The Imagineer's Chronicles

Heisenberg uncertainty principal: A Classical interpretation

theimagi — Wed, 01 Sep 2010 09:48:04 +0000

We have shown in "The Imagineer’s Chronicles" one can define a universe in terms of the existence of four *spatial* dimensions in a manner that makes predictions identical to those of both the General and Special Theories of Relativity while at the same time describing the theoretical advantages to doing so.

One of these is that it would allow for the development of a theoretical interpretation of the Heisenberg’s Uncertainty Principal in terms of the laws Classical of Physics.

The Heisenberg Uncertainty Principle states that certain pairs of physical properties, like position and momentum, cannot both be known to arbitrary precision. That is, the more precisely one property is known, the less precisely the other can be known. This is not a statement about the limitations of a researcher’s ability to measure particular quantities of a system; it is a statement about the nature of the system itself as described by the equations of quantum mechanics. According to the uncertainty principle, it is, for instance, impossible to measure simultaneously both position and velocity of a microscopic particle with any degree of accuracy or certainty.

The Uncertainty
Principal

In the article "Why is mass and energy quantized?" Oct 4, 2007 it was shown one can theoretically derive the properties of a particle in terms of a classically resonating system if one assumes it is a result of matter wave moving on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Additionally, it was showed why all energy exists in these resonant systems and therefore is quantized.

There are four conditions required for resonance to occur in a classical Newtonian environment, an object, or substance with a natural frequency, a forcing function at the same frequency as its natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial.

(In a latter article "The geometry of quarks" it will be shown how and why quarks join together to form these resonant systems in terms of the geometry of four *spatial* dimensions.)

The existence of four *spatial* dimensions would give three-dimensional space the ability to oscillate spatially on a "surface" between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

However, these oscillations in a "surface" of a three-dimensional space manifold, according to classical mechanics would generate a resonant system or "structure" in space. These resonant systems are known as particles.

The only way to dampen the frequency of a classically resonating system is to add or remove energy from it, which results in changing the characteristics of that system.

Additionally the energy in a classically resonating system is discontinuous and can only take on the discrete values associated with its fundamental or harmonic of its fundamental frequency.

However, these properties of a classically resonating system are the same as those found in a particle in that they are made up of discreet or discontinuous packets of mass/energy and when energy is either added or removed from it, its characteristics change.

The reason why we do not observe energy in its continuous wave form is that, as mentioned earlier all energy is propagated through space in the discrete components associated with its resonant structure. Therefore, when observing the energy of a wave function it would appear as though its energy was concentrated in a single point in space associated with the center of its resonant structure.

This is analogous to how the potential energy of water in a sink is release by allowing it to go down the drain. If all we could observe is the water coming out of the drain we would have to assume that it was concentrated in the region of space defined by the diameter of the drain. However, in reality the water occupies a much larger region.

However, this also defines a Classical reason for the validity of Heisenberg’s Uncertainty Principle, which states that certain pairs of physical properties, like position and momentum, cannot both be known to arbitrary precision.

Classical wave mechanics tells us a wave’s energy is instantaneously constant at its peaks and valleys or the 90 and 270-degree points as its slope changes from positive to negative while it changes most rapidly at the 180 and 360-degree points.

Therefore, the precise position of a particle could be only be defined at the peaks and valleys of the matter wave responsible for its resonant structure because those points are the only place where its energy or "position" is stationary with respect to a fourth *spatial* dimension. Whereas its precise momentum would only be definable with respect to where the energy change or velocity is maximum at the 180 and 360-degree points of that wave. All points in between would only be definable in terms of a combination of its momentum and position.

However, to measure the exact position of a particle one would have to divert or "drain" all of the energy at the 90 or 270-degree points to the observing instrument leaving no energy associated with its momentum left to be observed by another instrument. Therefore, if one was able to determine precise position of a particle he could not determine anything about its momentum. Similarly, to measure its precise momentum one would have to divert all of the energy at the 180 or 360 point of the wave to the observing instrument leaving none of its position energy left to for an instrument trying to measure it position. Therefore, if one was able to determine a panicles exact momentum one could not say anything about its position.

The reason we observe a particle as a point mass instead of an extended object is because, as mentioned earlier the article "Why is mass and energy quantized?" showed its energy must be packaged in terms of its resonant frequency. Therefore, when we observe or "drain" the potential energy continued in its wave function it will appear to come form a specific point in space similar how the potential energy of water flowing down a sink drain appears to be coming from a "point" source with respect the extended volume of water in the sink.

As mentioned earlier, all points in-between are a dynamic combination of both position and momentum. Therefore, the degree of accuracy one chooses to measure one will affect the other. For example, if one wants to measure the position of a particle to within a certain predefined distance "m" its wave energy or momentum within that distance will "move" or change by an amount defined by its wave function or the energy change within that distance or ("m"kg / s). Summarily if one wants to measure the momentum ("m"kg / s) of a particle in a predefined volume or distance ”m" its position will change within that distance.

However, because of the dynamic interaction between the position and moment component of the matter wave responsible for generating the resonant system associated with a particle defined in the article "Why is mass and energy quantized?" the change or uncertainty of one with respect would be defined by the product of those factors or m^2 kg / s

This defines the reason in terms of Classical Wave Mechanics for Heisenberg uncertainty principal and why it has the units of m^2 kg / s

Later Jeff

The "Shadows" of four spatial dimensions

(In a PDF format)

The geometry of the fundamental particles

theimagi — Sun, 15 Aug 2010 06:00:12 +0000

As Brian Greene pointed out in his book "The Elegant Universe", one of the unsolved mysteries of modern particle physics is why every fundamental particle encountered to date can be group into three families.

"Physicists have recognized a pattern among these particles displayed in the following table. The matter particles neatly fall into three groups, which are often called families. Each family contains two of the quarks an electron or one of its cousins and one of their neutrino species. The corresponding particle types across the three families have identical properties except for their mass, which grows larger in each successive family."

Family 1		Family 2		Family 3
Particle	Mass	Particle	Mass	Particle	Mass
Electron	.00054	Muon	.11	Tau	1.9
Electron Neutrino	< 10^-8	Muon Neutrino	< .0003	Tau Neutrino	< .033
Up Quark	.0047	Charm Quark	1.6	Top Quark	189
Down Quark	.0074	Strange Quark	.16	Bottom Quark	5.2

The answer to Brian Greene’s question regarding why the particles in the above table can be group into three families is related to the resonant "structures" that defined their properties in the article “Why is mass and energy quantized?” Oct. 4, 2007

Quarks | Standard Model Of Particle Physics

That article showed one can derive a particle’s properties in terms of a classically resonating system formed on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Additionally it was shown mass can only take on the energy values associated with its resonant or a harmonic of its resonant frequency.

If true, one should be able to derive the relative masses of each family member by extrapolating laws governing classical resonance in three-dimensional space to a fourth *spatial* dimension.

The article "Defining gravity" Dec. 15, 2007 showed one can derive the mass of objects and particles in terms of a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Additionally, it was shown the magnitude of their mass is directly related to a *separation* in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by that curvature.

(This curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is analogous to the space-time curvature the Einstein postulated is responsible for an objects mass.)

Finally the article "Defining potential and kinetic energy?" Nov. 26, 2007 showed one can derived all forms of energy, including gravitational, electrical and thermal, in terms of a spatial "separation" between different "surfaces" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

As mentioned earlier the article "Defining gravity" showed the mass of all objects including particles are a result of a separation in a "surface" of three-dimensional space manifold with respect to a fourth "spatial" dimension. However, as was shown in article "Defining potential and kinetic energy?" the separation between "surfaces" of a three-dimensional space manifold is dependent on the temperature or energy content of the environment associated with them. Therefore, the masses of all objects including particles would also be dependent on the energy content or temperature of the environment they are occupying.

Therefore, as was shown in the articles "Why is mass and energy quantized?" and "Defining gravity" the individual masses of each family member would be dependent on the energy of their associated resonant systems and energy of the environment they are occupying.

However, because there are only specific points in space where environments can resonant, each of the corresponding particle types across the three families would have a specific mass related to the energy of the environment in which they were created

The particles in the first family are found in relativity low energy environments, are relatively stable, and for the most part can be observed in nature. However, the particles in the second and third families are for the most part unstable and can be observed only in high-energy environments of particle accelerators. The exception is the Muon in the second family, which is only observed in the high-energy environment of cosmic radiation.

The relative masses of the fundamental particles increases in each successive family because as shown in the article "Defining potential and kinetic energy?" the higher-energy environments where they are generated in result in the corresponding particles in each successive family to be formed with a greater relative "separation" in the “surfaces” of a three-dimensional space manifold with respect to a fourth *spatial* dimension..

Therefore, the corresponding particles in the second family will have a greater mass than the particles in the first family because the "separation", with respect to a fourth *spatial* dimension of the three-dimensional space manifold associated with them is greater than the "separation", associated with the first family.

Similarly, the corresponding particles in the third family will have a greater mass than those in the second family because the "separation", with respect to a fourth *spatial* dimension, of the three-dimensional space manifold associated with them is greater than the spatial "separation", associated with the second family.

Additionally the corresponding particle types across the three families have "identical properties" because as shown in the article "The geometry of quarks" Mar. 15 , 2009 they are related to the orientation of the "W" axis of the fourth *spatial* dimension with the axis of three-dimensional space. Therefore, each corresponding particle across the three families will have similar properties because the orientation of the "W" axis of the fourth *spatial* dimension with respect to the axis of three-dimensional space is the same for the corresponding particles in all of the families.

This explains why "The corresponding particle types across the three families having identical properties except for their mass, which grows larger in each successive family” in terms of the properties of classical resonance and the existence of four *spatial* dimensions.

Later Jeff

The "Shadows" of four spatial dimensions

(In a PDF format)

The inertia of dimensional interactions

theimagi — Sun, 01 Aug 2010 10:15:31 +0000

We have shown throughout “The Imagineer’s Chronicles” it is possible to define a universe in terms of four *spatial* dimensions in a manner that makes predictions identical with those of Einstein’s General and Special Theories of Relativity. Additionally it has been shown there would be several theoretical advantages to adopting this perspective over that of his theories.

One is that it could allow for the development of a theoretical link between gravity, mass and inertia in terms of interactions between a third and fourth *spatial* dimensions.

3rd And 4th Dimensions

Newton, in his laws of motion defined how the inertia of an object interacts with its environment and the effects gravity has on them. However, he was unable to define the causality of gravity or inertia.

Einstein was able to define the causality of gravity and the relativistic properties of motion in terms of a four-dimensional space-time manifold but he was unable to define the causality of inertia.

However, one can define a casual or theoretical link between inertia, mass and gravity if one defines the universe in terms four *spatial* dimensions.

In the article "Defining energy" Nov. 26, 2007 it was shown all forms of energy including inertia or momentum can be derived in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

While the article "Why Space-time?" showed that one can derive the energy associated with the rest mass of an object or particle in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension. Additionally it was shown one can derive the causality of all accelerations including gravitational in terms of an interaction of that mass with the slope of a curvature in a "surface" of a three-dimensional space caused by that displacement.

(This curvature is analogous to a curvature in a four-dimensional space-time manifold Einstein theorized was the causality of gravitational accelerations.)

Therefore, according to the theoretical concepts presented in those articles the magnitude of inertia or momentum would be defined by the sum of two components. The first would be magnitude of a displacement in a "surface" of a three-dimensional space associated with the rest mass of an object, which as the article "Defining energy" showed is defined by its gravitational potential. The second would be the momentum or the magnitude of a displacement of the "surface" of the three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the energy of its relative motion. (The momentum of an object at rest with respect to other objects is zero so the displacement of three-dimensional space with respect to those objects would also be zero.)

To define the total momentum of an object or particle one would have to add the displacements in a "surface" of a three-dimensional space manifold associated with the energy of its rest mass to that associated with its relative motion.

However, the article Defining energy also showed that accelerations are caused by an object or particle interacting with a curved "surface" of a three-dimensional space manifold.

Therefore, as mentioned earlier if the momentum of an object is caused by a constant displacement of a "surface" of a three-dimension space manifold it would tent to stay rest or ones in motion would tend to stay in motion unless it interacted with a "surface" that was curved with respect to a fourth *spatial* dimension.

However, the inertia of an object would be defined in terms of the energy required to change a unit magnitude of its *spatial* displacement with respect to a forth *spatial* dimension. But as mentioned earlier, its rest mass is directly proportional to its gravitational potential. Therefore, because there is a 1 to 1 correspondence between it and the curvature in space associated with its gravitational potential, the energy required to make a unit change in its velocity will be directly proportional to its rest mass.

This defines a causal link between the inertia, mass and gravity in terms of a spatial interaction or displacement between a "surfaces" of a three-dimensional space manifold and a fourth *spatial* dimension.

Additionally it means the validity of Newton’s first law motion or inertia that "An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force" can be theoretically understood in terms of displacement of a "surface" of a three-dimensional space manifold with respect to fourth *spatial* dimension

Einstein could define the casualty of gravity but not inertia in terms of a four-dimensional space-time manifold because the "surface" of three-dimensional space cannot be spatially displaced with respect to time or a time dimension.

Later,

The "Shadows" of four spatial dimensions

(In a PDF format)

Why is the universe is flat?

theimagi — Thu, 15 Jul 2010 08:44:32 +0000

We have shown throughout “The Imagineer’s Chronicles” it is possible to define a universe in terms of four *spatial* dimensions in a manner that makes predictions identical with those of Einstein’s General and Special Theories of Relativity. Additionally we have shown there would be several theoretical advantages to adopting this perspective over that of his theories.

One it that it allow one to understand why the universe must be flat

A four dimensional universe can be geometrically open, closed, or "flat" and its shape is dependent on the mass and energy within it.

Carl Sagan
on the shape of the cosmos
(curved/saddle/flat)

In an opened universe, there is insufficient matter to halt the expansion initiated by the big bang. This will result in a saddle shape or open universe, which will continue to expand forever.

In a closed universe, the gravitational potential of its mass is large enough to overcome the expansive forces of the big bang. This will result in the universe having a spherical shape, which would be destined to collapse.

A universe will be flat if the attractive gravitational potential of matter just equals the expansive energy of the big bang. This will result in the expansion slowing and only stop after an infinite amount of time has passed.

However, recent observations by NASA’s WMAP satellite has shown the universe is flat to within a 2% margin of error.

But why the universe appears to be flat even after 14 billion years of expansion is still a mystery because a flat universe is like the top of a hill. If you are a little away from it – a bit open or a bit closed – the expansion of the universe soon drives you far away from this value, just as a ball that is a short distance from a hilltop will roll down to the bottom. Therefore, when the Universe was one second old, it must have deviated from flatness by less than one part in ten-thousand-trillion (10¹⁶). This is a problem because it is hard to understand how the amount of mass and the energy associated with the expansion could have been adjusted to such precision.

To resolve this issue physicist Alan Guth proposed the universe underwent a very rapid period of expansion increasing it size by more than a trillion in the first few nano-seconds after its birth. This resolves the flatness problem because its size is magnified by the inflation factor so much that locally it appears flat.

The reason for this can be understood by imagining what a two-dimensional creature who was living on a surface of a balloon would observe regarding the curvature of its surface. If the size of the balloon were small compared to his field of vision he would notice that it surface was curved. However, if its size was very large compared to his field of vision it would appear to him to be flat.

Inflation solves the flatness problem because it predicts the size of the universe increased so much in the initial expansion that portion we can observe appears to flat.

However, another reason why the universe appears to be flat is that all of its expansive energy must originate with its mass/energy. This is because if the universe is a closed system, the first law of thermodynamics tells us the sum of the gravitational potential of its mass/energy and its kinetic or thermal energy is constant.

As mentioned earlier, the curvature of our expanding universe is related to the ratio of total gravitational potential of its mass/energy to the total kinetic energy of its expansion.

However, as was shown in the article "Defining potential and kinetic energy?" Nov 26, 2007 the equivalence between kinetic energy and the gravitational potential of mass/energy can be defined in terms of equation E=mc^2 because it showed that, similar to Relativity mass is equivalent to energy. Therefore, energy in all its forms must also posses the gravitational potential energy associated with mass. Additionally the asymmetry of the equation E=mc^2 tells us kinetic energy is oppositely directed from the gravitational potential of mass/energy.

This means a balance must exist between the gravitational potential of the universe’s mass/energy and the oppositely directed kinetic energy associated with its expansion because, as mentioned earlier all of its expansive energy must come from its mass/energy. However, if one defines "m" as the total gravitational potential of the mass/energy of the universe, the equation E=mc^2 also defines the total energy available for its expansion. If one then substitutes "c" for "v" in the equation for kinetic energy (KE=1/2mv^2) one arrives at the equation 1/2mc^2. This equation defines the ratio of the total kinetic energy available to power the universe’s to its mass/energy This indicates there is a 1 to 1 ratio between the potential energy of the universe’s mass/energy and the total quantity of oppositely directed energy associated with its expansion.

Additionally because the kinetic energy of the universe’s expansion is defined by the non-linear equation m₀ = sqrt(E²/c⁴ – p²/c²) the ratio of the gravitational potential of its mass/energy will always maintain a 1 to 1 ratio to the its expansive energy if one assumes that its expansion has been as rapid as possible.

This means the universe will be flat now and throughout its history because as mentioned earlier there is a 1 to 1 ratio between the curvature associated with the gravitational potential of its mass/energy and oppositely directed curvature associated with the kinetic energy of its expansion, which means they will cancel each other.

Therefore, one does not have to assume the universe underwent an inflationary period to explain why it is flat now and has remained that way if one assumes the existence of four *spatial* dimensions, and that it has been expanding as rapidly as possible since the big bang.

This cannot be done in terms of four-dimensional space-time because time or a space-time dimension is observed to move only in one direction forward and therefore could not support the bidirectional movement required to define the symmetry between the potential energy of mass/energy and its kinetic energy.

However, for many this concept of a zero energy universe may sound strange, but it is rather simple to understand. A ball thrown up in the air has two forms of energy: kinetic and gravitational potential. If kinetic energy were considered as positive, the potential energy, due to the gravitational pull of the Earth, would be negative. If the positive portion of the energy beats the negative portion, the ball will escape from Earth. If the negative energy is greater, it will return. If the total energy is precisely zero the ball will barely escape – slowing to a stop when it is infinitely far away.

Many would disagree with this concept and point to the observations of Type Ia supernovae (SNe-Ia) which verified the existence of an expansive force or "Dark Energy" that opposes the contractive gravitational energy and is causing the universe to accelerating. However, physicists have been unable to define a source or mechanism responsible for this energy.

However, as mentioned earlier the equation E=mc^2 defines a dynamic oppositely directed relationship between the gravitational potential of mass/energy and its kinetic energy. In other words, in a closed system if the mass in a volume decreases the kinetic or thermal energy associated with that volume increase.

Therefore, due to the asymmetry between the quantity of mass and thermal kinetic energy in a closed system we should expect asymmetry between the quantity of forces those systems contain. In other words, we would expect a force to be generated that is oppositely directed with respect to the gravitational forces associated with mass when we convert mass to energy. This force would have to added to the linear expansion associated with the force of the big bang therefore, it would be viewed as acceleration. This force has been give the name Dark Energy and is responsible for the accelerated expansion of the universe.

Therefore, the mechanism responsible for generating the force called Dark Energy would be analogous to one that earlier defined the kinetic energy generated from a mass/energy. If the universe is a closed system then one must assume the sum of the potential energy of its mass and kinetic or thermal energy must is constant. This also means that when stars convert mass to energy in nuclear reactions a force must be generated that is oppositely directed with respect to the gravitational forces associated with mass.

However, the "concentration" of this Dark Energy relative to gravitational energy is also defined by the equation E=mc^2c were "c" equals the speed of light. This means its "concentration" and therefore its strength is 1/c^2 weaker than gravitational forces.

The reason why dark energy is so hard to detect is that, as show above its field strength is so small relative to gravitational.

Later Jeff

The "Shadow’s" of four spatial dimensions

(In a PDF format)

Dark matter: an alternative

theimagi — Thu, 01 Jul 2010 09:07:02 +0000

We have shown throughout “The Imagineer’s Chronicles” there are many theoretical advantages to assuming the existence of four *spatial* dimensions a continuous non-quantized form of mass.

One of them is that it would provide a more logical explanation of the observed properties of Dark Matter than can be found based solely on the quantum mechanical assumption that mass exists only in particle form.

Wikipedia tells us "The first person to provide evidence and infer the presence of dark matter was Swiss astrophysicist Fritz Zwicky, of the California Institute of Technology in 1933. He applied Newton’s law of gravity to the Coma cluster of galaxies and obtained evidence of unseen mass. Zwicky estimated the cluster’s total mass based on the motions of galaxies near its edge and compared that estimate to one based on the number of galaxies and total brightness of the cluster. He found that there was about 400 times more estimated mass than was visually observable. The gravity of the visible galaxies in the cluster would be far too small for such fast orbits, so something extra was required. This is known as the "missing mass problem". Based on these conclusions, Zwicky inferred that there must be some non-visible form of matter which would provide enough of the mass and gravity to hold the cluster together."

Many physicists believe the vast majority of the dark matter is in a non-baryonic form such as neutrinos, and entities such as axions, supersymmetric particles, or WIMPs.

However, none of these scenarios is supported by observations.

Neutrinos because of their mass would be characterized by high random speeds in the early universe. However, observations of the early universe indicate the matter that condensed to form galaxies was not hot enough to support the energy that would be associated with those high speeds.

The other particles, which could provide the missing mass fall into two classes: those which have been proposed for other reasons but happen to solve the dark matter problem, and those which have been proposed specifically to provide the missing dark matter.

Examples of objects in the first class are axions and the supersymmetric particles. Their properties are defined by the theory, which predicts them, by virtue of their mass, they can solve the dark matter problem only if they exist in the correct abundance.

The second class of particles contain entities such as the WIMP or "Weakly Interacting Mass Particle" whose properties are not specified. However, they are assumed to have properties that would allow them to explain the missing mass associated with dark matter along with other "ad hoc" ones that would explain why they have not yet been observed experimentally.

However, the existence of them along with axions and the supersymmetric particles is not based on observations so therefore there is no way to either confirm their existence or that they are responsible for the gravitational force associated with dark matter.

However, there is another theoretical possibility that is based on observations that has been overlooked by the scientific community.

In the article “What is Dark Matter?” Sept 10, 2007 it was shown that one could theoretically explain and predict the gravitational forces associated with Dark Matter in terms of a continuous non-quantized form of mass. This non-baryonic and non-particle form of mass would have all the observed properties dark matter in that it would not interact with ordinary matter via electromagnetic forces and since it is made up of mass it would add to the gravitational force of the particle matter in the universe.

However, unlike WIMPS its existence is supported by observations.

For example, the observation that energy in itself is not quantized because a photon can have any frequency greater than zero or less than infinity and the equation defining the relationship between mass and energy, E=m*c^2 indicates that mass is completely convertible to one or more photons with energies greater than zero or less than infinity.

This means a continuous non-quantized medium must be available to support the continuous properties associated with mass energy and the electromagnetic spectrum.

Additionally the existence of a continuous non-quantized form of mass is supported by the observation of Davisson and Germer, when, in 1927 they observed that electrons along with other particles are diffracted by crystals. This is because the only way to explain the observed wave properties of individual particles is to assume they must have the continuous non-quantized geometric substructure associated with a wave.

However, the most significant theoretical advantage to assuming its existence is that it would allow one understand, in terms laws of classical wave mechanics the quantum mechanical aspects of mass and energy.

In the article "Why is mass and energy quantized?" Oct. 4, 2007 it was shown that one could explain and predict the quantum properties of mass and energy in terms of a classically resonating system or "structure" form by a matter wave moving through a continuous non-quantized form of mass.

Classical wave mechanics tells us a resonant phenomenon will occur with all types of vibrations or waves: there is mechanical resonance, acoustic resonance, electromagnetic resonance, nuclear magnetic resonance (NMR), electron spin resonance (ESR), and resonance of quantum wave functions. Resonant systems can be used to generate vibrations of a specific frequency (e.g. musical instruments), or pick out specific frequencies from a complex vibration containing many frequencies.

However, as mentioned earlier the observation that particles mass has the continuous non-quantized geometric substructure associated of a wave means that according to classical wave mechanics a resonant system will be established is space. This provides observational evidence supporting the derivation of the quantum mechanical or particle aspects of mass and energy, as was done in the article "Why is mass and energy quantized?" in terms of discrete resonant systems formed by vibrations in a continuous non-quantized form of mass.

The are some who feel that the existence of substance like a continuous non-quantized form of mass permeating space validates the Newtonian concept of absolute space. However, as was shown in the article “Reference frames” July 1, 2008 this is not true.

Briefly, in the article "Defining energy" Nov. 26, 2007 it was shown the momentum or energy of an inertial reference frame can be derived in terms the displacement of its three dimensional volume with respect to a fourth *spatial* dimension.

Isaac Newton defined an inertial reference frame as one in which an object at rest will remain at rest, and an object in motion will remain in motion in a straight line at a constant speed.

However, as was shown in the article "Defining energy" the momentum or velocity of an inertial reference frame is defined by a constant displacement with respect to a fourth *spatial* dimension of the continuous non-quantized form of mass defining its volume.

Therefore, the existence of a continuous non-quantized form of mass does not validate the existence of absolute space because its motion can only be measured relative to other reference frames.

This shows there is viable alternative based solely on experimentally verifiable observations to the assumption that dark matter is made up of exclusively of matter in a particular form.

Later Jeff

The "Shadows" of four spatial dimensions

(In a PDF format)

Lorentz transformations contradict an objective methodological interdiction

Ravil — Sun, 20 Jun 2010 09:16:02 +0000

By Ravil Kalmykov

Ravil8@yandex.ru

Abstract
A fact of principled compatibility of a measured rod in one inertial system of coordinates and a measuring ruler in moving by other system only in the unique point by means of the elementary space-time diagram was proved evidently and convincingly. The methodological inadmissibility of intersystem comparison of any spatial or time pieces is accented. A conclusion on a methodological incorrectness Einstein’s way of synchronization of clocks and all known variants of a conclusion of Lorentz transformations on this basis is drawn. The other variant of space-time transformations is offered and its compatibility with the Michelson-Morley Experiment is shown. Philosophical reflections of the author about the true cognitive status of Lorentz transformations are adduced.

1. About a technique of comparison of spatial segments

Unfortunately, all former fair critical remarks of considerable number of sane fair researchers to address of Lorentz transformations customary in special relativity have not been perceived by scientific community to the right degree. Reasons of the author of this article about a methodological incorrectness of the process of deducing of these transformations have not considered too [1]. Apparently these failures should be referred on special world outlook and methodological complexity of a situation and for the present bad persuasiveness of the critical argument. We shall try to be more convincing well.

Not a secret, that the significant role of the invention of special four-dimensional Minkowski space-time in business of giving greater pictorial presentation to Special Relativity Theory (which have specially received by distortion of usual four-dimensional space-time by means of a doubtful way of synchronization of clocks and the artificial imposed thesis about invariance of an interval) in one’s time has played. We also shall resort to the elementary geometry for giving pictorial presentation to our reasons, but without specially invented elaborate distortions.

As it is accepted in all elementary textbooks, we shall consider a standard situation with mutual movement of two systems K and K ‘ with high speed along the combined axes x and x ‘. (See Fig.1):

Fig.1

In the further we shall exclude axes y, y ‘, z, z ‘ from consideration for simplicity and we shall represent a situation in the Cartesian orthogonal system of coordinates, on a bidimentional space-time plane. (See Fig.2).

Fig.2

By analogy to Minkowski space-time we shall consider, that each point on this plane, having the spatial and time coordinate, corresponds to world event in a described situation.

Here xOt – system of a stationary observer. During the initial moment of time as it is usual, reference marks of two systems O and O ‘ it is considered conterminous. Point O ‘ will move in the course of time on an axis x’ in this figure, representing the direct line located under a corner φ in relation to an axis t. At that φ = arctgV, where V-speed of movement of system K ‘ in relation to system K from the point of view of observer from system K.

Let’s consider, how movement of rod AB based in system K ‘ and located along an axis x’ will look here. Obviously, the rod in the course of time will slide on an axis x’ with all own points too. We shall note, that all points of a rod in system K ‘ coexist simultaneously, are in one temporal "section" or temporal "echelon".

From thought experiment with « Einstein’s train » we know, that the infringement of a principle of simultaneity of events in spatially divided points in two systems moving with high speeds takes place. This phenomenon has received the name « a relativity of simultaneity ». The essence of a phenomenon is evidently visible on Fig.2. All simultaneous events in system K lay on the straight lines parallel to axis Ox. For example, simultaneous events in points Ax and Bx here are. Nevertheless events, simultaneous in system K ‘, lay already on the straight lines parallel to axis Ox ‘. In particular, it is points A and B. It turns out, that two events, simultaneous in system K, do not be such in system K ‘ and on the contrary. Each schoolboy knows about it today.

Now we shall try to make the act of measurement of length of this rod, using opportunities and tools of stationary system K. In system K along axis Ox we shall arrange a measuring bar by means of which we shall try to measure length of a moving rod. We shall note, that all points of this bar coexist simultaneously (in one time section) on axis Ox into the combined moment of time t=0 and on an axis parallel to it into any other moment of time.

The standard technique of contact sensing of length of a line segment means superimposition its ends with point labels on a measuring bar. Means, a rod and a measuring bar should have two joint (coincident) world events. How business with it at us in this case is?

On Fig.2 it is evidently visible, that the rod can be superposed without effort by all own points or at least by two extreme with all measuring bars located in systems, moving with the same speed in relation to K. These bars are displayed on the lines parallel to axis Ox ‘ (for example, DE). However it is impossible to tell the same about axis Ox. It is obvious, that axes Ox and Ox ‘ are not parallel, therefore cannot be completely superposed, and can be crossed only in one point. This consequence of the elementary Euclid axioms. It turns out, that the rod can meet a bar into the certain moment of time per only one own end (generally – per only one point of own body). Superimposition of other end of a rod (generally – any its other point) with a bar becomes possible only into other moment of time, through a certain time interval. However it means that the second event occurs in other time echelon. During the specified time interval the first end of a rod and all other points of its body, certainly, "will depart" on significant distance so it will not turn out as the correct act of measurement. Essentially important fact is that all points of a body of a rod, except for one superposed, appear in other time echelons. Each point of a body of a rod for a meeting with a bar should wait exclusively the especial time echelon. The transparent conclusion from here follows, that the rod and a measuring bar cannot have two or more joint (coincident) world events and consequently their lengths essentially cannot be compared. This conclusion is so important, that deserve get-up in the form of special cognitive restriction or an interdiction that we shall make later. We already described this situation in details earlier [1], now this extraordinary occurrence is evidently visible per geometric visualization.

Perhaps, something will be changed with attempt of contactless remote measurement with use of transfer of the information by means of any signal? However signals from the ends of a rod, being are let out simultaneously in system of a stationary rod, with identical speed will move ahead to a measuring bar, being during any intermediate moment of time on direct, parallel axis Ox ‘ and consequently also cannot meet her simultaneously in system Ox. These signals during all time are within the limits of the own time echelon and cannot replace one time echelon with another at will. The situation will be similar at attempt of transfer of a signal in the opposite direction, from a measuring bar to a rod. Both these variants we already considered in details earlier [1].

For a case of usual small speeds this fact, maybe, has no so big methodological value. During described « defect of a simultaneity » the rod has not time "to depart" too far so distortion of its length observable from another system will be insignificant. However when the rod and a measuring bar mutually move with high near-light speeds, the problem gets basic value. If to adhere to strictly scientific objective methodological approach, it is necessary to ascertain, that

act of exact measurement of length of a rod and, in general, lengths of any line segments " in the air ", by measuring means of moving system turn out impracticable in principle.

Moreover, the objective methodological interdiction on any intersystem comparison of lengths of line segments and other extensive parameters along a line of moving of two systems takes place. As these pieces can have only one general world event, as we saw it on Fig.2, those parameters in these two systems which are entirely defined by frameworks of this dot event, for example, its spatial coordinates are supposed to comparison only. So, it is admissible to intersystem compare in moving systems with coordinates only one point.

2. Transformation of a time scale

In the classical mechanics with its small speeds axes t and t ‘ consider conterminous. Here transformations of coordinates of a point are reduced to transition from rectangular Cartesian system K to oblique-angled (affine) system K ‘ with one conterminous axis t (t ‘). Galilean Transformations are those:

x ‘ = x – V·t t ‘ = t

However we know that Galilean Transformations are not compatible to Maxwell’s Equations. For a case of movement with velocity of light or nearly other formulas should be found. Here again in all growth there is a following methodological problem: how to deduce formulas of transformations in conditions above the discovered objective interdiction on intersystem comparison of lengths of line segments? We shall recollect that all known variants of a conclusion of Lorentz Transformations are based on intersystem comparison of observable fragmentons, including infinitesimal (dx, dr, dS). Obviously, all this should be refer to incorrect procedures from the point of view of objective scientific methodology. Moreover, there is all the bases to assume, as Lorentz Transformations, being are deduced by the mentioned incorrect ways, cannot be necessary correct formulas of transformations. The scandalous circumstance appears.

How such methodological disorder could happen? Obviously, in days of creation special relativity the intuitive aspiration to prefer transformation of a spatial component to transformation of a time component has played with physicists a spiteful joke. The second, apparently, was too frightening theirs of the uncommonness. Therefore physicists have taken Lorentz’s idea about spatial "flattening" of objects at high speeds of movement and the corresponding formula of this deformation practically without alternative.

In those days empirical criticism was reign over the minds of physicists. And favorite of empirical critics the principle of economy of thinking in this case, apparently, has become a principle sparing their mind, leading thinking on a way of more habitual, less shocking schemes. But it has appeared, that this "sparing way" has brought as a result to the big bog of shocking consequences: as a result of Lorentz Transformations of coordinates have undergone to distortion both of space and time, and plus a phenomenon of a relativity of simultaneity in addition. And only now the fact of a methodological incorrectness of these transformations was found out. Obviously, it is necessary to search for other methodologically correct way, as well as possible really saving thinking and not leading to so grandiose transformations.

We have earlier already found out [1], that correct formulas can be received without any problems directly from the analysis of mental experiment with « Einstein’s train ». The saving thinking observer at station comes to conclusion, that the problem of a relativity of a simultaneity, that is a problem of a mismatch of hours in two systems can be easily solved if to admit the fact of presence of time displacement in spatially divided points. Hence, it is necessary to correct the formula of transformation of a time scale by means of addition of spatially dependent component.

We earlier already calculated size of a mismatch of scales t and t ‘ from the analysis of this mental experiment [1]:

xV

Θt = _{2 2}, where x – distance between described points on scale Ox

(c −V )

From the formula it is visible, that in case of coincidence of a direction of vectors x andV , the displacement will have positive size, and in case of discrepancy – negative. That is, for example, in case of a direction conterminous with movement of observable object, the relative delay of events on a time scale, and in case of an opposite direction – a relative forestalling will take place. One end of a train in mental experiment with « Einstein’s train » is for the observer along movement of a train, and another – against. So a relative forestalling of events on one end and a relative delay on other end compensate effect of displacement of a train during movement of a ray of light.

Thus, the situation for movement with near-light velocity on the elementary space-time plane will look geometrically as follows:

Fig. 3

As axes Ot and Ot ‘ are directed under a corner to each other, the above-stated reasonings for axes Ox and Ox ‘ will be fair for them too. It is necessary to ascertain, that pieces on a time scale or time intervals in two mutually moving systems too can have only one point of crossing. Thus, time intervals in two systems cannot be methodologically correct comparing with each other too. It is permitted an overlapping only one coordinate on a time scales.

3. Lorentz Transformations and the Einstein’s way of synchronization of clocks – outside of the law
Let’s sum up. On a way of attempt of correct measurement there is a basic methodological barrier. It appears impracticable in principle. It is found out, that superposition only one space-time point in two moving past each other systems (in case of four-dimensional space-time superposition on a cross-section plane y, z ) is admissible. Using terminology of Minkowski, it is necessary to approve: two such systems can have only one general world event. As such world event a start or a finish of light beams in the combined beginning of coordinates of two systems (See Fig.2) as it is made in Michelson-Morley Experiment or a meeting of two beams in the middle of a measured line segment in mental experiment with « Einstein’s train » can be chosen. But any second event in any second point is already cannot be correctly superposed. So mutual comparisons of lengths of spatial or time pieces in two such systems become absolutely impossible.

From here a particular conclusion: all calculations in which comparison more than one point in bidimentional and more than one plane in four-dimensional cases takes place, it is necessary to consider incorrect, to tell more precisely, in general wrongful. If to consider, that all variants of "conclusion" of Lorentz transformations for a bidimentional case are based on comparison of a different sort of pieces (spatial and time pieces, vectors, radius-vectors and intervals), let even infinitesimal (dx, dt, dr, ds) it is necessary to recognize all of them incorrect. Accordingly, it is necessary to recognize wrongful all transformations, received in this way. It is necessary to consider incorrect also the way of synchronization of the clocks offered by Einstein, based all on the same intersystem comparison of space-time pieces. Let’s repeat, we already brought these facts to attention earlier. Now all this is visible descriptive-geometrically.

Knowing size of a mismatch of time scales, it is possible to write the formula of transformation

x ⋅V

t’ = t-. It will mean on the bidimentional space-time plane, that the axis t ‘ will take up c^{2 −V ^{2 position under a corner ψ to an axis t. V}}

At that ψ = arcctg . c^{2 −V ²}

So, correct formulas of transformations for two moving systems will look like:

x ‘ = x – V·t x ⋅V

t ‘ = t -₂₂c −V

And it is not necessary to think out anything anymore here.

4. New system of transformations and the Michelson-MorleyExperiment
Obviously, it is necessary to show, as proposed system of transformations will be coordinated with experimental data. We shall consider it on an example of Michelson-Morley Experiment (See Fig.3):

Fig. 4

We accept that unique possible general world event for two systems – a meeting in space and time of two beams, longitudinal and transverse in a point O takes place. For the system connected with experimental installation, all it is so obvious. In system, concerning which this experimental installation moves with speed V, events occur in the same space points, but with displacement on the time. Size of displacement is considered of known mental experiment with « Einstein’s train » and equal:

r

Θx = ^xV, where x – distance between investigated points on scale Ox. (c^{2 −V ^{2) The observer to whom there "has arrived" the center O from point A, understands, that time spent for a way by a transverse beam, is equal}}

t1 = 2l/c + ΘAO (Taking into account a displacement of a time scales between points A and O). Time spent by a longitudinal beam on passage АВ, is equal

tAB = l/c + ΘAB (Taking into account a displacement of a time scales between points A and B). And time spent for passage ОВ, equal

tOB = l/c – ΘOB (Taking into account a displacement of a time scales between points O and B and changes of a sign at movement in an opposite direction). In sum АВ and ОВ are the general way of a longitudinal signal so time of longitudinal passage t2 will be equal, taking into account a difference of two displacements ( ΘAO = ΘAB – ΘOB ):

t2 = tAB + tOB = 2l/c + ΘAO = t1

Thus, times of passage of longitudinal and transverse shoulders of interferometer are equal for the moving observer too. The consent with experience obviously. One should think that similarly can be explained and results of all other experiments illustrating "relativistic" features.

Against the received formulas of transformations charges in their seeming "asymmetry" are possible. Really, the requirement of symmetry for record of transformations leads to the following:

x= x’ + V’ ·t’x′⋅V ′

t = t’ + c^{2 −V ′²}

However, it is necessary to pay attention, that V and V’, the speeds of mutual moving from the point of view of each of two systems, are the absolutely different parameters. Presence in two systems of only one conterminous world event excludes for us an opportunity of intersystem comparison of speeds which are defined by means of private from division of spatial and time pieces V = dx/dt, V’ = dx ‘/dt ‘. So formulas of direct and inverse transformations do not contradict each other, and no problem with a form of inverse transformations is present.

5. The Cognitive Status of Lorentz Transformations

The situation with an interdiction on comparison of space-time pieces should puzzle the researchers, wishing, nevertheless, to possess enough by the capacious information on events in other system. Perhaps, Lorentz transformations all the same will be useful to us in any cases? On Fig.1 it is visible, that moving rod AB casts the projection AxBx on axis Ox, and projection AtBt to axis Ot. In case of methodological inaccessibility of exact correct measurement the researcher, wishing definiteness and pictorialness, obviously, neglecting losses on displacement of a rod during time defect, can to set for itself a problem quasi-correct displays and to take advantage of the specified projections as substitutes of real parameters. For the lack of a normal mirror it is possible, alternatively, to try to use a distorting mirror. Lorentz’s formulas just it is necessary to reckon among such ersatz-representations. They obviously deform real characteristics of observable object and cannot be used in strict calculations; however nobody forbids using the approximate representations for the approximate calculations. But for all that it is important to remember about this quasi-correctness, to hold it in mind. It is necessary to recognize as the mistake of authors and adherents of the Special Relativity the fact, that they raise this quasi-correct representation in a rank of a unique reality with which it is necessary to deal. Actually with the aid of Lorentz Transformations it is possible to judge only scale of observable distortion of real parameters of moving by objects. It is solely the characteristic of a specific aberration of an observable picture at high speeds of movement – and no more that.

Lorentz Transformations give a local picture of observable distortions, it is a specific « observational physics», a version of the descriptive science, aspiring to absolutize the narrow private vision, to limit itself only to that is obviously found out in experience and by that to oppose with itself to the explanatory science opening causal bases of the phenomena. Strictly speaking, it should be referred to crude intermediate semi-empirical knowledge, poorly processed by scientific system of theoretical thinking, to an under-science.

At the article of D. Bohm [2] the bright example with two recessive travelers is made, each of which in opinion of another eventually decreases in the observable sizes. However everyone know, that in this case the observable angular sizes decrease only, and for nobody will come to mind to insist on the fact of real reduction of the sizes of travelers. It is possible to give an example also with heard distortion of a sound from a moving by source, known as Doppler’s effect: everyone know that it is only specific phenomenon caused by mutual movement of a source and the receiver, and it has no attitude to the basic physics of a sound. If to use photo-or the video equipment with the big exposure moving by subjects merge on a picture in one blurry stream. However, thankfully, nobody yet did not do a terrible conclusion from this fact about real loss of the precise outlines by the moving objects. For certain it is possible to give many examples of specific distortions and the aberrations, accompanying situations of mutual moving of a subject and the observer, it is possible even for the refined aesthetes to describe a special exotic local picture of the observable phenomenon, it is possible even to write the special exalted philosophy of the fascinated observer. However it is not necessary to try to absolutize it, try to substitute this perversion for the strict objective physical essence.

Unfortunately, we live during an epoch of domination of philosophy of empiricism in its several modern versions today. One of its branches is relativism, aspiring inadequately to overestimate a position of the observer and to belittle objective characteristics of objects of the nature. However in the milieu where the strict exact science have respect, nevertheless, there is strong an intuitive aspiration to a recognition of the fact of objective existence of the real world, independent of the observer and his cognitive situation. This spontaneous materialistic impulse, unfortunately, has not found a worthy embodiment in the traditional materialistic philosophy, proved unable to answer a number of key questions. However today it is possible to breathe with relief because, at last, appeared a healthy doctrine of the materialistic orientation, capable to overcome traditional stumbling-blocks of materialism and thus to develop the hand about a hand with other progressive philosophical currents. It is the synthesizing realism which is based on use of idea ring determinism [3, 4].

The situation with relativism, in our opinion, is evidently illustrated by a following example. We shall imagine the big branchy tree on each branch of which sits a raven, considering itself as wisest. It is clear, that each of them observing for world around under the special foreshortening, has before itself a special picture of the events and events pattern differing from others. If to stand up on a way of absolutization of an observable picture, favorite for relativists and other empiricists, it is necessary to deal with a great many of variants of the reality differing from each other that can lead to chaos in knowledge. Much more reliably and more conveniently, professing a principle of polyhedral (many-sided) monism [3, 4] to admit the fact of existence of a unique objective reality, visible different observers under specific foreshortenings and consequently naturally differing in their descriptions.

6. New Cognitive Situation

Following the great philosopher Kant we should inquire ourselves once again: what I basically can know about world around, in particular, on its extremely distant boundaries? Obviously, this situation has features of a basic originality and consequently should be characterized with use of a special principle which project is offered below.

Principle of the limited accessibility: in two systems moving rather each other with high speed cannot be compared (with a view of measurement or other purposes) anything more than one space-time point in a bidimentional case and anything more than one space-time plane, transverse to movement, in a four-dimensional case. Accordingly, in these systems those parameters which are completely defined in this point, for example, its space-time coordinates can be compared only. All other parameters appear inaccessible to comparison.

It, certainly, at all does not mean, that they disappear somewhere in "native" system, actually their exact value becomes inaccessible for moving by "relativistic" observer. If this observer adheres the philosophy of empiricism in its modern versions he can draw a conclusion, convenient for him, about real absence of these parameters inaccessible to him in general, completely exclude them from sphere of the consideration. However thus he risks subsequently colliding with them under the changed circumstances (for example, in case of alignment of speeds) and, besides, he can himself appear in a similar situation when parameters of his own system will be ignored by other observers.

It is necessary to note, that this situation is not so surprising nowadays and partly reminds that, which has developed in the mechanic of a microcosm where the significant set of combinations of some parameters describing movement of micro particles, becomes inaccessible to the macro observer. Unfortunately, unlike our case there the micro particle is deprived an opportunity « to stand up for itself », therefore physicists absolutely unpunishedly deprive it of right to possess these combinations of parameters objectively. In particular, they had taken away at it the right to have own trajectory of movement. There till now profess a primitive empirical principle: I do not observe – means, it is not present in the nature. And the principle of the limited accessibility which was assuming at them view as Heisenberg indeterminacy principle, they treat, as real absence of parameters, inaccessible to measurement, in the nature of micro particles.

Mankind collides with the specific restrictions in access to a number of interesting parameters in cosmology too. It too have objective character: limitation of speed of the signaling, not allowing to receive the current information on much removed objects, limitation of term of human life and mankind in comparison with cycles of passing of mighty space processes and the inaccessibility of supervision of the last concerned with it and so forth.

Anyway, speech in all these cases goes about one general cognitive problem: occurrence of specific objective restrictions on ways of knowledge of extremely distant areas of life of the person and the nature. It is necessary to ascertain, that the mankind at once on several sites of knowledge has clashed against a specific cognitive fencing, behind which it is possible to observe directly only a part of an interesting objective reality, to find out the incomplete, limited set of its parameters. Now comprehension of importance of an indisputable truth should come, at last: the person learns reality through a prism of special area of the contact with it, and from specific properties of this area depends, what picture of this reality he can depict for himself as a result. And the area of contact at times appears objectively enough narrow and uncomfortable. Thus objectively limited accessibility of direct empirical research opportunities creates a situation promoting growth of a topicality of substitutional ways of research: significance of dimensions of indirect parameters and more resolute and wide-ranging designing of system theoretical knowledge on this base increases. A topicality of this problem will be inevitable to increase with the further progress of knowledge on its remote boundaries, and it is necessary to be considered with this fact both to researchers, and philosophers of a science. So supporters of empirical and positivistic approaches to cognition inevitably should make place seriously. If to continue, as the empiricists recommend, to be limited to consideration of only those parameters that are accessible for direct supervision, excepting others from consideration, it is possible in general to lose ability to comprehend deep essence of the natural phenomena and to stop at a level of cleanly descriptive knowledge, to get confused in huge volume of poorly sensible information as it, for example, has occurred today in the physics of a microcosm.

References:

Ravil Kalmykov. Relativity of Simultaneity Versus Other Relativistic Effects. Jul. 4, 2007, in “The General Science Journal” http://www.wbabin.net/physics/kalmykov.pdf

David Bohm. The special Theory of Relativity. 1965. W.A.Benjamin Inc. N.-Y.-Amsterdam

Ravil Kalmykov. Ring Determinism: Solving the Problems of Scientific Materialism . Sep.30, 2007, in “The General Science Journal” http://www.wbabin.net/physics/kalmykov3.pdf

Ravil Kalmykov. The personal Internet-site in Russian. http://www.globalfolio.net/main/CMprov-p-336.phtml (the mirror http://sinthes.boxmail.biz/ )

Discovering quantum gravity

theimagi — Tue, 15 Jun 2010 10:18:24 +0000

The effort to unify all of the forces and laws of nature or find a "Theory of Everything" has primarily focused on explaining gravity in terms of the concepts contained in quantum mechanical particle theories.

However, it is unfortunate that some have not made an effort to find it by explaining the quantum mechanical properties of particles in terms of gravitational forces because if they had we may have found it by now.

A New Picture of
Gravity

We observe that all particles have mass, which is associated with gravitational force. However, for the past century the brightest minds of the scientific community have been unable to define how this force can be propagated by a particle using the current quantum mechanical paradigms. Additionally, even with the recent advancements in observational technologies, no one has observed the graviton or particle that many feel is responsible for the propagation of gravitational forces.

However, the fact that we have not been able to define a unifying mechanism either mathematically or conceptually for the observed quantum mechanical and gravitational properties of nature in terms of the current paradigms may not be related to their content but to how we are attempting to integrate them.

For example, the fundamental assumption of Quantum mechanics is that mass and energy is contained in discrete irreducible units or packets of energy called quarks and leptons.

However, the graviton or particle many physics associated with gravitational force has not, as mentioned earlier been observed. Some feel that this is due to the fact our instruments are not yet advance enough to detect it but it could also be because gravitational force is not propagated by a particle but by a continuous property of mass/energy.

This conclusion is supported by the observation of Davisson and Germer, when in 1927 they observed that electrons and along with other particles are diffracted by crystals. This means they must have a wave component because that is the only way to explain how they can generate a diffraction pattern. However, it also indicates that each individual particle must also have the continuous geometric substructure associated of a wave.

We have shown throughout “The Imagineer’s Chronicles” that observations of our environment suggest that space is composed of four *spatial* dimensions instead of four-dimensional space-time.

In the article "Defining gravity" Dec. 15, 2007 it was shown that one can theoretically derive the relativist properties of motion, gravity and the fact that it is equivalent to an accelerated reference frame in terms of a continuous geometric property of four *spatial* dimensions in a manner that makes predictions identical to these made by both The General and Special Theories of Relativity.

While in the article "Why is mass and energy quantized?" Oct. 4, 2007 it was shown that one can derive the quantum mechanical properties of mass in terms of a classically resonating system generated by a matter wave on a continuous "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

There are four conditions required for resonance to occur in a classical Newtonian environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial.

(In a latter article "The geometry of quarks" it will be shown how and why quarks join together to form these resonant systems in terms of the geometry of four *spatial* dimensions.)

The existence of four *spatial* dimensions would give a "surface" of three dimensional space the ability to oscillate spatially with respect to it thereby fulfilling one of the requirements for classical resonance to occur.

However, these oscillations in three-dimensional space would, according to classical mechanics would generate a resonant system or "structure" in it. These resonant systems are what defined a particle in the article "Why is mass and energy quantized?"

This cannot be done in terms of four-dimensional space-time because time or a space-time dimension is only observed to move in one direction forwards and therefore could not support the bi-directional spatial movement required to establish classical resonance.

The assumption that the quantum mechanical properties of mass are a result of a continuous properties of space is also supported by Davisson and Germer’s observation that all particles has a wave component because, as mentioned earlier it means they must have the continuous geometric substructure of a wave.

However, as mentioned earlier the properties of gravity can also be also derived in terms of the continuous property of four *spatial* dimensions.

This suggest that we may have already found a "A Theory Everything" if, as mentioned earlier we had tried to derive the discontinuous quantum mechanical properties of mass in terms of the continuous properties of gravity instead of deriving the discontinuous properties of particles in terms of continuous properties of gravitational forces.

Later Jeff

The "Shadows" of four spatial dimensions

(In a PDF format)

A Quantum "reality"

theimagi — Tue, 01 Jun 2010 07:41:04 +0000

Can we justify defining the reality of an environment based on our inability to define its reality.

The uncertainty principal of quantum mechanics tells us that we cannot know or observe the precise amount of energy contained in microscopic physical system over very short intervals of time.

Some physicists feel that because they cannot observe it in a microscopic system, it must fluctuate around a given point even though that volume is made up of a vacuum. They call the energy generated by this uncertainty quantum fluctuations or vacuum energy.

However, this means they are defining the reality of a vacuum in terms of their inability to define or observe the "reality" of the energy contain in that vacuum.

We have shown that it is more consistent with observations to define energy including that contained in a vacuum in terms the continuous properties of four *spatial* dimensions instead of four-dimensional space-time.

The observations many physicists associate with quantum fluctuations is one of those observations.

In the article “Why is mass and energy quantized?‘“ Oct. 4, 2007 it was shown that one can explain and predict the quantum properties of mass and energy in terms a resonant system caused by a matter wave moving on a continuous "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, this means one can define the "reality" quantum fluctuations in a vacuum based by extrapolating observations of our three dimensional environment to four spatial dimensions instead of relying, as many physicists seem to on their inability to observe them.

Vacuum or Zero point energy

Wikipedia describes the Casimir or the Casimir-Polder force as a physical force arising from a quantized field, which is responsible for zero point or vacuum energy. The typical example is of two uncharged metallic plates in a vacuum, placed a few micrometers apart, without any external electromagnetic field. In a classical description, the lack of an external field also means that there is no field between the plates, and no force would be measured between them. When this field is instead studied using quantum electrodynamics, it is seen that the plates do affect the virtual photons which constitute the field, and generate a net force either an attraction or a repulsion depending on the specific arrangement of the two plates. This force has been measured, and is a striking example of an effect purely due to second quantization. However, the treatment of boundary conditions in these calculations has led to some controversy.

Dutch physicists Hendrik B. G. Casimir and Dirk Polder first proposed the existence of the force and formulated an experiment to detect it in 1948 while participating in research at Philips Research Labs. The classic form of the experiment, described above, successfully demonstrated the force to within 15% of the value predicted by the theory.

Because the strength of the force falls off rapidly with distance, it is only measurable when the distance between the objects is extremely small. On a sub micrometer scale, this force becomes so strong that it becomes the dominant force between uncharged conductors. In fact, at separations of 10 nm—about 100 times the typical size of an atom the Casimir effect produces the equivalent of 1 atmosphere of pressure (101.3 kPa), the precise value depending on surface geometry and other factors.

In 1924, Louis de Broglie theorized all particles have a wave component. His theories were later confirmed in 1927 by Davisson and Germer when they observed that electrons are diffracted by crystals.

Observations of waves in a classical environment indicate the number of simple harmonic oscillators that can be established in a given environment is dependent on the distance or "gap" between the "end points" of their environments.

But same concept can be applied to two uncharged metallic plates in a vacuum, because even without any external electromagnetic field the electromagnetic components of the atoms in each plate are vibrating because if they are not at absolute zero they have thermal energy. These random vibrations of their electromagnetic components will result in a random electromagnetic field to be generated between the plates.

However, classical wave mechanics tells us these random electromagnetic vibrations would be reinforced at certain points in space. The number of simple harmonic oscillators or quantum fields in the space between two plates formed by this reinforcing would decreases as the gap between them decreases. In other words, the smaller the gap between the plates the fewer number of quantum fields or particles that gap could support.

This means as was shown in the article ”Why is mass and energy quantized?“ there will be a greater number simple harmonic oscillators or quantum fields impacting the plates from outside of the gap than between it. This will cause a force that will push the plates together because the energy density associated with harmonic oscillations outside of the gap would be greater than inside of it.

We know the reality of the wave properties of particles because Davisson and Germer physically measured and observed them.

However, we cannot observe the "reality" of the quantum fluctuations physicists associate with vacuum energy because, as mentioned earlier their existence is based on the fact we cannot observe them.

This suggests the Casimir effect may not be due to our inability to know the precise "reality" of the amount of energy contained in microscopic physical system but to the physical observable reality of the wave properties of a particle.

However, it also means the "reality" of quantum mechanics could be defined in terms of the reality of classical wave mechanics and the continuous properties of four *spatial* dimensions instead of non "reality" of the uncertainty principal.

It is not be possible to define the wave prosperities of a particle in terms of four-dimensional space-time because it cannot support the bi-directional movement required to explain the transverse wave motion Davisson and Germer observed in electrons.

Later Jeff

The "Shadows" of four spatial dimensions

(In a PDF format)

A new paradigm

theimagi — Thu, 20 May 2010 09:23:48 +0000

In Thomas Kuhn book "The Structure of Scientific Revolutions", he defines a new paradigm as one that replaces a previous worldview with a new one, which changes our fundamental understanding of reality.

History has shown that most if not all new paradigms are opposed by the establishment when first presented.

The Nature of Scientific Revolution

The Church at the time of Galileo tried to prevent his ideas from being seen by forcing him to recant because they contradicted what they believed in.

Although many will not admit it; today’s scientific establishment is not too different. Today one must have an idea published in a peer review journal before it can be "seen" by the scientific community.

Unfortunately, the existing scientific community determines which ideas are seen by them because they determine which ones are published.

In some cases they justifiably refuse to publish ideas because they are not back up by scientific facts however, in some cases they may prevent them from being published because they contradict what they believe in.

Science dictates that a theoretical model of our environment must explain and predict all observations. If it cannot it must be modified or discarded.

For example in the Ptolemaic or geocentric system of astronomy the existence of epicycles were used to explain the retrograde motion of the Moon, Sun, and planets.

It was not until scientific investigations were stimulated by Copernicus and advancements in observational technology, which allowed for direct observations of planetary motion did scientists realize epicycles did not exist.

This is true even though many Greek, Indian, and Muslim savants had published heliocentric hypotheses centuries before Copernicus.

However, why did it take almost two thousand years for science to realize that their ideas were correct?

The reason may have been that the scientific community assumed the existence of epicycles based only on their predicative powers. Therefore, they were able to justify suppressing the correct Greek and Muslim ideas for almost 2000 years because, using them, they were still able to make accurate predictions a planet’s position. This was true even though there was a more logical and accurate predicative methodology based as mentioned earlier on observations of the Greek, Indian, and Muslim cultures.

If one looks very closely one can see similarities between then and now.

The validity of Quantum theory is based primarily on their ability to make accurate quantitative predictions of our environment.

However, observations of Dark Matter appear to contradict the assumption made by it that all matter must be contained in particles.

This is because even with our advance observational technology, we have been unable to observe a baryonic or particle component.

History has shown the fact that a theoretical model can make accurate quantitative predictions does not justify not looking for a new paradigm when there are observations that contract its foundations,

Later Jeff

The crises of our time, it becomes increasingly clear, are the necessary
impetus for the revolution now under way. And once we understand
nature’s transformative powers, we see that it is our powerful ally, not a
force to feared our subdued.
Thomas Kuhn

(In a PDF format)

Entropy and the arrow of time

theimagi — Mon, 10 May 2010 10:20:59 +0000

In the natural sciences, arrow of time is a term coined in 1927 by British astronomer Arthur Eddington. He used it to distinguish a direction of time on a four-dimensional relativistic map of the world, which, according to Eddington, can be determined by a study of organizations of atoms, molecules, and bodies.

The Shape of time

Physical processes at the microscopic level are believed to be either entirely or mostly time symmetric, meaning the theoretical statements that describe them remain true if the direction of time is reversed However, the opposite is true in the macroscopic world in that there is an obvious direction (or flow) of time. In others words process in our macroscopic environment are observed to be asymmetric with respect to the direction of time.

Entropy appears to be the only quantity in the macroscopic world that "picks" a particular direction. Therefore, it is used by science to define the arrow of time. As one goes "forward" in time, the second law of thermodynamics says, the entropy or disorder of an isolated system will increase when no extra energy is consumed. Hence, from one perspective, entropy measurement is thought of as a kind of marker that determines the direction of time.

However, one cannot apply the concept of entropy to the microscopic world of atoms because the entropy or disorder of system composed of a signal atom does increase as it moves through time. In other words, the entropy of an atom moving to the left, while going forward in time is identical to the entropy of an atom moving to the right, while going backwards in time. Therefore, the one cannot use it to define a direction of time in most microscopic systems because it does not change as one changes direction in time.

This points out one of the problems with using entropy to "pick a particular" direction for time because using it does not give a universally consistent direction for it. For example, on microscopic or atomic level the entropy or energy of an isolated atom does not spontaneously increase over time therefore it cannot be used to define its direction. However, it can be used to define its direction in a macroscopic isolated system because in those systems entropy does spontaneously increase over time.

Another problem in assuming the second law of thermodynamics is responsible for determining the direction of time is that is statistical, so it does not hold with strict universality: any system can fluctuate to a state of lower entropy. This means the direction of the arrow of time in those system where it does will be reversed.

However, one could resolve this conundrum if one defines the arrow of time, as we have done in the article "Defining what time is?” Sept. 20, 2007 only in terms of the sequential ordering of the causality of events instead of the entropy of a system. This would give a consistent direction in all macroscopic multi component systems as well as single component microscopic ones such as an atom. This is because the ordering of the causality of all events would always move in the same direction forward.

For example, as mentioned earlier due to the statistical nature of the second law of thermodynamics it is possible for the entropy of gas molecules in a macroscopic environment to fluctuate or a move to a more orderly instead of a more disorganized arrangement. Therefore, in a system consisting of gas molecules, statistically speaking the arrow of time can be also reversed if one uses entropy to define it in a macroscopic system.

However, the causality of the fluctuation that reduced the entropy of the gas will always be different and later in time than all previous ones.

This also provides a consistent direction for the arrow of time in microscopic systems such as those containing a single atom because the causality of an atom moving to the left would always be proceeded by the causality of that the same atom moving to the right; even though the behavior of the atom is not qualitatively different in either case.

Therefore, defining the time only as a measure of the sequential ordering of the causality of an event, as we are suggesting would provide an unambiguous definition of arrow of time in both a macro and microscopic environment.

This shows why defining the arrow of time in terms of a measure of the sequential ordering of the causality of an event is more consistent with observations than defining it in terms of entropy.

Later Jeff

The "Shadows" of four spatial dimensions

(In a PDF format)

The Imagineer's Chronicles

Heisenberg uncertainty principal: A Classical interpretation

The geometry of the fundamental particles

The inertia of dimensional interactions

Why is the universe is flat?

Dark matter: an alternative

Lorentz transformations contradict an objective methodological interdiction

1. About a technique of comparison of spatial segments

As it is accepted in all elementary textbooks, we shall consider a standard situation with mutual movement of two systems K and K ‘ with high speed along the combined axes x and x ‘. (See Fig.1):

Fig.1

In the further we shall exclude axes y, y ‘, z, z ‘ from consideration for simplicity and we shall represent a situation in the Cartesian orthogonal system of coordinates, on a bidimentional space-time plane. (See Fig.2).

Fig.2

By analogy to Minkowski space-time we shall consider, that each point on this plane, having the spatial and time coordinate, corresponds to world event in a described situation.

The standard technique of contact sensing of length of a line segment means superimposition its ends with point labels on a measuring bar. Means, a rod and a measuring bar should have two joint (coincident) world events. How business with it at us in this case is?

act of exact measurement of length of a rod and, in general, lengths of any line segments " in the air ", by measuring means of moving system turn out impracticable in principle.

x ‘ = x – V·t t ‘ = t

We earlier already calculated size of a mismatch of scales t and t ‘ from the analysis of this mental experiment [1]:

xV

Θt = 2 2 , where x – distance between described points on scale Ox

(c −V )

Thus, the situation for movement with near-light velocity on the elementary space-time plane will look geometrically as follows:

Fig. 3

5. The Cognitive Status of Lorentz Transformations

6. New Cognitive Situation

Discovering quantum gravity

A Quantum "reality"

A new paradigm

Entropy and the arrow of time

Θt = _{2 2}, where x – distance between described points on scale Ox