PM [D01] Matter Waves

PM [D01] Matter Waves

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  © ABCC Australia2015 new-physics.com DE BROGLIE'S THEORY Matter-Waves [001]
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  © ABCC Australia2015 new-physics.com Wave Particle Duality of Light After fighting over hundreds of years, the issue of weather light is a particle or a wave is finally settled, or rather, compromised in the early twentieth century. It is now generally accepted that light is a particle as well as a wave. It is a hybrid called a wave-particle.
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  © ABCC Australia2015 new-physics.com Wavicles Some clever people coined the word ‘wavicle’ for a particle that is wave and at the same time as particle. The composite particles have dual characteristics, like the mythical hybrids in ancient Greek mythology.
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  © ABCC Australia2015 new-physics.com Light imitates material particles and becomes a wavicle. But what about the material particles themselves? There are many micro- particles such as electrons, neutrons, and protons and even quarks and gluons. Do they behave like waves as well? Material Particles?
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  © ABCC Australia2015 new-physics.com Matter Waves Photons are different from matter particles in that they are singularly characterized. Matter particles are traditionally believed to be solid, localized and unwavy – even when they are in motion. The idea of matter particles that waves like a photon was not known until 1924. Photon = Particle + Wave Matter particles and objects
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  © ABCC Australia2015 new-physics.com de Broglie Hypothesis In 1924, a young French nobleman named Louis de Broglie (1892-1987) submitted his doctoral thesis to the University of Paris under the title “Research in the Quantum Theory”[1]. It contained a new message that seemed to have the potential to completely revolutionize the classical view of matter. [1] Louis de Broglie: ‘Recherches sur la théorie des quanta (Researches on the quantum theory)’ Thesis (Paris), 1924; L. de Broglie, Ann. Phys. (Paris) 3, 22 (1925). Louis de Broglie (1892-1987)
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  © ABCC Australia2015 new-physics.com Particle Waves Based on the work of Max Planck (1858-1947)[2] and Albert Einstein (1879-1955)[3], de Broglie proposed in his thesis that material particles such as electrons should have both wave and particle properties, just like photons. [2] Max Planck: Energy of radiation [Link] [3] Albert Einstein: Relativistic energy [Link] Photon = Particle + Wave Matter particles
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  © ABCC Australia2015 new-physics.com Early Days of the Theory His thesis was so original that it was easily recognized. But there was not any experimental evidence of such a kind of wave at the time. So this new idea of matter-wave was not considered to have any physical reality. However, Paul Langevin (1872-1946) drew the attention of Albert Einstein (1879-1955) to the matter. Einstein immediately recognized its significance and promoted it to the attention of other physicists. Good stuff! [Because it came from my formula!]
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  © ABCC Australia2015 new-physics.com Nobel Prize Award Three years later in 1927, de Broglie’s idea was confirmed by experiments and he received the Nobel Prize for his discovery of the wave nature of electrons in 1929. This made him the first person to receive a Nobel Prize on a PhD thesis. Nobel Prize Medal
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  © ABCC Australia2015 new-physics.com Debut of Matter Waves de Broglie said in 1929: “We thus find that in order to describe the properties of Matter, as well as those of Light, we must employ waves and corpuscles simultaneously. We can no longer imagine the electron as being just a minute corpuscle of electricity: we must associate a wave with it.” [4]. [4] Louis de Broglie: Nobel prize speech 1929. Classical picture of an electron in motion Matter wave picture of an electron particle in motion
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  © ABCC Australia2015 new-physics.com Significance With this new discovery, de Broglie opened the gateway to the development of wave and quantum mechanics in the early 19th century. Although in the later stage of development, the precision descriptions of a particle in motion no longer prevailed and gave way to probabilistic interpretations, the discovery of de Broglie remained a historic landmark in physics.
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  © ABCC Australia2015 new-physics.com RELATIVISTIC ENERGY Aoppendix : Einstein’s
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  © ABCC Australia2015 new-physics.com Relativistic Energy The momentum 𝑝𝑝 in relativistic expression is: 𝑝𝑝 = 𝑚𝑚𝑜𝑜 𝑣𝑣 1 − 𝑣𝑣2 𝑐𝑐2 𝑚𝑚𝑜𝑜 is the rest mass of the particle; 𝑣𝑣 the velocity of the particle; 𝑐𝑐 the speed of light. Squaring both sides: (𝑝𝑝)2 = 𝑚𝑚𝑜𝑜 𝑣𝑣 1 − 𝑣𝑣2 𝑐𝑐2 2 We arrive at: 𝑝𝑝2 = 𝑚𝑚𝑜𝑜 2 𝑣𝑣2 1 − 𝑣𝑣2 𝑐𝑐2
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  © ABCC Australia2015 new-physics.com Multiplying both sides by 𝑐𝑐2 : 𝑝𝑝2 𝑐𝑐2 = 𝑚𝑚𝑜𝑜 2 𝑣𝑣2 𝑐𝑐2 1 − 𝑣𝑣2 𝑐𝑐2 Or: 𝑝𝑝2 𝑐𝑐2 = 𝑚𝑚𝑜𝑜 2 𝑣𝑣2 𝑐𝑐2 𝑐𝑐4 1 − 𝑣𝑣2 𝑐𝑐2 By adding and subtracting a term it can be put in the form: 𝑝𝑝2 𝑐𝑐2 = 𝑚𝑚𝑜𝑜 2 𝑣𝑣2 𝑐𝑐2 𝑐𝑐4 1 − 𝑣𝑣2 𝑐𝑐2 = 𝑚𝑚𝑜𝑜 2 𝑐𝑐4 𝑣𝑣2 𝑐𝑐2 − 1 1 − 𝑣𝑣2 𝑐𝑐2 + 𝑚𝑚𝑜𝑜 2 𝑐𝑐4 1 − 𝑣𝑣2 𝑐𝑐2 = −𝑚𝑚𝑜𝑜 2 𝑐𝑐4 + 𝑚𝑚2 𝑐𝑐4
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  © ABCC Australia2015 new-physics.com The term 𝑚𝑚𝑜𝑜 2 𝑐𝑐4 1− 𝑣𝑣2 𝑐𝑐2 is just the relativistic mass m. So: 𝑝𝑝2 𝑐𝑐2 + 𝑚𝑚𝑜𝑜 2 𝑐𝑐4 = 𝑚𝑚2 𝑐𝑐4 Or 𝑚𝑚2 𝑐𝑐4 = 𝑝𝑝2 𝑐𝑐2 + 𝑚𝑚𝑜𝑜 2 𝑐𝑐4 which may be rearranged to give the expression for relativistic energy 𝑚𝑚𝑚𝑚 = 𝐸𝐸𝑟𝑟𝑟𝑟𝑟𝑟: 𝑚𝑚𝑚𝑚 = 𝐸𝐸𝑟𝑟𝑟𝑟𝑟𝑟 = 𝑝𝑝2 𝑐𝑐2 + 𝑚𝑚𝑜𝑜 2 𝑐𝑐4 = 𝑝𝑝2 𝑐𝑐2 + (𝑚𝑚𝑜𝑜 𝑐𝑐2)2
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  © ABCC Australia2015 new-physics.com At the same time, Einstein's theory of relativity pointed out that for a particle like a photon of zero rest mass 𝑚𝑚𝑜𝑜 = 0. So the relativistic energy becomes: 𝐸𝐸𝑟𝑟𝑟𝑟𝑟𝑟 = 𝑝𝑝2 𝑐𝑐2 + (𝑚𝑚𝑜𝑜 𝑐𝑐2)2 = 𝑝𝑝𝑝𝑝 𝐸𝐸𝑟𝑟𝑟𝑟𝑟𝑟 = 𝑝𝑝𝑝𝑝
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  © ABCC Australia2015 new-physics.com THE EQUATION DERIVED BY DE BROGLIE To be continued in : Matter-Waves [002] ABCC