetism acts only between magnetic substances and not universally like other forces. It has a different explanation.) Consider an example:

A + B → C + D.

Here a force makes A interact with B to produce C and D. The same force doesn’t act on C and D as they don’t exist at that stage. If we change the direction of the force, B acts on A. Here only the direction of force and not the interval between the states before and after application of force (time) will change and the equation will be:

B + A → C + D and not B + A ← C + D.

Hence it does not affect causality.

There can be no negative direction for time or cause and effect.

A computer model can workout the data fed to it in the manner prescribed by the program writer. This puts severe restrictions on the computation, as the designer has to design within his limited knowledge. Since perception is time invariant (we perceive something at present in the same way as we had perceived something similar in the past), and it is the result of measurement of the impulses received by our sense organs that act mechanically, the World can theoretically be modeled as a digital computation. But it is physically impossible due to two inhibiting factors: the limitations of our perception and the mechanism of perception.

Take the example of time measurement. We perceive the day or the year, which is easily intelligible and fairly repetitive, as the unit of time and subdivide it to fix the duration of a second. But we know that the actual length of the day or the year varies. The atomic clock which fixes the pulses of the cesium atom at par with the classical second is also not precise. Since our unit is approximate, according to chaos theory it will lead to entirely different pictures every time. In fact this is the secret of evolutionary cycles – each cycle starts out similar (not same) but evolves differently from other cycles.

Objects are perceived in broadly two ways by the sensory organs. The ocular, auditory and psychological functions related to these follow action at a distance principle (homogenous field interaction). The tactile, taste and olfactory functions are always contact functions (discrete interaction). This is proved by the functions of mirror neurons. When we see or hear some actions or sounds at a distance, i.e. when disturbance generated by the objects travel in space as light or sound waves and reaches the field set up by our eyes or ears, it acts in the same way as a charged object when brought near a neutral object. The effect of such interaction is its operation.

In the case of visual perception, the neurons get polarized like the neutral object and create a mirror image impression in the field of our eye (like we prepare a casting), which is transmitted to the specific areas of brain through the neurons, where it creates the opposite impression in the sensory receptacles. This impression is compared with the stored memory of the objects in our brain. If the impression matches, we recognize the object as such or note it for future reference. This is how we see objects and not because light from the object reaches our retina. Only a small fraction of the incoming light from the object reaches our eyes, which can’t give full vision. We don’t see objects in the dark because there is no visible range of radiation to interact with our eyes. Thus, what we see is not the object proper, but the radiation emitted by it, which comes from the area surrounding its confinement - the orbitals.

Since the brain acts like the CPU joining all data bases, the responses are felt in other related fields in the brain also. When we see an event without actually participating in it, our mental activity shows as if we are actually participating in it. Such behavior of the neurons is well established in medical science and psychology. The auditory mechanism functions in a broadly similar way, though the exact mechanism is slightly different.

But when we feel an object through touch, we ignore the radiation because neither our eyes can touch nor our hands can see. Here the mass of our hand comes in contact with the mass of the object, which is confined. The same principle applies for our taste and smell functions. Till the object and not the field set up by it touches our tongue or nose (through convection or diffusion), we cannot feel the taste or smell. Mass has the property of accumulation and spread. Thus, it joins with the mass of our skin, tongue or nose to give its perception. This way, what we see is different from what we touch. These two are described differently by the two perceptions. Thus we can’t get accurate inputs to model a digital computer.

There is a deep, foundational reason why reality, which is purely analog, behaves in a digital way. We will briefly discuss it. Questions regarding singularity are often by-passed. But unless space and mass existed, what exploded into what at the big bang? The history of scientific inventions shows that wherever infinity appears in an equation, it points to some novel phenomenon or some missing parameters. Now big bounce has replaced big bang. Some say it hints at colliding galaxies. But the clue is hidden in the nature of the universe.

Inside atoms, protons and electrons with the help of neutrinos combine to create neutrons in a continuously reversible process. Atoms and molecules mix in different proportions to create all objects. The period of creation through combination culminates in the opposite process of devolution through disintegration – first to atoms and then to elementary particles. At singularity, the particles lose confinement and dissolve to create a field of uniform density. Without density variation, there is no unit to measure it. Hence the singularity. The field has three properties – stress, impedance and inertia. While stress and impedance that generate opposite forces during creation tend towards equilibrium, inertia of motion slows down to zero at singularity with corresponding increase in inertia of restoration8 (elasticity). This creates an instability and the reverse process starts with a bang. At that time the primordial soup was having the same density – stress and impedance at equilibrium. Stress overcomes impedance and moves at great velocity. This creates a bow shock effect which hinders its velocity to bring it down to zero. Before it finally stops, it cuts off a big volume. This is the cosmos. Then impedance takes over and there is a negative flow, which also stops at certain levels (√10). Thereafter it expands again slowly not in linear motion, but spin, for reasons to be discussed later. These are the closed universes. The second motion is called inflation.

Different forces are generated due to the operation of stress, impedance and inertia. These are like lumps confined by opposing forces. Inertia of restoration brings in equilibrium and thereby creates points of stability (ground) around which stress and impedance interact with different proportions to generate 3 x 5 = 15 different forces from the same stuff. The continuous symmetry braking creates mass and energy and provides variety and the various constants of Nature that leads to a digital description of the universe. If impedance overcomes stress, it becomes the confined particle with mass and positive charge that creates the nucleus. Otherwise it becomes the field with negative charge that confines mass. Their combination in specific ways makes all bodies. The primordial field confines all particles like islands in an ocean – not the raisin in pie model. Only this way we can unite all forces of Nature. We have a complete model9 for this.

Discrete models like cellular automata can be effective approaches to physics. Rule 110, which requires an infinite number of localized patterns to be embedded within an infinitely repeating background pattern, can be the basis. But unless we know how the images are generated, we would end up disappointed. The background pattern is fourteen cells wide and repeats itself exactly every seven iterations. The images are alien to modern physics though not for us.

NOTES.

1. String theory, which was developed with a view to harmonize General Relativity with Quantum theory, is said to be a high order theory where other models, such as super-gravity and quantum gravity appear as approximations. String theory comes in five different formulations, each of which covers a restricted range of situations. A network of mathematical connections links the different string theories into one overarching system called M-theory. Unlike super-gravity, string theory is said to be a consistent and well-defined theory of quantum gravity, and therefore calculating the value of the cosmological constant from it should, at least in principle, be possible. On the other hand, the number of vacuum states associated with it seems to be quite large, and none of these features three large spatial dimensions, broken super-symmetry, and a small cosmological constant. The features of string theory which are at least potentially testable - such as the existence of super-symmetry and cosmic strings - are not specific to string theory. In addition, the features that are specific to string theory - the existence of strings - either do not lead to precise predictions or lead to predictions that are impossible to test with current levels of technology. With its talk of D-branes, 10 or 11 dimensional universes and a myriad of possible solutions: 10500 at the last count – string theory looks more like an arcane branch of mathematics than tangible physics. It has not told us anything new about the real world, despite almost 40 years of trying. There are many unexplained questions relating to the strings. For example, given the measurement problem of quantum mechanics, what happens when a string is measured? Does the uncertainty principle apply to the whole string? Or does it apply only to some section of the string being measured? Does string theory modify the uncertainty principle? If we measure its position, do we get only the average position of the string? If the position of a string is measured with arbitrarily high accuracy, what happens to the momentum of the string? Does the momentum become undefined as opposed to simply unknown? What about the location of an end-point? If the measurement returns an end-point, then which end-point? Does the measurement return the position of some point along the string? (The string is said to be a Two dimensional object extended in space. Hence its position cannot be described by a finite set of numbers and thus, cannot be described by a finite set of measurements.) How do the Bell’s inequalities apply to string theory?

2. Particle-particle, Particle-field total interaction, particle-field partial interaction, field-field interaction.

3. Un-mathematical physics: Most of what is called as “mathematics” in modern science fails the test of logical consistency that is a corner stone for judging the truth content of a mathematical statement. For example, the Schrödinger equation was devised to find the probability of finding the particle in the narrow region between x and x+dx, which is denoted by P(x) dx. The function P(x) is the probability distribution function or probability density, which is found from the wave function ψ(x) in the equation P(x) = [ψ(x)]2. The wave function is determined by solving the Schrödinger’s differential equation: d2ψ/dx2 + 8π2m/h2 [E-V(x)]ψ = 0, where E is the total energy of the system and V(x) is the potential energy of the system. By using a suitable energy operator term, the equation is written as Hψ = Eψ. The equation is also written as iħ ∂/∂t

ψ› = H

ψ›, where the left hand side represents iħ times the rate of change with time of a state vector. The right hand side equates this with the effect of an operator, the Hamiltonian, which is the observable corresponding to the energy of the system under consideration. The symbol ψ indicates that it is a generalization of Schrödinger’s wave-function. The way the equation has been written, it appears to be an equation in one dimension, but in reality it is a second order equation signifying a two dimensional field, as the original equation and the energy operator contain a term x2. The method of the generalization of the said Schrödinger equation to the three spatial dimensions does not stand mathematical scrutiny. A third order equation implies volume. Addition of three areas does not generate volume and neither x+y+z ≠ (x.y.z) nor x2+y2+z2 ≠ (x.y.z). Thus, there is no wonder that it has failed to explain spectra other than hydrogen. The so-called success in the case of helium and lithium spectra gives results widely divergent from observation.

The probability calculations needed to work out the chance of finding an electron (say) in a particular place at a particular time actually depend on calculating the square of the complex number corresponding to that particular state of the electron. But calculating the square of a complex variable does not simply mean multiplying it by itself since it is not the same as a real number. Instead, another variable, a mirror image version called the complex conjugate is considered, by changing the sign in front of the imaginary part (if it was + it becomes - and vice versa). The two complex numbers are then multiplied together to give the probability. This shows that, truly it is not squaring, but a mathematical manipulation as the negative sign implies physical non-existence of the second term like the physical non-existence of a mirror image. If A has 5 apples and he gives it to B, then only B has those five apples and A is said to have -5 apples to signify his ownership of the five apples physically with B. Similarly, the mirror image does not make two objects, but only one real object and the other physically non-existent image. This is not mathematics, as mathematics deals with numbers, which is a characteristic of physical objects. Similarly, mathematically all operations involving infinity are void. Hence renormalization is not mathematical. The brute force approach where several parameters are arbitrarily reduced to zero or unity is again not mathematical, as the special conditions that govern the equality sign for balancing cause and effect are ignored. The arbitrary changes change the characteristic of the system. If we treat the length of all fingers as unity, then we cannot hold an object properly. There are innumerable instances of un-mathematical manipulation in the name of mathematics.

The requirement that all fundamental theories be presented within a concise mathematical framework virtually prevented serious theoretician from ever considering a non-field theory because of its mathematical complexities. The “mathematics” involved in field theories to describe events are simple and concise when compared with the “mathematics” of the same event in non-field terminology. Non-field theories are denied serious consideration because they cannot be given a precise mathematical description. Even if someone was able to develop a precise set of non-field equations, they would likely be so complex, mystifying and un-mathematical that only few mathematicians would be able to understand them.

4. Forces are not linearly additive: Suppose we are crossing a river 60 meters wide by a motor boat from West to East with a velocity of 4 m/s directly across the river. Suppose that the river was moving with a velocity of 3 m/s due North. How much time it would take to cross the river? The river current influences the motion of the boat and carries it downstream. The motor boat may be moving with a velocity of 4 m/s directly across the river, yet the resultant velocity of the boat will be greater than 4 m/s and at an angle in the downstream direction. While the speedometer of the boat may read 4 m/s, its speed with respect to an observer on the shore will be greater than 4 m/s. The resultant velocity of the boat is the vector sum of the boat velocity and the river velocity. Since the boat heads straight across the river and since the current is always directed straight downstream, the two vectors are at right angles to each other. Thus, the magnitude of the resultant will be: (4.0 m/s)2 + (3.0 m/s)2 = R2 or 16 m2/s2 + 9 m2/s2 = R2 Or 25 m2/s2 = R2 or R = 5m/s.

The direction of the resultant is the counterclockwise angle of rotation which the resultant vector makes with due East. This angle can be determined using a trigonometric function: tan (θ) = (3/4).

Hence θ = 36.9 degrees.

With the above data, let us calculate how much time does it take the boat to travel shore to shore and what distance downstream does the boat reach the opposite shore? The river is 60-meters wide. That is, the distance from shore to shore as measured straight across the river is 60 meters. The time to cross this 60-meter wide river can be determined by rearranging and substituting into the average speed equation:

Time taken = distance / (average speed)

The distance of 60 m can be substituted into the numerator. But what about the denominator? What value should be used for average speed? Should 3 m/s (the current velocity), 4 m/s (the boat velocity) or 5 m/s (the resultant velocity) be used as the average speed value for covering the 60 meters? With what average speed is the boat traversing the 60 meter wide river? The value of 5 m/s is the speed at which the boat covers the diagonal dimension of the river, but the diagonal distance across the river is not known in this case. Similarly, if one knew the distance from the position diagonally across from the initial position to where the boat reach the opposite shore downstream, then the river speed of 3m/s could be used to calculate the time to reach the opposite shore. And finally, if we consider the river width of 60m, then the boat speed of 4m/s could be used to calculate the time to reach the opposite shore.

In the above problem, the river width is 60 m. Hence the average speed of 4 m/s (average speed in the direction straight across the river) should be substituted into the equation to determine the time:

Time taken = 60m/ (4m/s) = 15 seconds.

It requires 15 seconds for the boat to travel across the river. During these 15 seconds of crossing the river, the boat also drifts downstream.

Distance = Time taken x (average speed) = 15 seconds x (3m/s) = 45 m. or

Time taken = 45m/ (3m/s) = 15 seconds, which is correct.

The boat is carried 45 meters downstream from the point opposite to the initial point during the 15 seconds it takes to cross the river. Now to calculate what distance downstream does the boat actually traveled to reach the opposite shore, we have to apply the formula:

(60 m)2 + (45 m2) = (75m)2. Hence the answer is 75 m.

The time taken is: Time taken = 75m / (5m/s) = 15 seconds, which is correct.

Thus, whichever way we calculate, we come to the same conclusion. If we change the speed of the river current to 5m/s so that the river current is faster than the boat speed, we come to the same conclusion about time taken. In this case only the distance downstream from the point opposite to the initial point changes to 75 m and the total distance actually traveled changes to about 96 m. If we use other speeds, the result remains similar. This would mean that an across-the-river variable would be independent of (i.e., not be affected by) a downstream variable. The time to cross the river is dependent upon the velocity at which the boat crosses the river. It is the component of motion directed across the river (i.e., the boat velocity) which affects the time to travel the distance directly across the river. The component of motion perpendicular to this direction - the current velocity - only affects the distance which the boat travels down the river. Since the across-the-river motion and the down stream motion are different induced by different forces, it proves that different forces coexist, but unlike mass, do not linearly couple with each other. They had to be squared for calculating non-linear motion provided they belong to the same category and act on the same body. Forces of different categories like gravitational forces and electromagnetic forces are never coupled.

5. SPACETIME: Newton thought that the Earth and the tree with the apple are stationary in space. The Earth pulls the apple through gravity. Einstein proposed that the mass of bodies caused the space and time around them to move as a curvature. According to him, the four dimensional grid of space-time occupied by the apple curved towards the Earth so that while the apple’s spatial and temporal coordinates moved, it remained inertially stationary like the Earth. In other words the space in-between curved so that interval between the apple and the Earth reduced with corresponding increase with the gap between the apple and the stem. His idea of space-time was space with motion through it, which implies time. This can be visualized by the example of a leaf floating on a river stream. The water flows and the leaf is stationary with reference to the water table. But to an observer from the shore, the leaf appears to move which is not correct. Similarly, this view of gravity is not correct. The leaf is physically moving away or moving towards the observer. There is no such repulsive force for gravity even though anti-gravity has been postulated by some. Secondly, the leaf is not dragged by the curvature of the river water, but it flows due to the flow of the river current which is independent of the masses of the tree or the leaf. Moreover, the leaf flows with it only after it falls on water due to a different force. This implies that the spacetime curvature is independent of the mass of the tree and the apple and the fall of the apple is not due to spacetime curvature, but due to the existence of a different force. Thus spacetime curvature is not an accurate description of the phenomenon. This problem can only be explained if we treat gravity as a force by which all particles interact with its analog “field” - which has a different dynamics. Thus, gravity calculation is done by treating the bodies as point particles, because the body with its internal dynamics acts as a whole. There is no need for the non-existent graviton or Higg’s particle to explain it. All problems relating to gravity can be solved if we take into account the stress, impedance and inertia of restoration and calculate gravity. This leads to seven types of gravitational interaction.

6. Superposition: When two waves of different heights move through each other, the amplitudes of the waves add up to give the total amplitude of the resulting wave. If one wave is at a crest at one point and another similar wave is at a trough at the same point, the amplitude of the two waves add up to zero. We see no wave but a plane surface. This principle of adding individual wave amplitudes to get the total amplitude is called the superposition principle. In such a case, we look at a state, whose perception is different from the causal state underlying it. What is seen as a plane surface really contained a crest and a trough of equal or comparable magnitude before the moment of their interaction. But at that “here-now” of their interaction, neither is visible. The plane surface might have arisen due to the interaction of waves of any magnitude, frequency and wave-length. We can’t predict with certainty about their frequency and wave-length unless we actually “observe” and “measure” it immediately before their interaction. But because of their dynamical nature, we can’t measure both their momentum and position (frequency and wave-length) simultaneously. They will not be visible as a similar crest and a trough after that moment. Thus, the plane surface that came out of a crest and a trough and then gets converted to something else – may be another crest and a trough - remains in a state of superposition of all probabilities for us except for the instant when we are actually observing it. This refers to the dynamical attributes of the wave. But its static attributes, like volume or mass or chemical composition, remain unchanged and thus, is not in a super-position of states. We must distinguish between these two aspects.

7. Please refer to our book: Vaidic Theory of Numbers (2005). For copy write to: mbasudeba@gmail.com.

8. Inertia of restoration. Please refer to our book: Vaidic Theory of Numbers. Inertia shows that application of force is momentary. The body moves and loses contact with the force, but moves due to inertia. If the inertia is retarded due to friction and the force is moving in the same direction, then the application of force may appear to be continuous. But actually, it catches up with the retarded body and pushes it again. Once a force is applied, the body as a whole responds to the field. If there is no variation in the field density, it moves unhindered. This is inertia of motion. The mental faculties of thought also function this way. However, the mechanisms for its retardation are different. We have proved mathematically that there is nothing called inertia of rest. It is the equilibrium state only. When the body is not rigid and when the applied force is not enough to completely displace the body, the partial displacement generates inertia in the opposite direction. This is elasticity.

9. The following are a few salient testable predictions contained in our forthcoming book:

“DEMYSTIFYING QUANTUM MECHANICS, QUANTUM FIELD THEORY & LOOP QUANTUM COSMOLOGY”.

1. The accepted value of the electric charge of quarks contains an error element of 3%. In stead of +⅔ and -⅓, it should be +7/11 and -4/11. Thus, taking the measured charge of electrons as the unit, the value of the electric charge of protons is +10/11 and that of neutrons -1/11. The residual negative charge is not apparent as negative charge always confines positive charge and flows towards the concentration of positive charge - nucleus. Hence it is not felt outside. It is not revealed in measurement due to the nature of calibration of the measuring instruments. This excess negative charge confines the positive charge (nearly 2000 times in magnitude) which is revealed in atomic explosions. Charge neutral only means the number of protons and electrons are equal.

2. The value of the gravitational constant G is not the same for all systems. Just like the value for acceleration due to gravity g varies from position to position, the value of G also varies between systems.

3. The value of the fine-structure constant α that determines the electromagnetic field strength as calculated by us theoretically from our atomic orbital theory is 7/960 (1/137) when correlated to the strong interaction (so-called zero energy level) and 7/900 (1/128) when correlated to the weak interaction (80 GeV level). There are 5 more values that determine the structure of the orbitals in the atomic spectra. Hence the physically available values of the s orbitals (principal quantum number) are restricted to n = 7, though theoretically, it can have any positive integer value.

4. There is nothing like Lorentz variant inertial mass. It has never been proved.

## Sunday, December 05, 2010

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