Put a neutron on an imaginary super-sensitive scale and measure its mass to be m n. You and a friend both earn $50,000 per year and pay the same tax. One pint + one pint in this case is not equal to one quart.Į. Now you pour a pint of water and a pint of alcohol together into a quart jar. You separately pour a pint of alcohol into another quart jar. You pour a pint of water into a quart jar. So both relativity theory and quantum theory slightly “besmirch” the superposition principle.Ĭonsider some examples where the superposition principle is not true.ĭ. Fields of arbitrary strength can share space without mutual “disturbance.” In quantum theory, not quite. Can they coexist in space without “bothering” one another? In classical electromagnetic theory (the theory of James Clerk Maxwell), the answer is yes. The truth of Example C at first seems more doubtful because fields occupy space. Masses are additive in classical Newtonian theory, but not in relativity theory. Example B may seem so, too (since it is consistent with ordinary experience), but in fact, the masses of two objects are not strictly additive when the objects exert forces on one another-forces that can change the energy and therefore the mass of the pair of objects. The same principle holds for magnetic fields.Įxample A may seem “obviously” true. At a certain location, the electric field arising from a collection of charges is the vector sum of the fields that would be produced at that location by the charges acting separately. (This implies the additivity of mass-valid up to a point!)Ĭ. When they are placed on a scale together, the recorded weight is W 1 + W 2. When force F = F 1 + F 2 is applied to the object, the resulting acceleration is a = a 1 + a 2 (these are vector sums).ī. Force F 1 applied to a certain object produces acceleration a 1 and force F 2 applied to the same object produces acceleration a 2. Here are some examples where it is a (mostly) valid principle:Ī. Simply stated, the principle of superposition is this: The result of several actions taken together is equal to the sum of the results of the actions taken separately. The Submicroscopic Frontier: Reductionism Physics At The End Of The Nineteenth Century: The Seeds Of Rel & QM The “System Of The World”: How The Heavens Drove Mechanics
#PRINCIPLE OF SUPERPOSITION IN MECHANICS DRIVER#
Faith In Simplicity As A Driver Of Science Early History Of Radioactivity And Transmutation Pauli Letter Proposing What Came To Be Called The Neutrino The Line Of Nuclear Stability Bends And Ends Why Are There No Electrons In The Nucleus? H-Atom Wave Functions And Classical Correspondence Bohr’s Triumph: Explaining The Rydberg Constant Planck’s Constant As The Particle-Wave Link Localization Of Waves Relation To Uncertainty Principle Why Is The Hydrogen Atom As Big As It Is? Waves And Particles (The de Broglie Equation) The Fourth Dimension: Spacetime And Momenergy Momentum In Relativity, And Another Approach To E = mc 2 Agreement And Disagreement: Relativistic And Classical Early Links Between Electricity And Magnetism Six Versions Of The Second Law Of Thermodynamics From Kepler’s Laws To Universal Gravitation Work And Its Relation To Kinetic And Potential Energy The Isotropy Of Space And Angular-Momentum Conservation
Space Homogeneity And Momentum Conservation Newton’s Third Law: Its Formulation, Its Significance \): The exact point of application of a force will impact how internal forces (stresses) are distributed, so the principle of transmissibility cannot be applied when examining internal forces.
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