An interesting special case occurs when the particles are connected by a lightweight, rigid rod, giving us a dumbbell. When a property is constant over a shift in time or space, that property is conserved and represents a universal property. Therefore, the energy needed to change from one standing wave to another must be quantized in order to maintain a whole number of wavelengths and avoid collapsing. Then it is not an initial condition, but rather a continuously-changing condition.

In this view Lorentz invariance is an emergent symmetry obeyed by our observations — for Bohmian mechanics a statistical consequence of quantum equilibrium that governs the results of quantum experiments. This is the opinion of Bohm and Hiley (1993), of Holland (1993), and of Valentini (1997). However — unlike nonlocality — violating Lorentz invariance is not inevitable , e.g. Creation and Annihilation Operators http://becomingvisibleconference.org/library/creation-and-annihilation-operators. There’s a theory discussed by most as if it were a proven fact. Yet we have Arp’s redshift anomalies and other factors that call it into question. Especially with an aether, cosmological redshift may not be recession velocity at all. But to question this interpretation; to question big bang theory, makes people accuse you of sacrilege. I recently read Helge Kragh’s seminal book, “Cosmology and Controversy.” It seems from my reading that big bang theory came about after Hubble discovered the proportionality between redshift and distance, and that this provided an answer to the missing force needed to counteract gravity to explain why the matter in the universe hasn’t collapsed into itself (his “cosmological constant”) , source: Satellite Technology: Principles and Applications http://blog.webdirectories.co/library/satellite-technology-principles-and-applications. Roychouhduri, 2009 Exploring divisibility and summability of ‘photon’ wave packets in non-linear optical phenomena, Proc. of SPIE, The Nature of Light III, 2009, 7421 74210A 46 - E. Schrödinger, 1982 Collected Papers on Wave Mechanics, Quantization as a Problem of Proper Values (Part I), Chelsea Publ. Co., New York, NY, USA, 1 12. 47 - W. Feng, 2008 Observation of a Push Force on the End Face of a Nanometer Silica Filament Exerted by Outgoing Light, PhysReview Letters, 101 24 48 - R , e.g. Waves in Fluids Waves in Fluids.

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