Niels Bohr, the founder of quantum mechanics summarized the complementary principal of quantum mechanics as follows:

"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.)

Yale university courses
The key experiments and wave-particle of nature

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. 

However it also 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.

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 defines the particle properties of waves in terms of the classical concept of resonant properties of a box because its physical properties define its frequency and energy.

This also provides the ability to understand the inseparability of the wave particle duality 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 these two different properties.

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


 

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Einstein told us that energy and mass are interchangeable in terms of the geometry of space-time however he did not define what mass is.  He only told us how mass interacts with it.

As Steven Weinberg said "Mass tells space-time how to curve while space-time tells mass how to move".

In other words Einstein did not tell us what mass is in terms of the principles he used to define their interactions.

While 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.

Searching for the Elusive Higgs Particle

But as Charles Seife mentions on page 142 of his book Alpha & 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 Higgs showed 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

Recently a particle that closely resembles the Higgs boson has been observed at the Large Hadron Collider (LHC) particle. If confirmed it would verify the existence of the Higgs field which according the Standard Model of Particle physics is responsible for mass.

But even if its existence is confirmed it still does not answer the question "What is mass?" in terms of first principles because it does not define what the Higgs field is made up it only confirms it existence.

As mentioned earlier Einstein told us that energy and mass are interchangeable in terms of the geometry of space-time however he did not define what mass is. 

However one can use his theoretical model and how we observe mass and energy to interact in a classical three-dimensional environment to understand what it is in terms of the (first) principles of a space-time universe if one converts or transforms it into one consisting of only four *spatial* dimensions.

(The reason will become obvious later.)

Einstein gave us the ability to do this when he used the constant velocity of light to defined 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 of our three-dimensional space.  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 his space-time universe in terms of the geometry of four *spatial* dimensions.

One of the primary advantage to doing this is that it, as was mentioned earlier would allow one to understand the physicality of the Higgs field and how and why it causes mass in terms of a fundamental property of the geometry of four *spatial* dimensions or the principles of the space-time environment exposed by Einstein because as was just shown their properties are interchangeable. 

For example 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.  In other words 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 measures it 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 mass of an object or particle while its energy with respect to the floor will correspond to the energy associated with its relative velocity.

In the article Why Space-time? ” Sept. 27, 2007 it was shown one can derive the rest or inertial energy/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 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 physicality of 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 this suggests that the magnitude of a physical displacement in the geometry of three-dimensional space with respect to a fourth *spatial* dimension may be responsible for the mass of an object or particle.  In other words it would allow one to derive the physicality of the Higgs field by extrapolating the observable field properties of three-dimensional space to a fourth *spatial* dimension.

Yet as was shown in the article “Defining energy” Nov 26, 2007 one can also derived the energy associated with the relative velocities in terms of a displacement of the three dimensional volume of an object or particle with respect to a fourth “spatial” dimension.  In other words it was able to show the energy of velocities are a result of a displacement of geometric properties of two masses in a “surface” of a three-dimensional space manifold with respect to a fourth “spatial” dimension.

(The energy of 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 of the velocity 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 momentum of an object at rest relative to other objects is zero so the displacement of three-dimensional space with respect to those objects would also be zero.) 

This also tells us the “relativistic” mass or inertia of an object or particle increases 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 with respect to the velocity of light.

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.

In other words this enables one to define the physicality of the Higgs field in terms of the field properties of space-time or four *spatial* dimensions and that the magnitude of its associated "drag" would be defined in terms of ratio of its rest or inertial energy/mass and the slope of the curvature in space it interacts with.

This also defines mass and the Higgs field in terms of the principles first put forth in Einstein’s General Theory of Relativity while showing that the properties of Higgs field are related to the irreducible the field properties of space because the result of removing or reducing space is nothingness.

It should be remember Einstein’s genius allows us to chose whether to solve all problems 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 and gives us a new perspective on questions regarding the origins of mass and a way of understanding how and why the Higgs field is responsible for mass.

Later Jeff

Copyright Jeffrey O’Callaghan 2014


 

The Imagineer’s
Chronicles
Vol. 4 — 2013

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E-book
$7.99

 

The Imagineer’s
Chronicles
Vol. 3 — 2012
 
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The Reality
of the Fourth
Spatial
Dimension
 
Paperback
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The Imagineer’s
Chronicles
Vol. 2 — 2011
 
Paperback
$8.32
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