{"id":12285,"date":"2014-04-01T05:06:35","date_gmt":"2014-04-01T09:06:35","guid":{"rendered":"http:\/\/www.theimagineershome.com\/blog\/?p=12285"},"modified":"2018-12-15T08:25:51","modified_gmt":"2018-12-15T12:25:51","slug":"the-geometry-of-a-particle-wave","status":"publish","type":"post","link":"https:\/\/www.theimagineershome.com\/blog\/the-geometry-of-a-particle-wave\/","title":{"rendered":"The geometry of a particle wave"},"content":{"rendered":"

Is it possible to define a “reality” behind the quantum world in terms of the classical laws of physics and the space-time environment defined by Einstein?<\/font><\/p>\n

In other words can one use our everyday experiences to understand the irrationality behind many of the assumptions made by quantum mechanics and integrate them into the space-time environment in which we all live<\/font><\/p>\n

For example the paradoxical wave\u00e2\u20ac\u201cparticle behavior of energy\/mass, one of the fundamental concepts defining Quantum mechanics defies the “reality” of the four dimensional world we live in because of its inability to describe\/define how quantum-scale objects can simultaneously exist as waves and particles.  Many have tried to explain it as a fundamental property of the Universe, while alternative interpretations explain the duality as an emergent, second-order consequence of various limitations of the observer. <\/font><\/p>\n

However, it is possible to explain the wave–particle duality of the quantum world in terms of the “reality” of classical concepts and four dimensional space-time by redefining Einstein’s space-time environment to its equivalent four spatial dimension counterpart because it will allow one to directly apply classical concepts of Newtonian space to the wave properties quantum mechanics associates with particles. <\/font><\/p>\n

(The reasons will become obvious latter.)<\/font><\/p>\n

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 four dimensional space-time universe to a unit of a space in an environment consisting  four spatial dimensions which 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. <\/font><\/font><\/p>\n

In other words by mathematically defining the geometric properties of time 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 <\/font>and gave us the ability to redefine the curvature or displacement he associated with energy\/mass in a space-time environment to a spatial displacement in a fourth *spatial* dimension.<\/span> <\/font><\/font><\/p>\n

This, as mentioned earlier will allow us to understand the reasons behind the paradoxical wave\u00e2\u20ac\u201cparticle duality of light when it is partially reflected by two surfaces, as outlined on pages 17 thru 23 of Richard P Feynman book “QED The Strange Theory of Light and Matter” in terms of the laws of classical physics.<\/font><\/p>\n

On those pages he writes that by placing two glass surfaces exactly parallel to each other one can observe how the photons of light reflected from the bottom surface interact with those reflected from the top surface.  Depending on the distance between the glass surfaces he can determine, by using a photo detector, that four percent or 4 out of 100 photons reflected from the lower surface of the glass could add up to as many as 16 or none at all when they interact with the photons reflected from the upper surface of the glass because of the reinforcement of the reflected wave energy from the bottom and top surfaces of the glass.<\/font><\/p>\n

In other words the 4 photons reflected from the surface of the bottom piece of glass would interact with the incident ones to that surface creating from 0 to 8 photons while the 4 photons reflected from the surface of the top piece of glass would interact with the incident ones to it creating 0 to 8 more photons for a total of 0 to 16 photons.<\/font><\/p>\n

These observations by Mr. Feynman support a wave theory of electromagnetic radiation because according to it, the energy associated with the interference of the 4 photons reflected from the bottom surface with 4 from the top will result in energy variations that corresponds to the energy of 0 to 16 photons.<\/font><\/p>\n

However, wave theory also predicts the energy variations should be continuous.<\/font><\/p>\n

In other words, the energy of the reflected photons should be able to take on any value between 0 and the combined energies associated with 16 photons.<\/font><\/p>\n

Unfortunately, for the wave theory of light, the energy of the reflected photons Richard Feynman observed in the above experiment only took on integral values equal to the energy of the photons that originally struck the surface of the glass.  This indicates that their energy is not transmitted by a wave but by a particle.<\/font><\/p>\n

However this observational paradox can be resolved if particles are, as mentioned earlier are viewed in terms four *spatial* dimension instead of four dimensions space-time because it shows their behavior can be described in terms of a resonant “structure” generated by a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.<\/font><\/p>\n

For example in the article “<\/font>Why is energy\/mass quantized?<\/font><\/a>” Oct. 10, 2007 it was shown one can derive both the wave and particle properties of energy\/mass and a photon by extrapolating the laws of classical of resonance in a three-dimensional environment to a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Additionally it showed that all energy must be propagated in these resonant systems.<\/font><\/p>\n

Briefly it showed the 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 would be meet by a matter wave on a \u00e2\u20ac\u0153surface\u00e2\u20ac\u009d of a three-dimensional space manifold with respect to a fourth *spatial* dimension.<\/font><\/p>\n

The existence of four *spatial* dimensions would give the \u00e2\u20ac\u0153surface\u00e2\u20ac\u009d of three-dimensional space (the substance) the ability to oscillate spatially with respect to a fourth *spatial* dimension thereby fulfilling one of the requirements for classical resonance to occur. <\/font><\/p>\n

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.<\/font><\/p>\n

Therefore if one extrapolates the laws of classical wave mechanics to a fourth *spatial* dimension these oscillations in a “surface” of a three-dimensional space manifold would generate a resonant system or “structure” in space.  <\/font><\/p>\n

Classical mechanics tell us resonant system can only have the incremental or discrete energy associated with its fundamental or a harmonic of its fundamental frequency. <\/font><\/p>\n

Similarly the incremental or discrete energies associated with individual photons in Richard Feynman’s experiment could be explained by assuming that they are a result of the fundamental or a harmonic of the fundamental frequency resonant properties of four *spatial* dimensions. <\/font><\/p>\n

This shows how one can derive the quantum mechanical properties of energy\/mass and a photon by extrapolating the laws of classical wave mechanics to a matter wave on a “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension. <\/font><\/p>\n

However, one can also describe the physicality of a particle in terms of the wave properties of its resonant structure.<\/font><\/p>\n

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.  <\/font><\/p>\n

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. <\/font><\/p>\n

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 associated with a particle in the article “<\/font>Why is energy\/mass quantized?<\/font><\/a>“<\/font><\/p>\n

This provides the ability to understand how and why a photon can have the properties of both a wave and a particle because it clearly defines their interdependence in terms of the laws of Classical wave mechanics<\/font><\/p>\n

However it also defines the physical reality of particle-wave duality in terms of the classical properties of a matter wave moving on the “surface” of a three dimension space manifold with respect to a fourth *spatial* dimension or four dimensional space-time environment because remember, as was show earlier they are equivalent<\/font><\/p>\n

For example, the wave like interference of photons he observed would be due to the wave properties of the resonant “system” defined in the article “<\/font>Why is energy\/mass quantized?<\/font><\/a>“.<\/font><\/p>\n

If the distance between the two glass surfaces in Richard Feynman’s experiment is equal to half of the wavelength of the resonant “system” associated with a photon, classical wave mechanics tell us the interference of its wave properties would interfere and will, as mentioned earlier yield the energy associated with 0 photons.<\/font><\/p>\n

If the distance between two glass surfaces is equal to its wavelength of they will reinforce each other and yield the energy associated with 16 photons.<\/font><\/p>\n

However, it also tells us the reason the energy variations caused by their interference are quantized and not continuous as wave theory predicts they should is because, as was shown in the article “<\/font>Why is energy\/mass quantized?<\/font><\/a>” the resonant properties of four *spatial* dimensions means that their energy would be propagated in the discrete quantized values associated with the fundamental or harmonic of fundamental frequency of four *spatial* dimensions or space-time environment they are occupying. <\/font><\/p>\n

Yet this also defines the reason the wave properties of 8 reflected photons reinforce themselves to create the energy associated with16 photons is because Classical wave mechanics tells us that when two waves of the same frequency interact their frequency will or does not change.  Therefore if energy is propagated in discrete quantized values associated with the wavelength or frequency of a resonant system the reinforcement of the wave properties of 8 photons must be carried away in the integral or discreet energies associated with resonant systems of up to 16 photons of the same frequency as those original 8 photons.<\/font><\/p>\n

This indicates that viewing the quantum mechanical world of wave\u00e2\u20ac\u201cparticle duality in terms of the geometric properties of a resonant “system” generated by a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension allows one to derive its “reality” by extrapolating the laws of classical mechanics in three-dimensional environment to a fourth *spatial* dimension. <\/font><\/p>\n

It should be remember Einstein\u00e2\u20ac\u2122s genius allows us to chose if we want to resolve all paradoxes between the microscopic world of quantum mechanics and the macroscopic world of Relativity 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 thereby giving us a new perspective on the physical relationship of particles and waves<\/font><\/p>\n

Later Jeff<\/font><\/p>\n

Copyright Jeffrey O’Callaghan 2014<\/font><\/p>\n","protected":false},"excerpt":{"rendered":"

Is it possible to define a “reality” behind the quantum world in terms of the classical laws of physics and the space-time environment defined by Einstein? In other words can one use our everyday experiences to understand the irrationality behind many of the assumptions made by quantum mechanics and integrate them into the space-time environment … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"sfsi_plus_gutenberg_text_before_share":"","sfsi_plus_gutenberg_show_text_before_share":"","sfsi_plus_gutenberg_icon_type":"","sfsi_plus_gutenberg_icon_alignemt":"","sfsi_plus_gutenburg_max_per_row":"","footnotes":""},"categories":[21,19,57],"tags":[20,319,763,880,923,925,621,344,401,291,400,320,495,396,924],"yst_prominent_words":[1565,1424,1430,2888,1716,1448,1408,1720,2548,1761,1482,1534,1409,1665,1418,1444,1420,1443,1415,1436],"class_list":["post-12285","post","type-post","status-publish","format-standard","hentry","category-theroetical","category-relativity","category-particle-physics","tag-quantum-mechanics","tag-einstein","tag-einsteins-space-time","tag-feynman","tag-four-dimensional-world","tag-fundamental-frequency","tag-newton","tag-newtonian-environment","tag-qed-the-strange-theory-of-light-and-matter","tag-quantum-world","tag-richard-p-feynman","tag-space-time","tag-wave-mechanics","tag-wave-particle-duality","tag-why-is-energymass-quantized"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.theimagineershome.com\/blog\/wp-json\/wp\/v2\/posts\/12285","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.theimagineershome.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.theimagineershome.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.theimagineershome.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.theimagineershome.com\/blog\/wp-json\/wp\/v2\/comments?post=12285"}],"version-history":[{"count":0,"href":"https:\/\/www.theimagineershome.com\/blog\/wp-json\/wp\/v2\/posts\/12285\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.theimagineershome.com\/blog\/wp-json\/wp\/v2\/media?parent=12285"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.theimagineershome.com\/blog\/wp-json\/wp\/v2\/categories?post=12285"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.theimagineershome.com\/blog\/wp-json\/wp\/v2\/tags?post=12285"},{"taxonomy":"yst_prominent_words","embeddable":true,"href":"https:\/\/www.theimagineershome.com\/blog\/wp-json\/wp\/v2\/yst_prominent_words?post=12285"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}