“However far the quantum physical phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms. The argument is simply that by the word “experiment” we refer to a situation where we can tell others what we have learned and that, therefore, the account of the experimental arrangements and of the results of the observations must be expressed in unambiguous language with suitable application of the terminology of classical physics.

This crucial point…implies the impossibility of any sharp separation between the behavior of atomic objects and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear…. Consequently, evidence obtained under different experimental conditions cannot be comprehended within a single picture, but must be regarded as complementary in the sense that only the totality of the phenomena exhausts the possible information about the object.”

In other words he did not think that it was possible to use classical concepts to integrate the wave and particle characteristics of a quantum particle into a single picture therefore he felt that there exits a physical division between the macroscopic world of classical objects and the microscopic world of quantum particles. 

However this may not be the true and one can understand why if one views the universe in terms of four *spatial* dimensions instead of four dimensional space-time.

(The reason will become obvious later.)

Einstein gave us the ability to do this when he used the velocity of light to define the geometric properties of space-time because it allows one to convert a unit of time in his space-time universe to a unit of a *spatial* dimension identical to those in our three-dimensional universe .  Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by mathematically defining the geometric properties of a space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions.

The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with energy in terms of four *spatial* dimensions is one bases for assuming as was done in the article “Defining energy?” Nov 27, 2007 that all forms of energy can be derived in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension. 

One of the advantage to doing is that allows one to understand the wave particle duality of energy/mass or its complementary property in terms of the concepts of classical physics.

For example the article, “Why is energy/mass quantized?” Oct. 4, 2007 showed that one can explain and understand the physicality of its particle properties in terms of the classical concept of waves by extrapolating the laws of resonance in a three-dimensional environment to a matter wave moving on “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension.  It also explains why all energy must be quantized or exist in these discrete resonant systems when observed.

Briefly it showed the four conditions required for resonance to occur in a classical 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 would occur in a matter wave moving in four *spatial* dimensions.

The existence of four *spatial* dimensions would give a matter wave 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, the oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established in four spatial dimensions.

Observations of a three-dimensional environment show the energy associated with resonant system can only take on the incremental or discreet values associated with a fundamental or a harmonic of the  fundamental frequency of its environment.

Similarly the energy associated with resonant systems in four *spatial* dimensions could only take on the incremental or discreet values associated a fundamental or a harmonic of the fundamental frequency of its environment.

Therefore these resonant systems in would be responsible incremental or discreet energy associated with quantum mechanical systems.

This allows one to define the particle properties of energy/mass in terms of the classical concepts of a wave.

However, one can define its wave properties in terms of the classical concepts of a particle in terms of the boundaries of its resonant structure.

For example in classical physics, a point on the two-dimensional surface of paper is confined to that surface.  However, that surface can oscillate up or down with respect to three-dimensional space. 

Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate “up” or “down” with respect to a fourth *spatial* dimension.

The confinement of the “upward” and “downward” oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries of the resonant system associated with a particle in the article “Why is energy/mass quantized?“

However it also provides the ability to understand the inseparability of the wave and particle properties of energy/mass because it clearly demonstrates how one is depend on the other.

However it also explains why quantum systems either display the properties of a particle or a wave when measured because if one wants to measure the total energy contained in a given volume of space one will observe it as a particle while if one want to measure how it is propagated through space one must observe its wave properties.

Additionally it defines a classical reason why particles sometimes behave like wave and sometimes like particle and why it is impossible simultaneously observe them.

As shown earlier the energy contained in a quanta of space associated with a particle would be defined by the energy associated with the wavelength of its resonate structure.  In other words to observe or measure the particle properties of a given volume of space one has to sample all of its energy leaving nothing of its wave component to measure.  Similarly if one wants to observe or measure fully the wave energy of a quantum of space one would have to sample all of its energy leaving none of its particle properties.

(If one does not want to observe all of the energy in a given volume of space then one would expect that the difference would be made up by the emission of a photon or other particle whose energy would correspond to that difference.)

The reason why one cannot simultaneously measure both its wave and particle properties is because as mentioned the energy of a particle is defined by the wave properties of its resonant structure.  Since the resonant system that defines a particle is the smallest unit of its resonate structure if one measures its particle properties there would be no wave energy left for measuring its wave proprieties while if someone measure its wave energy there would be no energy left to support its particle properties. Therefore making one of these measurements precludes the other.

This demonstrates how one can integrate the wave and particle characteristics of a quantum particle into a single picture and why the  physical division between the macroscopic world of classical objects and the microscopic world of quantum particles as was assumed by Bohr many not exist. 

Later Jeff

Copyright Jeffrey O’Callaghan 2014

The post Mass from first principles appeared first on Unifying Quantum and Relativistic Theories.

For example Kepler’s Laws are wonderful as a description of the motions of the planets.  However, they provide no explanation of why the planets move in that way.  Moreover, Kepler’s Third Law only works for planets orbiting the Sun and does not apply to moon’s orbiting around the planets.

However 1686, Isaac Newton presented his three laws of motion in the “Principia Mathematica Philosophiae Naturalis” which provided a more general explanation Kepler’s laws and allowed them to be applied not only to of the motions of the planets but also to those of their moons.

This is primarily because Kepler developed his laws directly from the quantitative observational records given to him by Tycho Brahe and did not attempt to generalize them.  Additionally he was unable or did not try to understand why those numbers appeared in nature but only to find a way of making the fit them into the consistent mathematical structure we now call Kepler’s laws.
However Newton was able to reformulate them by defining a gravitational mechanism that not only provide a theoretical understanding of their validity but also expanded, as mentioned earlier their domain to a much broader environment.

There are many aspects of modern physics that might gain the same benefits from the reformulation of existing ideas.

One in particular would be Einstein theories because it may allow one to derive a theoretical understanding of the casualty of Dark Energy and what Dark matter is.

Dark Energy or the mysterious force that is causing the accelerated, spatial expansion of the universe does not appear to be integrable into any of the currently accepted theoretical models of our universe.

This is true even though Einstein foresaw its existence when he used his intuition to arbitrarily insert a term, called a cosmology constant into his General Theory of Relativity that would create an expanding force very similar to that of Dark Energy.  Similar to Kepler he based this addition only on the observational records of his time that suggested space was static and unchanging and not on any theoretical principal.  Additionally like Kepler he either could not or did not try to integrate it or explain why it exists in terms of a theoretical model.

However there are some who feel that we may be able to use his intuitive genius and the concept laid down in his space-time theories to understand the causality of spatial expansion associated with Dark Energy even though Einstein called the insertion of his cosmological constant “His big blunder” when it was discovered that the universe was not static.

As   mentioned earlier Einstein either could not or did not try to conceptually  integrate his cosmological constant or an expansive force now called Dark   Energy into the theoretical structure of Relativity possibly because, as mentioned earlier they are   both related to how three-dimensional space expanded or was prevented from   contracting with respect to a higher spatial dimension not a time or   space-time dimension.   

Therefore to understand Dark Energy in terms of Einstein space-time theory one would have to add a new *spatial* dimension to the three that it already contain to define its spatial properties thereby significantly increasing the complexity of its theoretical structure.

This would be true if Einstein had not given us the ability reformulate his space time theories in terms of four *spatial* dimensions when he defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2.

As was just mentioned Einstein defined the geometric properties of a space-time universe in terms of a dynamic balance between mass and energy defined by the equation E=mc^2.  However when he used the constant velocity of light in that equation to define that balance he provided a method of converting a unit of space he associated with mass to a unit of space-time he associated with energy.   Additionally because the velocity of light is constant he also defined a one to one quantitative correspondence between his space-time universe and one made up of four *spatial* dimensions.

In other words by defining the geometric properties of a space-time universe in terms of mass/energy and the constant velocity of light he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions.

As mentioned earlier it is difficult to integrate and define the causality of why three-dimensional space is expanding towards a higher *spatial” dimension into Einstein space-time universe because it does not define a higher spatial dimension. 

However one can easily integrate it into one consisting of four *spatial* dimensions because of the fact that it would allow three-dimensional space to expand toward a higher fourth *spatial* dimension.

In other words if one reformulates Einstein’s equations and quantitatively defines energy in terms of a spatial displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimensions instead of one in a space-time environment one can understand how the observed spatial expansion of three-dimensional space associated with Dark Energy can occur.

We know from the study of thermodynamics that energy flows from areas of high density to area of low density very similar to how water flows form an elevated or “high density” point to a lower one.

For example if the walls of an above ground pool filled with water collapse the elevated two-dimensional surface of the water will flow or expand and accelerate outward towards the three-dimensional environment sounding it.

Yet we know from observations of the cosmic background radiation that presently our three-dimensional universe has an average energy component equal to about 3.7 degrees Kelvin. 

However this means that according to concepts developed in the article “Defining energy” (mentioned earlier) the three-dimensional “surface” of our universe which has an average energy component of 3.7 degree Kelvin would be elevated with respect to a fourth *spatial* dimension.

Yet this means similar to the two dimensional surface of the water in the pool three-dimensional space will accelerate and flow or expand outward in the four dimensional environment surround it.

This shows how reformulating Einstein space-time concept in terms of four *spatial* dimension can provide a theoretical understanding of the accelerative force called Dark Energy which can be generalize to broader environment than a space-time universe.

For example observations tell us that five to seven billion years ago, the expansion of the universe stopped slowing due to gravity and started to accelerate due to Dark Energy.

However this is exactly what one would expect if the theoretical model outlined above was correct because in the early universe the distance between it mass components was small relative to the its energy components.   Therefore gravitational forces would predominate.  However because gravitation force decease with the square of the distance there would come a time when the expansive forces associated with Dark Energy  would be predominate because they would, according the above model decease linearly with respect to gravities.

This shows why reformulating Einstein’s space-time universe into one of four *spatial* dimension allows it to be applied to a more broader more generalized environment and provide a theoretical understand of why we presently observed the expansive forces of Dark Energy overtaking the slowing force of gravity.

It should be remember Einstein’s genius allows us to chose weather to solve problems, such those associated with Dark matter or Dark Energy in either a space-time environment or one consisting of four *spatial* dimension when he defined the geometry of space-time in terms of energy/mass and the constant velocity of light. This interchangeability broadens the environment encompassed by his theories by making them applicable to both the spatial as well as the time properties of our universe similar to how Newton laws of gravity broaden domain of Kepler’s laws of planetary motion to their moons.

Later Jeff

Copyright Jeffrey O’Callaghan 2013 

The post Reformulating space-time appeared first on Unifying Quantum and Relativistic Theories.

All forms of mathematics are abstract by definition. However scientists feel that it can be used to extract, by quantification the underlying essence of a physical environment and thereby eliminate any dependence on real world objects with which it might originally have been connected.

Many of our most successful theories began as a mathematical study of real world problems. In other words scientists attempt to use mathematics to quantify real world environments and to establish the underlying rules that govern them.

However the fact that one can mathematically quantify an environment does not mean that they accurately defined the “reality” of the rules that govern it.
For example, Isaac Newton made qualitative observations of how objects in a “real world” environment interacted with the earth’s gravitational field. He then used the understanding develop form those observations and his knowledge mathematics to derive a theoretical model that could not only quantity them but also explain the rules as to why they interacted the way they did in terms of those observations.

In other words he was able to provide a direct physical connection between the abstract properties of his mathematics and how the components of his environment interacted through his observations.

However, with the advent of higher mathematics and advance computing technology physicists now feel they have to ability to define the “reality” of what we observe in purely abstract mathematical terms.

For example, String Theory is based purely on mathematically analyzing the quantitative observation of the real world and then, using only that information define its reality. In others words they not only define the quantitative properties of the environment but also the rules for why its component interact in terms of abstract mathematics without physically observing how those interactions are taking place.

Therefore, String Theory does not and cannot provide a physical connection to the observable universe because its description is based purely on abstract properties of mathematics and not on the physical observations as Isaacs Newton’s were, of how its components interact to form the environment they are describing.

These two different approaches to theoretical philosophies are called Empiricism and Realism.

On the surface they both to be appear to be viable methods for defining the rules that governing our observable environment even though their methodologies are different.

This is because Empiricists say that our theoretical models should only be concerned with the quantifiable properties of observations while the Realist tell us that our theories should not only make accurate quantitative predictions of an environment but also allow us to understand why nature behaves the way it does based on the observable properties of the environments they are describing.

For example empiricists feel that as mentioned earlier science should only be concerned with quantifying observations and that they should only be tested against the quantifiable properties of the natural world. In other words they are not interested in or feel that it is important to integrate the observations of how objects interact in the “real world” to create our observable environment. This is the attitude most string theorist take because they attempt to define not only observations but why the nature world behave the way is does in terms of the abstract properties of mathematics.

Realists, on the other hand believe that science should not only be concerned with quantifying experiences but also explaining why the natural world behaves the way it does based on observations. In other words they feel that mathematics should not only be used to quantify an environment but should also explain why object in the “real world” interact the way we do in terms of the observable properties of that environment. This, they feel would give the underlying essence of a physical environment developed by mathematics a stronger tie to its reality.

For example, Einstein who some would call a realist first developed a conceptual understanding of space-time, based, in part on the observation that the speed of light was constant in all reference frames. However unlike the Empiricists he then developed the theoretical structure of Special Relativity by forming a physical image of what it would be like to chase after a beam of light based on observable properties of the “real world” and then translated or transpose that understanding to define how and why matter and energy in motion would interact in a space-time environment. Later he developed the equations that quantified and verified the accuracy of his conceptual model based on observations of speed of light in the natural world.

However, the proponents of Empiricism take the opposite approach to science. They observe the quantitative results of observations and then, through trial and error define a series of abstract equations, which can accurately predict them. They then use those equations to define a theoretical structure which then predicts the reality or rules governing the underlying essence of that environment.

For example, Quantum Theories, which espouses the empiricist approach defines the observations of the quantum mechanical environment of energy/mass based solely on mathematical probability functions or equations. They then use those abstract equations to not only quantify those observations but to define the rules which govern of the environment they occupy.

However this circular method of predicting both observations and operating environments based on only on mathematics does not allow one to determine the physical reality of the environments they define because those mathematically created environments are by definition abstract and therefore are independent of the physical world they are defining.

But is there a way science can verify when a mathematical created environment defines the underlying essence of the “real world” when as just mentioned they are by definition abstract and therefore do not have a direct “physically connect” to it.

The realist answer to this is to connect the abstract environments created by mathematics as Newton and Einstein did to the physical environment they are defining though observations.

For example Quantum theory makes predictions based on the abstract mathematical environment of a probability functions. However because its abstract properties are not connected to any physical images of the “real world” all observations, no matter how inconsistent or bazaar they are can be incorporated into it.

This is in sharp contrast to the space-time environment defined by Einstein because he, as mentioned earlier developed the theoretical structure of a space-time environment based on a physical image of what it would be like to chase a beam of light in the real world. This not only gives the abstract properties of his mathematics a physical connection to the real world it also give science a way of checking its conceptual validity.

For example Einstein’s theory would be invalidated if it was found that something could travel faster than the speed of light because that would contradict the physical model he define.

If however if some observation happened to contradict principals of quantum mechanics such as simultaneously observing of both particle and wave properties of mass it could easily explained of in terms of the fact that its probabilities functions tells us that anything that can happen will eventually happen. However it is impossible to find any observation that would contradict the fact that anything can will and must happen at some time in the future.

Yet this can only happen in an abstract environment which is not bound by the physicality our observational world because in that world we observe that some things just do not happen.

But why should science put in the effort to understand the physical reality behind our world when both the abstract mathematical foundation of quantum mechanics and the physical imagery of Einstein’s theories make very accurate predictions of future events based on the past.

Because the mission of a science is to define reality in terms of what we observe in the world around us which, by definition is not an abstract property of mathematics.

Later Jeff

Copyright Jeffrey O’Callaghan 2013

The post The reality of our “mathematical worlds” appeared first on Unifying Quantum and Relativistic Theories.

One is that it would allow physicists to define a particles mass and inertia by using one’s imagination to extrapolate observations made in a three-dimensional environment to a fourth *spatial* dimension.

For the past 50 years, the Standard Model of particle physics has given us a complete mathematical description of the particles and forces that shape our world.  It predicts with so much accuracy the microscopic properties of particles and the macroscopic ones of stars and galaxies that many physicists feel that it is the ultimate theory of matter and energy.
But as Charles Seife mentions on page 142 of his bookAlpha & Omega “Taken literally the plain vanilla form of the Standard model does not say anything about particle mass at all: in fact if theorists try to put mass in to its equations they blowup and become meaningless.”

In 1964 Peter Higgsshowed that one can solve this problem and explain why particles have inertial or rest mass if one assumes space is permeated by what is called a Higgs field.

He was able to show that if a particle changes its velocity or accelerates, then the Higgs field should exert a certain amount of resistance or drag which according to his theory is the origin of mass.  In a slightly more precise terminology, the origin of mass is an interaction between a particle and the (nonzero) Higgs field.  It also assumes the disturbance created by mass as it moves through this field would have to generate the particle called the Higgs boson.

The only problem is that the Higgs boson has never been observed.

This is problematic for its proponents primarily because The Large Hadron Collider (LHC) the world’s most expensive and highest-energy particle accelerator has been able to attain the energy levels which most believe should make it observable.

However, if it cannot be observed in the high energy environment presently generated by the LCH, scientists are going to have to make a decision as to whether or not to continue to expend the resources looking for something that may not exist or expend even more to create a more powerful accelerator.

This is especially relevant because as mentioned earlier there is an alternative explanation for mass that is based on the observable and therefore verifiable properties of three-dimensional space which does not require the large expenditures in time and money as would be required for verifying the existence of the Higgs boson.

Observations of our three-dimensional environment tell us the total potential energy of an object or particle is related to the magnitude of its relative displacement.  For example the potential energy of water in a bucket is determined by the height or displacement of its surface relative to the surface of the table it is resting on.  However, its potential energy is greater if one measure it with respect to the relative to the floor on which the table is resting.

In the following discussion the potential energy of the water in the bucket relative to the table top will represent the rest mass of an object or particle while its energy with respect to the floor will correspond to the energy associated with its relative motion or velocity.

In the article “Why Space-time?” Sept. 27, 2007 it was showed one can derive the rest or inertial 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 its 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 responsible for gravitational accelerations)

This means that one could define the potential, inertial or rest energy of mass by extrapolating the observations of the potential energy of the water in a bucket resting on the surface of a table to a displacement in a “surface” of a three-dimensional manifold with respect to  a fourth *spatial* dimension.  In other words one could define the potential energy associated with inertial mass in terms of the displacement of a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension for the same reason as one can define the potential energy of the water in the bucket as being related to its displacement with respect to the table top.

However the article “Defining energy” Nov 26, 2007 derived the energy associated with the relative velocities in terms of a differential displacement of a volume of an object or particle with respect to a fourth “spatial” dimension.  In other words it was able to show the energy associated with velocities are a result of a differential displacement in a “surface” of a three-dimensional space manifold with respect to a fourth “spatial” dimension.

(The energy associated with relative velocities would be associated with the displacement of the surface of the table with respect to the floor in the example mentioned earlier.)

Isaac Newton defined inertia as being responsible for why 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.

This means, one could define the potential energy associated with the velocity or momentum of an object or particle in terms of the displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension associated with its rest mass plus that associated with its relative velocity because according to the concepts presented in those articles it would be defined by the sum of those components.

The first would be magnitude of the displacement in a “surface” of a three-dimensional space associated with the rest mass of an object.  The second would be the magnitude of the displacement of that “surface” 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.) 

This also defines why the “relativistic” mass or inertia of an object or particle increase as its velocity approaches that of light because its total energy/mass would, according to the concepts presented here be related to the relative magnitude of the total displacement in a “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension which in turn would be related to their relative velocities.

Yet, as mentioned earlier the article “Why Space-time?” showed that accelerations are caused by an object or particle interacting with a curved “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Therefore,  if as mentioned earlier the momentum of a particle or object is caused by a 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.

This means that one does not have to assume the existence of the Higgs Boson to explain why particles have both mass and inertia because it shows how one can use his or her imagination to explain it by extrapolating observations of a three-dimensional environment to a fourth *spatial* dimension.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

The post Mass, inertia, and the Higgs Boson appeared first on Unifying Quantum and Relativistic Theories.

The first involves developing a mathematical description by directly observing how its components interact.
For example, Isaac Newton developed his law of gravity by observing the movement of planets and realizing that they could be understood by assuming they exerted a force on their neighbors that was directly proportional to their mass.  He then derived a mathematical equation which allowed one to quantify their future movements based on those observations.  These equations could also be applied to the movement of planets that had not been observed.  For example the position of the planet Neptune was predicted before it was observed by the use of his equations.

In other words he first conceptually defined or understood their movements through observations and then derived a mathematical expression that quantified the reality of their world from that understanding.

The second involves extrapolating a conceptual understanding of the properties of our observable environment to an unobservable one.

For example Schrödinger developed an equation that defined the quantum mechanical properties of energy/mass by extrapolating an understanding of waves gained from observations of our three-dimensional environment to the unobservable one of subatomic particles.

In other words he mathematically defined the reality of a quantum mechanical world in terms of the reality of his observable properties of waves.

The third method involves developing a mathematical expression based not on a conceptual understanding of how the components of our observable universe interact as Newton and Schrödinger did but on analyzing the quantified result of those interactions.

For example string theorists analyze the quantified results of particle interactions and then developed mathematical expression that predicts them directly from those results.  They then define the reality of a “string” world based on a conceptual understanding of the equations that quantify them.

In other words string theorists define the “reality” of a “strings” environment based only on the mathematical structure of the equations that they use to define that reality.

For the last century researchers have favored the approach taken by string theorists in that they use the quantified result of observations to mathematically define how the components of an environment interact to generate those results. 

Why?

Because many feel they must rely totally on their imagination, intuition, and mathematics to guide them on the road to understanding because they cannot directly observe the worlds they are analyzing.

Unfortunately it is possible to use intuition and mathematics to create completely self contained worlds that can predict observations which may or may not be connected to their reality they are attempting to define.  Therefore the validity of the worlds they create can only be verified if they are anchored in a real non abstract world provided through direct observation of one’s environment.

For example the Copenhagen interpretation of Quantum Mechanics does not view the equations that define its theoretical concepts in terms of the observable properties of waves as Schrödinger had done but in only in terms of a mathematical probability based on them.

However history has shown the most powerful way to understand the physical properties of our environment are through observations.  Before Isaac Newton developed his law of gravitation scientists could still make accurate quantifiable predictions of planetary movements even though no one understood why they moved that way.

Some scientists of that period felt there was no need to look any further because they could still make accurate predictions of their motion without understanding why.  However, Newton by observing his environment developed an understanding that enabled one of what many feel is the greatest conceptual leaps in humankind understanding of the universe.

Presently we seem to be in a situation similar to that which occurred before Newton developed his gravitational theory.

Quantum mechanics can make extremely accurate predictions of the quantum mechanical properties of energy/mass based on a self contained mathematical environment called a wave function.  Yet no one can explain its physicality in terms of observable properties of our environment.

However, similar to the scientists who came before Newton many believe that the self contained abstract mathematical environment of quantum mechanics does not need explaining because it can make accurate a predictions of the properties of energy/mass.

Yet Newton demonstrated how important connecting a mathematical environment to an observational one is to our understanding of its reality.

Mathematics is a very powerful tool for helping us understand the world we live in but because of its abstract nature it can be used to create self contained environments which can predict our physical world and still not be connected to its reality.  The only way to make sure the reality they define is connected to our world is by anchoring it in physical observations of our environment.

Later Jeff

Copyright 2011 Jeffrey O’Callaghan

The post Mathematical verses observational reality appeared first on Unifying Quantum and Relativistic Theories.

For example, there are some who believe the best way is to observe the environment and then extrapolate those observations to the unobservable.

Isaac Newton used this approach to derive the law of gravity by making the assumption that mass generates an attractive gravitational force on all objects based on physical observations he made on the earth.  The universality of its existence is based on the fact that one can determine the motion of all objects in the universe by assuming this force was responsible for it.

However, we cannot “see” a gravitational force.  How then can we be sure that it really exists?

The answer is we cannot.  We can only assume it does based on the fact it allows us to predict and explain the motion of objects that at the time were unobservable.

For example the position of Neptune was mathematically predicted using Newton’s concept of gravity before it was directly observed.

However, there are some who take the opposite approach.

Quantum mechanics assumes one can define the laws of nature only in terms of mathematics and not the environment that surrounds them.

For example it defines the position of a particle by mathematically defining their probability distribution but says nothing about how it got there.   

This differs from the Newtonian method in that it defines the solution to where an object was in terms of how it got there whereas quantum mechanics as motioned earlier defines it only in terms of where it is.

Both of these methods are valid because they give scientists the ability to make accurate predictions of future events.

However physics as the name implies is the science that deals with physical properties matter, energy, motion, and force and not with abstract mathematics. Therefore, physicists should look to their observable properties as the primary vehicle to guide their understanding instead of mathematics.

The trouble with modern physics is that many have got lazy in their pursuit of reality.  Instead of taking the time and effort to observe it many scientists make a few observations and turn to mathematics not observations of the environment they occupy to interconnect them.

For example the article “Why is energy/mass quantized?” Oct. 4, 2007 can understand the quantum properties energy/mass by extrapolating the observations of a three-dimensional environment to a matter wave on a “surface” of a three-dimensional space manifold with respect to  a fourth *spatial* dimension.

Briefly it showed the four conditions required for resonance to occur in a classical 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 would occur in one consisting of four spatial dimensions.

The existence of four *spatial* dimensions would give a matter wave 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 to oscillate with the frequency associated with the energy of that event.

The oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established space.

Therefore, these oscillations in a “surface” of a three-dimensional space manifold would meet the requirements mentioned above for the formation of a resonant system or “structure” in four-dimensional space if one extrapolated them to that environment. 

Classical mechanics tells us the energy of a resonant system can only take on the discrete or quantized values associated with it fundamental or a harmonic of its fundamental frequency.

Hence, these resonant systems in four *spatial* dimensions would be responsible for the discrete quantized energy associated with the quantum mechanical systems.

This shows that one can contrary to what physicists tell us that one can understand why energy/mass is quantized by extrapolating observations of a three-dimension environment to the quantum mechanical world.

However this is not the only example because as we have shown throughout this blog there are many more. 

For example both the article “Is Quantum Mechanics a Fundamental or emergent property of space-time?” shows how one can integrate quantum mechanics with the classical properties of space-time and the article “The “reality” of the Higgs field“ explains why it is responsible for mass by extrapolating observations of a three-dimension world to their enviroments.

As mentioned earlier physics is the science that deals with physical properties matter, energy, motion, and force and not with abstract mathematics.  Therefore, the primary criteria for the acceptance or rejection of a theory should not be mathematical but observational.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

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